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GIFT   OF 


V 


A    NEW    TKEATISE 


ON   THB 


PRACTICE  OF  NAVIGATION  AT  SEA 


CONTAINING 


ALL  THE  DETAILS  NECESSARY  TO  ENABLE  THE  MARINER  TO  BECOME 

A  GOOD  PRACTICAL  NAVIGATOR. 


ILLUSTRATED    BY    A    NEW    MODE    OF 


ENGKAVED  DIAGRAMS  AND  FIGURES, 

DESIGNED  WITH  THE  INTENTION  OF  MECHANICALLY  INSTRUCTING  THE  LEARNER  IN  THE 

.  MEANING  AND  USE  OF  THE  VARIOUS 

PROBLEMS  IN  NAVIGATION  AND  NAUTICAL  ASTRONOMY, 

in  room  of  the  tedious  solutions  of  geometry  and  trigonometry.   the  usuai 
Tables  are  given  which  are  indispensable  in  a  work  of  this  kind, 

SOME   OF   which   ARE   IMPROVED,    AND   NEW   ONES   INTRODUCED  FO^ 

THE  FIRST  TIME,   WITH   A   VIEW   OF  SHORTENING   THE 

LABOR  OF   COMPUTATION. 

THE  WHOLE  BEING 

x^XPRESSLY  ADAPTED  FOR  THE  USE    OF  SEAMEN. 


BY   CAPTAIN   WILLIAM   THOMS, 


TWENTY-FIFTH   EDITION. 


NEW  YORK: 

PRINTED   FOR   THE   AUTHOR   AND   SOLD   BY   JOHN   BLISS   &   CO.. 

IIAVIGATION  WARKHOUSE,  '28  FRONT   STREET,  KEW  YORK;    F.  A.  ASHTON,  259  WINTHROP  STREET,  BROOKLrN, 

AND  ALJi  THE  PRINCIPAL  NAUTICAL  BOOKSTORES  IN  NEW   TORK  AND 

THROUGHOUT  THE  UNION. 

1902. 


7 


v^jf 


4,' 


.     Sntered  according  to  Act  of  Congress,  in  the  Year  One  Thousand  Eight  Hundred  and  Eighty 

BY  WILLIAM  THOMS, 
In  the  office  of  the  Librarian  of  Congress  at  Washiusitoa 


TO    THE 
COMMANDERS,    OFFICERS,    AND    SEAMEN, 

EMPLOYED  IN  THE 

MERCHANT    MARINE   OF    THE    UNITED    STATES, 

Cljis    i'olume, 

(THJB    FIRST   ATTEMPT   OF   THE    KIND   BY    A    MEMBER    OF   THAT   SERVICE,) 

IS   RESPECTFULLY    DEDICATED, 


•T 


THE  AUTHOR. 


288104 


PREFACE. 


This  work  is  intended  exclusively  for  the  use  of  seamen,  and  has  been  compiled  by  the  author 
from,  an  experience  of  more  than  twenty-five  years,  in  the  practice  of  navigating  a  ship  at  sea,  ia 
nearly  all  parts  of  the  world.  Consequently,  a  competent  knowledge  has  been  acquired,  during 
that  period,  of  what  is  actually  required  to  be  known,  in  order  to  become  an  expert  practical 
navigator.  This  work  is,  therefore,  confined  to  the  practice  at  sea  ;  that  is,  navigation  proper,  or 
that  which  has  reference  to  the  ship's  place  on  the  ocean. 

Thus  knowing  what  is  required,  and  also  the  distaste  which  seamen  have  for  long  and  tedious 
calculations.  I  have  endeavored  to  simplify  the  various  rules  and  tables,  and  to  strike  out  all 
jnnecessary  matter,  which  is  not  required,  and  in  the  room  of  which,  introduced  diagrams  of  the 
various  cases,  which  will  convey  mechanically  the  whole  state  of  the  case  to  the  mind  of  the 
reader  at  once. 

The  tedious  and  unprofitable  solutions  of  geometry  and  triginometry  are,  therefore,  abolished, 
together  with  the  tables  of  the  logarithms  of  numbers,  which  are  never  used  at  sea,  even  by  those 
persons  who  have  previously  studied  the  subject,  and  who  have  eventually  to  fall  back  upon  the 
method  now  used  in  this  work. 

The  sailings  are  therefore  explained  by  diagrams,  and  worked  out  by  inspection  of  the  traverse 
table;  only,  the  same  as  we  actually  do  at  sea,  and  which  is  correct  enough  for  all  practica] 
purposes ;  thus  relieving  the  learner  from  the  embarrassment  of  having  several  methods  given 
of  doing  the  same  thing. 

The  names  of  the  parts  of  the  diagram  are  inserted  against  them,  which  makes  it  easier  to 
comprehend  the  meaning  of  the  case,  and  will  be  found  an  improvement  upon  the  old  system  of 
marking  them  alphabetically  for  the  purpose  of  reference. 

Every  diagram  in  this  work  is  drawn  on  the  same  scale,  that  is,  with  the  chord  of  60",  taken 
from  the  plane  scale,  (and  which  is  in  general  use  on  board  ship.)  Instructions  are  also  given  how 
to  construct  the  diagrams,  so  that  the  learner  may  teach  himself  in  a  mechanical  manner,  and 
which  will  give  him  more  insight  into  the  nature  of  the  problem  than  the  study  of  geometry  and 
trigonometry  will. 

In  Parallel  and  Middle  Latitude  Sailings,  diagrams  of  semi-hemispheres  are  introduced,  showing 
the  contraction  of  the  meridians  towards  the  poles,  and  the  comparative  length  of  the  degrees  of 
longitude  in  the  various  parallels  of  latitude.  And  in  Mercator's  Sailing,  a  diagram  showing  the 
meridians  all  parallel  to  each  other,  and  the  expansion  of  the  degrees  of  latitude  towards  the  poles. 

Current  sailing  is  gone  into  at  some  length,  and  rules  given  as  they  are  applied  in  the  practice 
at  sea,  m  this  difficult  branch  of  the  study. 

Taking  departures,  or  ascertaining  the  ship's  place  by  the  bearing  of  the  land,  is  introduced, 
and  a  table  given  to  find  the  ship's  position  by  two  bearings  of  the  same  object,  having  the  course 
and  distance  sailed  between  them.  This  will  be  found  very  useful  to  a  ship  coasting  along  shore, 
a*  her  distance  oif  shore  can  be  easily  found  by  the  use  of  this  table ;  and  upon  the  same  prinoipla 
ber  distance  off  shore  may  be  ascertained  by  projecting  the  accompanying  diagram. 


n  PREFACE 

The  time  of  high  water  is  found  by  the  usual  rules,  and  is  only  an  approximation.  Local  tid« 
table  only  can  show  the  time  of  high  water  with  any  degree  of  certainty.  The  navigator  will 
naturally  consult  those  tables  in  preference  to  any  general  rule,  where  accuracy  is  required. 

A  short  account  of  the  prevailing  winds  and  currents  in  the  various  parts  of  the  world  are 
introduced,  chiefly  derived  from  my  own  experience,  and  will  be  found  interesting  and  useful  to 
ne  young  navigator. 

The  cause  and  effect  of  hurricanes  are  also  explained  in  a  short  and  familiar  manner,  and 
practical  rules  given  to  avoid  their  fatal  effects,  illustrated  by  diagrams  of  the  storm  circles  in 
both  North  and  South  latitude,  and  which,  by  giving  the  subject  a  little  attention,  will  be  easily 
understood.  The  rules  given  to  avoid  the  focus,  and  the  general  handling  of  a  ship,  on  approach 
ing  the  verge  of  the  storm  circle,  the  falling  of  the  barometer,  etc.,  are  also  derived  from  my  own 
experience,  the  facts  having  been  recorded  in  the  journals  I  have  kept  of  many  voyages,  where 
they  prevail. 

The  usual  rules  are  given  for  the  construction  of  a  general  chart  on  Mercator's  projection, 
illustrated  by  a  diagram  chart  of  part  of  the  North  Atlantic  Ocean.  The  use  of  it  is  explained, 
and  a  number  of  questions  proposed,  and  the  answers  given,  so  as  to  citable  the  learner  by  himself 
to  obtain  a  thorough  knowledge  of  this  most  important  subject. 

Rules  are  also  given  to  construct  a  coasting  chart  on  a  large  scale,  illustrated  by  a  diagram,  and 
the  use  of  it  explained,  under  all  the  possible  circumstances  in  which  a  ship  may  be  placed,  and 
questions  and  answers  given  in  like  manner,  which  will  be  found  of  much  importance  to  the  learner 

The  manner  of  sounding  with  the  lead  recommended,  on  a  ship's  approaching  the  coast  in  thick 
weather,  and  the  method  of  tracing  out  her  track,  by  soundings,  on  the  chart,  when  no  observations 
of  the  heavenly  bodies  can  be  obtained,  and  will  be  found  of  much  service  to  the  young  navigator. 

Nautical  astronomy  is  then  introduced,  containing  the  various  methods  of  finding  the  ship's 
place  on  the  ocean  from  astronomical  observations,  and  commences  with  a  diagram  of  the  solar 
system,  showing  the  real  state  of  the  case,  and  the  motion  of  the  earth,  and  of  those  planets  only 
which  are  used  in  navigation,  round  the  sun. 

Nautical  astronomy  is  then  defined,  and  diagrams  of  the  sphere  given,  showing  the  case  reversed 
and  the  earth  is  treated  as  a  mere  speck  in  the  centre  of  the  universe,  and  all  the  heavenly  bodies 
revolving  round  it,  the  spectator  being  supposed  to  be  situated  at  an  immense  distance  to  the 
Eastward  of  it. 

These  diagrams  will  be  found  of  great  importance  in  giving  the  learner  a  mechanical  knowledge 
of  the  nature  of  the  circles  and  angles  supposed  to  be  drawn  in  the  heavens,  and  will  show  at  once 
the  meaning  of  the  various  terms  used  in  nautical  astronomy,  and  which  any  amount  of  descrip- 
tion would  fail  to  do  without  them.  The  manner  of  constructing  those  diagrams,  from  the  use  of 
the  plane  scale,  and  the  measuring  of  the  various  circles  and  angles,  are  also  given,  with  the  view 
of  exercising  the  learner,  and  to  impress  the  figure  on  his  mind ;  and  they  are  generally  so 
arranged  that  the  description  is  given  on  the  page  facing  them. 

The  projection  of  the  heavens  in  two  hemispheres,  shows  at  once  the  nature  of  the  right 
a.scension  and  declination  of  the  heavenly  bodies,  the  sun's  path  in  the  heavens,  the  signs  of  the 
zodiac,  etc. 

And  the  diagram  of  motion  round  the  pole  will  give  a  distinct  idea  of  the  movement  of  the 
hour  angles  of  the  heavenly  bodies  in  an  opposite  direction  to  their  movements  in  right  ascension. 

As  it  is  of  much  importance  to  seamen  to  be  able  to  find  the  latitude  from  the  meridian  altitude 
of  a  star,  1  have  introduced  several  diagrams,  showing  the  nature  of  a  meridian  altitude,  and  how 
It  may  be  computed,  and  also  a  new  table,  containing  the  meridian  passages  of  those  stars  of  the 
first  magn'tudfe  which  are  t^enerally  used  at  sea,  for  avery  third  day  throughout  the  year,  by  which 
means  a  person  otherwise  unacquainted  with  the  stars  in  the  heavens  may  be  enabled  to  tind  any 
star  on  the  meridian  without  knoM'ing  it,  and  find  his  latitude  thereby. 

The  planets  are  also  found  by  the  same  method,  having  the  time  they  pass  the  meridian  from  the 
\autical  Almanac. 

Diagrams  showing  the  effect  of  the  dip  of  the  horizon,  refraction,  and  parallax,  which  is  fully 
explained  on  the  opposite  page 


PREFACE.  Tit 

A  diagram  showing  the  manner  of  observing  altitudes  of  the  he&venly  bodies  and  the  nature  of 
the  correction  for  semi-diameter. 

The  instruments  of  navigation  and  nautica.  astroncmy  are  then  explained,  and  the  manner  of 
reading  off  and  adjusting  them. 

The  use  of  the  quadrant  for  taking  altitudes,  and  the  sextant  for  measuring  angular  distance* 
Detween  the  sun  and  the  moon,  or  the  moon  and  stars,  are  fully  explained,  together  with  a  ne-w 
method  of  causing  the  moon  to  measure  her  own  distance  from  the  sun  or  a  star. 

The  artificial  horizon  is  explained,  and  a  diagram  showing  the  cause  of  the  double  reflection, 
this  being  a  most  useful  instrument  for  rating  a  chronometer  on  shore,  when  the  sea  horizon  ia 
not  visible. 

The  use  of  the  chronometer  is  now  explained,  and  the  various  practical  rules  given  for  its 
management  on  board  ships  at  sea,  which  will  be  found  of  great  service  to  the  young  navigator. 

The  azimuth  compass  is  next  explained,  and  the  manner  of  taking  azimuths  and  amplitudes,  aa 
practiced  at  sea. 

Then  follow  remarks  on  the  action  of  the  barometer  and  thermometer,  derived  from  experience 
in  the  use  of  these  instruments  for  the  last  twenty-five  years.  The  action  of  the  new  or  Aneroid 
Barometer  is  also  explained. 

The  sun  being  the  most  important  of  all  the  heavenly  bodies  on  which  observations  are  made, 
the  manner  of  correcting  his  declination  is  first  introduced,  and  the  latitude  deduced  from  his 
meridian  altitude,  illustrated  by  diagrams  of  all  the  various  cases,  which  will  give  the  learner  a 
complete  insight  into  the  meaning  and  nature  of  finding  the  latitude,  not  only  by  the  sun,  but  by 
the  meridian  altitude  of  any  other  heavenly  body.  • 

Finding  the  latitude  by  an  altitude  of  the  sun  out  of  the  meridian,  is  then  introduced,  having 
the  time  from  noon,  or,  which  may  be  deduced  from  the  Greenwich  time  by  chronometer,  and  bv 
the  help  of  a  new  table  for  that  purpose,  a  correction  is  found,  which,  added  to  the  observe 
•Ititude,  gives  the  meridian  altitude.     The  latitude  is  then  found  in  the  usual  manner. 

The  latitude  is  also  found  by  two  altitudes  of  the  sun,  misnamed  double  altitudes,  by  a  new 
method  of  using  the  hour  angle  of  the  lesser  altitude,  to  which  is  applied  the  interval  of  time 
between  the  observations,  corrected  for  the  ship's  change  of  longitude  in  time,  and  the  result  is 
the  inner  hour  angle,  or  the  time  from  noon,  at  which  the  greater  altitude  was  observed,  it  now 
becomes  the  same  case  as  if  only  one  altitude  had  been  observed.  This  will  be  found  a  more  direct 
and  easier  mode  of  solving  the  problem  than  by  the  old  and  tedious  methods  of  double  altitudes 
given  in  works  of  this  kind. 

A  method  is  also  given  of  finding  the  latitude  by  measuring  the  change  of  altitude  of  any  of  th5 
heavenly  bodies  on  the  prime  vertical  in  one  minute  of  time  ;  and  this  portion  of  altitude  found 
in  a  table  constructed  for  the  purpose,  will  point  out  the  latitude  corresponding,  within  certain 
limits. 

The  latitude  by  the  meridian  altitude  of  the  moon  is  found  in  the  usual  manner,  only  it  is  much 
simplified  by  the  introduction  of  a  new  table,  containing  the  correction  for  the  moon's  parallax  in 
altitude,  given  in  minutes  and  tenths  of  minutes,  and  taken  out  for  the  nearest  degree  of  apparent 
altitude  and  the  nearest  minute  of  parallax,  which  is  sufficiently  near  enough  for  all  practical  purposes. 
Becaurff ,  if  the  Greenwich  time  be  not  accurately  known,  the  moon's  declination  cannot  be  found 
within  ten  times  the  amount  of  the  difference  between  this  table  and  the  most  rigorous  method  of 
finding  this  correction,  a  new  table  is  also  given  to  correct  the  moon's  declination  to  the  Green 
wich  date. 

The  method  of  finding  the  planets  on  the  meridian,  and  the  latitude  obtained  from  their  meridian 
allitudv^  also  the  mode  of  finding  the  stars  on  the  meridian,  further  explained,  with  the  manner  of 
finding  the  latitude  from  their  meridian  altitudes  fully  explained,  and  which  may  be  put  in  practice 
by  any  person,  otherwise  unacquainted  with  the  stars  in  the  heavens,  ly  p'mply  followintr  the  direc- 
tions g'ven  in  this  work.  The  manner  of  finding  the  latitude  by  the  meridian  altitude  of  the  pole 
star,  both  above  and  below  the  pole,  and  the  usual  table  for  finding  the  latitude  by  that  stjir 
At  any  other  time  of  the  night,  which  has  heai  constructed  for  this  year,  but  will  serve  for  several 
years  hereafter. 


nil  ^  PREFACE. 

A  method  of  finding  the  correct  latitude  in  the  night  time,  when  the  horizon  :s  often  obsour«d 
and  doubtful,  by  observing  stars  both  North  and  South  of  the  meridian,  and  can  be  practiced  io 
either  hemisphere,  will  be  found  of  great  use,  from  its  extreme  simplicity,  as  will  also  the  finding 
of  the  latitude  by  the  moon,  planets,  or  stars  out  of  the  meridian.  For  instance,  if  the  latitude 
is  required  to  be  known  at  twilight,  (which  is  the  best  time  for  taking  altitudes  of  the  stars,  the 
horizon  being  then  distinctly  visible,)  it  may  happen  that  there  are  no  stars  on  the  meridian  al 
that  time.  Now,  if  an  altitude  of  a  star,  which  is  nearest  to  the  meridian,  be  observed,  and  th* 
apparpnt  time  of  the  observation  noted,  (as  in  the  case  of  the  sun,)  the  apparent  time  at  ship  ma^ 
be  deduced  from  the  Greenwich  time  by  chronometer,  it  is  easy  to  find  the  star's  distance  from 
the  meridian,  (which  with  the  sun  is  the  time  from  noon,)  and  is  used  in  the  tables  in  the  same 
manner,  by  which  means  we  obtain  a  correction  to  be  added  to  the  observed  altitude  of  the  star 
Thence  the  meridian  altitude  is  obtained  and  the  latitude  is  found  as  correctly  as  if  the  meridiaD 
altitude  had  been  actually  observed. 

The  finding  the  variation  of  the  compass  at  sea  by  amplitudes  and  azimuths,  is  now  introduceo, 
illustrated  by  diagrams  showing  the  real  state  of  the  case,  and  also  why  the  variation  is  called 
easterly  and  westerly. 

Then  follows  a  diagram  showing  the  effect  of  local  attraction  on  a  ship's  compass,  the  mannet 
of  detecting  the  same,  and  the  best  means  of  remedying  the  erro;,  and  remarks  on  fixing  up  r 
standard  compass. 

Diagrams  showing  the  nature  of  hour  angles,  and  the  terms  used  in  the  computation,  clearlj 
explained,  and  the  apparent  time  at  ship  found  from  a  set  of  altitudes  of  the  sun,  the  corresponding 
time  being  noted  by  a  watch  or  chronometer,  as  is  usually  done  at  sea.  The  time  tables  used  in 
/his  work  are  simply  the  co-secants  for  degrees  and  minutes  of  the  polar  distance,  the  secants  for 
ihe  latitude,  the  co-sines  of  the  half  sum,  and  the  sines  of  the  difference  or  remainder. 

The  apparent  time  from  the  preceding  noon  or  midnight,  in  the  case  of  the  sun,  or  the  hour 
anglea  of  the  other  bodies,  may  be  taken  out  at  once  from  these  tables. 

The  logarithms  in  these  tables  are  also  used  for  other  purposes  in  this  work.  The  old  standard 
tables  of  logarithms,  sines,  tangents,  secants,  etc.,  are  not  required. 

Finding  the  time  at  sunrise  and  sunset  is  illustrated  by  diagrams  showing  the  nature  of  the 
case,  and  the  degree  of  dependence  to  be  placed  thereon. 

The  method  of  finding  the  apparent  time  at  noon  from  equal  altitudes  of  the  sun,  is  also  intro- 
duced, and  is  valuable  from  its  extreme  simplicity. 

The  finding  the  time  on  shore  by  the  use  of  the  artificial  horizon.  •«► 

The  mode  of  finding  the  time  at  sea  by  an  altitude  of  the  moon,  planets,  and  stars,  and  also 
the  manner  of  finding  any  particular  planet  or  star  in  the  heavens  at  any  given  time,  when  abore 
the  horizon  ;  in  like  manner,  the  name  of  any  star  of  the  first  magnitude,  or  planet,  whose  altitude 
has  been  observed,  may  be  known. 

After  thus  having  given  all  the  various  modes  of  finding  the  time  at  ship,  the  longitude  by 
chronometer  is  then  gone  into,  and  every  possible  case  is  taken  notice  of  and  exemplified,  first 
by  the  sun,  in  which  the  cases  are  all  worked  out  in  full,  and  every  necessary  correction  fully 
explained,  to  which  are  added  the  practical  rules  as  they  are  worked  out  at  sea.  A  new  table  ia 
here  added,  to  correct  the  longitude  by  chronometer,  when  the  latitude  used  in  computing  the 
time  at  ship  is  proved  to  have  been  in  error ;  thus  saving  the  time  and  trouble  of  working  i 
over  again. 

ITie  longitude  by  chronometer  is  found  at  sun  rising  and  setting,  and  also  from  equal  altitude* 
at  noon,  and  from  the  altitudes  of  the  moon,  planets,  and  stars.  The  mode  is  also  given  of  com- 
bining observations  of  two  different  bodies,  with  the  view  of  finding  both  latitude  and  longitude 
by  chronometer,  at  the  same  instant  <^f  time. 

Sumner's  method  is  now  introduced,  explained  and  exemplified,  according  to  the  mode  [  have 
been  in  the  habit  of  using  myself  at  sea,  and  illustrated  by  a  diagram,  showing  its  great  utility 
and  use  to  the  navigator,  when  the  ship  is  approaching  land  or  a  danger. 

Tlie  method  of  rating  chronometers  at  sea,  from  time  "^o  time  during  the  voyage,  when  in  sight 
of  land,  is  full)   explained  and  exemplified,  and  also  when  in  port,  either  by  the  spa  or  by  ■■ 


PREFACE.  ts 

artificial  honzon.  This  is  worthy  the  attention  of  navigators  who  carry  chronometers,  from  th» 
(act  that  chronometers  generally  alter  their  rate  after  being  received  on  board,  and  acquire  what 
is  termed  a  sea  rate,  and  which  is  easily  ascertained  by  the  above  method. 

In  treating  of  lunar  observations,  diagrams  have  been  introduced,  showing  the  nature  of  the 
oorroctiins  required  in  clearing  the  lunar  distance,  and  a  case  projected  exhibiting  the  relative 
positions  of  the  two  bodies  in  the  heavens,  and  the  hour  angle  of  one  of  them  used  in  finding  the 
time  at  ship. 

The  various  methods  of  observing  and  writing  down  this  observation  is  given  as  practiced  at 
sea,  and  distances  exemplified  in  a.i  the  various  cases^  between  the  sun  and  moon,  and  between 
the  moon  and  planets  and  stars. 

In  clearing  the  lunar  distance,  one  method  only  has  been  adopted,  which  is  that  by  Lyons,  and 
IS  nearly  the  same  as  that  given  in  Thompson's  Tables,  and  which  I  have  found  from  experience  to 
be  the  most  simple  and  easiest  understood  of  any  mode  now  in  use,  and  is  correct  enough  in 
practice. 

Much  precision  in  clearing  the  lunar  distance  is  not  aimed  at  in  this  work,  therefore  many 
tedious  corrections  are  omitted,  which  only  tend  to  embarrass  the  navigator,  and  which  are  seldona 
applied  in  practice,  and  from  the  nature  of  errors  in  observing  the  distance  itself,  they  do  not 
seem  to  be  required. 

The  lunar  observation  in  this  work  is  therefore  considered  only  as  a  means  of  detecting  any 
Tery  gross  error  in  the  longitude  by  chronometer,  during  a  long  voyage. 

A  method  is  here  also  given  of  finding  the  longitude  by  a  lunar  observation  on  shore,  on» 
altitude  being  observed  in  the  artificial  horizon,  and  the  other  computed. 

I  have  also  introduced  a  new  method  of  my  own,  which  I  have  often  used  at  sea,  which  is  that 
of  finding  the  longitude  by  measuring  the  moon's  declination,  illustrated  by  diagrams  of  the 
meridian  altitudes  of  the  moon  and  a  star.  The  principle  of  this  method  is  simply  to  observe  th» 
distance  between  the  bodies  on  the  meridian.  Then  the  star's  declination  being  known,  (taken 
from  the  almanac  or  table,)  furnishes  the  moon's  declination.  Or,  the  meridian  altitudes  of  the 
bodies  being  observed,  (though  not  necessarily  on  the  meridian  together,)  the  star's  declination 
applied  to  the  difference  of  the  altitudes,  gives  the  moon's  declination.  Now,  where  this  declina- 
tion  so  measured  is  found  in  the  nautical  almanac,  will  give  the  Greenwich  time.  Then  the  dif- 
ference between  this  time  and  the  mean  time  of  the  moon's  passing  the  meridian  of  the  ship,  i» 
the  longitude  in  time,  etc. 

The  method  of  working  days  works  and  keeping  the  ship's  reckoning  at  sea,  adapted  to  the 
present  age,  is  thoroughly  explained  and  exemplified,  and  the  various  rules  given  in  the  first  part 
of  this  work  are  now  applied,  as  are  also  those  in  nautical  astronomy,  to  find  her  position  from 
celestial  observations. 

The  method  of  navigating  a  ship  is  now  introduced,  showing  the  mode  of  applying  all  the  details 
which  have  been  previously  gone  through,  and  many  useful  suggestions  given,  which  have  been 
derived  from  my  own  experience  of  a  sea  life,  and  will  be  found  of  service  to  the  young  navigator 
in  times  of  peril  and  danger. 

Amongst  which  the  rules  given  for  avoiding  a  collision  on  ships  meeting  each  other  at  sea,  will 
be  found  of  great  importance,  and  should  be  thoroughly  understood  by  every  seaman.  I  have» 
therefore,  put  them  into  a  practical  shape.  These  rules  are  recognized  by  courts  of  law  in 
deciding  cases  of  collision. 

The  method  of  keeping  a  log-book  is  explained,  and  various  remarks  made  thereon,  exemplified 
y  a  harbor  log,  the  manner  of  keeping  the  log  at  sea  by  civil  time,  and  also  in  the  usual  mod* 
by  sea  time.  The  whole  is  then  wound  up  by  the  journal  of  a  voyage  in  a  clipper  ship,  in  which 
every  circumstance  is  noted  in  the  log-book,  as  it  would  actually  be  done  at  sea,  and  showing  th» 
care  and  circumspection  necessarily  required  in  navigating  a  fast^sailing  vessel,  from  the  fact  that 
an  error  in  the  course  of  such  a  vessel  will  produce  an  error  in  the  dead  reckoning,  in  one  day'» 
run,  of  from  two  to  three  times  the  amount  greater  than  what  the  same  error  in  the  course  of  & 
■Jow-sailing  vessel  would  produce. 

Many  new  tables  have  been  introduced  into  this  work,  with  the  view  of  shortening  the  compa 


»  PREFACE. 

tations,  and  they  are  so  arranged  as  to  be  easily  referred  to  in  practice,  the  one  following  the  othet 
•8  they  are  required  to  be  used  at  sea. 

The  tables  usually  given  in  works  of  this  kind  are  rejected,  except  those  only  which  have  • 
direct  bearing  upon  the  practice  of  navigation  at  sea. 

The  tables  containing  the  times  of  high  water  at  full  and  change,  the  variation  of  the  compass  in 
early  all  parts  of  the  world,  deduced  from  actual  observation  at  sea,  and  the  very  important  one 
f  the  position  of  places,  which  is  taken  from  the  best  English  authorities  on  those  subjects,  in  which 
the  principal  headlands,  ports  and  islands  only  are  given,  with  the  view  of  enabling  the  navigator 
to  verify  his  chronometer  on  sighting  the  land  at  any  time  during  the  voyage,  or  rating  it  while 
in  port,  the  position  of  shoals,  etc.,  are  not  given,  the  navigator  will  naturally  look  for 
information  on  this  subject  from  his  chart,  which  will  furnish  the  most  proper  and  correct 
delineation  of  their  extent  and  position,  which  cannot  be  obtained  from  a  table. 

From  the  foregoing  prefatory  remarks,  it  will  be  perceived  that  no  very  great  amount  of 
mathematical  knowledge  is  required,  beyond  the  common  rules  of  arithmetic,  to  become  a  good 
practical  navigator. 

Practical  navigation  does  not,  therefore,  consist  of  a  tedious  set  of  oalculations,  with  a  view  of 
obtaining  a  very  nice  precision  at  any  given  time,  but  in  the  tact  with  which  the  navigator  can 
single  out  and  employ  the  heavenly  bodies,  in  finding  his  ship's  position  therefrom,  either  by  day 
■or  by  night,  and  by  increasing  the  number  of  observations,  serve  as  a  check  upon  each  other,  and 
thus  verify  her  position  in  short  intervals  of  time,  in  the  shortest  and  simplest  manner  possible, 
having  a  due  regard  at  the  same  time  to  its  general  correctness ;  and  which  has  been  the  aim 
of  this   work  to  accomplish. 

Having  been  engaged  for  some  years  in  the  instruction  of  seamen  in  navigation,  I  find  that  the 
chief  difficulty  lies  in  the  fact  that  the  generality  of  them  cannot  spare  time  sufficient  on  shore  for  the 
purpose  of  studying,  and  that  they  are  obliged  to  pick  up  scraps  of  it  here  and  there,  as  they  best 
can,  from  whatever  book  falls  in  their  way  ;  and  not  being  able  to  discriminate  between  what  i 
really  useful  in  practice  or  otherwise,  many  of  them  form  very  erroneous  ideas,  in  their  laudable 
attempt  at  self-instruction. 

Therefore  the  chief  inducement  I  had  in  writing  this  work,  was  to  place  it  within  their  reach, 
iivested  of  everything  but  what  has  a  direct  bearing  on  the  practice  at  sea,  whereby  they  might 
instruct  themselves  with  greater  ease  than  formerly,  as  it  will  lead  them  step  by  step  from  the 
Vowest  up  to  the  highest  branches  of  the  science,  and  it  embraces  everything  that  is  required  to 
form  a  good  practical  navigator. 

Here  1  may  remark,  that  the  entire  work  has  been  computed  and  written  by  myself,  from  the 
observations  and  memoranda  contained  in  the  journals  of  many  voyages  I  have  made  to  nearly 
all  parts  of  the  world,  the  examples  having  been  reduced  to  the  present  year  of  1854,  for  the  sake 
of  uniformity  ;  and  to  accommodate  those  persons  who  may  not  have  an  almanac  for  that  year  at 
hand,  I  have  added  a  table  of  extracts  from  the  Nautical  Almanac,  containing  the  data  for  working 
the  examples. 

Seamen  will  please  to  bear  in  mind  that  the  work  has  been  written  by  one  of  themselves,  and 
with  a  sincere  desire  for  their  improvement  and  instruction,  and  should  it  meet  with  their  approval, 
^equal  to  the  amount  of  labor  bestowed  on  it,)  would  leave  nothing  more  to  be  desired. 

And,  without  meaning  any  disrespect  to  the  generality  of  navigators,  I  may  add,  that  from  nQ.y 
«wn  experience  I  know  that  there  are  many  who  are  very  deficient,  not  from  the  want  of  the 
capacity  of  becoming  so,  but  from  the  want  of  the  proper  means  of  instruction,  and  which  would 
(Beem  to  verify  the  words  of  the  ancient  sage,  on  being  interrogated  by  the  youth.  "  My  son" 
said  he,  '■  when  you  come  to  the  years  of  manhood,  you  will  be  astonished  to  find  how  little  wisdom 
it  used  in  the  governing  of  the  worlds 

1  cannot  close  the  preface  to  a  work  of  such  immense  labor,  without  soliciting  the  indulgence 
of  the  reader  to  any  errors  or  inaccuracies  which  may  have  unavoidably  crept  in,  notwithstanding 
the  extreme  care  I  have  taken  in  revising  the  work  over  several  times,  both  before  and  after  com' 
mitting  it  to  the  press.  I,  however  flatter  myself  that  few  will  be  found  to  ex'jst  of  much 
importance.  WILLIAM  THOMSl 


CONTENTS. 


PAGE 

ImkOMicnoif  to  tbe  Practice  of  Navigation  at  Sea.  1 
Diagram  of  the  Earth — its  description  and  dimen- 

eious. 2 

Definition  of  the  imaginary  Circles  on  the  Earth's 

surface — Latitude,  etc^  explained S 

do.                     do.              Longitude  explained.  4 

Diagram  of  the  Earf.    h   'wo  Hemispheres 

Definition  of  Plant    •        2  and  the  properties  of  a 

Right-angled  Tr.     -      explained 6 

Instruments  of  Naviga„ u  defined  and  explained.. .  6 
Mariner's  Compass,  and  a  Table  of  the  Angles  each 

point  makes  with  the  Meridian 7 

The  Sailings — Great  Circle  described  on  the  Chart.  8 

Plane  Sailing,  by  Projection  and  Inspection 9 

•Questions  for  Exercise  in  Plane  Sailing 13 

IVaverse  Sailing  by  Projection  and  Inspection 14 

Parallel  Sailing  by  Projection  and  Inspection,  with 
a  Table  showing  the  number  of  minutes  and 
seconds  of   Departure  contained  in  one  degree 

of  Longitude,  f  t  every  degree  of  Latitude.  ...  18 

Middle  Latitude  Sailing  by  Projection  and  Inspection  20 

Questions  for  Exeicise  in  Case  Ist,  Mid.  Lat  Sailing  22 

do.                  do.       in  Case  2d,  Mid.  Lat.  Sailing  24 

Mercator's  Sailing  by  Projection  and  Inspection ....  25 

Questions  for  Exercise  in  Car",  1st,  Mercator's  Sailing  26 

do.                   do.      in  Case  2d,  Mercator's  Sailing  28 

Current  Sailing  explained 29 

Questions  for  Elxercise  in  Current  Sailing 30 

Taking  Departures,  or  finding  the  Ship's  Position 

from  the  Bearing  of  known  objects  on  the  Land  31 
Table  for  finding  the  Ship's  Position  by  two  Bear- 
ings of  the  same  object  on  the  Land,  with  the 

Rules 82 

Projection  of  a  case  of  finding  the  Ship's  Position  by 

two  Bearings 33 

Questions  for  Exercise  in  finding  the  Ship's  Position 

from  Beaiings    84 

Tides — Description  and  Cause  of  explained 35 

First  Method  of  finding  the  Time  of  High  Water.. .  36 

Second  Method  of  finding  the  Time  of  High  Water.  87 

Winds  in  different  parts  of  the  World  described. . .  SB 

Currents  of  the  Ocean  described 39 

Hurricanes — their  Nature  and  Cause  described.  ...  41 

Diagram  of  the  Storm  Circle  in  North  Latitude.. . .  42 

do.                            do.               South  Latitude....  43 

Remarks  on  Handling  a  Ship  in  a  Hurricane 44 

The  Construction  of  MercJitor's  Chart 46 

Diagram  of  a  Chart  of  Part  of  the  Atlantic  Ocean, 

and  Ship's  Track 

Construction  of  a  Coasting  Chart  on  a  large  scale. .  47 
fhe  Use  of  Mercator's  Chail,  Pricking  off  the  Ship, 

Shaping  a  Course,  etc_ 48 

Questions  for  Exercise  in  Using  the  Chart 49 

(J«e  of  the  Coasting  Chart  and  Questions  for  Exer- 
cise.    60 

Span  lings  on  the  Coast,  witli  Remarks  *^reon. ...  62 


NAUTICAL  ASTRONOMY. 

Diagram  of  the  Solar  System,  and  explanation   ...  54 

Description  of  the  Planets  used  in  Navigation 6fi 

Diagram  of  the  Sphere,  projected  and  explained. .  56 

Definition  of  Nautical  Astronomy 67 

Diagram  of  the  Sf^-'re,  and  the  definitions  explained  58 

Projection  of  the  Heavens  in  two  Hemispheres 60 

Signs  of  the  Zodiac,  and  the  Change  in  the  Seasons 

explained fil 

Diagram  of  the  Motions  of  the  Heavenly  Bodies 

round  the  Pole 6S 

Definitions  of  Tmie •"••... 68 

Diagrams,  showing  the  Method  of  finding  the  Stars 
in  the  heavens  from  their  computed  Altitude 

and  Meridian  Passage 64 

Diagrams,  showing  tbe  Dip,  Refraction  and  Parallax  66 

Definitions  of  the  Dip,  Refraction  and  Parallax 67 

Diagram,  showing  the  manner  of  taking  Altitudes .  f.8 

The  Instruments  of  Nautical  Astronomy  explained  69 

To  Adjust  the  Quadrant 70 

To  Measure  Altitudes  with  the  Quadrant 71 

To  Adjust  the  Sextant 72 

To  find  the  Index  Error  of  the  Sextant 73 

The  Use  of  the  Sextant  in  measuring  Angular  Dis- 
tances     74 

To  find  any  Heavenly  Body  (used  in  the  Lunar  Dis- 
tance)  by   computing   its   Distance  from   the 

Moon 75 

Remarks  on  Telescopes,  and  a  New  Method  of  tak- 
ing Lunars 7(j 

The  Artificial  Horizon  explained 77 

Diagram,  showing  the  prinxjiples  of  the  Artificial 

Horizon 7  g 

The  Chronometer  explained — stopping,  setting  ago- 
ing, etc 79 

General  Remarks  on  tbe  Use  of  the  Chronometer. .  80 
The    Azimuth   Compass    explained — Taking    Azi- 
muths and  Amplitudes 81 

Use  of  the  Thermometer,  and  General  Remarks  on 

the  same §2 

Use  of  the  Barometer,  and  Practical  Remarks  on 

the  same 88 

To  Correct  the  Sun's  Declination,  with  Remarks. . .  84 
Questions  foi'  Exercise  in  Correcting  the  Declination  86 
Finding  the  Latitude   by  the   Sun's   Meridian  Alti- 
tude   85 

Diagrams  and  Examples  of  finding  the  Latitude  by 

the  Sun 87 

Questions  for  Exercise gg 

Diagram  of  tiie  Sun  in  the  Zenith,  and  Examples. .  89 

Finding  tlie  Latitude  by  observing  the  Sun's  centre  89 
Finding  the  Latitude  by  a  back  observation  with  a 

Sextant ^ 

Finding  the  Latitude  by  a  Meridian  Altitude  of  the 

"^un  below  the  Pole ,,,.  %f 


CONTENTS, 


FAOE 

Fio.liDg  the  Latitad«  on  Shore  bj  the   Artificial 

Horizon 92 

Fiiuling  the  Latitude  by  the  Sun  out  of  the  Meridian  98 
Questioos  for  Exercise   in  findiog  the  Latitude  out 

of  the  Meridian 94 

Finding  the  Latitude  by  two  Altitudes  of  the  Sun. .  96 
QuertUoni^  tor  Exercise   in  finding  the  Latitude  by 

two  Altitudes 99 

Fiiiiiiiig  the  Latitude  from  the  Sun's  change  of  Alti- 
tude on  the  Prime  Vertical,  with  a  Tjible  con- 
taining the  Sun's  change  of  Altitude    in    one 
minute  of  time  for  ev^rj  degree  of  Latitude. . .    100 
Finding  the  Latitude  by  the  Meridian  Altitude  of 

the  Moou .' 101 

Examples  of  finding  the  Latitude  by  the  Moon. . . .  103 
Finding  the  Latitude  by  the  Meridian  Altitude  of  a 

Planet 104 

Examples  of  finding  the  Latitude  by  a  Planet  ....  105 
Finding  the  Latitude  by  the  Meridian  Altitude  of  a 

Star 106 

To  find  the  Star  in  the  heavens  from  its  computed 

Altitude  and  Meridian  Passage 107 

Examples  of  finding  the  Latitude  by  a  Star. 108 

Finding  the  Latitude  by  the  Meridian  Altitude  of 
the  Pole  Star,  and  also  at  any  other  time  when 

risible 109 

Finding  the  Latitude  by  the  Meridian  Altitude  of 
two  Stars,  North  and  South  of  the  Meridian, 

when  the  horizon  is  obscured 110 

Finding  the  Latitude  by  an  Altitude  of  a  Star  out  of 

the  Meridian Ill 

To  compute  the  Logarithm  of  the  Latitude  and  De- 
clination when  the  latter  exceeds  26* 112 

Finding  the  Latitude  by  two  Stars,  one  of  them  out 

of  the  Meridian 118 

Finding  the  Latitude  by  an  Altitude  of  the  Moon 

out  of  the  Meridian 114 

Finding  the  Latitude  by  an  Altitude  of  a  Planet  out 

of  the  Meridian 116 

Diagram  of  an  Amplitude,  and  solred  by  Inspec- 
tion     116 

Finding  the  Variation  of  the  Compass  by  an  Ampli- 
tude.    117 

Diagraui  of  an  Azimuth,  and  Rule  for  computing 

the  same 118 

Finding  the  Variation  by  an  Azimuth 119 

Diagram,  showing  the  EflFect  of  Local  Attraction  on 

the  Ship's  Compass 120 

Remedy,  when    Local    Attraction  exists   on  board 

Ship  at  Sea 121 

Finding  the  Time  at  Sea  by  the  Sun 122 

Diagrams  of  the  Hour  Angles,  with  North  and  South 

Declinations 123 

Method  of  Obserring  Altitudes  of  the  Sun  for  Time, 
and  Gkneral  Rules  for  finding  the  Time  at  Ship, 

with  Examples 124 

Diagram  of  the  Hour  Angles,  when  both  the  Sun 
and  the  Ship  are  on  the  Equator,  with  Exam- 
plea  of  finding  the  Time 127 

Finding  the  Time  by  the  Sun's  Rising  or  Setting. .  128 
Diagrams  of  the  Hour  Angles  at  Rising  or  Setting.  128 
Finding  the  Time  from  Equal  Altitudes  of  the  Sun 

near  Noon 130 

Finding  the  Time  on  Shore  by  the  Artificial  Horizon  181 

Finding  the  Time  by  an  Altitude  of  the  Moon 132 

Finding  the  Time  by  an  Altitude  of  a  Planet 134 

Finding  the  Time  by  an  Altitude  of  a  Star 1 36 

Remarks  on  finding  the  Longitude  by  Chronometer  138 
Finding  the  Longitude  by  Chronometer  by  the  Sun  140 
Fizamples  of  the  Ship  crossing  the  Opposite  Merid- 
ian to  Orcenwich 148 

To  Correct  the  Longitude  at  Noon,  wben  the  Lati- 
tude worked  with  is  in  error. 144 


Finding  the  Longitude  by  Gbrononaeter  at  Sunri»« 
or  Sunset 

Finding  the  Longitude  by  Chronometer  at  Noon, 
from  Equal  Altitude* 

Finding  the  Latitude  bv  the  Sun,  and  the  Longitude 
by  the  Chroiioineter  "jy  the  Meon 

Finding  the  Latitude  by  a  Star,  and  the  Longitude 
by  Chronometer  b}      Planet 

Finding  the  Longitude  b)  Chronometer,  and  the 
Variation  of  the  Compass  by  an  Azimuth,  from 
the  same  Altitude  ot  the  Sub 

Finding  the  Ship's  Positioi  at  Sea  by  Sumner's 
Method 

Diagram  of  Sumner's  Method 

Continuation  of  the  same  Example 

Rating  the  Chronometer  at  Sea 

Examples  in  West  Longitude 

do.  East  Longitude 

Rating  the  Chronometer  on  Shore 

Questions  for  Exercise  in  finding  the  Longitude  by 
Chronometer 

Lunar  Observations.  Diagram  showing  the  Efi'ect 
of  Parallax  on  the  Lunar  Distance 

Remarks  on  Lunar  Observations 

Methods  of  Observing  a  Lunar,  with  or  without  as- 
sistants  

Diagrams  of  a  Lunar  Observation 

Finding  the  Longitude  by  a  Lunar  Observation  by 

the  Sun 

do.  do.     Lunar  Ob8<»'v"'ion  by  a  Star. . 

do.  do.         do.  by  a  Planet 

To  find  the  Error  in  the  Meap'         .distance 

The  Bodies  being  too  near  the  ...pridian  to  get  the 
correct  time  from  their  Altitude.  Time  found 
afterwards  and  applied 

Rule  to  Compute  the  Altitude  of  any  heavenly  body 

To  Compute  the  Altitudes  at  the  time  of  observing 
the  Distance 

Finding  the  Longitude  by  Lunar  Observations  on 
Shore 

New  Method  of  finding  the  Longitude  from  the 
measurement  of  the  Moon's  Declination 

Diagram  of  the  Moon  and  a  Star  on  the  Meridian . . 

New  Method  of  finding  the  Longitude  from  the  Me- 
ridian Altitudes  of  the  Moon  and  a  Star 

Diagram  of  the  Meridian  Altitudes  of  the  Moon  and 
Star ,;,..    

Method  of  Keeping  a  Ship  s  Reckoning  at  Sea.. . . . 

The  Log  Board  explained 

Allowing  for  Leeway  and  Variation 

Remarks  on  Keeping  the  Reckoning  at  Sea 

Rules  for  Working  a  Day's  Work 

Example  of  a  Day's  Work,  outward  bound 

do.  do.         at  Sea 

do.  do.         inward  bound 

Finding  the  Departure  and  Longitude  from  Equal 
Distances  of  Sun  or  Star  from  the  Meridian  . . 

Navigating  the  Ship,  appUcationof  the  above  Rules, 

etc. 

do         Indications  of  Stormy  weather,  discovery 
of  Danger 

Rules  to  Prevent  CollisiM  on  meeting  Ships  at 
Sea,  etc. 

Lying  to  under  a  Drag.  Construction  of  a  Tempo- 
porary  Rudder 

Making  the  Land.     Signs  of  Land  being  near. 

Methods  of  Keeping  the  Log-Book 

Keeping  the  Harbor  Log,  outward  bound 

Method  of  Keeping  the  Log-Book  in  Civil  Time  . . 

Usual  Method  of  Keeping  the  Log  in  Sea  Time,  ex- 
emplified in  a  Journal  from  Santa  Cruz  to  St 
John's 

Abstract  of  the  Journal 


147 
148 
14« 

150 

151 
159 
154 
15C 
156 
158 
169 

160 

161 
163 

168 
164 

16& 
167 
168 
169 


170 

172 

178 

174 

176 
177 

178 

17» 
180 
181 
182 
188 
184 
185 
186 
187 

188 

188 

18» 

1»> 

19) 
19i 
193 
194 
19fi 


19« 
9M 


NOTICE   TO    THE   THIRD   EDITION. 

This  edition  has  been  furtker  revised  and  corrected  ;  and  a  new  and  complete  set  of  Tablei, 
for  finding  the  Time  at  Ship  (and  thence  the  Longitude  by  Chronometer),  have  been  added. 

NOTICE    TO   THE   SECOND    EDITION. 

This  work  has  been  revised  and  corrected,  and  an  addition  made  of  a  separate  Explana- 
tion of  the  Tables^  and  it  is  hoped  that  no  error  of  importance  will  now  be  found  to  exist. 
It  may  be  necessary  here  to  say,  that  the  author,  in  writing  this  work,  did  not  consider  a  separata 
Explanation  of  the  Tables  requisite,  as  he  had  beep  particular  irt  explaining  them  in  difftrent 
parts  of  the  work  when  they  were  used.  But  as  some  navigators  have  recommended  it,  the  fol- 
lowing has  been  added,  which  will  be  found  useful,  as  by  glancing  over  tliem  you  can  rapidly  see, 
what  the  book  contains,  where  the  tables  can  be  found,  how  and  where  they  are  used. 

EXPLANATION  AND  USE  OF  THE  TABLES. 

Note. — The  number  of  the  page,  which  is  placed  on  the  same  line  with  the  number  of  the 
table,  refers  to  the  second  part  of  this  work,  where  the  table  will  be  found,  and  the  numbers  of 
pages  in  the  margin  refer  to  the  first  part  of  this  work,  where  the  table  is  used  and  explained. 

TABLES  I.  AND  II.— Page  1  to  6L 

Difference  of  Latitude  and  Departure. 

These  tables  are  of  very  extensive  use  in  Navigation,  afibrding  an  easy  and  expeditious  method 
of  solving  problems  in  right-angled  plane   trigonometry,  and   consequently   applicable   to  every 
variety  of  sailing.     Table  I.  contains  the  difference  of  latitude  and   departure  (m  whole  numbers 
And  tenths)   answering  to  distances  not  exceeding  300,  and  for  courses  to  every  point      p        „ 
of  the  compass.     Table  II.  is  of  the  same  nature  and  extent,  but  for  courses  consisting  °„ 

of  whole  degrees.     The  courses  are  set  down  at  the  top  of  the  pages  when  they  do 
not  exceed  4  points  or  4.^  degrees,  and  at  the  bottom  when  they  are  greater  than  these  quantities; 
and  it  must  be  observed  that  when  the  courae  is   taken  from  the  /o/>  of  the   page,  the  diff.  of  Lat. 
and  Dip.  must  be  taken 'from  the  top  also,  but  when  the   course  is  taken  from  the  bottom  the  diff. 
of  Lat.  and  D(p.  must  be   taken    from   the  bottom.     Hence,  wnen  these  tables   are      „        ,„ 
applied  in  Farallcl  or  Middle  Latitude  sailing  the  co.  lat.  or  co.  mid.  lat.  is  taken  as  a         ''i'f 
course,  the  departure  or  meridional  distance  is  found  in  the  Dep.  coiumn,  and  the  dif- 
ference of  longitude  in  the  Dist.  column.     In   Mercator's  sailing,  the  meridional  dif-      p        „. 
ference  of  latitude  is  taken  out  in  the  Lat.  column,  and  difference  of  longitude  in  the        "^*     ^ 
Dep.  column.     When  any  of  the  given  parts  (excepting  the  courses,)  exceed  the  limits 
of  the   table,  any  aliquot  part,  as  a  half,  third,  fourth,  &c.,  is  to  be  taken  ;  and  those  found  cor 
responding  are  to  be  multiplied  by  the  same  figure  that  the  given  number  is  divided  by. 

TABLE  III.— Page  62  to  G7. 

Meridional  Parts. 


This  table  is  used  in  resolving  problems  by  Mereator's  sailing,  and  in  constru' ting      „        „_ 
eharts  on  Mereator's  projection.     The  meridional  parts  are  to  be  taken  out  fo»   the     ^nl 
degrees  answering  to  the  given  latitude,  at  the  top  or  bottom,  and  for  the  minutes  at 
either  side  colunm. 

•   1*  TABLE  IV.— Page  68. 

Mean   Refraction 

Thl.*  table  contains   the   mean  refraction   of  the   heavenly   bodies,   in   minutes  and      p        «- 
•econis,  at  a  mean  state  of  the  atmosphere,  and  corresponding  to  their  observed  alti-        °f  an 
tudes      This  correction  is  always  to  be  substracted  from  the  observed  altitude  of  the     " 
ohject. 


tn  EXPLANATION    AND    USZ    OF    THE    TABLES. 

•2  TABLE  v.— Paqb  69. 

Dip  of  the  Horizon 

_        ^^_  The  corrections  taken  out  from  this  table,  answering  to  the  height  of  the  eye,  ftboT* 

^fl_  the  sea  in  feet,  are  to  be  subtracted,  from  an  altitude  taken  by  a  fore  observation,  or 

*****      '         added  to  those  taken  by  a  back  one. 

*3  TABLE  VL— Paok  69. 

Sun^s  Parallax  in  Altitude. 

Foffe  67  This  correction  is  to  be  taken  out  opposite  the  Sun's  altitude,  and  is  always  ad 

and  86,         ditive  to  it. 

•  Ifot* — ^Th«  joint  effect  of  the  oorrections  taken  from  theBe  three  tables,  togetb«r  with  the  Sun's  semi-diameter,, 
tma  b«  taken  at  onoe  from  Table  IX.  when  the  altitude  of  the  Sun's  lower  limb  is  tr.ken  by  a  fore  obaerTation. 

TABLE  VIL-Page  69. 

Moon^s  Augmentation. 

_        .f..  The  Moon's  apparent  horizontal  semi-diameter,  as  given  in  the  Nautical  Almanacs, 

t^age  .  j^  ^.^  ^^  increased  by  a  number  of  seconds,  called  the  augmentation,  taken  out  from 
this  table,  answering  nearest  to  her  altitude.  I^ote. — In  practice  this  is  seldom  used,  except  in 
working  a  Lunar.     See  page  165. 

TABLE  VIII.— Page  69. 

Dip  at  Different  Distances. 

p       _»  When  that  part  of  the  horizon   immediately  under  the  Sun   is  obstructed  by  land,. 

"^  '  the  dip  is  to  be  taken  fi-om  this  table,  (with  the  height  of  the  eye  at  the  top,  and  th« 
estimated  distance  from  the  land  in  miles  in  the  side  column)  instead  of  Table  V. 

TABLE  IX.— Page  70. 
To   Correct  the   Observed  Altitude  of  the  Sun''s  Lower  Limb. 

n       Qrt  This  table  is  intended  to  simplify  the  usual  method  of  correcting  the  observed  altitude 

"^*  ■  of  the  Sun's  lower  limb,  when  taken  by  a  fore  observation,  by  showing  the  correc- 
tion at  once  for  the  joint  effect  of  the  Sun's  semi-diameter,  dip  of  the  horizon,  refraction,  and 
parallax.  These  corrections  I  ing  computed  to  minutes  and  tenths,  the  tenths  may  easily  be 
reduced  to  seconds  by  multiplymg  them  by  six.  In  this  table  the  Sun's  semi-diameter  is  assumed 
at  16  minutes,  and  its  variation  from  that  quantity  in  each  month  of  the  year,  given  at  the 
bottom  of  the  tal)le,  is  to   be  applied  to   the  corrections  found  in  the  table  according  to  the  sign 

-|-  or  —  prefixed  it. 

TABLE  X.— Page  71  and  72. 

Sun's  Declination. 

The  Sun's  declination  is  given  in  this  table  in  degrees  and  mmutes  for  the  years  1854-55- 
66-57,  at  noon  on  each  day  of  the  year  under  the  meridian  of  Greenwich ;  but  will  answer  for 
leveral  subsequent  years,  by  applying  the  corrections  from  Table  XII. 

TABLE  XL— Page  73. 

To  Correct  the  Suit's  Declination  for  Longitude  and  for  Time. 

T*      Al  "^^  ^^^  Sun's  declination   in  table  X.  is  adapted   to  the  meridian  of  Greenwich  at 

^Qfr  noon,  when  the  ship  is  to  the  eastward  or  westward  of  that   meridian,  it  should  be 

corrected  by  this  table;  also  when  it  is  required  for  any  other  time  than  noon,  it  can 

oe  corrected  by  this  table,  and  applied  as  directed  below  the  table.     J!iote. — Rules  for  correcting 

the  declination  (taken  from  the  Nautical  Almanac")  to  Greenwich  time,  at  page  124 


EXPLANATION    AND     IISK    OK     II IK    TABLKS.  «•• 

TABLE  XII.— Page  73. 

Correction  of  the   Sun's  Declinatu  n  evert/  4  years. 

This  table  is  intended  to  correct  the  Sun's  declination  given   in   Table  X-,  for  the  chanc[e  that 
takes  place  in  periods  of  four  years.     See  note  below  the  Uible. 

TABLE  XIIL— Paok  74. 

Sun's  Right  Ascension. 
* 
The  Sun's  mean  right  ascension  contained  in  this  table,  is  to  be  taken  out  with  the      p       ^»^ 
month  at  the  top,  and  the  day  in  the  side  column.     When  great  accuracy  is  necessary,  ' 

it  must  be  taken  from  Nautical  Almanac. 

TABLE  XIV.— Page  74. 

Equation  of  Time  and   Table  of  Corrections. 

The  Equation  of  time  for  apparent  noon   at   Greenwich,   is  given  in  this  table  for  the  years 
1854-55-i56  and  '57,  and  which  will  answer  nearly  for  sixteen  years.     A  table  adjoin-      „       ,j>^ 
ing  is  given  for  correcting  the  Equation  of  time  for  Longitude  and  for  time.     This  table  " 

is  entered  with  the  daily  change  of  the  variation  at  the  top,  and  the  Longitude  at  the  left  side,  (or 
if  for  time,  at  the  right  side)  and  the  angle  of  meeting  points  out  the  correction  in  sec.  and  tenths 
of  sec.  to  be  applied  as  directed  at  the  bottom  of  the  table.  Note. — Rule  for  correcting  th» 
Equation  of  time  from  the  Nautical  Almanac  is  given  at  page  124. 

TABLE  XV.— Page  75  to  80. 

J'hr  Finding  the  Latitude  out  of  the  Meridian. 

This  table  was  first  calculated  and  published  by  the  author  in  a  separate  form,  (call-      „       ^j- 
ed  Thorn's  Tables)  but  on  writing   this  work  was  introduced   in  it ;  it  is  divided  into  ^ 

five  parts,  and  explained  at  Page  93. 

TABLE  XVI.— Page  81  to  83. 

Apparent   Time,  of  Sun's  Rising  and  Setting. 

This  table  is  entered  with  the  declination  at  the   top  and  the  latitude  at  the  side,  and  the  angl* 
tC  meeting  will  point  out  the  time  of  rising  and  setting   from  the  top  when  the  Latitude  and  de- 
clination are  of  the  same  name,  or  from  the  bottom  when  they  are  of  contrary  names. 

To  Find  the   Time  of  Rising  and  Setting  of  any  other   Celestial   Object. 

This  table  also  exhibits  half  the  time  that  an  object  continues  above  the  horizon  in  Moon^s 

the  column  of  Sett.,  and  half  the   time  that  it  continues  below  in  the  column  of  Ris.,  M.  P., 

from  the  top  of  the  page,  when  the  latitude  and   declination  of  the  object  are  of  the  FagelOl. 

same  name,  and  from  the  bottom  when    they  are   of  contrary   names.     Therefore,  to  Star's 

find  the  time  of  the  object's  rising,  subtract  half  the  time  that  it  continues  above  the  M.  P., 

horizon,  from  the  time  of  t7s  passing   the   meridian,  and  to  find   the   time  of  setting  Fage  \0Q. 

add  half  the  time  that  it  continues  above  the  horizon  to  the  time  of  its  passing  the  Planet's 

meridian.     Note. — The  rule  for  computing  the  meridian  passage  of  the  Stars  is  given  M.  P. 

It  page  in.     Table  XVIIL  al^o  gives  the  Mn.  Passages  of  the  Stars  Page  85  to  90.  Page  115. 

TABLE  XVII.— Page  84. 

Altitudes  by  which  the  Apjyarent   Time  may  be  found  with    the  greaictit  accuracy. 

When  the  latitude  and  declination  of  an  object  are  of  the  same  name,  by  entering  this  tabU 
with  the  declination  at  top  or  bottom,  and  the  latitude  at  the  side,  the  angle  of  meeting  p^^  j23, 
points  out  the  altitude  of  the  object  nearly,  when  it  is  in  the  prime  vertical,  or  at  its 
nearest  approach  thereto,  and  which  is  the  best  altitude  for  ascertaining  the  apparent  time.  When 
the  latitude  and  declination  of  an  object  are  of  contrary  names  the  olject  is  nearest  the  prinw 
vertical,  when  in  the  horizon,  but  an  altitude  less  than  6°  or  7°  stould  not  be  used  on  account  ot 
\ite  uncertainty  of  refraction  at  low  altitudes. 


«T»  EXPLANATION    AND    USE    OF    THE    TABLES, 

TABLE  XVIII.— Page  85  to  90. 

Fof  finding   the  Apparent    Time  of  24   Principal  Stars  passing  the   Meridian  throughout  th» 
Page  106.     year. 

TABLE  XIX.— Paob  9L 

"age  106.  Sight  Ascension  and  Declination  of  24  Principal  Start. 

TABLE  XX.— Page  91. 

Fbr  Correcting  the  Observed  Altitude  of  a  Star  or  Planet. 


Page  108. 


Pag  109 
mtdll. 


This  table  contains  the  corrections  in  minutes  and  tenths  to  be  subtracted  from  th» 
observed  altitude  of  a  Star  or  Planet  to  find  its  true  altitude,  being  the  joint  effect  of 
refraction  and  dip  of  the  horizon. 

TABLE  XXI.— Page  92. 

To  find  the  Latitude  by  an  Altitude  of  the  Polar  Star. 

This  table  is  explained  on  its  own  page,  and  on  the  right  hand  column  is  the  varia- 
tion of  the  correction  in  10  years,  which  is  to  be  substracted  from  the  correction  for 
that  period  of  time. 

TABLE  XXII.— Page  93. 


For  Correcting  the  Time  of  the  Moon's  M.  Passage  at   Greenwich  to  the  time  of  her  passing  over 

any  other  Meridian. 

This  table  is  entered  with  the  daily  variation  of  Moon's  M.  Passage  to  the  nearest      „       i<\j 
minute  at  the  top,  and  the  longitude  of  the  place  in  the  left  side  colunm,  and  the  angle  ^ 

of  meeting  points  out  the  minutes  to  be  added  to  the  time  of  Moon's  passing  the  Meridian  of 
Greenwich  in  west  longitude  or  subtracted  in  east.  The  sum  or  remainder  will  be  the  time  of 
her  passing  the  Meridian  of  the  place. 

TABLE  XXIII— Page  94. 

For  Reducing  the  MoorCs  Declination  to  the  Greenwich  Time  of  the  Observation. 


Page  102. 


This  table  is  only  used  with  an  Almanac  that  has  the  Moon's  Declination  given  for 


every  noon  and  midnight. 

TABLE  XXIV.— Page  95. 

To  Correct  the  Moon''s  Semi-diameter  and  Horizontal  Parallax. 

Pag§  101.         This  table  is  explained  at  Page  95,  below  the  table. 

TABLE  XXV.— Page  9G. 

Bage  102,  To  Cor'-ect  the  Moon's  Apparent  Altitude. 

TABLE  XXVI.— Page  97. 

To  Turn  Time  into  Degrees  or  Degrees  into  Time. 

p       \At\         T^s  table  is  entered  with  degrees  in  one  column,  and  opposite  the  time  correspond 
rage  14U.     j^^    .^  ^^^^^ 

TABLE  XXVIL— Page  98  to  106. 

logarithms  of  the  Latitude  and  Polar  Distances. 

P       1«M»  T^&  table  contains  Logs,  of  latitude  and  polar  distance  for  finding  the  time,  and 

^  '  thence  the  longitude  by  chronometer.  The  latitude  in  degrees  is  taken  from  the  top  and 
miles  from  left  hand  side,  the  polar  distance  in  degrees  is  taken  from  the  bottom  and  miles  from 
right  hand  side,  except  when  the  polar  distance  is  above  90°.  it  is  then  taken  from  the  top. 


EXPLANATION    AND    USE    OF    THE    TABLES. 

TABLE  XXVIIl.— Paob  107,  115. 

Logarithms  of  the  Half  Sum  a«td  Difference. 

This  table  contains  the  Logs,  of  the  half  sum  and  difference  for  finding  Jie  time,     p       j^^ 
4nd  thence  the  longitude  by  chronometer.     The  half  sum  is  tak«jn  from  the  top  and        ^ 
difference  from  bottom. 

TABLE  XXIX.— Page  116  to  124. 

Logarithms  of  Apparent  Tin\e  or  Hour  Angle. 

For  explanatioa,  sm  note  at  bottom  of  page  125,  first  part  of  this  work.  Paiye  12S. 

TABLE  XXX.— Page  125. 

^or  Correcting  the  LongihuU  hy   Chronometer  for  the  effect  of  an  error  in  the  Latitude  used  m 

finding  Time. 

TTiis  tabl*  saves  the  trouble  of  working  the  sights  over  again   at  noon,  when  you     Page  144 
€nd  you  have  used  a  wrong  latitude  in  finding  the  time  at  s«»»  in  the  morning.  and  145. 

TABLE  XXXI.— Page  126  to  137. 

Logarithms  of  the  Apparent  Lunar  Distance. 

This  table  0(mtains  the  Logs,  sines  and  Logs,  tangent  of  the  apparent  lunar  distances.     Page  165. 

TABLE  XXXII.— Page  138  to  152. 

Logarithms  of  the  First  and  Second  Corrections. 

Tliis  table  contains  the  first  and  second  corrections  to  be  applied  to  the  apparent     „       .__ 
<li3tanoe.  -r  opre  I06, 

TABLE  XXXIII.— Page  154  to  205. 

Logarithms  of  the  Third  Correction. 

This  table  contains  the  third  correction  to  be  added  to  the  first  and  second  oorreo-     p       .  _- 
tions  and  apparent  Lunar  distance  to  find  the  true  distance.  ***" 

TABLE  XXXIV.— Page  206  to  220. 

Proportional  Logarithms. 

Tlis  table  is  explained  at  bottom  of  page  133,  first  part  of  this  work.  Pag^  133. 

TABLE  XXXV.— Page  221,  222. 

Amplitudes. 

This  table  is  intended  to  expedite  the  method  of  finding  the  variation  of  the  compass.     Pag9  IM. 

TABLE  XXXVI.— Page  223  to  225. 

Extracts  from  the  Nautical  Almanac. 

This  table  contains  extracts  from  the  Nautical   Almanac  for  the  year  1854,  for  the  purpose  vi 
working  out  the  examples  given  in  this  work. 

TABLE  XXXVII.— Page  226  and  227. 

Variation  of  the  Compass. 

This  table  contains  the  approximate  variation  of  the  compass,  and  is  to  be  entered  with  tk» 


trtu  EXPLANATION    AND    USE    OF    THE    TABLES. 

p      J  jg     longitude  at  top  of  page  226  when  west,  or  227  when  east,  and  the  Istitade  at  th« 
^^       '     side,  and  the  angle  of  meeting  points  out  the  degrees  of  variation  and  is  marked  easi 
or  west.     The  longitude  is  given  for  every  10  degrees,  and  the  latitude  for  every  2  degrees.     If 
the  variation  be  required  for  any  intermediate  position,  it  may  be  found  by  taking  jthe  mean  be 
tween  the  two  or/our  variations  which  are  given  for  places  on  each  side  of  the  required  position.. 

TABLE  XXXVIII.— Page  228  to  230. 

Times  of  High    Water  at  the  principal  Ports. 

This  table  contains  the  times  of  high  water  at  the  full  and  change  of  the  moon.  It  is  alphabeti- 
cally arranged,  and  entered  accordingly ;  when  opposite  the  name  of  the  place,  will  be  found  th« 
time  of  high  water. 

TABLE  XXXIX.— Page  231  to  243. 

Position  of  Places. 

TTiis  table  contains  the  Latitudes  and  Longitudes  of  the  most  prominent  places  in  the  world ;  thf 
manner  of  finding  any  required  place,  supposing  its  situation  nearly  known — ^needs  no  explanation. 

TABLE  XL. — Page  244  to  the  end. 

Positions  of  Places. 

In  this  Table  the  Latitudes  and  Longitudes  of  Places  has  been  extended,  and  some  places  ot. 
tmoortance  (omitted  in  Table  XXXIX)  have  been  inserted. 

TABLE  AT  PAGE  18— First  Part  of  this  Work: 

p       .g  Shows  the  number  of  minutes  and  seconds  contained  in  each  degree,  or  60  mile* 

^       *       of  longitude^  for  every  degree  of  latitude. 

TABLE  AT  PAGE  32— First  Part  of  this  Work. 

Page  32.       Por  finding  the  distance  of  an  object  by  two  bearings  and  the  distance  sailed  between  th^m.. 

This  table  is  particularly  useful  to  coasters. 

TABLE  AT  PAGE  37— First  Part  of  this  Work. 

p       «-  This  table  is  used  for  finding  the  time  of  high  water  at  any  place  by  correcting  for 

^       *       the  moon's  horizontal  parallax. 

TABLE  AT  PAGE  100— First  Part  of  this  Work. 

To  find  the  Latitude  from  Sun's  change  of  Altitude. 

P       inn  This  table  contains  the  Sun's  change  of  altitude  in  one  minute  of  time  for  every 

^         *     degree  of  latitude  when  on  the  Prime  Vertical. 

TABLE  AT  PAGE  153— Second  Part  of  this  Work. 

This  table  contains  the  Sun's  change  of  altitude  in  one  minute  of  time  for  every  degree  of  iat> 
bude  when  not  on  the  Prime  Vertical. 

JAMES  H.  BROWNLOW 


PRACTICAL    NAVIGATION 


INTRODU.CTION. 

Navig  A.TION  is  the  art  of  conducting  a  ship  from  one  port  to  another,  through  the  wide  and 
trackless  ocean,  with  the  greatest  safety,  in  the  shortest  time  possible,  and  to  find  her  position  on 
the  globe  at  any  given  time. 

To  be  able  to  do  this,  the  mariner  is  required  to  have  a  knowledge  of  certain  imaginary  circles, 
Bupposed  to  be  drawn  on  the  surface  of  the  earth,  together  with  the  most  practical  and  easy 
method  of  finding  a  ship's  position  thereon,  from  the  course  steered  by  the  compass,  and  lier 
distance  sailed,  and  also  the  course  and  distance  to  her  intended  port.  This  constitutes  what  is 
called  Navigating  by  Dead  Reckoning;  but  as  it  is  liable  to  be  greatly  in  error,  even  in  short  dis- 
tances run,  from  many  causes  (which  will  be  explained  in  this  work),  it  cannot  therefore  safely  be 
depended  on. 

Consequently,  the  mariner  must  have  some  other  resource  to  apply  to,  with  the  view  of  ascer- 
taining his  ship's  true  positioa.  This  can  only  be  derived  from  the  observations  of  the  heavenly 
bodies ;  but  to  do  this,  he  is  required  to  have  e  knowledge  of  certain  imaginary  circles  supposed 
to  be  drawn  in  the  heavens,  corresponding  to  those  already  supposed  to  be  drawn  on  the  earth's 
surface ;  by  which  means  he  obtains  the  positions  of  the  heavenly  bodies  themselves,  in  the  same 
manner  as  the  position  of  the  ship  is  indicated  by  the  circles  on  the  earth  ;  and  it  will  be  the  object 
of  this  work  to  instruct  him  how  to  find  his  ship's  position,  from  the  observations  of  any  of  the 
heavenly  bodies  which  may  be  visible,  either  by  day  or  by  night,  and  avoiding  all  the  tedious 
details  and  intricate  calculations  which  are  not  necessary,  thereby  saving  much  valuable  time  and 
labor  ;  the  results,  by  this  method,  having  been  found  from  actual  experience  to  be  sufficiently 
accurate  for  all  practical  purposes. 

In  this  work  the  mariner  will  therefore  not  be  required  to  go  through  a  tedious  training  in 
decimal  and  logarithmical  arithmetic,  nor  is  it  required  that  he  should  have  a  previous  knowledge 
of  either  geometry  or  trigonometry,  which  are  usually  given  in  works  of  this  kind ;  all  the  matter 
which  treats  on  those  subjects  is  therefore  discarded,  except  such  part  of  it  as  has  a  direct  bearing 
on  the  practice  of  navigation  at  sea. 

All  that  is  then  required  of  him  is  to  have  a  previous  knowledge  of  the  common  rules  of  arith- 
metic; that  is,  addition,  subtraction,  multiplication,  division,  the  rule  of  three,  and  the  practice 
of  aliquot  parts ;  or  that  amount  of  education  only  which  would  be  required  to  fit  a  person  to  ful- 
fil the  ordinary  business  of  life. 

In  the  room  of  the  above-mentioned  discarded  matter.  Diagrams  or  figures  of  the  subject  under 
consideration  will  be  introduced  in  their  proper  places,  and  the  explanation  of  each  Diagram  facing 
it  on  the  same  or  opposite  pages,  thereby  enabling  thf  learner  to  comprehend  mechanically  the 
whole  case  at  one  view. 

The  construction  and  use  of  both  General  and  Coasting  Charts,  with  the  manner  of  taking  Sound- 
ings on  the  Coast,  tiie  prevailing  Winds  and  Currents  in  different  parts  of  the  world,  and  Storms 
and  Hurricanes,  will  all  be  explained,  and  practical  rules  given  to  avoid  the  latter,  derived  from 
actual  experience.  The  Instruments  of  Navigation  will  also  be  explained,  and  the  manner  of 
adjusting,  correcting,  and  using  them  at  sea. 

In  treating  of  Nautical  Astronomy,  the  subject  will  be  illustrated  by  Diagrams,  and  the  case* 
proved  by  projection  only,  in  the  room  of  going  into  the  tedious  solutions  of  Spherical  Trigonom- 
etry, except  in  those  cases  where  a  Rule  is  required ;  and  much  new  matter  on  this  subject  will 
W  introduced,  in  connection  with  the  use  of  the  Chronometer.  Many  new  Tables  will  also  b« 
-Dtroduced,  with  a  view  of  shortening  the  labor  in  the  computations. 

Although  this  work  is  intended  to  treat  only  on  those  subjects  which  have  reference  to  the  place 
of  the  Ship  on  the  Ocean,  nevertheless  much  useful  matter  will  be  found  which  will  be  interesting 
to  the  young  officer,  in  regard  of  Navigating  the  Ship.  The  who.e  being  original  matter,  which 
the  author  of  this  work  has  derived  f^om  a  personal  experience  of  more  than  a  quarter  of  a  cen- 
tury, in  Navigating  Ships  to  nearly  all  parts  of  the  world.  The  work  will  be  closed  with  the 
methods  of  Keeping  a  Log-Book,  exemplified  by  a  journal  of  a  Voyage,  with  remarks  on  th» 
same,  as  would  actually  be  done  at  sea. 


fJEOGRAPHY. 


/♦  ,1.  .^ 


DIAGKAM   OF  THE  EARTH, 

Aowng  Ut  inclination  to  the  Plane  of  its  Orbit  of  23*  28',  and.  the  imaginary  Circles  drawn  or.  it    mtfjtt 

FlQ.    1. 


DESCRIPTION    AND   DIMENSIONS  OF  THE    EARTH. 

The  Polar  Diameter  is  7899,  and  the  Equatorial  Diameter  7926  miles;  the  latter  being  the  greatest,  it 
Mtosed  by  the  revolution  of  the  Earth  on  its  axis,  and  as  the  greater  portion  of  the  surface  is  covered  with 
water,  it  recedes  from  the  poles  towards  the  Equator,  until  its  tendency  to  run  back  towai-ds  the  poles  just 
balances  the  effects  of  the  centrifugal  force.  This  causes  the  Equatorial  Diameter  to  be  about  27  miles  greater 
than  the  Polar  Diameter.  If  the  Earth  should  stop  revolving  on  its  axis,  the  water  at  the  Equator  would 
■ettle  away  towards  the  Poles  until  it  assumed  the  form  of  a  Globe  as  near  as  possible.  Thus,  large  por- 
tions of  land  in  the  Torrid  Zone  which  are  now  covered  by  the  ocean  would  be  left  dry,  and  new  conti* 
Bents  and  islands  formed. 

The  Polar  Axis  is  not  perpendicular,  but  inclines  to  the  plane  of  its  orbit  at  an  angle  of  23°  28',  and  per- 
forms its  revolution  round  the  sun  in  one  year,  or  365  days  6  hours,  or  at  the  rate  of  68,000  miles  an  hour; 
at  the  same  time  it  performs  its  daily  revolution  round  its  axis  at  the  rate  of  15°  to  the  hour — equal  to  90* 
miles,  or  15  miles  in  1  minute  of  time. 

Latitude  is  measured  in  Degrees,  Minutes,  and  Seconds  from  the  Equator  towards  the  Poles,  from  which 
H  is  90*  distant ;  each  Degree  contains  60  Minutes,  and  each  Minute  contains  60  Seconds.  1  Minute  ©r 
Nautical  Mile  contains  6082  feet,  or  1013  fathoms,  and  therefore  a  Second  is  about  101  feet,  or  17  fathomi 
nearly. 

The  Circumference  of  the  Earth  at  the  Equator  is  360  Degrees  of  the  same  length  as  the  Degrees  of  Lati- 
tude ;  consequently,  Degrees  of  Latitude  and  Longitude  are  the  same  length  on  the  Equator.  But  on  sail- 
ing North  or  South  from  the  Equator,  the  Meridians  contract,  and  the  Degrees  of  Longitude  become  less, 
(but  still  contain  or  are  divided  into  60  minutes,)  until  they  finally  meet  at  the  Poles,  where  there  is  ne 
Longitude. 

The  Earth  revolves  from  West  to  East,  which  if  th/*  '•aiise  of  all  the  heavenly  bodies  appearing  to  rise 
in  the  East  and  set  in  the  West. 


DEFINITIONS    OF   GEOGRAPHT. 


GEOGRAPHY, 

iS    APPLIED    TO    THE     PRACTICE    OF    NAVIGATIOW    AT    SEA. 


DEFINITIONS. 

Practical  Navigation  relates  to  two  methods,  independent  of  each  other — the  first  is  that  usually  called 
Oead  Reckoning,  and  the  other  by  Astronomical  Observations ;  but  in  practice  they  are  generally  carried 
♦n  together,  as  a  check  upon  each  other. 

The  first  of  these  methods  requires  a  knowledge  of  the  imaginary  lines  and  Circles  on  the  surface  of  the 
Globe,  or  Earth,  which  we  inhabit,  and  which  turns  round  once  in  every  24  hours  ;  the  line  round  which  it 
revolves,  and  which  is  the  shortest  diameter,  is  called  the  Polar  Axis,  and  drawn  between  the  North  and 
South  Poles 

90°  from  the  Poles  is  the  great  Circle,  called  the  Equator,  passing  round  the  earth  and  dividing  it  into 
"two  equal  parts,  or  Hemispheres.  At  all  places  on  this  circle  the  sun  rises  and  sets  at  6  o'clock  all  the  year 
round,  and  the  days  and  nights  are  equal,  being  divided  into  12  hours  each. 

A  Meridian  is  a  circle  passing  through  both  poles,  and  cutting  the  Equator  at  right  angles.  Places  situ- 
ated on  this  Circle  are  said  to  be  on  the  same  meridian  North  or  South  of  each  other. 

Latitude  is  the  distance  from  the  Equator,  measured  in  Degrees  and  Minutes,  on  a  meridian  towards  Ihe 
North  or  South  Poles,  and  named  accordingly. 

The  Co-latitude  is  the  difference  between  a  given  Latitude  and  90*.  or  the  Pole. 

Parallels  of  Latitude  are  Circles  parallel  to  the  Equator,  running  East  and  West.  Places  on  this  circle 
.*re  said  to  lie  on  the  same  parallel  of  latitude. 

The  Difference  of  Latitude  of  two  places  is  the  portion  of  the  meridian  included  between  their  parallels. 

The  Difference  of  Latitude  of  a  Ship  is  therefore  the  distance  she  makes  good  in  a  North  or  South  direc- 
'Uon. 

It  is  evident  that  when  two  places  are  on  the  same  side  of  the  Equator,  their  difference  of  Latitude  u 
ifound  by  subtracting  the  lesser  latitude  from  the  greater,  and  that  when  they  are  on  opposite  sides  of  tha 
Equator,  that  is,  when  one  place  is  in  North  Latitude,  and  the  other  in  South  Latitude,  the  sum  of  their 
l«alitudes  is  the  difference  of  Latitude. 


EXAMPLE  1. 

Find  the  difference  of  Latitude  between  New  York 
tnd  CharleatoD,  S.  C. 

New  York,  Latitude 40*  43'  N. 

Charleston "    • 32   46  N. 

Difference  of  Latitude. .    .  7°  67'. 

EXAMPLE  2. 

Find  the  difference  of  Latitude  between  Cape  Henry 
<ftnd  Cape  St  Roque. 

Cape  Henry,  Latitude. .  36°  56'  N. 
Cape  SL  Roque..    " 5    28    S. 

Difference  of  Latitude  .  .42°  24'. 


EXAMPLE  8. 

A  ship  Bails  from  Latitude  50°  19'  N.  to  48°  12'  If. 
find  her  difference  of  Latitude. 

Latitude  left 60*  19'  N. 

Latitude  in 48    12  N. 

Difference  of  Latitude. .  ..2°    7'  —  127  mile* 

EXAMPLE  4. 

A  ship  sails  from  Latitude  1°  11'  N.  to  0°  13'  S,  find 

her  difference  of  Latitude. 

Latitude  left 1°  11' N. 

Latitude  in 0    LS   S. 

Difference  of  Latitude  1°  24'  or  84  milei 


Note. — When  a  Ship  in  north  hititiide  sails  North,  she  evidently  increases  her  latitude,  and  so  likewise  when  in  south 
.<«titude  she  sails  South,  because  in  these  cases  she  increases  her  distance  from  the  Equator,  at  which  the  latitud* 
"betrins. 

But  if  in  north  latitude  she  sails  South,  or  in  south  latitude  she  sails  North,  she  diminishes  her  latitude ;  hence,  when 
WIS  latitude  and  the  difference  of  latitude  are  given  the  ether  atitude  is  easily  found. 

EXAMPLE  1. 

A.  Sliip  from  43°  30'  S.  sails  219  miles  South,  required 
•er  latitude  iu. 

I.iititude  left ...     4:3*  30' S. 

Diff  ',f  Lat.  219  divided  by  60  —     3    39   S. 

Latitude  in 47°    9' S. 

EXAMPLE  2. 

A  Ship    from  latitude  43°  11'  N.  makes   194  mile* 
«onthing,  required  her  latitude  in. 

Latitude  left 43*  11'  N. 

Difference  of  Latitude 194  —     3    14   S. 

Latitude  in     39*  57'  N 


EXAMPLE  3. 

A  Ship  from  Latitude  1°  3'  N.  sails  123  miles  SoutK 
required  her  latitude  in. 

Latitude  left T  5'  N. 

Difference  of  Latitude  123  —    2    8    8 
Latitude  in 1*  Q'  & 

NoTX.— The  Ship  being  in  1<>  8',  or  63  milta  N.  of  th« 
Equator,  munt  evidently  be  in  South  Latitude  after  nutkisg 
128  miles  southinff. 

Thus,  in  subtracting  one  of  the  quantities  from  tba  oinar, 
the  difference  takes  the  name  of  the  greater. 


GEOGRAPHY. 


Longitude  is  th«  distance  xneasured  on  the  Equator,  between  the  Meridian  of  a  giren  plaoe  and  another^ 
•ailed  the  first  meridian.  The  choice  of  a  first  meridian  is  arbitrary.  The  Americans,  English,  and  othat 
nations  adopt  Greenwich  Observatory  in  England  as  the  first  Meridian. 

The  Longitude  of  a  place  is  named  East  or  West,  according  as  it  is  East  or  West  of  Greenwich,  as  far  w- 
J  80',  and  which  is  the  opposite  meridian  to  Greenwich,  or  one-half  of  the  circumference  of  the  Earth.  A 
Ship  sailing  East  beyond  180°  East  Longitude,  would  then  be  in  West  Longitude,  and  sailing  West  beyond 
180*  West  Longitude,  would  then  be  in  East  Longitude. 

Longitude  is  measured  either  in  Degrees,  Minutes,  and  Seconds,  or  in  Time,  that  is,  in  Hours,  Minutes, 
and  Seconds,  each  hour  being  equal  to  15°  ;  for  the  Sun,  which  regulates  the  time,  returns  to  the  same- 
meridian  again  after  describing  a  complete  circle,  or  360  ,  in  24  hours,  and  15*  multiplied  by  24,  makes 
360*. 

The  Difference  of  Longitude  of  two  places  is  the  portion  of  the  Equator  included  between  their  meridians. 
To  measure,  therefore,  the  difference  of  Longitude  between  two  places,  we  must  follow  down  their  meridian* 
to  the  Equator,  and  then  take  the  included  portion  of  the  Equator  itself, 

The  Degrees  of  Latitude  and  Longitude  are  of  the  same  length  on  the  Equator ;  but  as  the  meridians 
contract  and  meet  at  the  Poles,  the  greater  the  Latitude  the  Degrees  of  Longitude  become  less ;  that  is,  the 
space  contained  in  a  Degree  of  Longitude  becomes  less  as  the  Latitude  increases,  until  at  the  Poles  the 
Longitude  ceases  altogether. 

When  two  places  are  on  the  same  side  of  the  first  meridian,  their  difference  of  Longitude  is  found  by 
subtracting  the  lesser  from  the  greater. 

When  two  places  are  on  opposite  sides  of  the  first  meridian,  that  is,  when  one  place  is  in  East  Longitude 
and  the  other  in  West  Longitude,  the  sum  of  their  Longitudes  is  the  difference  of  Longitude. 

When  one  Longitude  is  East  and  the  other  West,  and  their  sum  exceeds  180°,  subtract  from  360'  will 
fire  their  difference  of  Longitude. 

EXAMPLE  5. 

Find  the  difference  of  Longitude  between  New  York 
and  )£anilla. 

New  York,  Longitude 74°     1'  W. 

Manilla "   121       2    B 

Sum 


EXAMPLE  1. 

Find  the  difference  of  Longitude  between  New  York 
and  CbailestoD,  S.  C. 

New  York,  Longitude 14'    0'  W. 

Charle«ton "    79    64  W. 

Difference  of  Longitude. ...  6*  64'. 

EXAMPLE  2. 

Find  tk«  differenee  of  Longitude  between  the  Cap«  of 
)ood  Hope  and  Cape  St  Roque. 

Cape  of  Good  Hope,  Longitude    18*  30'    E. 

Oape  St  Roque " 86    17'  W. 

Difference  of  Longitude, 63*  47'. 

EXAMPLE  8. 

A  Ship  sails  from  Longitude  60*  10'  W.  to  60°  80* 
W,  find  the  difference  of  Longitude. 

Longitude  left 60*  10'  "W. 

Longitude  in .60    30  W. 

Difference  of  Longitude. .  10*  20'. 

EXAMPLE  4. 

A  Ship  sails  from  Longitude  6°  40'  W.  to  2*  10'  R 
find  her  difference  of  Longitude. 

Longitude  left 6*  40*  W. 

Longitude  in 210    £. 

Difference  of  Longitude. .  .7*  60'. 


195"     3'. 

Subtract  ftom 360      0. 

Difference  of  Longitude..     164°  57' 

Fig.  2. 
THE    EQTUTOR. 


NoTB.— A  Ship  in  East  Longitude  sailing  East,  or  in  West  Longkuda  sailing  "We8t,  increases  her  Longitude,  b-n  ir 
But  Longitude  sailing  West,  or  in  West  Longitude  sailin^r  Eastj  she  dimir.iahea  her  longitude  ;  and  when  the  Lonir' 
ide  exoeedg  180",  subtract  it  from  860,  will  give  the  Longitude  m  of  a  contrary  name. 

EXAMPLE  7. 


EXAMPLE  6. 

A  Ship  from  Longitude  85*  26'  "W.  sails  East  8*  40', 
fad  the  Longitade  in. 

Longitude  left 86'  26'  W. 

Difference  of  Longitude    8    40    E. 
longitude  in 81*  46'  W. 


A  Ship  from  Longitude  179'  32'  E.  sails  East  2° 
find  the  Longitude  in. 

Longitude  left 179'  32'  K. 

Difference  of  Longitude . .  2     30  B. 

Sum 


sy. 


182° 

Subtract  from 360 


2' 
0 


Longitude  in   177°  68'  W, 


DEFINITIONS     Or    PLANE     SAILING 
Fic.  4. 

DIAGRAM    OF    THE    RIGHT-ANGLED    TRIANGLE. 


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PRINCIPLES    OF    THE    RIGHT-ANGLED   TRIANGLE. 

The  Course  steered  is  the  angle  between  the  Meridian  and  the  Ship's  head ;  the  Course  made  good  ir 
(he  angle  between  the  Meridian  and  the  Ship's  real  track  on  the  ocean. 

The  Course  is  reckoned  from  the  Meridian  accordingly,  North  or  South  towards  the  East  or  West,  if  lew- 
than  eight  points,  or  90  Degrees. 

The  Course  is  measured  in  points  of  11*  15'  each,  or  in  Degrees  and  Minutes. 

The  Rhumb  line  is  the  Ship's  track  when  crossing  all  the  Meridians  at  the  same  Angle. 

The  Distance  between  two  places,  or  the  Distance  sailed  by  the  Ship  on  a  certain  course,  is  measured  ia 
autical  miles  of  60  to  the  Degree  of  Latitude,  each  containing  6,082  feet. 

Three  such  miles  make  a  League. 

The  Departure  is  the  Distance  made  good  by  the  Ship  due  East  or  West,  or  the  distance  she  departs  froiB' 
her  first  Meridian,  and  are  always  of  the  same  length  as  the  miles  of  Distance,  or  difference  of  Latitude, 
it  is  also  called  Easting  or  Westing,  and  always  expressed  in  miles.  When  a  Ship  sails  East  or  West  she 
makes  no  difference  of  Latitude. 

The  difference  of  Latitude  is  the  space  contained  between  two  parallels  of  Latitud«»,  and  is  counted  oB' 
the  meridian.     When  a  ship  sails  North  or  South  she  makes  no  Departure. 

Taking  a  departure  means  taking  the  bearing  of  any  object  by  compass,  or  its  angle  with  the  Meridian, 
and  estimating  its  distance  from  the  Ship  on  leaving  the  land. 

The  above  figure  represents  a  case  in  Plane  Sailing,  in  which  all  the  above  terms  are  explained.  The 
thick  lines  form  a  Right-Angled  Triangle,  of  which  the  Perpendicular  is  the  Difference  of  Latitude. 
The  Base,  the  Departure ;  the  Angle  between  them  is  a  Right  Angle,  or  90° ;  and  the  Hypothenuse  is  the 
Distance  sailed  ;  the  Angle  between  the  Hypothenuse  and  the  Perpendicular  is  the  Course  reckoned  from 
the  Meridian  ;  and  the  opposite  Angle  is  found  by  subtracting  it  from  90° ;  because  these  two  Angles  are 
equal  to  the  Right  Angle,  or  90°.  We  have  now  the  four  terms  of  a  Right-Angled  Triangle,  corresponding 
to  the  Course.  Distance,  Difference  of  Latitude,  and  Departure,  and  by  the  well-known  properties  of  thai 
figure,  any  two  of  which  being  given,  the  other  two  can  readily  be  found  by  the  rules  given  for  projecting 
the  case ;  and  to  obviate  the  labor  of  calculating  the  terms  by  Logarithms,  Tables  have  been  long  in  use 
containing  all  that  is  necessary  for  solving  the  problems,  sufliciently  accurate  for  the  purpose  intended 
They  are  called  the  Traverse  Tables,  and  the  quantities  are  taken  out  by  inspection ;  and  as  this  is  the 
method  invariably  used  at  sea,  ull  the  other  methods  are  neglected,  and  never  used  even  by  those  who  have 
a  thorough  knowledge  of  Trigonometry,  and  many  navigators  consider  them  a  useless  appendage  to  a  work  on. 
Practical  Navigation. 

INSTRUMENTS    OF    NAVIGATION. 

The  Instruments  used  in  Navigation  are  the  Compass,  the  Log,  and  Glass.     The  former  shows  the  diree 
tlon  of  the  Ship's  track,  and  by  means  of  the  latter  her  distance  run  is  measured. 

The  Log  Ship  is  a  small  triangular-shaped  piece  of  wood,  one  side  being  loaded  so  as  to  cause  it  to  •wim 
apright ;  sometimes  a  funnel-shaped  bag  is  used  instead.  This  is  attached  to  the  line  in  such  a  manner 
that  when  the  glass  has  run  out,  and  the  line  checked,  one  of  the  corners  (being  fastened  by  a  peg  of  wood 
•r  bone),  is  released,  or  the  bag  reversed,  which  allows  it  to  be  easily  hauled  on  board  again.  At  12  or  lA 
ffcthoniB  from  the  Log  Ship  the  line  is  marked  with  a  strip  of  Rag  ;  this  is  called  the  Stray  line,  which 
enables  the  Log  to  go  clear  of  the  Ship  before  the  time  is  counted,  or  the  Glass  turned.  From  this  marh 
the  line  is  measured  and  divided  into  Knota  and  Half  Knots,  and  marked  at  each  Knot  with  a  bit  of  string 
with  the  number  of  Knots  upon  it. 

The  length  of  a  Knot  depends  upon  the  number  of  seconds  which  thi  Glass  measuren. 


[NSTRUMF.NTS    OF    NAVIGATION. 


Fic.  5. 

THE    MARINER'S    COMPASS. 


As  tLe  Ship'8  Course  is  sometimes  expressed  in  Points  and  sometimes  in  Degrees,  the  foDowiiig  Tabi 
»ill  be  found  useful  for  reference. 


1 

ROBTH   A.fD  KAST. 

NORTH   AND    WEST. 

SOOTH  AND  EAST. 

(ODTB  AND  WEST. 

POINTS. 

D.  H.  ■. 

North. 

N.JE. 
N.  ♦E. 
N.  f  E. 

North. 

N.  i  W. 
N.  i  W. 

N    j  W. 

Soiiih. 

S.  iK. 
S.  i  E. 
S.  JE. 

South. 

S.  i"W. 
S.  i  W 
S.  J  W. 

0 

i 
t 

2  48  45 
5  37  30 
8  36  IS 

N.  by  E. 

N.  by  E.  i  E, 
N.  by  EiE. 
N.  by  E.  }  E. 

N.  bv  W. 

N   bv  W.  J-  \V. 
N.  by  W.  iW. 
N.  by  W.  i  W. 

S.  byE. 

S.  byE.  JE. 
S.  byE.  iE. 
S  byE  j  E. 

S.  by  W. 

S.  by  W.  i  W. 
S.  by  W.  i  W. 
S.  bv  W.  f  W. 

1 

1* 
U 
1* 

11  15  00 
14    3  45 
16  53  30 
19  41  15 
22  30  00' 
25  18  45 
28    7  30 
30  56  15 

N.  N.  K. 

N.  N.  E.  i  E. 
N.  N.  E.  iE. 
N.  N   E.  f  E. 

N.  N.  VV. 

N.  N.  W.  1  W. 
N.  N.  \V.  i  VV. 
N.  N.  W.  i  W. 

S.  S.  E. 

S.  S.  E.iE. 
S.  S.  E.  JE. 
S.  S.  E.»E. 

S.  s.  w. 

s.  s.  W  i  w. 
S  S.  W.  i  w. 
s  s.  W.  JW. 

it 

2* 

2» 

N.  E.  by  N. 

N.  E.  f  N. 

N.  E.  i  N. 
N.  E.  J  N. 

N.W.  byN. 
N.  W.  }  N 

N.  W.  i  N 
N.  W.  iN. 

S.  E.  by  S. 

S.  E  JS. 
S.  E.  k  S. 
S.  E.  k  B. 

S.  W.  by  S. 

S.  VV.  J  S. 
S.  W.  i  s. 
S   W.js. 

3 

3i 
31 
3* 

33  45  00 
36  33  45 
39  22  30 
42  11   15 

N.E. 

N.  E.JE. 
N.  E. i  E. 
N.E.»E. 

N.  W. 

N.  W.  1  W. 
N.  W.  i  W. 
N.  W.  }  W. 

8.  B. 

S.  E.  1  B. 
S.  E.iE. 
S.E.J  E. 

s.w. 

S.  W.  i  w. 
S.  W.  i  w. 
S.  W.  }  w. 

4 

*i 
4» 

45  00  00 
47  48  45 
50  37  30 
53  26  15 

N.  E.  by  E. 
N.  E.  by  E.JE. 
N.E.  by  Ei  E 
N.E.  by  E.|  E. 

N.  W    by  W. 
N.  W.  by  "W  J  W. 
N.  W.  by  W.  i  W. 
N.W.  by  W.  1  W. 

S  E.  byE. 
S.  E.  byE.  »  K. 
S.  K.  by  E    i  E. 
S.  E    by  E.  1   E. 

E.  S.  E. 

E.  byS.  1  S. 
E.  by  S.  i  S. 
E.  by  S.  iS. 

S.  W.  by  W. 
S.  W.  by  W.  1  W. 
S.  W.  by  W.  1  W. 
S.  W.  by  W.  J  W. 

5 
5* 
5* 
5» 

56  15  00 
59    3  45 
61  52  30 
64  41   15 

B.N-E. 

E.  by  N.  f  N. 
E.  by  N.  i  N. 
K.  by  N.  *  N. 

W.  N.  W. 

W. bv  N.  J  N 
W.  by  N.  i  N. 
W.  by  N.  i  N. 

w.  s.  w. 

W.  by  S.  }  S. 
W.  by  S.  4  S. 

W.  by  S.  i  S. 

6 
6* 

67  30  00 
70  iS  45 
73     7  30 
75  56  15 

E.byN. 

E.iN. 
E.i  N. 
E.iN. 
Batt. 

W.  by  N. 

W.J  N. 
W  i  N. 

W.  i  N. 
West. 

E.  by  S. 

E.fS. 

K.  iS. 

E.  iS. 
Eh.iL 

W.  by  S. 

W.  }3. 

W,  i  S. 

vV.  iS. 
West. 

7 

?i 

78  4S    0 
81  33  .."i 
84  22  3b      1 
87  11  15      ' 
90  00  00     ^ 

INSTRUMENTS    OF    NAVIGATION.  *> 

The  length  of  a  nautical  mile  being  about  6,080  feet,  the  30  Second  Glass  should  have  a  length  of  T  *t 
oearly  51  feet  To  determine  the  length  of  Knot  to  any  length  of  glass,  the  Rule  is,  as  3f  Seconds  u  tc 
SI  feet,  so  is  38  Seconds  to  the  Knot  of  47  feet,  and  so  on. 

But  in  practice  a  45  feet  length  of  Knot  is  found  to  correspond  best  with  a  28  Second  Glass.  The  dif- 
ference is  caused  by  the  Log  Ship  coming  home  when  hove,  ana  47  feet  gives  the  Distance  run  too  small. 

Before  the  line  is  measured  it  should  be  well  stretched,  and  then  made  wet.  Nails  should  be  placed  in 
•Hie  Deck  at  the  proper  length  of  the  measured  Knot,  so  as  to  verify  the  marks  frequently,  as  the  line  is 
!hable  either  to  stretch  or  run  up. 

Sometimes  the  Knots  and  half  Knots  only  are  inserted  in  the  Log  Board,  but  in  general  the  Knot  is 
•divided  into  10  fathoms,  and  the  odd  fathoms  inserted  for  handiness  in  adding  up.  This  laihom  is  noi  i 
feet,  but  the  tenth  part  of  the  Knot  only. 

The  Log  line,  after  being  thus  measured,  is  fastened  to  a  Reel  and  wound  up.  ready  for  use.  The  mail- 
ner  of  heaving  the  Log  can  only  be  learned  at. Sea,  but  it  may  be  useful  to  remark  that  the  line  is  faked  in 
the  hand,  not  coiled,  and  the  Log  Ship  is  to  be  thrown  well  out  to  Leeward  of  the  Ship's  wake,  and  in  such 
a  manner  that  it  may  take  hold  of  the  water  at  once,  and  that  before  a  heavy  Sea  the  line  should  be  paid 
out  rapidly  wlien  the  Stern  is  rising,  and  retarded  a  little  when  the  Stern  is  falling. 

Whichever  length  of  Glass  is  adopted,  there  should  always  be  another  of  half  the  length,  usually  called 
the  short  glass,  and  used  when  the  Ship  is  going  rapidly  through  the  water,  as  only  half  of  the  length  of 
line  is  required,  and  by  doubling  the  number  of  Knots  run  out,  the  same  result  is  obtained  as  if  the  whols 
•line  had  been  used. 

The  Glass  should  be  kept  dry,  and  verified  occasionally  with  the  second  hands  of  a  Chronometer. 

THE    COMPASS. 

The  Mariner's  Compass  consists  of  a  circular  card,  the  edge  being  divided  into  32  Points,  Half  Points 
»nd  Quarter  Points,  and  into  360  Degrees. 

The  four  principal  points,  or,  as  they  are  called,  the  cardinal  points,  are  North,  South,  East,  aad  Waal,, 
the  East  being  towards  the  right  when  facing  the  North. 

A  farther  description  of  this  well-known  Instrument  is  not  required,  except  that  in  North  Latitude  the 
North  Pole  of  the  magnetizpd  bar  is  drawn  or  attracted  in  that  direction,  and  in  South  Latitude  the  South 
Pole  is  attracted  towards  the  South.  The  Dip,  or  attraction  towards  the  centre  of  the  Earth  is  greatest  in 
high  Latitudes,  and  is  frequently  the  cause  of  a  sluggish  movement  of  the  Card  in  common  compasses* 
The  magnetic  pole  dipping,  a  balance-weight  of  Sealing- Wax  or  other  substance  is  required  at  the  othei 
«nd  of  the  bar,  to  make  it  swing  freely  round,  which  can  be  removed  again  in  low  Latitudes.  The  pin  on 
which  the  card  is  balanced  sometimes  becomes  blunt  by  constant  use,  which  can  be  sharpened  with  a  fine- 
grained file  or  a  set  stone. 

The  Lubber's  Point  is  a  perpendicular  mark  in  the  centre  of  the  forward  part  of  the  Compass  Bowel 
uid  represents  the  line  of  the  Ship's  Keel,  (or  a  line  parallel  to  it)  By  endeavoring  to  keep  a  given  poin< 
«f  the  Compass  cam  at  this  mark,  constitutes  what  is  called  steering  a  course  by  Compass. 

THE     VARIATION     OF    THE     COMPASS. 

The  Needle  points  to  the  Magnetic  North,  which  in  few  pajts  of  the  world  agrees  with  the  true  Nerth, 
<he  difference  between  them  is  called  the  Variation  of  the  Compass.     See  page  116. 

The  Variation  is  named  Easterly  when  the  North  end  is  drawn  towards  the  East  of  the  true  North,  and 
Westerly  when  drawn  to  the  Westward.  The  variation  is  different  in  different  places,  and  is  constantly 
'though  slowly  changing. 

To  correct  compass  courses  and  bearings  for  variation,  if  the  variation  is  Easterly,  apply  it  to  the  right 
hand  of  the  Compass  course  or  bearing.  When  Westerly,  apply  it  to  the  left  hand,  looking  towards  ths 
|>oint  representing  the  given  course  or  bearing. 

A  True  course  or  bearing  is  reduced  to  the  Compass  course  or  bearing  by  applying  the  variation  the  con- 
Irary  way. 

LOCAL     ATTRACTION. 

The  Compass  in  every  Ship  is  more  or  less  affected  by  the  Iron  used  in  her  construction,  and  by  Iron  on 
Iward  as  cargo.  It  is  most  sensibly  felt  when  the  Ship's  head  is  East  or  West,  because  in  North  Latitude 
the  North  Point  is  drawn  forward,  and  the  reverse  in  South  Latitude ;  but  when  her  head  is  North  and  ■ 
Bouth,  the  Magnetic  and  true  meridians  nearly  coincide  with  the  disturbing  force,  situated  in  the  forward 
part  of  the  Ship,  and  the  effect  is  not  so  sensible.  It  may  be  detected  by  taking  frequent  observations  to 
find  the  variation  of  the  Compass,  (which  will  include  the  Local  Attraction ;)  then  the  difference  between 
that  and  the  variation  laid  down  on  the  Chart  will  be  the  Local  Attraction.  Th'S  subject  will  be  found 
treated  of  more  at  length  at  page  120. 


PRACTICAL    NAVIGATION. 


INTRODUCTION    TO    THE    SAILINGS. 

Th«  Methods  used  in  navigating  a  Ship  by  Dead  Reckoning  are  the  Plane  and  Traverse  Sailings,  Paral 
lei,  Middle  Latitude,  a,nd  Mercator  Sailings ;  Current  Sailing  being  merely  a  modification  of  the  others,  all 
•f  "Which  will  be  explained  and  exemplified  under  their  proper  heads. 

It  has  not  been  deemed  necessarily  •vrithin  the  scope  of  this  work  to  include  Great  Circle  Sailing,  simply 
because  the  track  of  a  Ship,  as  given  by  the  general  rules  in  Great  Circle  Sailing,  cannot  be  practicallT'' 
adopted  by  a  Sailing  Vessel,  from  many  causes  which  it  is  not  necessary  here  to  explain,  and  which  ha* 
been  the  cause  of  leading  many  vessels  astray  that  had  adopted  it. 

A  Ship  may,  however,  adopt  a  modification  of  the  Track  on  the  Great  Circle  without  reference  to  any- 
general  rules,  as  follows : 

Great  Circle  Sailing  supposes  a  Ship  to  Sail  on  a  circle  on  the  Earth's  surface,  having  the  Centre  of  th» 
Earth  as  a  Centre.  When  a  Ship  sails  true  North  or  South,  she  sails  on  the  Arc  of  a  Great  Circle;  and 
when  she  sails  true  East  or  West  on  the  Equator,  she  also  sails  on  the  Arc  of  a  Great  Circle,  because  these 
Circles  have  the  Earth's  Centre  for  a  Centre ;  but  in  sailing  on  a  straight  Rhumb  line  in  any  other  direo- 
tion,  which,  although  it  may  appear  perfectly  straight  on  the  Chart,  nevertheless,  if  her  positions  at  Nooa 
were  laid  off  on  a  Terrestrial  Globe,  it  would  be  found  that  she  had  described  a  Curve  with  its  back  to- 
wards the  Equator,  and  been  sailing  on  a  Small  Circle.  Now  the  object  to  be  attained  in  Great  Circle- 
Sailing  is  to  adopt  a  curve  or  track  on  the  Chart,  the  back  of  which  shall  be  turned  towards  the  Pole  of  that 
Latitude  in  which  she  is  Sailing.  Then,  supposing  her  positions  at  Noon  to  be  laid  off  on  the  Globe  as  be- 
fore, it  will  be  found  that  she  has  been  sailing  on  a  circle  which  has  the  centre  of  the  Earth  as  a  centre,, 
the  distance  measured  between  any  two  places  on  this  Great  Circle  is  the  least  distance  between  them  j. 
but,  as  before  observed,  this  is  not  always  practical.  A  modification  may  be  adopted  by  tracing  upon  a 
Chart  of  the  intended  voyage  a  curved  Track  from  Port  to  Port,  having  its  back  towards  the  North  in  North 
Latitude,  or  towards  the  South  in  South  Latitude,  and  which  shall  keep  the  Ship  free  from  being  entangled 
with  the  Land,  and  at  the  same  time  placing  her  in  the  most  favorable  position  to  take  advantage  of  the 
prevailing  Winds  and  Currents. 

The  manner  of  doing  this  is  simply  to  draw  a  line  between  the  two  places  on  the  Chart,  and  to  mark 
the  extent  to  which  the  curve  may  be  judiciously  made  on  the  polar  side  of  the  middle  of  that  line ;  thei* 
through  th«>se  three  points  trace  a  curved  line,  which  will  approximate  to  that  of  a  Great  Circle.  Now  it 
is  evident  that  to  sail  on  this  curved  track,  the  course  must  be  shaped  accordingly,  and  that  it  will  be 
required  to  be  reshaped  or  changed  at  the  end  of  every  60  or  100  miles  of  Distance  run  by  the  Ship.  The- 
extent  <  f  this  curve  must  be  greatest  in  high  Latitudes,  and  on  crossing  the  Equator  it  changes  to  the  oppo- 
site side  of  the  straight  line.  See  the  Great  Circle  track  from  Santa  Crux  to  St.  Johns,  on  the  Chart  a^ 
Dace  4* 


PLANE    SAILING. 

Plane  Sailing  is  the  Art  of  Navigating  a  Ship  on  ^lano  surface,  supposing  the  surface  of  the  Earth  M 
♦©  an  extended  plane,  and  the  meridians  all  parallel  to  each  other.  This  supposition  is  nearly  true  foi 
•mall  portions  of  the  Earth's  surface,  and  for  a  considerable  space  on  each  side  of  the  Equator. 

But  as   the  Meridians  contract  in  Sailing  from  the  Equator  towards  the  Poles,  the  sides  of  the  Right 
ijogled  Triangle  do  not  bear  the  same  relation  to  each  other  on  large  portions  of  the  Earth's  surface. 

Plane   Sailing   also  supposes   the  parallels  of  Latitude  to  be   at  right  angles  to  the  Meridians,  and  th 
i»ngth  of  a  degree  on  the  Meridian,  Equator,  and  parallels  of  Latitude,  everywhere  equal. 

CASE    L       , 

The  Course  and  Distance  given  to  find  the  Difference  in  Latitude  and  Departure. 

Example. — A  Ship  from  Latitude  48°  30'  N.  Sails  North-East  by  North  300  miles.  Required  he'  Latitude 
an  and  Departure  from  the  Meridian. 

BY    PROJECTION    ON    THE    PLANE    SCALE. 

Fig.  6. 


Draw  a  horizontal  line  representing  the  parallel  of  Latitude  sailed  from ;  then  with  the  Chord  of  6P '  u 
the  dividers,  and  one  foot  on  this  line,  describe  a  Semicircle ;  divide  this  Semicircle  ,into  equal  parts  of  fO" 
each,  (oi  a  Quadrant) ;  divide  the  right  hand  Quadrant  into  8  equal  parts,  which  transfer  to  a  line  dravvTi  aoroai 
the  Quad.-ant,  will  give  the  line  of  Rhumbs.  Divide  the  left  hand  Quadrant  into  9  equal  parts,  and  transfer 
them  to  a  line  drawn  across  the  Quadrant  in  like  manner,  will  give  l^e  line  of  Chords.  Those  figures  ar« 
always  drawn  so  that  the  upper  part  represents  the  North,  and  the  ship  is  supposed  to  sail  from  the  centre  on 
a  given  course  towards  the  circumference  or  horizon,  the  course  North-East  by  North,  300  miles  given.  Taka 
3  points  from  the  line  of  Rhumbs  and  lay  it  off  from  the  North  towards  the  East,  and  draw  the  Rhumb  line, 
which  will  represent  the  Ship's  Course,  and  on  which  measure  off  the  Distance  Sailed ;  this  will  give  the 
Ship's  place.  Draw  a  parallel  of  Latitude  through  this  place,  and  through  the  Meridian  wailed  from,  and 
the  space  between  the  Parallels  of  Latitude  is  the  Difference  of  Latitude  made,  measured  on  the  Meridiaa. 
f>raw  a  Meridian  through  the  Ship's  place  parallel  to  the  Meridian  sailed  from,  and  the  space  between 
the  Meridians  is  the  Departure  made. 

BY    INSPECTION.    TRAVERSE    TABLE. 

Conroe  North-East  by  North,  or  3  Points,  and  Distance  300  miles.     In  the   Traverse   Table  gives 

Difference  of  Latitude. , . .  )249.4  miles,  and  the  Departure  167  mfle*. 

—  4°    9'  N 

Latitude  left 48    30'  N. 

Latitude  in... 52°  39'  N 

Note. — ^These  Tables  contain/ui/r  terms,  any  two  of  which  being  given,  the  other  two  can  be  found  by  inspecJuni . 
md  it  must  be  observed  that  in  using  these  Tables  the  terms  Distance,  Latitude,  Departure,  must  be  found  at  the  top,  if 
the  Course  is  found  there  :  but  if  the  Course  is  found  at  the  bottom,  those  names  or  terms  must  be  found  at  the  bottom 
Thus,  the  Course  North-East  by  North,  or  8  Point*,  is  found  at  the  top,  and  the  columns  headed  Latitude  and  Departure 
•re  to  be  used  from  the  top,  and  against  Distance  800  stands  Difference  of  Latitude  249.4,  and  Departure  1M.7.  £n 
practice,  should  the  tenths  bo  less  than  6,  we  throw  them  away  ;  if  more  than  6,  we  call  the  sum  one  mile  more. 

When  the  Dibtance  is  more  than  800,  or  if  any  of  the  other  terms  be  too  great  for  the  Tables,  we  take  one  half,  enft 
third,  one-fourth,  or  on«-tenth,  and  multiply  the  termu  thus  found  by  the  same  quantity  that  they  were  reduced  ^r- 


10  PLANE    SAILING 

CASE  II. 

The  Dijfference  of  Latitude  and  Course  given  to  find  the  Distance  and  Dep.  •  'ure. 

Example. — A  Ship  from  Latitude  52°  39'  North,  sails  South- West  by  South  until  her  Latitude  obserred 
48*  30'  North.     Required  the  Distance  run  and  her  Departure  from  the  Meridian. 


Fio.  7. 


Latitude  left. 
Latitude  in . . 


,52' 
48 


39' N. 

30  N. 


Fio.  8. 


Latleft..82*  81'  >. 
Latin...  30    10  N 

2°  21'  • 
60 


Diffi  Lat  141 


PROJECTION    BY    THE    PLANE    SCALE. 

Draw  a  Horizontal  line  to  represent  the  parallel  of  Latitude  sailed  from,  then  with  the  Chord  of  6( '  a 
the  dividers,  and  one  foot  on  this  line  as  a  Centre,  make  the  Arc  of  a  Circle  towards  the  right  hand  d<-wn- 
firards,  and  which  will  represent  the  South-East  quarter  of  the  Compass.  Take  90°  in  the  dividerb,  and 
*ith  one  foot  on  the  line  where  the  circle  meets  it.  extend  the  other  downwards,  and  mark  the  Circle ;  thei 
A  line  drawn  through  this  mark  to  the  Centre  will  form  a  Right  Angle  with  the  oth"-  line,  and  represent* 
the  Meridian  sailed  from.  Lay  off  the  Difference  of  Latitude,  141,  oa  the  Meridian.  'Jom  the  parallel  of 
Latitude  sailed  from  downwards,  or  towards  the  South,  and  draw  the  parallel  of  Lativr  de  come  to. 


4°    9'  N. 
60    0 

T3iff.  of  Lat.. . . 249  miles. 

PROJECTION   BY   THE    PLANE    SCALE. 

Draw  a  horizontal  line  to  represent  the  parallel  of  Lati- 
tude Sailed  from  ;  then  with  the  Chord  of  60°  in  the  divi- 
ders, and  one  foot  on  this  line  as  a  Centre,  make  the  Arc 
of  a  Circle  towards  the  left  hand  downwards,  which  will 
represent  the  Southwest  Quadrant.  Take  90°  in  the  divi- 
ders, and  with  one  foot  on  the  line  where  it  joins  the  Cir- 
cle, extend  the  other  downwards,  and  mark  the  Circle. 
A  line  drawn  through  this  mark  to  the  Centre  will  form 
a  Right  Angle  with  the  other  line,  and  represents  the 
Meridian  sailed  from.  Lay  off  the  Difference  of  Latitude 
on  this  Meridian  towards  the  South,  and  draw  the  parallel 
of  Latitude  come  to.  Take  3  Points  from  the  line  of 
Rhumbs,  and  lay  it  off  from  the  Meridian  South,  towards 
the  West,  and  draw  the  Rhumb  line,  and  where  it  cuts 
the  parallel  of  Latitude  is  the  Ship's  place,  and  gives  her 
Distance  Sailed.     Draw  a  line  parallel  to  the  Meridian 

through  the  Ship's  place,  will  give  the  Meridian  come  to.  and  the  space  between  the  Meridians  is  th* 

Departure, 

BY    INSPECTION.     TRAVERSE    TABLES. 

I  open  the  Table  at  a  3-Point  Course,  and  find  the  Difference  of  Latitude  249  miles  in  its  column,  (a 
ne  top  ot  the  page,  marked  Latitude,)  and  against  it,  in  the  Distance  column,  stands  300  miles,  the  Di» 
tance  required,  and  opposite,  in  the  column  marked  Departure,  stands  the  Departure  required,  167 

CASE    III. 

The  Difference  of  Latitude  and  Departure  given  to  find  the  Course  and  Distance. 

ExAMPLi. — A  Ship  from  Latitude  32°  81'  North  sails  between  the  South  and  East  until  her  Latitude  in  is  80"  10'      * 
N  ortih,  having  made  265  miles  of  Departure.     Required  her  Course  and  Distance  sailed. 


PLANE   SAILING. 


n 


From  the  meridian  line  towards  the  East,  or  right  hand,  lay  off  the  Departure,  265  miles,  and  dra\»  th* 
meridian  come  to  parallel  with  it.  Then  where  this  meridian  cuts  the  parallel  of  Latitude  come  to  is  th* 
Bliip's  place.  Draw  the  Rhumb-line  between  th«  Ship's  place  and  the  centre,  which  will  give  the  Distano* 
Sailed ;  and  where  this  line  cuts  the  Circle  will  be  the  Course  5i  Points  measured  from  the  meridian  lin*^ 
w  from  the  South  towards  the  East. 

BY  INSPECTION.     TRAVERSE  TABLES 

With  tlie  difference  Latitude  141,  and  the  Departure  265,  I  enter  the  Table  for  Points,  and  I  find  theM 
©  agree  nearly  to  the  Course  5^  Points,  and  the  Distance  opposite  is  300  miles. 

Or,  in  the  Table  for  Degrees  the  nearest  is  264.9  and  140.8,  which  gives  the  Course  Sailed  62*  E.,  ai^ 
•stance  300  miles.     The  Departure  being  the  greatest  the  C^ourse  is  found  at  the  bottom  of  the  page 

CASE    IV. 

The  Difference  of  Latitude  and  Distance  Sailed,  given,  to  find  the  Course  and  Departure. 

A  Ship  from  Latitude  38*  20'  N.  sails  296  miles  between  the  North  and  West,  until  the  Latitude  ofc» 
•••rred  was  40"  13'  N.     Required  her  Course  and  Departure. 

Fig.  9. 


J?ara/lcly(/'/ Za^     co-rtiS'  io 


/   Jfe/o   ^7^ 


Lat.  left, 
Lat.  in, 


380 
40 

20 
13 

N 
N 

1* 
60 

53 

Dif.  Lat.       113' 


J^uretUel   ef  Zai.  <Sculeil  rre^c/ 


PROJECTION  BY  THE  PLANE  SCALE. 

Draw  a  horozontal  line  representing  the  parallel  of  Latitude  sailed  from.  Then  with  the  Chord  of  iO* 
ia  the  dividers,  and  one  foot  on  this  line  as  a  Centre,  draw  the  Arc  of  a  Circle  to  the  left  hand  upwards, 
which  will  represent  the  N.  W.  quarter  of  the  Compass.  Take  90°  in  the  dividers,  and  with  one  foot  OB' 
this  line  -w^ere  the  circle  meets  it.  extend  the  other  upwards  and  mark  the  circle,  draw  a  line  through  this 
mark  to  the  centre,  and  it  will  form  a  Right  Angle  with  the  other  line  and  will  represent  the  meridian 
•ailed  from.  Lay  off  the  Difference  of  Latitude,  113,  on  this  meridian  line  from  the  parallel  of  Latitude 
sailed  from  towards  the  N.  and  draw  the  parallel  of  Latitude  come  to.  Take  the  Distance  296  miles  in 
the  dividers,  and  with  one  foot  on  the  centre  extend  the  other  and  cut  the  parallel  of  Latitude  come  to, 
which  is  the  Ship's  place.  Draw  the  Rhumb  line  between  the  Ship's  place  and  the  Centre,  and  where  ii 
euts  the  circle  shows  the  Angle  of  the  Course  N.  6  points  W.  Through  the  Ship's  place  draw  a  line  par 
allel  to  the  meridian  sailed  from,  which  will  be  the  meridian  come  to,  and  the  space  between  the  meridian* 
U)  the  Departure. 

BY  INSPECTION.     TRAVERSE  TABLES. 

With  the  Distance  296  miles  and  Difference  Latitude  113,  I  enter  the  Table  for  Degrees,  and  find  them 
to  agree  between  67°  and  68°,  or,  N.  67*  30'  W.,  and  the  Departure  274.  The  manner  of  doing  it  is  thus 
I  take  the  Distance  296  miles  and  the  nearest  Difference  Latitude  greater  than  the  one  sought,  is  found  to 
be  115.7  at  Course  67",  and  the  nearest  less  Difference  Latitude  110.9  at  Course  68°.  The  half  between 
them  is  the  course  required.  The  Departure  at  Course  67==  is  272.5,  and  at  68°  is  274.4.  The  mean  or 
half  between  the  two  is  274,  nearl)',  which  is  the  Departure  required. 

Or,  enter  the  Table  of  Points  with  Distance  296  and  Difference  Latitude  113.  The  nearest  to  it,  113.3. 
gives  a  six  point  Course,  and  the  corresponding  Departure  is  273.5. 

Non. — In  all  those  oaaes  where  the  Course  is  required,  consider  whether  the  DiflTerence  of  Latitude  or  the  Departor* 
is  the  ereatest.  If  the  Depsirture  is  the  greatewt,  the  Course  is  found  at  the  bottom  of  the  page ;  but  if  the  Departur* 
Is  ^he  least  of  the  two,  the  course  will  be  found  at  the  Top  of  the  page. 

Because  those  Tables  are  calculated  as  far  aa  Four  Points  or  45"  at  the  Top,  for  Distance,  DiflTerence  of  Latitude,  and 
Departure ;  they  then  commence  at  the  Bottom  of  the  page,  and  go  backwards  for  tiio  remaining  Points  or  Degrees  of 
the  Quadrant,  and  the  angle  of  the  Course  beips'  jrreater,  the  Latitude  and  Departure  columns  are  reversed  at  fh<»  BoV 
',  and  miU'Ket'  voordipi?!''. 


12 


PLANE    SAILING. 


CASE  V. 

The  Course  and  Departure  given  to  find  the  Distance  and  Difference  of  Latitude. 

Example. — A  Ship  from  Lat.  2°  7'  N    sails  South-West  by  West  half  West   until  she  has  made  8fi0  inOtf  «i 
Departure.     Required  her  Latitude  in  and  Distance  Sailed. 

Fig.  10. 


Latitude  left  2°  T  N. 
Diff.  of  Lat..3__7  S. 
Latitude  iu..V~Q'  S 


PROJECTION    BY    THE    PLANE    SCALE. 

Draw  a  horizontal  line  to  represent  the  parallel  of  Latitude  sailed  from.  Take  the  Chord  of  60°  in  th« 
dividers,  and  with  one  foot  on  this  line  as  a  Centre,  make  the  Arc  of  a  Circle  towards  the  left  downwards, 
which  will  represent  the  South- West  quarter  of  the  Compass.  Take  90°  in  the  dividers,  and  with  one  foot 
on  the  line  where  the  Circle  joins  it,  extend  the  other  and  mark  the  Circle.  A  line  through  this  mark  to 
the  Centre  will  form  a  Right  Angle  with  the  other  line,  and  which  will  represent  the  Meridian  sailed  from. 
Take  5^  Points  from  the  line  of  Chords,  and  lay  it  off  from  the  South  towards  the  West,  and  mark  it  on  the 
Circle.  Draw  the  Rhumb  line  through  this  mark  to  the  Centre,  and  it  will  form  an  Angle  with  the 
Meridian  or  the  Course. 

Lay  off  the  Departure  350  miles  from  the  Meridian  towards  the  West,  and  draw  the  Meridian  come  to 
parallel  with  the  other;  then  where  it  cuts  the  Rhumb  line  is  the  Sliip's  place.  Extend  the  dividers  b»> 
tween  this  place  and  the  Centre,  will  give  the  Distance  sailed  396  miles.  Through  the  Ship's  place  draw 
the  parallel  of  Latitude  come  to.  and  the  space  hetween  the  parallels  of  Latitude  is  the  Difference  of  Lati- 
tude, 187,  or  3°  7'  South,  and  the  Latitude  in  is  1°  00'  South.     In  this  case  the  Ship  has  crossed  the  Equator. 

B^  INSPECTION.  TRAVERSE  TABLES. 
Find  the  Course  5^  Points  at  the  bottom  of  the  page  of  the  Table  for  Points.  Take  half  the  Departure, 
JJ50  miles,  which  is  175,  in  its  column,  the  nearest  to  it,  is  174.6;  opposite,  in  the  Distance  column,  standi 
198,  and  in  the  Latitude  column  93.3,  which  is  half  the  Distance  and  half  the  Departure,  which,  being 
doubled  gives  the  whole  Distance,  396  miles,  and  the  whole  Difference  of  Latitude  186.6,  or  divided  by  60, 
3°  7'  South.  The  Latitude  sailed  from  was  2°  7'  North,  which,  subtracted  from  the  Difference  of  Lati- 
tude made,  gives  the  Latitude  in  1  °  0'  South,  and  the  Ship  in  this  case  has  crossed  the  Equaior 

CASE  VI, 
The  Distance  and  Departure  given  to  find  the  Course  and  Difference  of  Latitude 
ExiMPLE. — A  Ship  from  Latitude  1°  0'  South  sails  between  the  North  and  East  896  miles,  until  her  D«partar» 
ii  860  miles.     Required  the  Ootirse  steered  and  her  Latitude  in. 

Fio.  11. 


J^i:'ju//('/    r/      Acy.      ':<'r,,<  /< 


""-^  llf/>  jy/T 


I' f /,  f ''//..■■/    r/"  /^aJ^  SufU<^^-  ^y't'iTh 


PLANE     SAILING  IS 

PROJECTION  BY  THE  PLANE  SCALE. 

Draw  a  horizontal  line  to  represent  the  parallel  of  Latitude  sailed  from.  Take  the  Chord  of  60'  in  th« 
dividers,  and  with  one  foot  on  this  line  as  a  centre,  make  the  Arc  of  a  circle  towards  the  right  hand 
upwards,  which  will  represent  the  North-East  quarter  of  the  Compass.  Take  90°  in  the  dividers,  and  with 
one  foot  on  this  line  where  the  Circle  joins  it,  extend  the  other  upwards,  and  mark  the  Circle.  A  lina 
drawn  thTough  this  mark  to  the  Centre  will  form  a  Right  Angle  with  the  other  line,  and  which  will  rep- 
resent the  Meridian  sailed  from.  Lay  off  the  Departure  350  miles  from  the  Meridian  towards  the  right  oi 
the  Ea=t,  and  draw  the  Meridian  come  to  i)arallel  with  the  other.  Take  the  Distance,  396  miles,  in  the 
dividers,  and  with  one  foot  on  the  centre,  extend  the  other,  and  cut  the  Meridian  come  to,  which  will  be  the 
Ship's  place.  Draw  the  Rhumb  line  between  the  Ship's  place  and  the  centre,  and  where  it  cuts  the  Circle 
will  be  the  Course  North  5i  Points  East,  and  measured  on  the  line  of  Rhumbs.  Through  the  Ship's  place 
draw  the  parallel  of  Latitude  come  to,  and  the  space  between  the  parallels  is  the  Difference  of  Latitude, 
487  miles,  or  3°  7',  the  Latitude  in  being  2°  7'  North. 

In  this  case  the  Ship  has  crossed  the  Equator. 

BY    INSPECTION.     TRAVERSE    TABLES. 

Take  half  the  Distance,  198.  and  half  the  Departure,  175.  Seek  in  the  Tables  till  opposite  the  former, 
the  nearest  to  the  latter  is  found  to  be  174.6,  adjoining  to  which  stands  half  the  Difference  of  Latitude, 
■93.3,  which  doubled  is  186.6,  or  3°  7'  North,  from  which  subtract  the  Latitude  left,  1°  0'  South,  gives  the 
Latitude  m  2°  7'  North,  and  the  Departure  being  greater  than  the  Difference  of  Latitude,  the  Course  i* 
found  at  the  bottom  of  the  page  to  be  North  5i  Points  East,  or  North  62°  E.  in  the  Table  for  Degrees. 


The  above  Six  cases  comprehend  all  the  varieties  of  Plane  Sailing,  but  as  it  is  of  great  importance  tt 
have  a  thorough  knowledge  of  the  principles  of  Plane  Sailing  before  going  into  the  other  Sailings,  (because 
it  is  us^d  in  all  the  other  Sailings,)  and  also  to  exercise  the  learner  in  the  use  of  the  Traverse  Tables,  the 
following  questions  are  given  for  exercise. 

Question  1.  A  Ship  from  Latitude  36°  30'  North  sails  South-West  by  West  420  miles.  Required  her 
Latitude  in  and  her  Departure  from  the  Meridian. 

Answer.  Latitude  in  32°  37'  North,  and  Departure  349.2   West. 

Question  2.  A  Ship  from  Latitude  3°  54'  South  sails  North- West  i  West  until  her  Latitude  in  is  2*  14 
North.     Required  her  Distance  run  and  Departure  made  good. 

Answer.   Distance  618  miles,  and  Departure  496.4  West. 

Question  3.  A  Ship  from  St.  Helena,  in  Latitude  15°  55' S  sails  South-South-East  i  East  till  she  has 
made  115  miles  of  Departure.     Required  her  Latitude  in  and  the  Distance  run. 

Answer.  Latitude  iji  19°  30'  South,  and  Distance  244  miles. 

Question  4.  A  Ship  from  Latitude  28°  20'  North  sails  between  the  North  and  East  486  miles,  and  finds 
ty  Observation  that  she  is  in  Latitude  32°  17'  North;  what  Course  has  she  steered,  and  what  Departure 
feas  she  made  ? 

AxswEii.   Course  N.  61°  East,  or  North-East  by  East  i  East  nearly,  and  Departure  425  East. 

Question  5.  A  Ship  sails  between  the  North  and  West  170  Leagues  from  a  Port  in  Latitude  38°  42' 
North  until  her  Departure  be  98  leagues.     Required  her  Course  and  Latitude  in. 

A.nswer.  Course  North  35°  West,  or  North- West  by  North  i  West  nearly,  and  Latitude  in  45°  40' 
North. 

Question  6.  A  Ship  from  Sandy  Hook  in  Latitude  40°  28'  North,  sails  between  the  South  and  East  until 
her  Latitude  observed  is  38°  20'  North,  and  having  made  100  miles  Departure.  Required  the  Course  and 
Distance  Sailed. 

Answer.  Course  South  38°  East,  Distance  163  miles. 

Question.  7.  A  Ship  off  Cape  Henry  in  Latitude  36°  56'  North,  is  bound  to  Bermuda,  in  Latitude  32°  19' 
North,  and  which  lays  552  miles  to  the  Eastward  of  the  Cape.     Required  her  Course  and  Distance  to  it. 

Answer.  Course  South  63°  East,  or  South-East  by  East  i  East  nearly,  and  the  Distance  618  miles. 

Question  8.  Five  Days  ago  we  were  in  Latitude  3°  10'  North,  and  since  then  have  sailed  on  a  South- 
West  Course,  at  the  rate  of  10  knots  an  hour.  Required  the  Latitude  in  and  the  Departure  made  to  the 
A'estward. 

Answer.  The  Latitude  in  is  10°  59'  South,  and  the  Departure  made  is  849  to  the  Westward. 

Question  9.  A  Ship  from  Latitude  4°  10'  South  is  bound  to  a  Port  in  Latitude  3°  10'  North,  and  bearing 
trom  the  Ship  North-North- West.  Required  how  far  that  Port  lies  to  the  Westward,  and  the  Ship's  Dis- 
tance from  it. 

Answer.  The  Port  lies  183  miles  to  the  Westward,  and  the  Distance  is  478  miles. 

Question  10.  Required  the  Bearing  and  Distance  between  Neversink  Light  in  Latitude  40°  24'  North 
<tnd  the  Island  of  Porto  Rico  in  Latitude  18*  29'  North,  and  which  lies  413  miles  to  the  Eastward  of  the 
former. 

Answer.  The  Bearing  is  South  17°  30'  East,  or  South  by  East  i  East,  and  tie  Distance  1,380  milcfc. 


14 


/ 


TRAVERSE    SAILING. 


This  u  a  Tariety  of  Plane  Sailing  in  which  the  Ship  makes  two  or  more  Courses  in  succession,  and  tilt 
OMthod  of  reducing  these  several  Courses  and  Dista».»s  into  a  single  Course  and  Distance  is  called  woririn^ 
%  Traverse. 

TO  WORK    A    TRAVERSE 

Make  a  Table,  and  divide  it  into  six  columns ;  in  the  first  of  these  set  down  the  several  Courses,  and 
©pposite  to  them,  in  the  second  column,  their  corresponding  Distances.  The  third  and  fourth  columns  are  te 
be  marked  North  and  South  at  the  top,  and  are  to  contain  the  Differences  of  Latitude.  The  fifth  and  sixth 
are  to  be  marked  East  and  West,  and  to  contain  the  Departures. 

Find  the  Difierence  of  Latitude  and  Departure  corresponding  to  each  Course  and  Distance  by  the  method 
of  Plane  Sailing.  Set  these  down  opposite  the  Distance  in  their  proper  commns,  that  is,  if  the  Difference 
of  Latitude  is  north,  it  must  be  placed  In  the  North  column,  and  if  South  in  the  South  column,  and  that  if 
the  Departure  is  Easterly  it  mu^  be  placed  in  the  East  column,  and  if  Westerly  it  must  be  placed  in  the 
West  column.  When  the  Course  is  due  North,  South,  East,  or  West,  set  down  the  Distance  in  that  column 
answering  to  it.  Add  up  the  columns  of  Northing,  Southing,  Easting,  and  Westing,  and  set  down  the  sum 
df  each  at  the  bottom,  then  the  difference  between  the  sums  of  the  North  and  South  columns  will  be  the 
whole  difference  of  Latitude  made  good,  of  the  same  name  as  the  greater,  and  the  Difference  between  the 
•unu  of  the  East  and  West  columns  is  the  whole  Departure  made  good  of  the  same  name  as  the  greater; 
then  with  the  whole  difference  of  Latitude  and  Departure  made  good,  find  the  direct  Course  and  Distance. 


EXAMPLE  1. 

A  Ship  takes  her  Departure  from  an  Island  in  Latitude 
North-West  10  miles,  and  sailed  on  the  following  Courses 


35*  10'  North,  the  centre  of  which  b^re  West- 
North-East  30  miles.  West  by  North  60  miles, 


South-South- West  36  miles.  East  20  miles.  South  14  miles.  East  by  North  50  miles,  and  Soutt-West  by 
West  70  miles.  Required  her  Latitude  in,  the  Course  and  Distance  made  good,  and  the  bearing  and  Dis- 
Unce  of  th«-  Island. 


TRAVERSE  TABLE. 


Dirf .  OF  LAT. 

DEPAKTDBB. 

couKaif. 

DIST. 

NORTH. 

iOOTH. 

BAIT. 

WBBT. 

Bearinir  W   N  W    . 

Opposite  Pt  E.  S.  E. 

10 
30 
60 
36 
20 
14 
60 
70 

9.8 

8.8 

9.2 

21.2 

"49.6** 

13.8 

W  bv  N 

East       

S3.S 

*  20.0 

South 

"V.s" 

14.0 
88.9 

E.  by  N 

49.0 

'  '58.2*  * 

S.  W.by  W 

Diff  of  Lat.  made . . . 

40.8 

90.0 
40.8 

99.4 

121.0 
99.4 

49.2  S., 
85    10  N. 

34*  21'  N. 

<fc  Dep.  mi 

ide  21.6 

Lat.  of  the  Island . . .  • 

West                    1 

Lat  of  the  Ship 

Witli  the  Difference  of  Latitude  49.2,  and  Departure  21.6,  seek  in  the  Table  for  the  nearest  corree- 
ponding  sams,  which  are  found  to  be  49.3  and  22.0,  and  opposite  to  them  stands  the  Distance,  54,  in  its 
•oltunn.  and  the  Course  is  found  at  the  top  of  the  page,  because  the  Departure  is  less  than  the  Difference 
•f  Latitade.  The  Course  made  good  'n  this  case  is  South  24*  West,  or  South-South- West  i  West  nearly, 
and  the  Distance  54  miles. 

The  Bearing  of  the  Island  from  the  Ship  is  just  the  reverse  of  the  Course  made  good,  that  is,  North  84* 
East,  because  the  Departure  was  taken  from  it,  and  the  Distance  is  the  same  as  the  Distance  made  good  bj 
*he  Ship,  which  is  54  miles. 


TRAVERSE    BAILING. 


1ft 


PROJECTION    BY    THE     PLANE    SCALE. 
Fio.  12. 


llarallel  o/'Zdro/^u.^Jaan(//35  '  vo  ^' 


-East    2C 


^.    4   el 


Para_^/r/  -^Xr/^  Lai 


y    J)ep     27   c 


come  tr>    .,//    i/  .A' 


With  the  Chord  of  60°  describe  a  Circle.  Take  90'  in  the  dividers,  and  mark  the  circumferenoe  of  il 
mto  lour  equal  parts,  representing  the  Points  of  the  Compass,  and  mark  it  North  at  the  top.  South  at  th^bot- 
»K    I  on  the  Right,  and  West  on  the  left  hand,  and  mark  the  Centre  as  the  place  of  the  Island      Tak« 

^LTfvf  w'*?  ^  ^i*'."*^  ^^'*'  ^"  ^^^  dividers,  from  the  line  of  Rhumbs  and  lay  it  off  from  the  North 
^r^hiM  '  !'  e"  '?''*V-^^"®  *°  *^®  ^^"*'"®'  ^^'«^'  prolonged  to  the  opposite  side,  will  pass  through 
the  Ship  s  pxace  to  South  6  Points  East.  Take  the  distance  of  the  Ship  from  the  Island,  10  miles  in^a 
aimers,  and  lay  it  off  from  the  centre  on  this  line,  which  will  be  the  Ship's  place  at  the  time  of  taking  ber 
aeparture.  1  ake  4  Points  in  the  dividers,  and  lay  it  off  from  the  North  towards  the  East,  and  mark  it  oa 
Pnnilo*;  iu  L  f  ^?=''  ""^  ^^®  parallel  ruler  over  this  mark,  and  that  of  the  Centre,  and  transfer  thi« 
frnm  tt  cl-  >  P  '  P  ?^'  ^"^  ^^'^^'  ^  ^^"^^  ^'^  *^^*  direction;  take  30  miles,  in  the  dividers,  and  lay  it  off 
W  fi  f  n  ^^  ^  P^Tt.''  "^^P^rture  on  this  line,  and  which  will  be  the  Ship's  second  place  after  corapletin- 
ner  first  Course  and  Distance.  fio"", 

thi'l«!l't>r''''°f  lu^l.''^  """  1^^  ''*^^''  ^^"'■'*'  ^"^  Distances.     Then  draw  a  parallel  of  Latitude  throagb 
nr.»     v%         u    J,"P'  ^"^  ^^®'"®  "^  <="t^  t^«  Meridian  will  be  the  Difference  of  Latitude  made  49 
n^^r  ^A^        u    cf  ^^"^''^to  the  Ship's  place,  and  where  it  cuts  the  Circle  will  be  the  Course  made  good.' 

Z^Zt.    T  M  '  -^"''^  ?'    ^^^*'  *"^  *^«  D'«^^"«^'  5^  '"il^^-     ^^  "^«  drawn  through  the  Ship's  pW 
KrnL!f  )t  ^^f"dian  of  the  Island,  will  give  the  Meridian  come  to,  and  the  space  between  them  is  the 

i«S  K'k   oi^i^'\     }'u    ''.^^""^  °^  ^"^^  ^'^^"d  ^"■°'"  ^^'«  Ship  is  the  opposite  point  to  the  Course  mad« 
good  '  Distance  from  the  Island  is  54  miles,  which  is  equal  to  the  Distance  madt 


lA 


TRAVERSE     SAILING. 


EXAMPLE  2. 
A  Ship  from  Latitude  43*  10'  North,  is  bouud  to  a  port  in  Latitude  42°  20'  North,  and  which  lies  50  miles  to  tL 
Westward  of  the  Ship.     But  by  reason  of  contrary  winds,  and  other  causes,  she  has  sailed  on  the  following  Courses^ 
n*. :  N.  N.  W    SO  miles,  E.  S.  E.  30,  South  20,  W.  i  S.  39,  S.  E.  15,  and  W.  by  S.  22.     Required  the  Bearing  and 
L/istanceof  the  Port  rrom  her  first  position,  her  Course  and  Distance  made  good,  her  Latitude  come  to,  and  tM 
bourse  and  Distance  to  her  intended  Port. 

TRAVERSE  TABLE. 


To  find  the  Bearing  and  Distance  of   the   f\ir1 
from  the  Ship's  first  position. 


DIFF.   LAT. 

DEP. 

1 

COURSES. 

N.  N.  W. 
E.  S.  E. 
South. 
W.  i  S. 

S.  E. 
W.  by  S. 

DIST. 

NORTH. 

SOUTH. 

EAST. 

WEST 

30 
30 
20 
89 
15 
22 

27.7 

11.5 

11.5 
20.0 

3.8 
10.6 

4.S 

27.7 

10  6 

■    -   .    •  •  •  •  • 

38.8 
21.6 

1 

27.7 

5(1.2 
27  7 

38.3 

71.9 
38.3 

.43°  10'  N. 
.42    20' N. 


Diff.  Lat , 

Lat  left. 43° 


Lat  of  the  Ship. 
Lat.  of  the  Port. 

Diff.  Lat 60    Dep.  50, 

Gives  the  Bearing S.  W 

And  the  Distance 70  mile* 


22.5  S.     and  Dep. . .  33.6  W.,  gives  the  Course  made  good,  S.  56°  W.,  or  S.W.  by W 
1 0'  N.  and  the  Distance  40  miles. 


Lat.  come  to 42°  47'.         To  find  the  Bearing  and  Distance  of  the  intended  Port.     Take  the  whoI« 

Difif.  of  Lat.  between  the  Ship's  1st  position  and  that  of  the  Port,  which  is  50  miles,  and  the  whole  Departure  50. 
From  which  subtract  the  Diff.  Lat.  made  good 23     "        and  Dep.  made  good ...  .34. 

Leaves  the  Difference  of  Latitude  to  make 27     "        and  the  Dep.  to  make. .  .16 


Port 


These  agree  in  the  Tables  to  the  Course  31°,  or  2|  points,  nearly,  and  the  Distance  31  miles';  and  as  the  inteodW 
)rt  lies  to  the  South  and  West  of  the  Ship,  she  must  steer  S.  31    W.,  oi 


or  S.  S.  W.  S  W.,  31  miles. 


PROJECTION  BY  THE  PLANE  SCALE. 
Fig.  13. 


II 


TRAVERSE    SAILING. 


n 


l>raw  a  figure  as  in  the  preceding  example,  the  Ship's  position  being  in  the  Centre.  Draw  her  parahel 
«f  Latitude  and  her  Meridian;  from  the  Centre  lay  off  the  first  Course  Norlk  2  Points  West  30  miles;  lay 
off  6  Points  from  the  South  towards  the  East  for  the  second  Course,  and  mark  it  on  the  Circle.  Lay  the 
parallal  ruler  over  this  mark  and  the  centre,  and  transfer  this  Course  to  ihe  Ship's  place,  and  dra>y  a 
line,  on  which  lay  off  the  Distance,  30  miles.  Lay  off  the  other  Courses  and  Distances  in  like  manner, 
and  at  the  end  of  the  last  one  is  the  Siiip's  place.  From  the  Ship's  place  draw  a  line  to  the  Centre,  which 
will  be  the  Distance  made  good.  40  miles,  and  the  Angle  which  thi«  line  makes  with  the  Meridian  is  the 
Course  made  good  South  5  Points  West.  Through  the  Ship's  place,  draw  the  parallel  of  Latitude  como 
to,  and  the  ^ace  between  the  parallels  of  Latitude  is  the  difference  of  Latitude  made  good,  23  miles.  Draw 
a  Mer.dian  line  through  the  Ship's  place,  and  the  space  between  the  Meridians  is  the  Departure  mad©  good, 
34  miles. 

Take  the  Difference  of  Latitude  between  the  Latitude  saile^  from,  and  the  Latitude  of  the  intended  Port, 
50  miles.  Lay  this  off  to  the  South  on  the  Meridian  sailed  from,  and  draw  the  parallel  of  Latitude  of  the 
Port  on  this  line.  Lay  off  50  miles,  which  the  Port  lies  west  of  the  Meridian  of  the  Ship,  and  draw  the 
Meridian  of  the  Port ;  where  these  lines  intersect  each  other,  is  the  intended  Port.  Draw  a  line  between  the 
uitended  Port  and  the  Ship's  place,  will  give  the  Distance  from  it,  31  miles,  and  the  Angle  between  this 
line  and  the  Meridian  of  the  Ship  will  be  the  Course.  Lay  the  ruler  along  this  line,  and  transfer  it  to  the 
Centre,  and  where  the  edge  of  the  ruler  cuts  the  Circle  is  the  measurement  of  the  Course  South  31°  West 
to  her  intended  port.  Draw  a  line  between  the  Port  and  the  Ship's  first  position  in  the  Centre,  will  give 
its  Distance,  70  miles,  and  the  Angle  between  this  line  and  the  Meridian  of  the  Ship  is  the  bearing  of 
the  Port,  which  is  South- West. 

EXAMPLE  3. 

A  Ship  from  a  Port  in  Latitude  38°  42'  North,  bound  to  another  Port,  situated  in  Latitude  36*  32'  North, 
and  137  miles  to  the  Ea.stward,  sails  on  the  following  Courses;  South  by  West  i  West  55  miles,  South- 
West  by  South  i  West  37  miles.  South  60  miles,  East-South-East  40  miles,  South-East  by  South  i  East  32 
miles,  and  North-East  by  East  i  East  58  miles.  Required  her  Course  and  Distance  made  good,  her  pres- 
ent Latitude,  and  the  direct  Course  and  Distance  to  her  intended  Port. 

Answer.  The  Course  made  good  is  South  23°  30'  East,  and  the  Distance  169  miles,  the  Latitude  in  36* 
y  North  the  Course  t»  the  intended  Port  North  70°  East,  and  the  Distance  74  miles. 

EXAMPLE  4. 

A  Ship  takes  her  Departure  from  Cape  Henry  Light  House,  in  Latitude  36°  56'  North,  bearing  West- 
North- West  7  leagues,  bound  to  the  Island  of  Bermuda,  in  Latitude  32°  19'  North,  and  which  lies  552  miles 
to  the  Eastward  of  the  Cape,  but  by  reason  of  contrary  winds  has  sailed  on  the  following  Courses:  South- 
East  by  East  50  miles,  South-South-East  40  miles,  South  20  miles,  East  60  miles.  East  by  North  J-  North 
30  miles,. North-East  i  East  40  miles,  and  East  by  South  i  South  50  miles.  Required  the  Difference  of 
Latitude  and  Departure  made  good,  her  direct  Course  and  Distance  made  good,  her  present  Latitude  and 
the  Bearing  and  Distance  of  Bermuda  Island. 


COUSSB8. 


E.  S.  E. 

S.  E.  bv  E. 

S.  S.  E. 

South. 

East. 

E.  by  N.  i  N. 

N.  E.  i  E. 
E.  by.  S.  i  S. 


21 

50 
40 
20 
60 
30 
40 
50 


8.7 
25.4 


34.1 


8.0 
27.8 
37.0 
20.0 


14.5 


19.4 
41.6 
15.3 


60.0 
28.7 
30.9 
47.8 


WEST. 


243.7  of  Easting. 


Difference  of  Lat  made  good  is 

or'r  13'  S. 

Latitude  of  Cape  Henry 36    66  N.    v.^  c-  i  o  oc?  „il«i 

LaUtud«of  theShip... '35°  43' N.    by  S  i  S.  254  mile.. 


107.3 
34J 

73.2  and  Dep.  243.7,  gives 
the  Course  and  Dis- 
tance made  good  E. 


Latitude  of  Cape  Henry  36°  56'  N. 
Latitude  of  Bermuda...  32    19   N. 


4°  37' 
60 


Whole  Diff.  of  Latitude  277  S.,  and  Dep.  652  K 
Diff.  of  Latitude  made, .  73  S.,  and  Dep.  244  E. 

Leaves  Diff  of  Lat 204' and  Dep 308mile8 

to  make. 

One-tenth  of  these  Sums  are  found  to  agree 
nearly  to  a  Course  of  56°  and  the  Distance  correa- 
ponding  370  miles. 

The  true  Bearing  of  Bermuda  from  the  Ship  ia, 
therefore,  South  56°  East,  or  South-Eaat  by  &*ai 
nearly  distant  370  miles. 


18 


PARALLEL    SAILING. 


fn  Plane  Sailing  the  Earth  is  considered  to  be  an  extended  plane,  and  the  Meridians  all  parallel  to  eacB 
other,  and  the  length  of  a  Degree  everywhere  equal,  which  supposition  will  give  just  conclusions,  so  far  u 
the  Course,  Distance,  Difference  of  Latitude  and  Departure  are  concerned ;  because  a  Sliip,  when  sailing 
on  a  Rhumb  line,  makes  equal  Angles  with  the  Meridian. 

But  as  the  E-artli  is  a  Globe  or  Sphere,  and  the  Meridians  meet  at  the  Poles,  it  is  evident  that  the  Dis- 
tance between  any  two  Meridians  must  vary  in  every  Latitude  :  their  greatest  Distance  being  at  the  Equator 
on  which  tlie  Difference  of  Longitude  is  measured  ;  hence  tlie  difference  of  Longitude  always  exceeds  the 
Departure  or  Meridian  Distance,  (except  on  the  Equator,  where  they  are  the  same),  in  proportion  as  the 
given  places  are  situated  farther  from  the  Equator. 

The  following  Table,  showing  the  number  of  Minutes  and  Seconds  contained  in  each  Degree  or  60  milea 
•f  Longitude  for  every  Degree  of  Latitude,  will  be  found  useful. 


LAT. 

MIN.       SEC. 

LIT. 

MIN.      SEC. 

LAT. 

MIN.      SEC. 

LAT. 

MIN.      EEC. 

LAT. 

MIN.      8EC. 

• 

tt 

• 

/       II 

o 

1       II 

o 

1       II 

• 

1      II 

1 

59.59 

19 

66.44 

37 

47.55 

65 

34.26 

73 

17.33 

2 

69.58 

20 

66.23 

38 

47.15 

56 

33.30 

74 

16.83 

S 

59.56 

21 

66.00 

39 

46.38 

57 

32.41 

75 

15.31 

4 

59.51 

22 

65.38 

40 

45.58 

58 

31.48 

76 

14.31 

6 

59.46 

28 

55.14 

41 

46.17 

59 

30.64 

77 

13.30 

6 

59.40 

24 

54.49 

42 

44.35 

60 

30.00 

78 

12.28 

7 

69.33 

25 

54.23 

43 

43.53 

61 

29.06 

79 

11.27 

8 

69.25 

26 

53.56 

44 

43.10 

62 

28.10 

80 

10.26 

9 

69.16 

27 

53.28 

45 

42.26 

63 

27.16 

81 

9.24 

10 

59.06 

28 

52.59 

46 

41.41 

64 

26.18 

82 

8.21 

11 

58.54 

29 

52.29 

47 

40.55 

66 

25.22 

83 

7.19 

12 

58.41 

30 

51.58 

48 

40.09 

66 

24.24 

84 

6.16 

13 

58.28 

31 

51.26 

49 

39.22 

67 

23.26 

85 

8.14 

14 

68.14 

32 

50.53 

50 

38.44 

68 

22.28 

86 

4.12 

15 

57.68 

33 

50.19 

51 

37.46 

69 

21.30 

87 

3.09 

16 

67.41 

34 

49.45 

52 

36.57 

70 

20.31 

88 

2.02 

17 

57.23 

35 

49.09 

53 

36.07 

71 

19.32 

89 

l.OS 

18 

57.04 

36 

48.33 

54 

35.18 

72 

18.33 

90 

0.00 

DIAGRAM 

Showing  the  Contraction  of  the  Meridians  from  the  Equator  towards  the  Pole,  and  the  Parallel!  of  Lot* 

tude  crossing  the  Meridians. 


Fig. 


Parallel  Sailing  is  the  method  of  finding  the  Distance  between  two  places  in  the  same  Parallel  of  Latituie 
when  their  difference  of  Longitude  is  known,  or  of  finding  the  difference  of  Longitude  answering  to  th« 
Distance  or  Departure  made  good  when  a  Ship  sails  due  East  or  West.  Distance  sailed  and  Departure  ar« 
Ihe  same  thing  in  Parallel  Sailing. 

Note  —This  Sailing  ia  particularly  useful  in  making  a  small  or  low  Is'and,  in  which  case  it  is  usual  to  run  into  the 
Ltttitud'e,  and  then  steer  East  or  West,  care  being  taken  that  the  Ship  ia  on  the  proper  side  of  the  Meridian  of  th« 
Ulaad. 


PARALLEL    SAILING.  19 

CASE    I. 
Hu  Difference  of  Longitude  between  two  Places,  both  in  one  Parallel  of  Latitude,  given,  to  find  their  Du'oncc 

EXAMPLE. 

A  Ship  fc  the  Latitude  of  32*  a'  N.  and  Longitude  69*  50'  W.,  and  bouud  to  Bermuda,  in  the  same  Latitude,  and 
Longitude  64*  60'  W.,  what  distance  must  she  run  to  the  Eastward  to  arrive  at  the  Island  ? 

BY    INSPECTION. 

Longitude  of  the  Ship.  .69°  50'  W.  )  u  i    *  t   ^-^    i      e  ^\     t  i     j  o^.  «-  -kt 

Lon|itude  of  Bermuda.  ^*_50'  W.  ^  ^  "'■''^"^1  ^^  Latitude  of  the  Island  32*  9'  N. 

6°    0' 
60 

Role. — Take  the  Parallel  of  Latitude  32*  as  a  Coura« 


•nd  the  Difference  of  Longitude  in  miles  300  in  the  Distance  Column,  and  the  Distance  (or  Departure)  264.4  will 
b«  i)und  in  the  Latitude  Column.  The  Ship  has,  therefore,  to  run  254  miles  to  the  Eastward  to  aniye  at  tb« 
blaud. 

CASE  II. 

The  Distance  between  two  places  given,  both  in  the  same  Parallel  of  Latitude,  to  find  the  Difference  of  Lon- 
gitude. 

EXAMPLE. 

A  Ship  from  the  Island  of  Bermuda,  in  Latitude  32*  9'  N.  and  Longitude  64*  60'  W.,  saild  du^  W.  254  miloA 
E«quirea  her  Longitude  in. 

Rcu. — Take  the  Parallel  of  Latitude  32*  as  a  Course,  and  the  Distance,  254,  in  the  Latitude  Oolunco,  and  UM 
Difference  of  Longitude  will  be  found  in  the  Distance  Column,  300  miles. 

Longitude  of  Bermuda.  .64*  60'  W. 

Diff  Long,  made  300. .  —  5      0  W. 

Longitude  in. . .  .69*  60'  W 

CASE    III. 

The  Difference  of  Longitude  and  Distance  between  two  places  in  the  same  Parallel  of  Latitude  given,   (• 

firxd  the  Latitude  of  that  Parallel. 

EXAMPLE. 

A  Ship  sails  due  East  264  miles,  and  then  finds  she  has  altered  b«r  Longitude  SOO  miles.  Required  the  Paralld 
•f  Latitude  she  sailed  in. 

Rdlx. — Seek  in  the  Tables  until  the  Difference  of  Longitude,  300,18  found  in  the  Distance  Column,  and  the  Distanes 
«ailed,  254,  is  found  in  the  Latitude  Column ;  then  the  Course  32',  at  the  top  of  the  page,  will  be  the  Parallel  of 
Latitude  sailed  in,  because  254  is  found  in  the  Column  headed  Latitude  at  the  top  of  the  page. 

QUESTION  FOR  EXERCISE. 

A  Ship  from  Latitude  48*  89'  N.  and  Longitude  60°  10'  W,  sails  due  "Wept  350  miles.    Required  her  Longitude  in. 

With  Latitude  48°,  and  half  the  Distance,  175,  (the  whole  being  too  great  for  the  Tables,)  in  the  Lati- 
tude Column,  I  find  half  the  Difference  of  Longitude,  262,  in  the  Distance  Column.  Then,  with  Latitude 
49°  as  a  Course,  and  Distance  175  in  the  Latitude  column,  I  find  267  in  the  Distance  column.  Add  these 
Differences  of  Longitude  together,  and  take  their  half  Sum  for  the  Difference  of  Longit  ide,  corresponding  to 
the  Latitude  48°  30',  which  doubled  will  give  the  required  Difference  of  Longitude,  529=8°  49'  W  and 
Longitude  in  68°  59'  W.,  as  follows  : 

Latitude  48*  difference  Longitude  262 
Latitude  49*  difference  Longitude  267 

)529 


Half  Difference  cf  Longitude  264.5 

2 


Whole  Difference  of  Longitude.   629.0  miles. 

Which  divided  by  60*  gives 8°  49'  W. 

Longitude  left fin  10  W. 

Longitude  in 68°59'  W. 


20 


MIDDLE    LATITUDE    SAILING. 

This  method  is  founded  upon  the  same  principle  as  Parallel  Sailmg ;  that  is,  of  converting  the  Depart 
ore  into  Difference  of  Longitude,  and  Difference  of  Longitude  into  Departure.  When  the  Ship's  Courst 
lies  obliquely  across  the  meridians,  that  is,  when,  besides  Departure,  she  makes  Difference  of  Latitude  she 
leaves  a  certain  Parallel  of  Latitude  and  arrives  at  another,  the  Space  or  Departure  between  the  Meridians 
•ailed  from  and  come  to  differ,  the  one  being  greater  than  the  other,  and  it  is  evident  neither  of  these 
Departures  can  be  used  singly,  to  find  the  Difference  of  Longitude. 

But  if  we  take  the  Middle  Parallel  of  Latitude  between  the  Latitudes  sailed  from  and  come  to,  we  get 
the  middle  Departure  between  them.  In  the  greater  Latitude  the  Departure  is  less,  and  in  the  less  Lati- 
tnde  the  Departure  is  greater,  than  the  Departure  corresponding  to  the  Middle  Latitude.  Hence  thi» 
method,  which  is  compounded  of  Plane  and  Parallel  Sailings,  is  called  Middle  Latitude  Sailing. 

The  Middle  Latitude  is  half  the  Sum  of  the  two  Latitudes  when  they  are  of  the  same  name.  Near  the 
Equator,  when  the  Latitudes  are  of  contrary  names,  no  sensible  error  can  arise  from  taking  the  Departure 
itself,  made  good  from  day  to  day  as  the  Difference  of  Longitude,  because  the  Degrees  of  Latitude  and  Lon- 
gitude are  of  the  same  length  on  the  Equator,  and  the  latter  is  only  diminished  by  1  mile  at  the  lOtb 
Parallel  of  Latitude;  therefore  in  practice  at  Sea,  Longitude  and  Departure  may  be  considered  the  same  for 
several  Degrees  on  each  side  of  the  Equator. 

In  using  the  Traverse  Tables,  it  is  enough  to  take  the  Latitude  for  the  nearest  Degree. 

In  greater  distances  between  places  whose  Latitudes  are  of  contrary  names,  the  proper  rule  is  to  take 
half  the  greater  Latitude  as  the  Middle  Latitude*      (See  the  annexed  Diagram.) 

The  Difference  of  Longitude  found  by  this  Sailing  is  true  at  the  Equator,  and  very  nearly  true  for  short 
distances  in  all  Latitudes,  especially  when  the  course  is  nearly  East  or  West.  In  High  Latitudes,  when 
the  Distance  is  great  and  the  Course  oblique,  the  error  becomes  considerable  ;  but  the  result  may  be  made 
nearly  true  by  subdividing  the  Distance  Sailed  into  small  portions,  and  finding  the  Difference  of  Longitude 
for  each  portion  separately,  and  then  adding  the  whole  together. 

In  like  manner  the  Bearing  and  Distance  between  places  near  the  Equator  by  this  Sailing  are  correcl 
But  in  High  Latitudes  the  result  cannot  be  rendered  accurate  by  subdividing  the  Distance  into  small  por- 
tions, as  above,  because  it  is  not  known.     Such  cases  are  truly  solved  by  Mercator's  Sailing 

DIAGRAM, 
Showing  the  Middle  Latitude  between  the  Parallels  of  Latitude  North  and  South  of  the  Equator 

Ffo.    15 


•  Or  ndd  together  the  half  of  the  greater  Latitude  to  the  half  of  the  less  Latitude,  and  their  half  sum  will  J*  the 
Hidcfie  Latitide  required.    See  al8.:^  the  Note  at  page  28. 


I 


MIDDLE    LATITUDE    SAILING.  SI 

CASE    I.  • 

ihte  Latit  ide  and  Longitude^  Course  and  Distance  given,  to  find  the  Difference  of  Latitude  arui  Longttudt. 

EXAMPLE  L 

A  Ship  from  Latitude  62*  6'  N.  and  Longitude  36°  6'  W_  sailed  S.  W.  by  W.  256  u  ilea.     Required  her  Latitud* 
■nd  Longitude  in. 

Course  S.  6  pta.  W,        ) 

Distance      256  miles,     )  gives  the  Diff.  Lat.   )142  and  the  Dep.  212.9,   the  half,   106.4,  taken  in   the   Latitudk 

^     Diff.  Lat 142    S.  Diffi  Lat..  .2*  22'  S.       CoL  of  Mid.  Lat  61*.  as  a  Course,  then  Half  DiH  of 

I     Departure 218W.  Lat  left.  52°    6' N.       Long- is  found  in  the  Dist  Column  to  be  1 99 


Lat  in 49°  44'  N.  Lat  in. .  49°  44' 


)388 


'^      Diff  Long....  6°  38'  W.-  Sum...  101   .60 

T          •            ^.^OiAf  Tir                      \M  J  T   t  rr.»  r r/                                            Diff  Loug.  made..   5'  88'  W. 
Long.  m. ...  40  44   W.  Mid.  Lat  60   66'  L^^  ij 35^^  ^ 

Long.  in. . . . 40*  44'  W. 

The  Difference  of  Latitude  and  Departure  are  found' a«  in  Plane  Sailing.  The  Latitude  in,  and  thence 
the  Middle  Latitude,  by  adding  the  two  Latitudes  together,  and  taking  their  half  Sum  for  the  Middle  Lati- 
tude. The  Departure  being  too  great  for  the  Tables,  the  half  is  taken.  Then,  with  Middle  Latitude  as  » 
Course  and  half  the  Departure  in  the  Latitude  column,  half  the  Difference  of  Longitude  is  found  in  the 
Distance  column.  This  being  doubled  and  divided  by  60  gives  Degrees  and  Minutes.  Ship  in  West  Lon- 
gitude sailing  West,  add  Difference  of  Longitude  to  Longitude  left. 

This  is  the  usual  case  at  Sea  in  working  a  day's  work. 

Two  Latitudes  and  Course  given,  to  find  the  Distance  and  Difference  of  Longitude 

EXAMPLE  2. 

A  Ship  from  Latitude  49*  44'  N.  and  Longitude  40*  44'  W,  sails  N.  E.  by  E.  until  by  obserTation  she  is  in  Late 
tade  62*  6'  N.     Required  her  Distance  run  and  Longitude  in. 

GoHTse  N.  6  pte.  E.  Lat  left  . .  .45"*  44'  N.  Lat  left 49*  44'  N 

Dist 266  Latin 62*    6  N.  Latin 62      6   N 

Diff.  Lat. .  142  N.  2*  22  Sum 101    .50 

Dep. 218  K  ^0 Mid  Lat, .  .60*  66' 

Lat  Ob.  62*  6'    N.     Course  6  pts.  and  142  Difference  Latitude  in  its  column  gives  the  Dep.  )213  and  Dist  266-, 

Diff  Long.  6*  88'  K  Mid.  Lat  61*  as  a  Course,  and  half  the  Departure, 1 06.5  in  tiie  Lai- 

Loa  in.  .36*    6'W.  Column,  half  the  Diff.  of  Long,  is  foimd  in  the  Dist  Column  to  b«   169 

2 
)338 

Diff  of  Long. 6°  38'   E. 

Long,  left 40   44   W. 

Long,  in 36°    6'  W. 

In  a  fast-sailing  ship,  where  it  is  found  difficult  to  measure  the  Ship's  rate  of  sailing  by  the  Log  thi» 
Example  may  be  used  with  advantage. 

Two  Latitudes  and  Distance  given,  to  find  the  Course  and  Difference  of  Longitude. 

EXAMPLE  3. 

A  Ship  from  Latitude  3°  20'  N.  and  Longitude  22*  80'  W.,  runs  for  4  days  between  the  South  and  West,  at  the- 
rate  of  10  knots  an  hour,  and  then  by  observation  finds  her  Latitude  to  be  10°  40'  S.  Requred  the  Course  and  the. 
Longitude  in. 

Lat  left 3*  20'  N.  Greater  Lat 10*  40'    S.     Run. ,  4  days. 

Course &  29*  W         Latin 10   40   S.  The  half  of  which,  6°  20'  24 

i^     Diet 960  ,  Diff  of  Lat  14°    0'  to  be  taken  as  Mid  Lat  . .        "96  hours 

I      Diff  Lat....  840  S.  _60^  '  10  knots 'an  hour. 

I      Dep 466  W.  The  10th  part  of  840  Differ.  Latitude  and  10th  part  of  the  Distance,  "960"    are   fcund   te 

eg      Lat  ic 10*  40'    S.         agree  at  Course  S.  29°  W,  and  gives  the  tenth  part  of  the  Departure  46  5  then  witb 

Diff  Long..  7    47  "W.         half  the  greater  Lat  5°  for  the  Middle  Latitude  as  a  Course,  and  the  t<  nth  part  of  th» 
Long.  in.  .30    17   W         Dep.,  46.5,  in  the  Latitude  column,  the  tenth  part  of  the  Diff.  of  Long,  is  found  in  the 

Distance  column  to  be  46.7,  and  the  whole  is    )467 

Diff  Long.         7°  47'  W. 
Long,  left       22   30    "W 

Long,  in  80*  17'  W. 

By  this  Example  it  appears  that  there  are  only  2  miles  difference  between  the  Departure  and  the  Differ 
•Dce  pf  Longitude  as  found  in  the  run  of  noarly  1 000  mi.'  aa. 


«2 


MIDDLE    LATITUDE    SAILING. 


One  Latitude,  Ccrnrse  and  Distance  given  in  a  Hi°;h  Latittide,  to  find  the  Latitude  and  Longitude  tn. 

EXAMPLE  4. 

A  Ship  from  Latitude  68*  30'  S.  and  Longitude  178*  10'  W.,  sails  S.  W,  by  W.  300  miles.  Required  Ler  Correei 
Latitude  aud  Longitude  in.  By  taking  Short  Distances  run,  and  also  the  same  by  the  Whole  Distance  run,  in  th« 
oauol  way.  V 


TRAVERSK    TABLE. 

D.  LAT. 

DKP. 

LONGITUDE    TABLE. 

Course. 

Dist 

s. 

W. 

Lat  Left. 

Lat  in. 

M:  1.  Lat 

Dif.  Long.  made. 

S.  W.  by  W. 

14 
f( 
M 
M 

(( 

S.  W.  by  W. 

Diff.  Lat 
Lat  left 

50 
50 
50 
50 
50 
50 

300  m 

.  2*  47' 
58°  30' 

27.8 
27.8 
27.8 
27.8 
278 
27.8 

.=166.8 

S.  Dep 
S. 

41.6 
41.6 
41.6 
41.6 
41.6 
41.6 

)249.6 

124.8  ' 

58°  30'                  58°  58' 

58  58                    59  26 

59  26                    69  54 

59  54                    60  22 

60  22                    60  50 
60  50                    61    18 

Summary. 

W .=249.5         Course.  .S.  W.  by 
2         Dist 800 

68°  44' 
69  12 

59  40 

60  8 

60  36 

61  4 

W.          Diff  of  ] 
Long,  lei 

80' 
81 
82 
83 
*84 
86 

)496' 

Long.  8°  16'  W. 

■t..l78*  10'  W. 
186°  26' 
360*    0' 

. . .  178*  84'   E. 

LaL  in    61°  17' 

S. 

Diff  Lon 

The  Shoit  E 
Whol<»  Tlistji 

)499.0         Diff  Lat 167 

119°  47' 
Mid.  Lat   59°  54' 

g...8*  19  W.  Dep 250 

Lat  in 61°  17 

istances  give  Diff.  Long 8°  1( 

iDce do 8*  19 

'    S.      Long,  in 
)'  W. 
'  W. 
'   E. 

Long 

'.  in  is. 

173*  34 

In  this  Example,  by  taking  Short  Distances  on  the  same  Course  and  finding  the  Difference  of  Longitude 
corresponding  to  each,  and  adding  the  whole  together,  there  appears  to  be  a  difference  of  3  miles  between 
ihat  and  the  Difference  of  Longitude  found  from  the  whole  Course  and  Distance,  the  former  being  the  correct 
Difference  of  Longitude,  the  Distance  in  this  Example  not  being  great. 

One  Latitude,  Course  and  Departure  given,  to  find  the  Latitude  and  Longitude  in. 

EXAMPLE  5. 

A  Ship  from  Latitude  38*  40'  S.  and  Longitude  1*  .16'  W,  tails  N.  R  i  E.  jntil  her  Departar«  is  860  mOM 
Required  the  Latitud*  and  Longitude  in. 

Cours« 4i  pte.         and  half  the  Departure,  125,     gives  half  the  Dist  162,  and  half  Diffi  Lat    102.8 

Z  2 

^     Dist 324  Dht     824                    Diff  Lat    )20S.g 

2      Diff  Lat.  .206  Mid.  Lat  87*  and  half  the  Dep.  126— D.  Long.  167                                               8*  26'  N. 

I      Dep 260  £.  Lat  left 38*  40'  & 

J      Lat  in.. . 35°  14'  S.  J314_  Lat  b .85*  14'  8. 

DiffLong.  5*  14'K  Diff  of  I^ng..  .6*  14'    K  Sum 78°  64' 

Long.  in.  .3°  59'  E.  Long,  left .1*  18'  W,  Mid.  Lat ...    86*  87' 

Long,  in 8°  59'    E. 


QUESTIONS    FOR    EXERCISE. 

Question  1.— A  Ship  from  Latitude  25*  35'  N.  and  Longitude  60*  W.,  sails  N.  N.  E.  296  miles.     Re 
quired  her  Latitude  and  Longitude  in. 

Answer. — Latitude  in  30*  9'  N.  and  Longitude  57*  52'  W, 

Ques.  2. A  Ship  from  Latitude  3°  10'  N.  and  Longitude  25°  0'  W.  sails  on  a  S.  W.  by  S.  Course  until 

iher  Latitude  observed  was  2°  16'  S.     Required  the  Distance  run  and  Longitude  in. 
Jns. — The   Distance  run  is  392  miles  and  the  Longitude  in  28°  38'  W. 

Ques.  3. A  Ship  from  Latitude  30*  15'  S.  and  Longitude  178°  10'  E.,  sails  on  a  N.  E.  Course  until  her 

Departure  is  150  miles.     Required  the  Distance  run  and  the  Latitude  and  Longitude  in. 
Ans. — Distance  sailed  212  miles,  Latitude  in  27°  45'  S.  and  Longitude  in  178*  58'  W. 

Ques  4. A  Ship  from  Sandy  Hook,  in  Latitude  40*  28'  N.  and  Longitude  74*  C  W.,  sails  between  the 

fiouth  and  East  until  her  Latitude  observed  is  37*  6'  N.  and  her  Departure  made  good  is  500  miles.  Re^ 
paired  the  Course  and  Distanr-e  sailed  and  the  Longitude  in. 

Ans. — Course  S.  68°  E.,  Distance  540  miles,  and  the  Longitude  in  63*  '«'  W 


MIDDLE    LATITUDE    SAILING.  St 

CASE    II. 

Two  L  *itudes  and  Longitudes  given,  to  find  the  Bearing  and  Distance. 

EXAMPLE  1 

Required  the  Beaiiug  and  Distance  between  Cape  Henry,  in  Latitude  36°  66'  N.  and  Longitude  76'  0'  W,  and 
Om  IsLnd  of  Bermuda,  iu  Latitude  32°  18'  N.  and  Longitude  64°  50'  W. 

LaL  Cape  Henry 36°  6«'  N.  36°  56'  N.  Long,  of  Cape  Henrv      76°  C    W 

Lat  Bermuda 32    18  N.  32    18  N.  Lnjug.  of  Bermuda.  .'.     64    6C  W 

4°  38'  b9M7"  rr°  10   . 

60  3^o  37'  Middle  Latitude.  60 


Diffi  Lat.  in  miles 278  '  Diff.  Long,  iu  miles. . .  670 

Rule. —  With  Middle  Latitude  34°  30'  as  a  Course,  taken  out  first  with  34°  and  then  with  35°,  and  the  tenth  pait 
of  the  Diifeience  of  Longitude,  67.0,  iu  the  Distance  Columns,  the  tenth  part  of  the  Meau  Departure,  55.2,  will  be 
found  in  the  Latitude  Columns.  Then  with  this  Departure,  55.2,  and  the  tenth  part  of  the  Dittereuce  of  Latitude, 
57.8,  enter  the  Tables  again,  and  where  they  are  fouud  to  agree  in  their  columns,  gives  the  Course  at  the  bottom 
of  the  pa^,  63°,  because  the  Departure  is  greater  than  the  Difference  of  Latitude,  and  the  corresponding  Distance 
opposite  is  61.5,  which  multiplied  by  10  gives  the  Whole  Distance,  615  miles. 

Hence  the  Bearing  of  Bermuda  from  the  Cape  is  S.  63°  E.,  because  the"Latitude  and  Longitude  of  the  former  ki 
to  the  Southward  and  Eastward  of  the  latter,  aud  the  Distance  beween  them  is  615  miles. 

Two  Latitudes  and  Longitudes  given^  to  find  the  Course,  Distance  and  Departure. 

EXAMPLE  2. 

A  Ship  from  Latitude  30°  15'  N.  and  Longitude  45°  20'  W.,  sails  between  the  North  and  West  until  by  observa- 
tion she  18  in  Latitude  33°  46'  N.  and  Longitude  60°  10'  W.  Required  the  Course  and  Distance  made  good,  and  hoi 
Departure  from  the  Meridian. 

^     Course. .  .N.  60°  W.        Lat.  left 30°  15'  N Long,  left 45°  20'  W. 

I      Dist 822  Lat.  in .33    45    N.      Lat.  left 30°  15'  N.      Long,  in 60    10'  W. 

I      DiflL  Lat. 210  3°  30'  ^at.  in -33    45    N.      Difj  Long -^  50' 

^     D^p 246  60  Sura 64  .0  60 

DifF.  Lat 210  N.  Mid.  Lat .32°  as  a  Course,  and  290  in  the  Distanc* 

column  gives  the  Departure  in  the  Latitude  column  245.9.     Then  with  half  the  Diiference  of  Lati 

ude,  105,  and  half  the  Departure,  123,  found  in  their  columns,  where  they  agree  nearest,  and  the  Course  must  b« 
taken  from  the  bottom  of  the  page  at  50°,  (because  the  Departure  is  greater  than  the  Difference  of  Latitude,)  and  half 
the  Distance  is  found  opposite  to  be  161,  which  doubled  gives  322  miles.  Hence  the  True  Course  and  Distanot 
■ailed  is  N.  60*  W,  or  N.  W.  i  W.,  822  miles,  aad  the  Departure  from  the  Meridian  246  miles. 

One  Latitude  and  Longitude,  with  the  Difference  of  Lct»i.uue  and  Departure  given,  to  find  the  Latitude  and 
Longitude  in,  and  the  Bearing  and  Distance  of  the  Inte7id€d  Port. 

EXAMPLE  3. 

A  Ship  from  Montauk  Point,  in  Lat.  41*  4'  N.  and  Longitude  71*  51'  W.,  and  bound  to  Santa  Cruz  (one  of  the 
Cape  Verd  Islands)  in  Latitude  17"  2'  N.  and  Longitude  26*  15'  W.,  sails  between  the  South  and  East  -mtil  she  has 
made  800  leagues  of  Southing  and  400  leagues  of  Easting.  Required  the  Latitude  and  Longitude  in.  and  the 
Course  and  Distance  to  her  intended  port 

Course.  .S.  53°  E.         Diff.  Lat  300  Leagues.     Dep.  400  Leagues. 
Dist  1500  miles  sailed.  3  3 

Dep.  in  miles.  1200  The  tenth  part  of  the  Departure,  120,  found 

in  the  Lat  column,  of  the  Middle  Latitude, 
33,  gives  the  10th  part  of  the  Diff.  Long,  in 
Dist.  column,  143.      Middle   Lat  34°,  in  like 
manner  gives  145,  the  mean  of  which  is  144 
this  multiplied  bv  10  gives  the  proper 

"Diff.  of  Long.)1440  miles. 

Diff  Long 24°    0'    E. 

Long,  of  Ship  47°  51'  W.  Long,  of  Montauk  Point.  71    51    W. 

"  Santa  Cruz  25    15  W  Long,  of  the  Ship 47°  51'  W. 

Diff.  Long.... 22°  36' 

60     with  Mid.  Lat  21°  and  22°,  and  the  tenth  part  of  the 


Diff.  Lat  in  miles 

)  900 

Diff.  Lat 

.15°    0'   S. 

Lat.  Montauk  Point. 

.41      4   N. 

Lat  of  the  Ship. . . . 

.26°    4'N. 

Sum 

.67°    8' 

Mid.  Lat 

83°  34' 

Lat  of  the  Ship  26°  4' N , 

"    Santa  Cruz  17    2'N.     Lat  26°    4'N. 

Diff.  Lat ..   9°  2'  Lat.  n 2  N. 

^Q  Sum  43*    6'" 


Diff.  Lat 642         ^i(j   Lat  21°  33  

'■ Diff.  Long.  135.6  in  the  Dist.  column,  the  tenth  part  of  the  Departure 

126,  is  found  in  tlie  Lat  column.     Then  with  the  tenth  part  of  the  Difference  Latitude  54.2,  and  the  Departure  126 
the  Course  to  SanCa  Cruz  is  found  to  be  S.  67°  E.  or  E.  S.  E.,  and  the  Distance  1870  miles. 

Note. — The  rule  in  the  Epitomes,  which  directs  that  half  the  Difference  of  Latitude  between  two  places  on  opposite 
Bides  of  the  Equator  must  be  used  for  the  Middle  Latitude,  beiiip  incorrect,  (as  may  be  perceived  by  inspecting  Fig.  16, 
page  20,)  the  deficiency  is  supplied  by  the  following  Rule  :  (See  Example  4,  which  is  worked  out  iu  the  following  page.) 
Add  the  half  of  the  Grejiter  Latitude  to  the  half  of  the  Less  Latitude,  and  take  their  half  Sum  for  the  Middle  Latitude. 
If  one  Latitude  he  great  and  the  other  small,  take  the  half  of  the  Greater  Latitude  alone  for  the  Middle  Latitude.  The 
Example  referred  to  comes  out  exactly  the  same  by  Mercator's  Sailing,  which  proves  this  Rule  to  be  correct.  But  when 
the  Ship  sails  a  greater  distance  on  one  side  of  the  Equator  than  on  the  other,  a  greater  weight  should  be  given  to  that 
li»liturte  which  corresponds  to  the  greater  dislanne.     (See  the  Last  Example  in  this  Sai'ing.) 


^  MIDDLE    LATITUDB    SAILIN*. 

Tvo  Places,  whose  LaiitiuUs  and  Longitudes  are  of  contrary  names,  given,  tn  find  the  correct  Bearing  tmS 

Distance  between  them. 

EXAMPLE  4. 

Required  the  Bearing  and  Distance  between  New  York,  in  Latitude  40°  43'  N.  and  Longitude  74*  0'  W,  »nd  th» 
Cfep«  of  Good  Hope,  in  Latitude  84°  22'  S.  and  Longitude  18*  80'  E. 

Lat  of  New  York 40*  48'  N.  Half  of  the  greater  Lat 20'  21'         Long,  of  New  York 74*    0'  W 

"     Cape  G.Hope.,  84    22   &                ..         «       less  Lat .17    11  "      Cape  Good  Hope.  18    SO   EL 

75*    5'                   Sum 37°  82'  92°  SO' 

60  Half  Sum  for  Mid.  Lat.  ...  18°  46'  ^Q 

Diflt  Lat  m  miles. . .  .4506  Diff.  Long,  in  miles 6551 

In  this  Example  we  have  to  take  the  100th  part  of  these  Sums  to  get  into  the  Tables,  as  follows:  With 
Middle  Latitude  19*  as  a  Course,  and  the  lOOth  part  of  the  Difference  of  Longitude.  55.5,  in  the  Distance 
Column.  By  taking  parts  we  get  the  Departure  in  the  Latitude  Column,  52.45.  Then  with  this  Departure 
and  the  lOOth  part  of  the  Difference  of  Latitude,  45.05,  enter  the  Table  again,  and  they  are  found  to  agree 
to  the  Course  49*,  and  Distance  69°.     Multiply  this  Distance  by  100,  which  is  the  Distance  required. 

Hence  the  Bearing  of  the  Cape  from  New  York  is  S.  49°  E.,  or  S.  E.  k  E-,  nearly,  and  that  of  New  York 
from  the  Cape  N.  49°  W.,  or  N.  W.  k  W.     Distance  6900  miles. 

This  Example,  worked  by  Mercator  Sailing,  comes  out  the  same  as  above  ;  but  by  the  Old  Rule,  half  the 
Difference  of  the  Latitudes  in  this  case  would  be  3*  10' for  the  Middle  Latitude;  which  is  manifestly 
incorrect. 

The  following  Exanaple,  though  not  of  much  practical  utility,  may  exercise  the  learner. 

EXAMPLE  6. 

A  Ship  from  36*  32'  North  Latitude,  sails  between  the  Soutn  and  West  until  she  has  made  480  miles  of  Departure 
and  560  miles  Difference  of  Longitude.     Required  her  present  Latitude,  Course  steered  and  Distance  rua 

RiHJC. — -Enter  the  Table  with  the  10th  part  of  the  Departure,  48,  in  the  Latitude  Column,  and  the  10th  part  of 
the  Difference  of  Longitude,  56,  in  the  Distance  Column,  they  are  found  to  agree  to  the  Course  at  the  "Top  of 
the  page,  81',  and  which  is  the  Middle  Latitude  the  ship  has  sailed  in.  Take  the  Difference  between  this  Middl« 
Latitude  and  the  Latitude  left  which  is  5°  32',  and  subtract  it  from  the  Middle  Latitude,  because  the  ship 
has  been  sailing  S»uth,  will  give  the  present  Latitude,  25°  28'  N. 

Take  the  Difference  between  the  Latitudes  sailed  from  and  come  to,  which  is  664,  and  the  Depar*,ure,  480, 
enter  the  Tables  with  the  tenth  part  of  the  Difference  of  Latitude,  66.4,  and  the  Departut  e,  48.0,  found  in  their 
respeotive  columns,  the  Course  is  found  to  be  36°,  and  the  Distance  82,  which  multiplied  by  10  gives  820.  Heoo« 
the  Latitude  in  is  25°  28'  N.,  and  the  Course  S.  36*  W.,  or  S.  W.  i  S,  Distance  820  miles. 

Diff.  Long.  56  and  Dep.  gives  the  Mid.  Lat  31°    0'       Lat  left.  .86' 32' N.      - 

Lat  left.. 36    32'       Lat  in... 25   28  N. 

Difr.  between  Mid.  Lat  and  Lat  left .T5°  32'  N.  11°    4' 

Mid.  Lat. 81      0  60 

Lat  in ...  25°  28'  N.    Diff.  Lat  664  and  Dep.  480»=Cour8e  S.  86*  W.,  Dist  820  m 

QUESTIONS    FOR    EXERCISE. 

Question  1.— A  Ship  from  Latitude  60°  10'  N.  and  Longitude  30°  15'  W.,  is  bound  to  a  Port  in  Latitude 
49*  10'  N.  and  Longitude  50°  10'  W.     Required  the  Course  and  Distance. 
Answer. — The  Course  is  S.  46°  W.,  or  S.  W.,  nearly.     Distance  950. 

Ques.  2. — A  Ship  on  the  Equator,  in  Longitude  25°  40'  W.,  and  bound  to  the  Port  of  Rio  Janeiro,  and 
wishing  to  shape  a  Course  for  Cape  Frio,  in  Latitude  23°  1'  S.  and  Longitude  41*  50'  W.  Required  the 
correct  Course  and  Distance  to  it. 

Ans. — The  Course  is  S.  35°  W.,  or  S.  W.  by  S.,  nearly,  and  Distance  1685  miles. 

Ones.  3. — Required  the  Bearing  and  Distance  between  the  Cape  Verd  Islands,  (say  Cape  St.  Anthony,} 
in  Latitude  17°  12'  N.  and  Longitude  25°  19'  W.,  and  the  Island  of  St.  Helena,  in  Latitude  15'  55'  S.  and 
4°  45'  West  Longitude. 

Ans. — Bearing  is  S.  30*  30'    E.,  and  Distance  2300  miles 

Que*.  4. — Required  the  Bearing  and  Distance  between  Cape  Horn,  in  the  Latitude  of  55°  59'  S.  and  Lo» 
gitude  67°  16'  W.,  and  San  Francisco,  in  Latitude  37'  48'  N.  and  Longitude  122'  21'  W. 
Ar^. — The  Bearing  is  N.  27'  W.,  and  the  Distance  6300  miles. 

NoTB. — In  the  last  Example,  half  the  greater  Latitude  ie  taken  as  a  Middle  Latitude,  and  which  is  incren«e('  by  !•, 
ttMaose  the  (jreateat  disUnoe  had  to  t)e  ran  to  the  Southward  of  the  Equator.     The  Middle  Latitude  allowed  is  80 


aft 


MERCATOR'S    SAILING. 

Thi«  Sailing  is  used  lor  the  same  purposes  as  Middle  Latitude  Sailing,  and  is  more  correct  in  long 
Autances,  except  when  the  Course  is  large ;  tliat  ie,  near  the  East  or  West  points. 

Mercator  Sailing  is  the  Art  of  finding  on  a  Plane  Surface  the  position  of  a  Ship,  which  shall  be  true  ta 
Course,  Distance,  Latitude  and  Longitude. 

This  method  is  derived  from  the  Projection  of  Mercator's  Chart,  in  which  the  Degrees  of  Longitudfl  are 
«very  where  equal,  the  Degrees  of  Latitude  expand  towards  the  Poles,  and  the  Parallels,  Meridians,  and 
Rhumb  Lines  are  all  represented  by  straight  lines.  In  Middle  Latitude  Sailing  the  Meridians  contract 
and  meet  at  the  Poles,  and  the  length  of  the  Degrees  of  Longitude  also  decrease  from  the  Equator  towards 
the  Poles.  But  in  Mercator  Sailing  the  Meridians  are  all  parallel  to  each  other,  and  a  Degree  of  Longitude 
is  60  miles  in  length,  measured  on  the  Equator,  in  all  parts  of  the  World.  To  remedy  this,  the  Degrees 
of  Latitu  le  are  expanded  from  the  Equator  towards  the  Poles,  and  the  miles  of  Latitude  grow  larger  ;  so  that 
in  the  Latitude  of  60*  the  miles  of  Latitude  are  twice  the  length  they  are  on  the  Equator,  and  the  Degree 
of  Longitude  is  only  30  of  these  miles  long  ;  near  the  Pole  one  mile  of  Latitude  is  nearly  the  length  of  60 
miles  on  the  Equator,  and  the  Degree  of  Longitude  only  1  mile  long.  But  as  the  Polar  Seas  are  not  navi- 
gable much  above  80°,  Charts  or  Tables  on  this  projection  are  rarely  published  beyond  that  paralleL 

DIAGRAxM    OF    MERCATOR'S    SAILING, 

thowing  the  Expansion  of  the  Parallels  of  Latitude  for  every  10  Degrees,  and  the  Meridians   (or  ParalUU 
of  Longitude)  all  Parallel  \o  each  other  at  10  Degrees  Distance. 

Fio.  16. 


90        80      -70      60         50     40       30 
W  E  5  T      L  0  N   CT     ^ 


o      io       ao 


EAST      LOnC 


PROJECTED    BY    THE    FOLLOWING    TABLE 


And  the  Measurements  taken  from  the  Degrees  on  the  Equator. 


From  the  Equator 

to  Lat.  10° 

the 

Expansion 

is  0° 

3' 

From  Lat  10°  to  20 

(( 

0 

25 

l( 

20    to  30 

« 

1 

28 

t* 

30    to  40 

" 

3 

43 

M 

40    lo  50 

it 

7 

54 

U 

50    to  60 

t. 

15 

27 

« 

60    to  70 

ti 

29 

26 

u 

70    to  80 

u 

69 

35 

Distance  of  1st  Parallel  from  the  Equat<jr  is  10*  •* 


2d 

3d 

4th 

5th 

6tb 

7th 

8th 


** 

20  26 

*' 

81  28 

i* 

43  48 

1* 

57   64 

(( 

75  27 

it 

99  26 

*^ 

139  86 

Vyn. — The  Calenlations  in  this  Sailingr  are  pertorined  by  the  help  of  a  Tablo  of  Meridianal  Parts,  (Table  III.,.)  8n*ir- 
a>e  the  Expansion  of  the  miles  of  Latitude  from  the  Equator  towards  the  Poles. 

To  find  the  Meridiiiiial  Difference  of  Latitude.  When  the  Latitudes  are  of  the  same  tmme,  take  the  differeno*  of  tiM 
Meridianal  Parts  for  the  two  Latitudes.    When  of  contrary  rames,  take  the  sum  of  the  Meridianal  Part*. 


2d  MERCATOR'S    SAILING. 

CASE    I. 

One  Latitude  and  Longitude.  Course  and  Distanit  given,  to  find  the  Latitude  and  Longitud4  m. 

EXAMPLE  1. 

A  Ship  from   Latitude  62°  6'  N.  and  Longitude  35*  6'  W,  sails  S  W.  by  "W.  266  miles.      Required  her  Latitud* 
uxi  Longitude  in. 

Here,  as  in  Middle  Latitude  Sailing,  the  Difference  of  Latitude  and  Departure  are  found  from  tha  Coon* 
&nd  Distance  by  the  rules  in  Plane  Sailing. 

Course  S.  6  pts.  W^         ) 

and  Diutance  256  miles   f  gives  the  Difference  of  Lat,  )142  and  the  Dep.  213. 

Diff.  Lat  in  Degrees 2°  22'   S. 

Lat.  left 62*    6'  N Meridianal  parts 8676  ),p,,    jj, 

Lat.  b 49°  44'  N Meridianal  parts 8460  J 

Rule. — With  the  Couise  6  pMnts,  and  the  Meridianal  Difference  of  Latitude  226  in  the  Difference 
of  Latitude  column,  (here  we  find  it  to  be  too  great  for  the  Tables,)  we  take  the  half,  112.5.  Then  half  the  Diff  ol 
Longitude.  168.8,  is  found  against  it  in  the  Dep.  Column,  which  doubled  gives  the  whole  Diff  of  Long.  )327.6 

Diff.  of  Long,  in  Degrees 5°  38'  W 

Long,  left tb'    6'  W. 

Long,  b 40°  44'  W 

Two  Latitudes  and  Course  gtVen,  to  find  the  Distance  and  Difference  of  Longitude. 

EXAMPLE  2. 

A  Ship  from  Latitude  49°  44'  N.  and  Longitude  40°  44'  W.,  saUa  N.  R  by  R  until  by  obserration  she  is  in  Lati 
tuda  62°  6'  N.     Required  her  Distance  run  and  Longitude  in. 

Lat.  left 49°  44'  N.     Merid.  parts 8460 

Lat  in  62°    6'  N.     Merid.  parts 8676 

Diff  Lat 2°  22'  N.     Merid.  Diff.  Lat ,  )226 

^Q  112.5 


Rule. — With  the  Course  5  pts.  and  the  Diff.  of  Lat  142  in  its  column,  then  opposite  to  it  in  the  Dist  Column  stand* 
the  Distance,  266  miles.  Again,  with  the  same  Course,  6  points,  and  half  the  Merid.  Diff.  of  Latitude,  112.6,  taktm 
in  the  Latitude  column,  then  half  the  Difference  of  Longitude,  168.8,  is  found  in  the  Departure  column,  whidi  doubled 
gives  the  whole  Difference  of  Longitude,  337.6,  or, 6°  38'  K 

Long,  left 40°  44'  W. 

Dbtance  sailed,  266  miles,  and  Long,  in 35°    6'  W. 

Two  Latitudes  and  Distance  given,  to  find  the  Course  and  Difference  of  Longttude 

EXAMPLE    8. 

A  Ship  from  Latitude  8*  20'  N.  and  Longitude  22*  30'  W.,  runs  4  days  between  the  South  and  West  until  her 
Latitude  observed  is  10°  40'  S.  Her  rate  of  sailing  -was  10  knots  an  hour.  Required  the  Course  she  baa  mad«  and 
ber  Longitude  ia 

Latleft 8°  20' N.         Merid.  parts 200  Run  of  4  days. 

Latin 10'  40'  S.         Merid.  part* 644  24  bonra, 

Diff  of  Lat 14*  "O^  Mer.  Diff  Lat ..   844  96  hours. 

60  10  knot*. 

Rule. — Enter  the  Table  with  the  tenth  part  of  Diff  Lat,  84.0,  and  the  tenth  part  of  the  Distance,  96.0  miIes,aod 
they  will  be  found  to  agree  at  Course  29°.  Again,  with  the  same  Course,  29*,  and  the  tenth  pari  of  the  Meridiaoali 
Difference  of  Latitude,  84.4,  in  the  Latitude  colimin,  then  the  tenth  part  of  the  Difference  of  Longitude  is  found  ia 
the  Departure  column  47,  which  multiplied  by  10  gives,  470,  the  whole  Difference  of  Lon^^itude. 

Diff.  Long,  in  Degrees T°~5b'  W. 

Long,  left 22°  30'  W. 

The  Course  steered  is  S.  29'  W.  and  Longitude  m,  .80°  20'  W. 

NoTK. — The  above  three  Examples  are  the  same  as  are  used  in  Middle  Latitude  Sailing,  and  the  answers  oome  oat 
<he  same  by  Merciitor's,  and  all  the  others  may  be  done  in  the  same  way  ;  observing  that  we  must  use  the  Two  Terma 
/iven,  as  in  a  case  of  Plane  Sailingr.  Then  with  the  Course  made  pood,  and  the  Meridianal  Difference  of  Latitude  found 
ID  the  Latitude  colunan.  the  Difference  of  Longitude  required  is  found  opposite  to  it,  in  the  Departure  column. 

EXAMPLE  4. 

A  Ship  from  Latitude  88*  40'  S.  and  Longitude  1°  16'  W.,  sails  N.  E.  i  E.  until  her  Departure  is  250  mue* 
Required  the  Latitude  and  Longitude  in. 

The  Course  4^  points,  and  half  the  Departure,  125,  in  its  column,  half  the  Difference  of  Latitude  is  found  to  h» 
102.8  in  its  column,  which  doubled  gives  205.6,  or  3°  26',  and  the  Latitude  in  36°  14'  S.  Find  the  Meridianal  Differ 
ence  of  Latitude,  which  is  268.  Then  with  the  same  Course,  4^  points,  and  half  the  Meridianal  Difference  of  Lati- 
tude. 129.  half  the  Difference  of  Longitude,  166.9,  is  found  in  the  Depar*'i'~>  wluma  The  whole  Difference  of 
Loogituc'e  is  813.8,  or  5°  14',  and  the  Longitude  in  8°  69'   East 


MERCATOR'S    SAILING.  Tt 

CASE  II. 
Tipo  Latitudes  and  Longitudes  given,  to  find  the  Bearing  and  Distane4. 

EXAMPLE  L 

Required  the  Bearing  and  Distance  of  Cape  Henry,  in  Latitude  36*  66'  N.,  and  Longitude  76*  0'  W,  and  the  leUa^ 
f  Bermuda,  in  Latitude  32°  18'  N,  and  Longitude  64°  60'  W. 

Latof  Cape  Henry 36*  66'  N.  Merid.  parts 2388      Long 76*  00'  W. 

Lat.  of  Bermuda 32    18   N.  Merid.  parts 2050      Long 64    60   W. 

4°  38  Merid.  diffi  Lat    ...  ..888  S.  11*  10'  W. 

60  .  60 


Diff.  of  Lat  in  miles 278  Diff  Long,  in  miles  670 

RUT.E. — Seek  in  the  Tables  with  the  tenth  part  of  the  Meridian  Difference  of  Latitude  38.8.  and  the  tenth  part  of 
the  Difference  of  Longitude  67.0  until  they  are  found  to  agree  in  the  Latitude  and  Departure  columns,  as  if  thej 
were  Difference  of  Latitude  and  Departure.  If  the  Difference  of  Longitude  be  greater  than  the  Meridian  Differeno* 
©f  Latitude,  the  Course  must  be  taken  from  the  bottom  of  the  page,  but  if  let-i,  from  the  top.  They  ai"e  found  to 
agree  in  this  case  nearly  to  the  Course,  63*.  Then,  with  the  tenth  part  of  the  proper  Difference  of  Latitude,  27.8, 
in  its  column  on  the  same  page,  will  be  found  opposite  to  it,  in  the  Distance  column,  the  tenth  part  of  the  Distaneer 
•1.6,  which,  multiplied  by  10,  gives  the  whole  Distance,  616  miles.  Hence,  the  Bearing  is  South  63*  East,  beoauie 
Bermuda  lies  towards  the  South  and  East  from  the  Cape,  and  the  Distance  is  615  miles. 

Fwo  Latitudes  and  Longitudes  given,  to  find  the  Course  and  Distance. 

EXAMPLE  2, 

A  Ship  from  Latitude  30*  15'  N.,  and  Longitude  46'  20'  W.,  sails  between  the  North  and  West  imtil,  by  obeerra- 
tion,  she  is  in  Latitude  33°  46'  North,  and  Longitude  60*  10'  West     Required  the  Course  and  Distance  mad*  ([oo<L 

Lat  left 30*  15' N.     Merid.  parts 1906      Long.  left 45°  20' W. 

Latin .33    45   N.     Merid.  parte .2153      Long,  in .50    10  W. 

3*  80'  N.     Merid.  Diff  Lat 247  4°  60'  W. 

60  60 

Di£  Lat  in  miles. .  210  Diff.  Long,  in  miles. .  .290 

RcLS. — Seek  in  the  Table,  with  half  the  Meridian  Difference  of  Latitude,  123.6,  and  half  the  Difference  of  Loa- 
jitude,  145,  and  the  nearest  are  found  together  at  the  Course  50*.  Again,  with  this  Course,  50°,  and  half  the  Differ- 
ence of  Latitude,  105,  found  in  its  column,  then  half  the  Distance  is  found  opposite  to  it  in  the  Distance  columo.  161^ 
which  doubled,  gives  the  whole  Distance  826  miles. 

Hence,  the  Course  made  good  is  N.  50'  W,  or  N.  W.  ^  W.  nearly.     Distance  326  miles. 

'I\90  Places  whose  Latitudes  and  Longitudes  are  of  contrary  names,  given,  to  find  their  Bearing  and  Distance 

between  them. 

EXAMPLE  3 

Required  the  Bearing  and  Distance  between  New  York,  in  Latitude  40*  43'  North,  and  Longitude  74°  00'  Westj 
Bfid  the  Cape  of  Good  Hope,  in  Latitude  34*  22'  S.,  and  Longitude  18*  30'  K 

Lat  of  New  York 40°  43'  N.     Merid.  parts 2679      Long,  of  New  York 74°  00'  W. 

Lat  of    Cape  Good  Hope. 34    22    S.     Merid.  parte .2198      Long,  of  Cape  Good  Hope      18°  80'  E. 

75°  06'         Merid.  Diff  Lat 4877  92*  30' 

60  60 

Diff  Lat  in  miles 4606  Diff.  Long,  in  milea 6650 

Rule. — Take  the  100th  part  of  the  Meridian  Difference  of  Latitude,  48.77,  and  the  100th  part  of  the  Difference 
•f  Longitude,  55.50,  and  seek  in  the  Table  until  they  are  found  to  agree  as  Difference  of  Latitude  and  Departure, 
which  give*  the  Co:.rse,  49°.  Again,  with  this  Course  and  the  lOOtb  part  of  the  proper  Difference  of  Latitude,  46.06, 
taken  in  the  Latitu  le  column,  then  the  Distance,  69,  will  be  found  opposite  to  it,  which,  multiplied  by  100,  give*  the 
:rhoIe  Distance,  69(i0  miles,  and  the  Bearing  South  49*  East  or  S.  K  i  K  nearly. 

One  Latitude.,   'bourse  and  Difference  of  Longitude  given,  to  find  the  Distance  and  Difference  of  LatitxuU 

EXAMPLE  4.* 

A  Ship  from  L  ititude  34*  29'  North  sails  South  41*  West  till  her  Difference  of  Longitude  is  682  mileSb  Reqiurad 
«r  present  Latit  ide  and  Distance  sailed. 

Rule. — Enter  the  Table  with  the  Course  41*  and  the  tenth  part  of  the  Difference  of  Longitade,  ^8.2,  in  the  Def^ 
tlumn,  opposite  to  which,  in  the  Latitude  column,  stands  the  Meridian  Difference  of  Latitude,  78.t. 

Lat  left 34*  29'  N.         Merid.  parte 2207 

Merid.  Diff  of  Lat . .  J786     Subtracted  from  the  Merid.  part*  of  Lai  left 

Gives  the  Lat  in  23 3'  N  —  Merid.  parts 1422  of  the  Lau  m. 

Diff.  of  Lat 11*  26' 

60 
Conn*  41*,  and  D.  I..  686  in  the  Lat  column,  gives  the  Distance  910  mileSb 

*  This  Example  cannot  be  solved  by  Middle  Latitude  Bailing. 


9M 


MEROATOR'S    SAILING 


QUESTIONS    FOR    EXERCISE. 

QvEsriON  1.  Required  the  Course  and  Distance  from  the  Cap«  of  Good  Hope  in  Lai.  34*  24'  S.,  and 
Long.  18*  32'  E.  to  the  Island  of  St.  Helena  in  Lat.  15°  55'  S.,  and  Long.  5*  44'  W. 

Answer.  By  Middle  Lat.  Sailing  the  Course  is  N.  50"  W.,  and  Distance  1725  miles.  By  Meroator  Sail 
ing  the  Course  is  N.  50*  W.,  and  Distance  1725  miles. 

QuMTioN  2.  A  Ship  from  Lat.  60°  10'  N.  and  Long.  30"  15'  W.  is  bound  to  a  port  in  Lat.  49"  10'  N 
and  Long.  50"  10'  W.     Required  the  Course  and  Distance. 

Answer.  By  Middle  Lat.  Sailing  the  Course  is  S.  46°  W.,  or  S.  W.  nearly,  and  Distance  950  miles. 
By  Meroator  Sailing  the  Course  is  S.  46°  W.,  or  S.  W.  nearly,  and  Distance  950  miles. 

Question  3.  A  Ship  on  the  Equator  in  the  Long,  of  25°  40'  W.,  and  bound  to  the  port  of  Rio  Janeiro. 
Required  to  shape  a  Course  to  Cape  Frio  in  Lat.  23°  1'  S.,  and  Long.  41*  59'  W.  Find  the  Course  and 
Distance  to  it. 

Answer.  By  Middle  Lat.  Sailing  the  Course  is  S.  35°  W.^  Distance  1685  miles.  By  Mercator  Sailing 
the  Course  is  South  34*  40'  W.,  Distance  1683  miles. 

Question  4.  Required  the  Bearing  and  Distance  between  Cape  St.  Anthony  (one  of  the  Cape  Verd 
Islands)  in  Lat.  17*  12'  N.  and  Long.  25°  19'  W.,  and  the  Island  of  St,  Helena  in  Lat.  15°  55'  S.  and  Long. 
6'  44'  W. 

Answer.  By  Middle  Lat.  Sailing  the  Bearing  is  S.  30*  30'  E.,  Distance  2300  miles.  By  Mercator  Sail- 
ing the  Bearing  is  S.  30"  0'  E.,  Distance  2295  miles. 

Question  5.  Required  the  Bearing  and  Distance  between  Cape  Horn  in  Lat.  55°  59'  S.  and  Long.  67°  16' 
W..  and  San  Francisco  in  Lat.  37°  48'  N.,  and  Long.  122°  21'  W. 

Answer.  By  Middle  Lat.  Sailing  the  Bearing  is  N.  27'  W..  EHstanoe  6310  miles.  By  Meroator  Sailing 
ihe  Bearing  is  N.  27°  W.,  Distance  6300  miles. 

Question  6.  A  Ship  from  Lat.  29°  47'  N.,  and  Long.  24"  36'  W.  sails  S.  S.  W.  i  W.  320  leagues.  Re- 
quired her  present  Latitude  and  Longitude. 

Answer.  By  Middle  Lat.  Sailing  the  Lat.  in  is  16°  4'  N.,  and  Long.  33"  36'  W.  By  Mercator  SailiBg 
the  Lat.  in  is  16*  4'  N.  and  Long.  33°  34'  W. 

In  the  preceding  examples,  both  by  Middle  Latitude  and  Mercator  Sailing,  we  have  always  supposed  tA« 
Ship  to  sail  on  a  direct  Course,  but  when  she  makes  more  than  one  Course  they  must  be  reduced  to  a  single 
Coursf.  by  the  Traverse  Table,  and  the  Latitude  and  Longitude  found  as  in  the  following  example. 


COURSE 

DIST. 

NORTH. 

SOUTH. 

EAST. 

WEST. 

N.  K 

86 

1 

26.5| 26.6 

13.7i ..:  2.7 

N.  by  W 

14 
oS 
42 

29 

N.  E.  by  E. 
N.  by  E. 
K  N.  E.  . . 

iK 

27  .S 
41.2 
11.1 



61.2 

8.2 
26.8 



iDiff  La\ 

)1188 

111.7 

2.7 

Suppose  a  Ship  from  Latitude  32°  86'  N.  and  Longitude  61 
45'  W.,  sails  N.  E.  36  miles,  N.  by  W.  14,  N.  E.  by  K  ^  K  58, 
N.  by  E.  42,  and  E.  N.  E.  29.     Required  her  Latitude  and  Lon- 
gitude in 

BY  MERCATOR  SAILING. 

Mer.  Parts,  2071 


Lat  left 32 

Diff.  Lat  119,  or 1 


36' N. 
59 


Latin 84°  85 


or     r 

Lat  left ^ 

Lat  in 34 

Sum 


59'N.  2.7 

36     Dep.  109.0  in  the  Lat 


Mer.  Parta,  2214 
Mer.  Diff.  Lat    143 


36     Column  tbeD.  Long.  131, 

67    11     Is  found  in  the  Dist  col, 

Middle  Lat 83    36 —  D  Long.  131 —2"  11' E. 

Long,  left 61    46  W. 

Long,  in 69"°  34  W. 


Diff.  of  Lat  118.8  and  Dep.  109,  gives  the  course42''30' 
This  course  and  the  Mer.  diff.  of  Lat  143  in  the  Lat. col- 
umn, the  Diff.  of  Long.  )131  is  found  ib  the  Dep.  culumiL 
2°  11  K 

Long,  left 61    45  W. 

Long,  in 69°  34  W 


Lat  118.8  and  Dep.  109  gives  the  course  N.  42°  30  E. 

Dist 161  miles. 

Diff  Lat 119  N. 

Dep. 109  E. 

Latin.. 34"36'N. 

DiALoDg 2"  11   E 

J  owr  «  ii'»°  W  W 


2tf 


CURRENT    SAILING. 

Cunent  Sailing  is  the  most  perplexing  subject  connected  with  Navigation,  on  account  of  the  uncerHuntf 
«  their  direction  and  velocity.  Even  those  which  are  ascertained  to  exist  and  are  well  established,  hav« 
Deen  known  to  change  their  rate  of  running  frequently,  and  sometimes  even  to  run  in  a  ccntrary  direction. 

The  only  safeguard  is  for  the  Navigator  to  be  constantly  on  the  alert,  and  to  obtain  his  Ship's  Position 
from  Celestial  observations  (when  the  weather  will  permit)  as  often  as  possible  in  the  course  of  the  24 
hours,  both  by  day  and  night,  from  the  altitudes  of  the  Sun,  Moon,  Planets  or  Stars,  and  comparing  her 
position  so  found  with  that  given  by  the  Dead  Reckoning  from  time  to  time  ;  the  difference  between  which 
will  point  out  the  direction  and  velocity  of  the  Current  from, the  effect  it  has  had  upon  the  Ship's  Courna 
«nd  DistfHice  as  given  by  the  Compass  and  Log,  provided  the  Compass  is  free  from  local  attraction.* 

When  a  Ship  is  sailing  in  a  known  Current,  the  Course  is  sometimes  changed  so  as  to  counteract  its  effect 
a«  much  as  possible,  so  that  the  vessel  may  be  continued  on  her  required  Course.  Or,  when  a  Ship  crosses 
«  known  Current  obliquely,  the  direction  or  set  of  the  Current  is  taken  as  a  Course,  and  its  velocity  or  drift 
per  hour  as  a  Distance,  and  which  is  entered  in  the  Traverse  Table,  along  with  the  Courses  and  Distanoea 
the  vessel  may  have  made  during  that  day. 

CASE    I. 

Given,  the  effect  of  a  Current  acting  on  a  Ship.     Required,  its  Direction  and  Velocity. 

EXAMPLE  1. 

A  Ship  from  Latitude  S9°  25'  N.  and  Longitude  65°  10'  W^  by  Observation  and  Chronometer,  and  on  the  following 
day  the  Latitude  in  was  36°  40'  N.  and  Longitude  62°  80'  W.,  by  Observation  and  Chronometer;  the  Dead  Reckon- 
ing carefully  kept  from  her  position  at  the  preceding  noon,  gave  the  Latitude  in  36°  02'  N.  and  Longitude  63°  18' 
W.     Required  the  Set  (or  direction)  and  Drift  of  the  Current  per  hour. 

Lat  left 39°  25'  N.  Lat  left 39°  25'  N.  Long,  left 65°  10'  W.  Long,  left 65°  10'  W. 

Lat  by  Obs.. . .  .36    40'  N.  Lat  by  D.  Reck..  36_02'  N.  Long.Chron 62    30  W.  Long.  D.  Reck.. .  .63    18  W. 

Diff  Lat  by  Obs.  2°  45'  S.  D.  Lat  by  D.  R..     3°  23'  S.  D.  Lon.by  Chron.  "2^40'  E.  D.  Long,  by  D.  R.T°^'   E. 

"      by  Obs.. .    2    4*5  S.  D.  Long,  by  Chron.  2    40 

Ship  Set  to  the  Northward 38  miles.         Ship  Set  to  the  Eastward , .  48  m. 

[of  Longituda 
Middle  Latitude  88°  and  Difference  of  Longitude  48'  in  the  Distance  column,  gives  the  Departure  38  in  the  Lati- 
tude column.     Then  tlie  Difference  of  Latitude,  38  miles,  and  the  Departure,  38  miles,  gives  the  Course  or  Set  of  the 
Current  N.  45°  E.,  and  the  Drift  or  Velocity  64  miles  in  24  hours,  or  at  the  rate  of  2^-  miles  an  hour. 

EXAMPLE  2. 

At  6  A.  M.  the  Latitude  observed  was  23°  10'  N.  and  Longitude  56°  10'  W.,and  at  6  P.M.  the  Latitude  observed 
was  22°  08'  N.  and  the  Longitude  by  Chronometer  5t°  01'  W.  In  the  interval  the  Ship  had  made  a  Course  good 
S.  60°  E.,  and  the  Distance  run  by  Log,  US  miles,  which  gives  the  Latitude  in  22°  12'  N.  and  Longitude  53°  22  W 
by  Dead  Reckoning.     Required  the  Set  and  Velocity  of  the  Current 

Lat  in  at  6  P.  M.  by  Observa. 22°  03'  N.  Long,  by  Chron.  at  6  P.M 54°  01'  W. 

"       by  Dead  Reckon 22    12  "      by  Dead  Reckoa 53    22 

Ship  set  to  the  Southward 9  miles.         Ship  Set  to  the  Westward 39  miles  of  Longitude. 

With  Middle  Latitude  23°  as  a  Course,  and  Difference  of  Longitude  39  miles,  the  Departure  36.9  is  obtained. 
Then  with  Difference  of  Latitude  9,  and  Departure  36,  the  Course  or  Set  of  the  Current  is  found  to  be  S.  76°  W,  or 
K.  by  8.  J  S,  true,  and  the  Distance,  or  Drift  of  the  Current,  37  miles  in  12  hours,  or  3  knots  an  hour,  nearly. 

EXAMPLE  3. 

'  A  Ship  in  the  Gulf  of  Florida,  in  Latitude  26°  44'  N.  and  Long.  79°  28'  W.,  the  Gun  Key  Lights  in  sight,  bearing 
Ea«t-  distant  13  miles,  shaped  a  true  North  Course  at  8  o'clock  in  the  evening,  her  rate  of  sailing  all  night  being  6 
knots  an  hour.  At  midnight  the  Latitude  oberved  by  Stars  North  and  South  of  the  Meridian  was  26°  24'  N,  and 
at  4  A.  M.  the  Latitude  observed  by  Meridian  altitude  of  the  Moon  was  27°  08'  N.,  and  at  6  A.  M.  the  Latitud« 
observed  by  the  planet  Venus  was  27°  28'  N.  and  the  Longitude  by  Chronometer  79°  20'  W.  Required  th« 
Velocity  of  the  Stream  at  the  various  intervals,  and  the  direction  and  drift  of  the  Current  from  8  o'clock  in  th« 
€venii^  until  6  o'clock  next  morning. 

Oonrse  from  8  P.M.  to  Mid't,  North 24  miles.  From  Midnight  to  4  A  M.  Dist  run 24  mile*. 

Lat  left,  26°  44'  N.,  Lat  obs.  26°  24'  N,  Diff. .  ._A0  Lat  Mid.  26°  24'  N.,  Lat  4  A.M.  27°  8'  N,  Diff.  44 

Northerly  Set  in  4  hours   16  miles.  Northerly  Set  in  4  hours 20  mil«« 

Position  of  the  Ship  at  3  P.  M,  Lat 25°  44'  N.  Long 79°  28'W, 

"    at6A.M.,I.At 27    28  Long 19    20  W. 

1°  44'  Diff.  Long 8     equal  to  7  miles  Depi 

60 


Diff  Lat  by  observation  in  miles 104 

Dist  run  from  8  P.M.  to  6  A.M.,  10  h.  at  6  knots    60 


Ship  S«t  t«  the  Northward 44  miles,  and  to  the  Eastward  7  miles.      This  gives  the  CourM 

•r  toue  du-ection  of  the  Current  N.  9°  E,  and  the  Distance  or  Drift  in  10  hours,  46  miles,  or  at  the  rate  of  4^  mil«a 
mn  hour. 

•  An  error  in  the  reckoning  is  frequently  caused  by  local  attraction  affecting  the  Ship's  Compass,  and  niistaken  tor  a 
Carrent,  where  none  exists.     (See  page  120..1 


30 


CURRENT    SAILING. 


When  a  Current  is  ascertained  to  exist,  either  from  recent  observations  or  from  the  proximity  of  the  Shipa 
Position  to  where  a  certain  Current  runs,  whose  rate  and  drift  is  known,  it  is  allowed  for  in  the  dav'a  work 
M  follows  : 

CASE  II. 

The  Direction  and  Velocity  of  a  Current  given,  to  find  its  effect  on  the  Ship. 

EXAMPLE  1. 

A  Ship  from  Latitude  89°  25'  N.  and  Longitude  65°  10'  W.,  by  observation  and  cbronometer,  makes  a  Coiirw 
good  S.  23°  30'  E.,  and  Distance  222  miles,  until  the  Noon  of  the  following  day,  during  which  time  a  Current  hai 
been  setting  to  the  N.  E.  (true)  at  the  rate  of  2{  miles  per  hour.  The  Latitude  observed  at  Noon  was  36°  40'  N 
■nd  Longitude  by  Chronometer  62'  30'  W.  Required  the  position  of  the  Ship  by  Dead  Reckoning,  allowing  for  the 
Onrrent 


COURSB. 

DIST. 

NORTH. 

SOUTH. 

EAST. 

South  23°  30'  East 

.222. 

.  ...203. ... 

88 

N.  E.  Current  24  h.  at  2^-  knots  drift. 

.54.. 

38. 

38 

Diff.  Lat...38., 


Diff.  Lat.  made 2' 

Lat  left 39 

Position  of  the  Ship  at  Noon,  Lat.  in 

EXAMPLE  2. 


. .203  S Dep.l  26  with  M.  Lai  88 

38  N.  gives  the  Difil  Long...  160 

)166  or  2°  •tO'     B 

45'  S.  Long,  left .65    10 

25    N.  Long,  by  D.  Rec.  62°  30' 


W 


36°  40'  N.  by  Dead  Reckoning. 


A  Ship  fromLatitude  23'  10'  N.  and  Longitude  66*  10'  W.,  sails  12  hours  on  a  true  Course  S.  60°  E.,  llBmilea, 
and  during  which  time  a  Current  has  been  setting  her  to  the  W.  by  S.  ^  S.  (true)  at  the  rate  of  3  knots  an  hour 
Required  the  Latitude  and  Longitude  ia 


COURSK. 

DtST. 

SBVTH. 

EAST. 

WEST. 

South  60°  East 

115. 

57.5. 

9.0. 

99.6. 

35.0. 

Current  W.  by  S.  i  S.,  12  h.  at  3  knots 

..36. 

Difference  Latitude 66.6.  .Dep..  .99.6.  .Dep. 

86.0 


.86.0 


Difference  Latitude  made ... .    1°    7' S.  

Latleft 23    10  N..  .Dep..  64.6  Gives  Diff.  Ln.  69 

Lat  in  by  D.  Reckon 22    03  N 


r09'  E. 
Long,  left 55   10  W 

Long,  by  D.  Reck.  54°  01'  W 
CASE    III. 
Given,  the  Bearing  and  Distance  of  the  Port,  and  the  Set  and  Rate  of  the  Current,  it  is  required  to  shape  the 

Course  so  as  to  keep  the  Port  on  the  same  bearing. 

HxTLB. — When  the  Bearing  of  the  Port  and  the  Set  of  the  Current  are  nearly  at  right  angles  to  each  other,  or  the 
Current  sets  obliquely  across  its  direction,  take  their  Sum.  But  when  it  runs  in  the  same  or  opposite  directions,  tak» 
the  Difference.  ' 

With  this  Sum,  (or  what  it  wants  of  16  points,  or  180°,  if  it  exceeds  8  points,  or  90°,)  or  Difference  as  a 
Course,  and  the  Rate  of  the  Current  as  a  Distance,  find  the  Departure. 

With  this  Departure  as  Departure,  and  the  rate  of  the  Ship's  Sailing  as  a  Distance,  find  the  Course. 

This  Course  being  applied  to  the  bearing  of  the  port  on  the  opposite  side  to  that  towards  which  the 
Current  is  drifting  the  Ship,  gives  the  Course  required. 

EXAMPLE  1. 
The  Port  bears  S.  45*  "W.,  the  Current  sets  S.  E.  by  S.,  or  S.  84*  E.,  S  miles  an  hour,  the  Ship'g  rate  of  sailing  lU 
knots  an  hour.     Required  to  shape  the  Course  so  as  to  keep  it  on  the  same  Bearing. 
Bearing  of  the  Port  S.  45°  "W. 
Current  oblique. . .  S.  34    E. 

Take  their  Sum,  79°,  as  a  Course,  and  rate  of  the  Current,  3  miles,  as  Distance,  gives  the  Departure,  2.i», 
This  Departure  and  the  rate  of  the  Ship,  10  miles,  as  Distance,  gives  the  Course,  17°.  This  applied  to  the  rigbt^ 
»r  added  to  the  bearing,  45°,  gives  the  Course,  S.  62°  W. ;  because  in  facing  towards  the  S.  W.  tiie  running  of  the 
Current  is  towards  the  3.  E.  by  S.,  or  to  the  left  of  the  bearing  of  the  Port 

EXAMPLE  a.'-k    -■-'. 

The  Port  bears  N.  45*  K,  the  Current  South,  3  knots,  rate  of  sailing  8'knots.  Shape  the  Course  so  as  to  keep  the 
Port  on  the  same  bearing. 

South  giving  no  angle,  the  first  Course  is  46',  which  with  Distance,  8  knots,  gives  Departure,  2.  The  Distaoee, 
or  rate  of  sailing,  8  and  Departure,  2,  gi-es  Course,  15°,  which  applied  to  the  left  of  the  bearing,  gives  N.  80*  K.; 
beeause  in  facing  towards  the  ¥.  E.  the  Current  is  setting  to  the  right  of  the  bearing. 

EXAMPLE  8. 

The  Port  bears  E.,  the  Current  sets  S.  W.  by  S.,  3  knots,  rnte  of  sailing  4  knots.  East  is  8  points,  or  90*,  which 
ia  one  of  the  opposite  quarters  to  S.  W.  The  Difference  between  them,  which  is  6  points,  as  a  Course,  and  Distance 
8,  the  rate  of  the  Current  gives  the  Departure.  2.5.  This  Departure,  and  Distanee,  4,  (the  rate  of  the  ship,)  gives 
the  Course,  89°.  •  which  appUed  to  the  left  of  East  the  bearing  of  the  Port  gives  the  Course  to  be  steered  N.  51*  E 

EXAMPLE  4. 

The  Port  bears  N.  82°  E.,  the  Current  S.  10'  W.  4  knots.  Ship's  rate  of  sailing  8  knots.  N.  E.  and  S.  W.  be<np 
spposite  points,  the  Difference  is  72°,  as  a  Course,  and  rate  of  Current  4,  as  Distance,  gives  Departure,  8.8  This 
Departure  bfing  greater  than  the  ship's  rate  of  sailing,  8  knots,  which  is  impossible,  shows  that  the  Ship  cauDot 
nauitaiii  the  beiuiuf  of  the.  Fort 


OF  THE  SHIPS  POSITION. 


TAKING  DEPARTURES,  OR  FINDING  THE  POSITION  OF   THE  SHIP   FROM  THE  BB.AR'MG 

OF   KNOWN  OBJECTS  ON  THE  LAND. 

CASE    I. 

By  a  single  Bearing  and  estimated  Distance. 

Set  the  Bearing  by  the  Compass,  and  estimate  the  Distance*  off.  This  is  the  common  method,  and  ■ 
person  may  soon  acquire  the  tact  of  estimating  Distances  with  much  preci.'^^ion  by  adopting  the  following 
fuggestion  :  Compare  the  Distance  required,  in  your  mind,  with  the  known  Distances  of  the  surrounding 
objects,  in  a  locality  which  is  well-known  and  familiar  to  you,  and  take  the  one  that  seems  to  correspond 
nearest  to  the  required  Distance. 

RuLS.  To  find  the  ship's  Position,  take  the  opposite  point  to  the  bearing  of  the  object,  correct  for  magnetio  raruitioa 
Enter  the  Traverse  Table  with  it  as  a  oourse  and  the  estimated  distance,  and  find  the  Diff.  Lat  and  Den. 
Take  from  the  Table  of  Positions  the  Latitude  and  Longitude  of  the  object  Apply  the  DiS.  of  Lat  to  that  Lat^ 
▼hich  will  give  the  Lat  of  the  ship.  Then  with  Mid.  Lat  as  a  course,  and  the  Dep.,  find  the  Diff  of  Long.  This 
apphed  to  the  Long,  of  the  object  will  give  the  Long,  of  the  ship. 

EXAMPLE  1. 

The  lighthouse  on  Neversink  bore  W.  by  N.  i  N.  20  miles.  Magnetic  Variation  i  point  Westerly.  Required  th* 
position  of  the  ship. 

Bearing  W.  by  N  -J  N.        Lat  of  Neversink 40°  23'  N.    Long,  of  Neversink 73°  69'  W 

Opposite  ptE.  by  S.iS.     Var.ipt=- E.  i.S.  20  m.  D  L._0 4   S.    Dep.  19  6K  Mid.Lt  40°give8D.Ln.    0   28    K 

Latitude  of  Ship 40°  19 'N.    Longitude  of  Ship 73*  88'  W. 

EXAMPLE  2. 

Bamegat  light-bouse  bore  N.  |  K  12  miles.  Variation  i  pt.  "Westerly.  Required  the  position  of  the  ship.  (Thin 
«  useful  in  rateing  a  chronometer.) 

N.  i  K  opposite  pt  S.  i  W     Var.  i  pt  W.  —  South  12  miles.  D.  Lat.    0°  12'  a    Dep.  0  D.  Long 0°  0 

Lat  of  Bamegat 39   46  N.     Longitude ..74   6' W 

Latitude  of  the  Ship.    89°  34'  N.     Long,  of  Ship 14^6'  W 

EXAMPLE  8. 

Neversink  light-houses  bore  by  compass  W  ^  N.  20  miles.      Variation  i  pobt  W.      Required  the  position  of  Vmi 
ihip. 
Bearing  W.  i  N.  Opposite  pt  E.  i  S.  Var.  i  pt  W.  —  E.  20  m  —  D.  Lat     0°    0'      Dep.  20  Ml.  L.  40°  —  D.  L.    0°  26'  Tt 

Lat  of  Neversink  40   28  N.  Long,  of  Neversink 73  69  W. 

Lat  of  the  Ship     40°  28'  N.  Long,  of  the  Ship 73°  Si'W. 

A  ship  on  leaving  the  land  and  commencing  a  voyage,  her  departure  is  taken  from  the  bearing  of  an 
jbject  whose  position  is  known,  and  its  estimated  distance  off,  similar  to  the  above,  the  opposite  point  to 
which  is  taken  as  a  course,  and  being  corrected  for  the  variation  of  the  compass,  it  is  entered  into  the 
Traverse  Table,  along  with  the  other  courses  and  distances  the  vessel  has  sailed,  up  to  the  following  noon. 
Her  position  is  then  deduced  from  the  Latitude  and  Longitude  (taken  from  the  Table  of  Positions)  0/  th^ 
sbject  she  took  her  departure  from. 

CASE    II. 

By  two  Ptarings  of  different  Objects  at  right  angles  to  each  other. 

RuLK,  To  find  the  Ship's  position,  the  object  bearing  true  East  or  West,  gives  the  Ship's  Latitude,  and  the  one 
aearing  true  North  or  South  gives  the  Ship's  Longitude,  because  she  is  on  the  same  parallel  of  Latitude  as  tb« 
former,  and  on  the  tame  meridian  as  the  latter. 

EXAMPLK 
Baroegat  light-house  bore  N.  ^  E.,  and  Little  Egg  Harbor  light  W.  \  N.     Required  the  position  of  the  Ship. 

bearing  N.  ^  K     Var,  ^  pt        —  true  North.  Long,  of  Barnegat 74*    6'  W.  )  Long,  of  the  Ship   74*    6'  W 

iJwing  W.  i  N.    Var.  i  pt  W.  —  true  West  Lat  of  Egg  Ear.  Light.  .89   30  N.   \  Lat  of  the  Ship. .  .&»   80  N. 

CASE  III. 

,  The  Latitude  of  the  Ship  and  the  Bearing  of  a  known  Object  given. 

'  Rui-a.  Enter  the  Traverse  Table  with  the  True  Bearing  of  the  object  as  a  Course,  and  the  Diff.  Latitude  between 
he  Ship  and  the  object  in  its  column.  The  Distance  will  be  found  in  its  column — that  is,  the  Distance  i-  the  cbjeel 
rem  the  Ship.  '' 

EXAMPLE. 

The  Latitude  observed  was  40°  10'  N.  At  the  same  time  Neversink  Highland  bore  N.  W.  ^  W.  by  CompaM,  at 
f.  W.  by  W.  true.     Required  the  Ship's  distance  off. 

True  Bearing  N.  W.  by  W.  or  5  points.     Latitude  of  Neversink  40°  23'  N. 

Latitude  of  the  Ship      40°  10'  N. 
Tru*  Bearing  6  points  as  a  Course  ami  Diff  Latitude         13'  gives  the  Distance  off  lA  mtlea 


S2  FINDING  THE  SHIP'S  POSITION. 

FINDING  THE  SHIP'S  POSITION  FROM  TWO  BEARINGS  OF  THE  SAME  OBJECT. 

CASE  IV. 
Given  the  Bearing  and  Distance  of  the  nearest  Object  from  the  Ship^  and  the  Bearing  and  Distance  of  ^nothe* 
from  the  first  Object,  to  find  the  Bearing  arid  Distance  of  the  second  Object  from  the  Ship.  , 

EXAMPLE. 
The  Bearing  and  DisUace  of  Neversink  Lighthouse  from  Fire  Island  is  known  to  be  W.  S.  W.,  true,  37  miles.    Th» 
jint  at  right  angles  to  that  Bearing  is  N.  N.  W.     The  ship  having  Fire  Island  Light  on  that  Bearing,  (allowing  th   ', 
rariation  of  llie  Compass),  and  distant  15  miles,  required  the  Bearing  and  Distance  of  Neversink. 

Enter  the  Traverse  Table  with  37  miles  as  Departure  and  15  as  Difference  of  Latitude,  which  will  give  the  CourM; 
6  points  and  the  Distance  40  miles.  Add  this  6  points  to  the  bearing  of  Fire  Island,  which  was  N.  2  points  W.,  and 
the  bearing  of  Neversink  will  be  obtained  N.  8  points  W.,  or  due  West,  distant  40  miles. 

TABLE    FOR    FINDING   THE    DISTANCE  OF  AN  OBJECT    BY  TWO  BEARINGS,  AND    THB 

DISTANCE  BETWEEN  THEM. 


=  g 

DirKKaEMCB    BETWEK.W    THE    OOURSK    AND   THE    FItt.ST    BE.\aiNQ. 

5  0  S 

POINTS    OF    THE    COMPASS. 

P  •<N 

pnt's 

2 

H 

3 

H 

4 

^ 

5 

H 

6 

6i 

7 

H 

8 

8i 

9 

n 

10 

3* 

1.00 

4 

1.00 

H 

0.81 

1.23 

5 

0.69 

1.00 

1.45 

' 

H 

0.6U 

0.85 

1.17 

1.66 

6 

0  54 

0.741.00 

1.35 

1.85 

6i    0.49 

0  670.88 

1.14 

1.50 

2.02 

7     |C  46 

0.61 

[0.79 

1.00 

1.27 

1   64 

2.17 

^ 

0.43 

0.57 

0.72 

0.90 

1.11 

1.39 

1.77 

2.30 

8 

0  41 

0.53 

0.67 

0.82 

1.00 

1.22 

1.50 

1.87 

2.41 

8^ 

0.40 

0.51 

0 .  63 

0.76 

0.92 

1.09 

1.31 

1.58 

1.96 

2.50 

9 

0.39 

0.49 

0.60 

0.72 

0.85 

1.00 

1.18 

1.39 

1.66 

2.03 

2.56 

n 

0.38 

0.48 

0  58 

0.69 

0.80 

0.93 

1.08 

1.2.5 

1.46 

1.72 

2.0S|2.60 

10 

0.38 

0.47 

0.57 

0.66 

0.76 

0.88 

1.00 

1.14 

1.31 

1.51 

1  .76  2.11 

2.61 

m 

0.38 

0.47 

0.56 

0.65 

0  74 

0.84 

0.94 

1.06 

1.19 

1.35 

1.53  1.79 

2.12 

2.60 

11 

0.39 

0.47 

0  56 

0.64 

0.72 

0.81 

0.90 

1.00 

1.11 

1.24 

1.391.57 

1.80 

2.11 

2.56 

IH 

0.40 

0.48 

0.56 

0.63 

0.71 

0.79 

0.87 

0.95 

1.05 

1.15|l.27;i.41 

1.58 

1.79 

2.08 

2.50 

12 

0.41 

0.49 

0.57 

0.64 

0.71 

0.78 

0.85 

0.92 

1.00 

1.08 

1.18 

1 .  29 

1.41 

1.57 

1.76 

2.03 

2.41, 

1-2^  ,0.43 

0.51 

0.58 

0.65 

0.71 

0.77 

0.83 

0.90 

0.97 

1.03 

1.11 

1.20 

1.29 

1.41 

1.35 

1.72 

i.9d 

Rule  Ist.  To  find  the  Distance  of  the  object  when  the  last  Bearing  was  taken,  enter  the  table  with  the  number  otl 
points  at  the  top,  contained  between  the  first  Bearing  and  the  ship's  head,  and  the  number  of  Pointe  at  the  side  coi> 
taifled  between  the  second  Bearing  and  the  ship's  he«d.  At  the  angle  of  meeting  take  out  the  tabular  number, 
which  multiply  by  the  number  of  miles  of  Distance  made  good  by  the  ship.  The  result  is  the  Distance  in  milea  off 
•bore  at  the  time  the  last  Bearing  was  taken. 

Rule  2d.  To  find  the  Distance  when  the  first  Bearing  was  observed,  enter  the  table  with  the  differe-Me  between] 
these  Bearings  and  16  points ;  the  second  Bearing  in  this  case  must  be  taken  from  the  top,  and  the  first  Bearing  from  the 
side  column.  Take  out  the  tabular  number  corresponding  and  multiply  it  by  the  number  of  miles  of  Distance  made 
good  by  the  ship.     The  result  is  the  Distance  of  the  ship  off  shore  at  the  time  of  the  first  Bearing. 

CASE  1. 
Finding  the  Ship*s  Position  from  two  Bearings  of  the  same  Object. 

EXAMPLE  L 

At  8  P.  M.  Fire  liknd  Light  bore  N.  W.  ^  N.  by  Compass.  Ship's  course  W.,  at  the  rat«  of  7  knots  an  hour,  and 
at  10  P.  M.  the  same  light  bore  N.  N.  E.  |  E.     Required  her  Distance  off  at  both  stations. 

let  Beariner  N.  W.  4  N.  )   .      i     . ,     ,.        2d  Bearing  N.  N.  E. -J  E.  )   .      ,    ,^,     ^      .        xu    t  u  i      xr  noA 

Course  West.  J  Angle  4i  pts.      Course  W^st,  f  Angle  lOi  pts.  gives  the  Tabular  Num.    0.84 

Taken  at  the  top  of  the  Table.  Taken  at  the  side  of  the  table.  Dist  sailed  2  h's  at  7  knots       14m 

~336 

The  Tabular  Number  multiplied  by  14,  the  Distance  sailed,  and  the  two  right  hand  figures  struck  off  (being     "'^ 
Decimals)  gives  the  Distance  off  at  10  P.  M.  llf  miles  nearly,  or  -  11.76 

To  find  the  distance  off  at  8  P.  M., 

The  first  angle  being 4-J  points,     the  second  angle  10^  points  )      The   Tabular  number  is  .......  0.95 

Subtract  from 16        "  subtract  from       16         "       \      Distance  sailed 14iB 

Taken  at  the  aid*  of  the  Table  TTT     "  Taken  at  the  top'  6^      "       )  880 

95 
Giv»8  th«>  distance  off  at  8  P.  M.  l^i  miles,  or  13.80 


/ 


FINDING  THE  SHIPS  xuSiTlON. 


EXAMPLE  2 

At  6  P.  M.  Barnegat  Light  came  in  eiglit,  bearing  by  conipasa  S.  W.  by  W.     Ship  sailed  on  a  S.  by  W.  ^  W 
iouree,  at  the  rate  of  8  kuots  an   houi-.  with  n  2kiiot  tide  in   iier  favor,  until  7h  3f>m  P.  M.,  when  the  same  light 
waa  observed  to  bear  N.  W.  by  W.     Required  her  distance  off  at  both  stations. 
Ist.  bearing  S.  W.  by  W.  )  .       ,  2d  bearing  N.  W.  by  W.  )  , 

Course  S.  by  W.  ^  W.       \  ^"^^^  ^*  P^"      Curse  S.  by  W.  ^  W.      f  ^"^'^  ^*  P^ 

Takeu  at  tke  top  of  the  Table.  Taken  at  the  side  of  the  Table,  glTes  the  Tabular  Number 0.6» 

Distmice  sailed  in  1^  hours.  .  12  milea.       Multiply  by 16 

Add  for  tide 3  ~346 

Distance  made  good 16  miles.  6t» 

The  siiip's  distance  off  the  Light  at  7h  3(lm  P.  M.  is  10^  milea,  or   lOM 
To  tiad  the  distance  oflf  at  6  P.  M., 
Che  first  angle  was    3^  points,     2d  an^le       V-^  points.  ) 

4ub»r<.cl  from  16         "  Sub.  from  16         "        \      The  Tabular  Number  is  found  to  be 1.08 

l*k8  at  the  side      T2i  points.     At  the  top  ~6i  points.  )      Distance  made  good _16 

61fi 
10  S 

The  ship's  distance  off  the  Light  when  peen  at  6  P.  M.,  was  16^  miles,  o.    1*44 


PROJECTION  OF  THE  ABOVE  EXAMPLES, 
Skmcing  the  Distances  found  by  the  Tables  to  be  correct,  as  measured  in  the  Diagram. 

Fig.    17. 


Ce^ur.ie  ms'l  J)isl  H^fftlcs 


SCALE  of  MILE5 


t  i  6  T  t  2         IC 


94  FINDING    THK    SHIPS    POSITION. 

FINDING  THE  SHIP'S  POSITION  FROM  TWO  BEARINGS  OF  THE  SAME  OBJECT. 

CASE  II. 

Given,  two  Bearings  by  Compass  of  an  Object  on  Shore,  with  the  Distance   sailed  between  them,  to  ^nd  ilu 

Ship's  correct  Position  in  Latitude  and  Longitude. 

This  case  is  useful  in  finding  the  Sea  Rate  of  the  Chronometer.     (See  page  155.) 

EXAMPLE  1. 

At  6  o'clock  A.  M.,  Neversink  Light-House  bore  by  Compass  W.  by  S.  i  S.     Ship  then  sailed  on  a  S.  |  W.  Course, 
«t  the  rate  of  6^  knots  an  hour,  until  7  A.  M.,  when  the  same  object  bore   N.  W.  by  N^  variation  ^  point  West 
Required,  the  Ship's  Latitude  and  Longitude  at  the  time  of  each  Bearing. 
Fbe  Ist  Bearing  W.  by  S.  i  S.  by  Compass.  2d  Bearing  N.  W.  by  N.  by  Compass. 

Corr.  for  i  pt  W.  var.  is  W.  S.  W.,  j   .'   „,    „  ,.+=  Corr.  for  ^  pt  var.  N.  W.  ^  N.  |   .  „„,    ,  „,     .. 

Course  S.iW         -        South,        [AngleGpts.  Course..!.^ true  S.  f  ^^^"  ^^i  pts 

Tabular  Number 97 

2  hours  at  5^  knots=Distance  sailed 11 

Distance  off  at  time  of  2d  Bearing  at  7  A.M 10.67  miles. 

Tte  op.  pt  to  the  2d  Bear,  is  S.  E.  i  S.,  Dist.  10^  miles,  gives  D.L.  0°    8'  S.,  and  Dep.  6.7==D.  Long.. .  0°    8'  46"   K 

Lat  of  Neversink, 40    24  N.  Long,  of  Neversink.  .78    58   48     "W. 

At  7  A.  M.  the  Lat  of  the  Ship  was 40°  16'  N.  and  Long 73"°  50'    ?"  W. 

To  find  the  Position  of  the  Ship  at  5  A  M.,  or  time  of  the  1st  Bearing. 

Ist  Angle  was 6  points.  2d  Angle  -was 12^  points. 

;  Subtractfrom 16     "  Subtractfrom 16 

Take 10  points  at  the  side  of  the  Table,  and 3^  at  the  toj*. 

Tabular  Number 66 

Distance  Sailed 11 

Diet  off  at  time  of  1st  Bear.  5  A.  M 7.26',  or  7i  miles,  nearly. 

l^e  pp.  pt  to  1st  Bear,  is  E.  N.  E,  and  Dist  7i,  gives  Diff.  Lat. . .   0°     8'  N.     Dep.  6.7— D.  Long.     0°    8'  45"  E. 

Lat  of  Neversink  .40    24   N.  Long.. . .   73    68   48    W 

At  5  A.  M.  the  Lat  of  the  Ship  was 40°  27' N.  Long 73°  60'    8"W. 

The  Ship  having  made  a  true  South  Course,  she  has  sailed  on  the  Meridian  of  73°  50'  3"  West,  and  was  is  Um 
Hme  Longitude  at  7  A-  M.  as  at  5  A-  M.,  and  her  Difference  of  Latitude  is  equal  to  the  Distance  sailed. 

EXAMPLE  2. 
At  Noon  the  N.  W.  end  of  St  Anthony  (one  of  the  Cape  Verde  Islands)  bore  S.  E.  by  E.  by  Compass.     Shij)  tnen 
•ailed  on  a  South  Course,  at  the  rate  of  10  knots  an  hour,  until  4  P.  M.,  at  which  time  it  bore  N.  E.  by  E.  -J  E.  the 
Magnetic  Variation  here  being  1^  points  "Westerly.      Required  the  Lat  and  Long,  of  the  Ship  at  the  time  of  each 
Beaoing. 

The  Ist  Bear.  S.  E.  by  E.  by  Compass.  2d  Bear.  N.  E.  by  E.  ^  K  by  Compass. 

Cor.  for  U  pts.  W.  var.  =E  by  S.  i  S.  )    .      ,    -    ,  Cor.  for  1^  pts.  var.=N.  E.        |   .      ,    ,„, 

Course  South,  corrected,=S.  by  E.  |  E.  f  ^^S^^  ^  P^  True  Course. . .  .S.  by  K  i  K   f  ^"^le  lOi  ptiL 

Tabular  Number 0.94 

4  hours  at  10  knots Dist . .  40 

Dist  off  at  the  time  of  the  2d  Bear,  at  4  P.  M .37.60  miles. 

'Qie  op.  pt  to  the  2d  Bear.'is  S.  W.,  and  Dist  37^  miles,  ^ives  D.  L.    0°  26'  80"  S.     Dep.  26.5=-D.  L.    0°  27'  40^  W 

Lat  of  the  N.  W.  Point  of  St  Anthony 17    12     0   N.     and  Long.  do.. .  .26    19     0    W 

At  4  P.  M.  the  Lat  of  the  Ship  was 16°  45' 30"N.     and  Long 25°  46' 40"  W 

To  find' the  Position  of  the  Ship  at  Noon,  or  time  of  1st  Bearing 

The  1st  Angle  was. ...  5  points.  2d  Angle  was 10^  points. 

Subtract  from .!&_   "  Subtract  from. .  ._16        "  )  Tabular  No. . .  1.00 

Take 11  points  at  the  side  of  the  Table,  and   . .   5^  at  the  top.  \  Dist  sailed . . .  40 

Dist  off  at  time  of  1st  Bearing,  or  Noon 40.00  miles. 

The  op.pt  to  the  1st  Bear,  is  W.byN.iN.,  and  Dist40=D.  L.    0°  11'  36"  N.      Dep.  38.3  W.=D.  Long.    0°  40'  "W 

Lat  N.  W.  Point  of  St  Anthony  is .17    12     0    N.  Long.. . .  25    19    W 

Lat  of  the  Ship  at  Noon  was 17°  23'  36"  N.  Long.. . .  25°  59'  W 

This  method  of  finding  the  Position  of  the  Ship  when  in  .sight  of  Land,  by  two  bearings  of  the  same 
•bject,  will  be  found  of  great  value,  when  a  cross-bearing  cannot  be  obtained.  All  that  is  necessary  to  do, 
is  to  select  an  object,  the  position  of  which  is  given  in  the  Table  of  Latitudes  and  Longitudes,  and  to  take 
a  correct  bearing  of  it  by  the  Ship's  Compass,  and  note  the  time  by  Watch  ;  and  after  the  bearing  has 
altered  not  less  than  3  points,  take  a  2d  bearing  and  note  the  time  by  the  Watch.  Thus  having  the  interval 
of  time  between  the  1st  and  2d  bearings,  and  the  rate  of  sailing  per  hour,  the  Distance  sailed  ia  the  interval 
may  easily  be  obtained,  and  the  Ship's  correct  Latitude  and  Longitude  found,  as  explained  in  the  above 
Examples,  at  either  of  the  Bearings. 

This  will  be  found  of  importance  wnen  the  Ship's  Chronometers  require  to  be  verified,  at  times  during 
a  voyage,  when  in  sight  of  any  known  land.  Because  if  the  Sights  are  taken  for  Time,  the  Bearing  of 
the  Land  can  be  taken  at  the  same  time,  and  another  Bearing  taken  either  before  or  after  that  time,  with 
the  Course  and  Distance  run  in  the  interval,  will  give  the  Ship's  exact  Latitude  ani  Longitude  at  the  time 
the  Sights  were  taken. 


ss 


TIDES.  . 


The  Tidal  Wave  is  caused  by  the  joint  Attractions  of  the  Sun  and  Moon,  but  chiefly  of  the  latter  body, 
whereby  the  Sea  is  raised  or  drawn  up  by  that  power,  in  the  form  of  a  Swelling  Wave,  and  following  th« 
motion  of  the  Moon  round  the  Earth,  advances  at  a  prodigious  rate.  This  Water  does  not,  however,  partaxe 
of  any  onward  motion,  but  merely  rises  and  falls.  The  motion  of  a  Tide  Wave  is  represented  by  the 
fluttering  of  an  Awning  or  the  shaking  of  a  Sail. 

If  the  Earth  was  entirely  covered  with  water,  the  Course  of  this  Wave  would  be  from  the  East  towards 
the  West ;  but  as  large  Continents  and  Islands  exist,  which  obstruct  its  free  passage,  it  diverges  into  other 
directions,  and  the  meeting  with  those  obstructions  causes  the  water  to  acquire  a  motion  conforming  to  ths 
direction  m  which  the  land  lies  ;  but  still,  to  a  certain  extent,  under  the  governing  influence  of  the  Sur 
and  Moon,  and  branching  off"  in  all  directions  until  it  finds  its  level. 

The -Interval  of  time  which  the  Moon  takes  in  passing  the  Meridian  of  any  place,  and  returning  to  th« 
same  again,  consists  of  24  liours  49  mmutes,  being  the  length  of  a  Lunar  day.  This  occasions  two  floods 
and  two  ebbs  of  the  Tide  Wave  in  that  time.  Therefore  one  flood  and  one  ebb  will  occupy  about  12  hours 
24  minutes,  and  the  Flood  tide  will  run  6  hours  12  minutes,  and  the  Ebb  in  a  contrary  direction  the  same 
len^iii  of  time. 

But  as  the  JMoon  comes  to  the  Meridian  nearly  an  hour  later  every  day,  the  time  of  High  Water  is  that 
much  later  every  day.  When  it  is  High  Water  on  the  shore,  or  when  the  Tide  has  done  rising,  it  continues 
running  longer  in  the  offing.  Three  hours  longer  is  called  Tide  and  Half  Tide,  one  hour  and  a  half  longer, 
Tide  and  Quarter  Tide. 

On  the  day  of  the  full  and  change  of  the  Moon,  the  time  of  High  Water  is  noted  at  the  various  Ports  and 
places  of  the  World,  and  published  in  a  Table,  and  which  is  called  the  E..tablishment  of  the  Port  or  place 
And  all  that  would  require  to  be  done  to  find  the  time  of  High  Water  on  any  other  given  day,  would  be  to 
add  the  time  of  the  Moon's  Meridian  passage  to  the  fetablishment  of  the  Port.  But  on  account  of  the 
irregular  influence  of  the  Sun  and  Moon,  and  other  causes,  together  with  the  effect  of  gales  of  wind  in 
accelerating  or  retarding  the  times  of  High  Water,  an  approximate  result  only  can  be  obtained  from  any 
general  rule.  In  some  parts  of  the  world  Local  Tide  Tables  are  constructed,  containing  the  times  of  High 
Water  at  the  various  places  on  that  Coast,  predicted  from  long  experience  of  tidal  observations,  and  which 
is  of  great  importance  to  vessels  which  are  about  to  enter  a  Harbor  where  there  is  a  great  rise  and  fall  of 
the  Tide.  In  many  parts  of  the  world  there  is  very  little  rise  and  fall ;  nevertheless,  the  tide  runs  with 
considerable  velocity. 

And  where  a  Bay  or  Inlet  is  exposed  to  the  Set  of  the  Flood  Tide,  which  not  having  any  outlet,  the 
water  naturally  rises  to  a  great  height,  as  we  see  in  the  case  of  the  Bay  of  Fundy,  and  other  places.  In 
inland  Seas,  such  as  the  Mediterranean,  Baltic,  &c.,  which  are  composed  of  narrow  stripes  of  water,  there 
is  not  sufficient  room  for  the  formation  of  the  Tidal  Wave  ;  consequently,  the  tides  there  are  scarcely 
perceptible. 

In  some  rivers,  which,  on  account  of  tlie  great  quantity  of  water  they  discharge,  run  longer  and  with 
greater  velocity  on  tlie  ebb,  the  flood  tide  is  thereby  kept  back,  until  accumulating  strength,  it  rises  like  a 
wall  above  the  level  of  t.ie  ebb,  and  advancing  m  the  form  of  a  Crested  Wave,  rushes  upwards  with  great 
strength  until  it  finds  its  level.     This  phenomena  ic  called  the  Bore  of  the  Tide. 

When  the  Sun  and  Moon  are  on  the  Meridian  together,  their  actions  concur,  and  the  tide  is  higher 
than  at  any  other  time.  The  same  holds  good  when  they  are  in  opposition  to  each  other.  These  highest 
tides  are  called  Spring  Tides,  and  occur  a  day  or  two  after  New  and  Full  Moon.  But  when  the  Sun  and 
Moon  are  90°  apart,  their  actions,  or  power  of  attraction,  neutralize  each  other,  and  the  tide  is  lower  than 
at  other  times.     These  are  called  the  Neap  Tides. 

The  highest  tides  happen  in  the  month  of  January  ;  because  the  Earth  is  nearer  to  the  Sun  and  Moon 
then,  than  at  any  other  time  of  the  year ;   consequently,  the  hignest  Spring  Tides  happen  in  that  month. 

When  the  Moon's  Declination  is  0,  the  tides  are  equally  high  on  that  day  ;  and  while  the  Moon  has  Nortk 
Declination  the  higest  tides  are  in  the  Northern  Hemisphere,  when  she  is  above  the  horizon,  and  the  reverse 
when  her  Declination  is  South.  The  Tides  risp  h'ghest  at  places  where  the  Moon  is  in  the  zenith;  they 
Are  also  highest  at  the  Equator  and  lowest  at  the  Poles. 

The  common  method  of  finding  the  time  of  High  Water  is  as  follows : 

1.     TO  FIND  THE  MOON'S  AGE. 

Rule. — Add  together  the  Epact  of  the  Year,  the  Epact  of  the  Month,  and  the  Day  of  the  MontL  The  Sum,  if  it 
does  not  exceed  30,  is*  the  Moon's  Age  ;  if  the  Sum  exceeds  30,  subtract  80  from  it,  and  the  remainder  will  be  tb« 
Moon's  Age  on  that  day  of  the  month  reauired. 


M  TIDES. 

TO  FIND  THE  TIME  OF  THE  MOON'S  PASSING  1  HE  MERIDIAN 

IhrLK. — Multiply  the  Moon's  Age  by  8,  and  point  oflF  the  right  figure  under  the  days,  then  the  left  hand  figur«,  ot 
figures,  yriW  be  the  hours,  and  multiply  the  right  hand  figure  (which  was  pointed  off)  by  6,  will  be  the  minutes  past 
Boon  when  the  Muon  passes  the  Meridian.  If  the  hours  exceed  12,  subtract  12  uours  from  it,  which  will  be  thf 
lim«  vf  her  Morning  passage. 

TABLES  FOR  FINDING  THE  MOON'S  AGE 


THE  KPACT  OK  THE  YEAR. 

186S. 

1854. 

1856. 

1866. 

1867. 

1858. 

1859. 

1860. 

1861. 

1862. 

1863.  1864. 

1865 

1866. 

1867. 

1868. 

d  h. 
6.  8 

1869. 

d.  h. 

20.  1 

d.  h. 
I.  3 

d.  h. 
11.18 

d.  h. 
23.10 

d.  h. 
4.12 

d.  h. 
15.  3 

d.  h. 
25.17 

d.  h. 
7.21 

d.  h. 
18.12 

d.  b. 
29.  8 

d.  h.  d.  h. 
10.  6  21.21 

d.  h. 
2.23 

d.  h. 
13.15 

d.  h. 
24.  6 

d.  d. 
16.23 

THE  EPACT  OF  THE  MONTH. 

1 
1 

Jkn. 

Feb. 

Marcli, 

April. 

May. 

June. 

July. 

Aug. 

Sept. 

Oct 

Nov. 

Dea 

d.  h. 
0.  0 

d.  h. 
1.11 

d.  h. 
29.11 

d.  h. 
1.10 

d.  h. 
1.21 

d.  h. 
3.  8 

d.  h. 
3.20 

d.  h. 
6.  7 

d.  h. 
6.18 

d.  h. 
7.  6 

d.  h. 
8.17 

d.  h. 
9.  4 

TO  FIND  THE  TIME  OF  HIGH  WATER.— l5t  Method. 

Role. — To  the  time  of  the  Moon's  Meridian  passage  on  the  given  day,  add  the  time  of  High  Water  at  the  givei 
pliice  on  the  Full  and  Change  days,  or,  as  it  is  called,  the  Establishment  of  the  Port  Their  Sum  is  the  time  of 
High  Water  past  noon  on  the  given  day.  If  this  Sum  exceed  1 2  hours  24  minutes,  which  is  the  interval  between 
Mich  succeeding  tide,  subtract  12  hours  24  minutes  from  it ;  or,  if  it  exceed  24  hours  48  minutes,  subtract  24  boor* 
48  minutes  from  it,  and  the  remainder  will  be  the  time  of  High  Water  in  the  afternoon  of  the  given  dav. 

EXAMPLE  1. 

Required,  the  time  of  High  Water  at  Sandy  Hook,  October  2,  1854,  (Civil  time.) 


Epact  for  the  Year,  1854,  is 1.3 

"  "        Month,  Octf)ber, 7.5 

Day  of  the  Month,  October 2.0 

Moon's  Age 10.8 


Moon's  Age,  October  2,  1854 10.8 

Multiply  by. 8 

8h.  '2.16 
6 

Moon's  Meridian  Passage 8h.l6 

Establishment  of  Sandy  Hook 7    36 


Time  of  High  Water  in  the  morning 15    51 

Subtract.. 12    24 


Time  of  High  Water  at  Sandy  Hook. . . .    8h.27  in  the  aftemooa 


EXAMPLE  2. 
itequired,  the  time  of  High  Water  at  Cape  Henry,  December  6th,  1854,  (Civil  time.) 


Kpaet  for  the  Year,  1854,  is 13 

"  "      Month,  December, 9.4 

Day  of  the  Month,  December, 6.0 

Moon's  Age 16,7 


Moon's  Age,  December  5th, 16.7 

Multiply  by 8 

13.  '0.8 
6 

Moon's  Meridian  Passage 13h.  2.0 

Establishment  of  Cape  Henry 7    40 

Time  of  High  Water  in  the  morning 20   42 

Subtract 12    24 

do. 


Do. 


in  the  evening 8h.l8 


As  this  Rule  gives  only  a  rough  estimate  of  the  Time  of  High  Water,  and  may  be  as  much  as  two  houi» 

in  error,  caused  by  the  variation  in  the  time  of  the  Moon's  daily  passage   over  the   Meridian,  and  which 

aries  from  about  40  minutes  to  66  minutes,  at  different  times   n  the  year.     This  Rule  assumes  the  interval 

f  her  Meridian  passage  to  be  48  minutes  or  four-fifths    of  au  hour.      It,  however,  may  be  useful  when 

Jiere  is  no  Nautical  Almanac  at  hand. 

The  Second  Method  is  more  to  be  depended  on.  In  this  case  the  Moon's  Meridian  Passage  at  Green- 
wich  is  taken  from  the  Nautical  Almanac,  and  corrected  to  the  time  of  her  passing  the  Meridian  of  tbt 
Ship,  and  which  is  further  corrected  for  her  Horizontal  Parallax  by  the  annexed  Tables. 

FINDING  THE  TIME  OF  HIGH  WATER.— 2<i  Method. 

R;u.  Take  out  the  time  the  Mooo  passes  the  Meridian  at  Greenwich  from  the  Nautical  Abnanac,  for  the  day 
Mqnired,  and  apply  the  Equation  of  time  the  contrary  way  to  the  precept  at  the  head  of  the  column,  which  will  b« 
lk»  appM-«nt  time  at  Greenwic)  of  her  Meridian  passage.     Enter  the  tide  toble  with   the  Longitude  of  the  pU«a 


TIUKS. 


S7 


and  Uke  oat  a  number  of  miauteB,  to  be  adat>d  to  the  Meridian  passage  if  the  Longitude  be  Went  but  subtracted 
if  Eaet,  will  be  the  App.  time  of  the  Moon's  Meridian  passage  at  the  place.  Take  out  the  Moon's  Hor.  Pari 
Dearest  to  this  time  on  the  given  day,  from  the  Nautical  Aimanaa  Enter  the  Table  below,  with  the  time  of  the 
Meridian  passage  at  the  side  and  the  Hor.  Pari,  at  the  top.  and  take  out  a  correction  to  be  applied  as  directed  in  th* 
table,  to  the  apparent  time  of  the  Moon's  Meridian  passage  at  the  place,  to  which  add  the  establishment  of  the  port^ 
and  the  result  is  the  time  of  High  Water  in  the  afternoon,  if  less  than  12  hours.  If  it  exceed  12  hours,  it  is  the 
time  of  High  Water  next  morning  ;  and  to  obtain  the  time  for  P.  M.  on  the  present  day,  subtract  12h.  24  m.  from  it 
If  the  sum  exceeds  24  hours,  it  is  the  apparent  time  of  High  Water  P.  M.  the  next  day.  For  the  P.  M.  of  the  prc^- 
poted  day,  subtract  24h.  48m. 


Long. 

Corr. 

of   th« 

ia 

TABLE  FOR  FINDING  THE  TIME  OF  HIGH  WATER. 

?Hce. 

Min. 

» 

, 

• 

f 

Moon'* 

Moon 

'•  Horizontal  Parallax. 

Moon's 

Moon's 

Moon 

't  Horizontal  Parallax. 

Moon's 

0 
10 
20 
80 

0 

1 

3 
4 

Mer. 
Passage. 

Mer. 
Passage. 

Mer. 
Passage. 

Mer. 
Passage. 

64' 

56' 

68' 

60' 

64' 

66' 

68' 

60' 

Add 

Add 

Sub. 

Sub. 

40 

6 

h   m 

h    m 

h   m 

h   m 

h   m 

h   m 

h   m 

h    m 

h   ro 

h   ra 

h   m 

h    m 

60 

6 

0     0 

0     6 

0     2 

0     1 

0     8 

12     0 

6  50 

0  45 

0  42 

0  40 

n  38 

18  50 

60 

8 

Sub. 

Sub. 

7     0 

0  37 

0  35 

0  34 

0  33 

19     0 

70 

9 

0  20 

0     1 

0     4 

0     6 

0     7 

12  20 

7  10 

0  29 

0  28 

0  28 

0  27 

19   10 

80 

10 

0  40 

0     8 

0  10 

0  11 

0  12 

12  40 

7  20 

0  22 

0  22 

0  22 

0  22 

19   20 

90 

12 

1     0 

0  16 

0  16 

0  17 

0  17 

13     0 

7  30 

0  16 

0  15 

0  16 

0  17 

16  30 

100 

13 

1  20 

0  22 

0  22 

0  22 

0  22 

13  20 

7  40 

0     8 

0     9 

0  11 

0  12 

19  40 

110 

14 

1  40 

0  29 

0  28 

0  28 

0  27 

13  40 

7  60 

0     0 

0     3 

1     6 

0     6 

19  60 

120 

15 

2     0 

0  37 

0  85 

0  33 

0  32 

14     0 

Add 

Add 

Add 

130 

17 

2  20 

0  43 

0  41 

0  38 

0  37 

14  20 

8     0 

0     9 

0     4 

0     1 

0     1 

20     0 

140 

18 

2  40 

0  6C 

0  46 

0  44 

0  42 

14  40 

Add 

160 

19 

3     0 

0  56 

0  52 

0  49 

0  46 

15     0 

8  20 

0  17 

0  12 

0     8 

0     6 

20  20 

160 

21 

S  20 

1     3 

0  57 

0  53 

0  51 

15  20 

8  40 

0  29 

0  22 

0  17 

0  13 

20  40 

170 

22 

3  40 

1     8 

1     2 

0  67 

0  54 

16  40 

9     0 

0  31 

0  24 

0  19 

0  15 

21     0 

180 

23 

4     0 

1   13 

1     6 

1     1 

0  58 

16     0 

9  30 

0  36 

0  29 

0  23 

0  19 

21   80 

4  30 

1   18 

1   11 

1     5 

1     2 

16  30 

10     0 

0  35 

0  27 

0  22 

0  18 

22     0 

5     0 

1   21 

1   13 

1     7 

1     3 

17     0 

10  30 

0  30 

0  23 

0  18 

0  15 

22  80 

5  80 

1   18 

1   11 

1     6 

1     2 

17  80 

11     0 

0  23 

0  17 

0  13 

0  10 

23     0 

6     0 

1   13 

1     6 

1     1 

0  58 

18     0 

11   30 

0  15 

0  10 

0     6 

0     4 

23  30 

6  20 

1     2 

0  56 

0  53 

0  50 

18  20 

Sub. 

Sub. 

6  40 

0  53 

0  49 

0  46 

0  44 

18  40 

12     0 

0     6 

0     2 

0     1 

0     3 

24     0 

EXAMPLE  1. 

Required  the  time  of  High  Water  at  Sandy  Hook,  Oct.  2d,  1854.  (Sea  time.) 

Moon's  Mer.  Passage  Oct  Ist,  N.  A 8h  11m     "      "    "      ~    • 

Equa.  of  Time  the  contrary  way,  add 10 

Apparent  time  of  Meridian  passage 8h  21m 

Long,  of  Sandy  Hook  74°  W.,  add 10 

^pp.  time  of  the  M.  Mer.  pass,  at  Sandy  Hook.   8h  31m 


At  Sandy  Hook,  Apparent  time  of  High  Water,  in  the  afternoon . 


Moon's  Hor.  Pari,  at  time  of  the  Mer.  passage  is  59'.  Then- 
with  the  Mer.  pass  at  the  side  of  the  table,  and  between 

68  and  60  at  the  top,  the  Corr.  is Oh  Km 

to  be  added  to  the  Meridian  passage 8    31 

8h  41m 

Add  the  Establishment  of  the  place 7    35 

Time  of  High  Water  in  the  morning 16h  16m 

Subtract 12h  24m- 

3h  52ui 


EXAMPLE  2. 

Required  the  time  of  High  Water  at  Cape  Henry,  December  6th,  1864.     (Sea  time.) 

Moon's  Mer.  passage,  December  5th,  N.  A ISh    8m     Moon's  Hor.  Pari,  at  time  of  the  Mer.  passage  55'.     Then 

with  the  Moon's  Mer.  passage  at  the  side  of  the  tal 


9_ 

18b  12m 
10 


passage  at  tiie  side  oi  ine  table,  and 
between  64  and  56  at  the  top,  the  Corr.  is. . . .  Oh  22m 
■which,  subtracted  from  the  Meridian  passage  .13    22 

13h    On? 
Add  the  Establishment  of  the  place 7    40 

At  Cape  Henry,  apparent  time  of  High  Water  in  the  morning 20h  40ni 

12    24 


Equa.  of  time  the  contrary  way,  add. 

Li)ng.  of  Cape  Henry  76°  West,  add. 

App.  time  of  the  Moon's  Mer.  passage 13h  22m 


TW«  of  nigh  Water  oc  the  afternoon  of  the  same  day 


8b  16i 


WINDS. 


The  fjilownng  short  description  of  the  prevailing  Winds  may  be  found  useful,  in  the  absence  of  the  regu- 
alar  sailing  directions  for  the  voyage,  which  should  contain  all  the  necessary  information  on  this  head: 

The  Earth  revolving  on  its  axis  from  West  to  East,  together  with  the  great  heat  near  the  Equator,  caused 
toy  the  Sun  being  always  vertical  in  some  part  or  other  of  the  Torrid  Zone,  produces  the  Trade  Winds. 

The  motion  of  the  Earth  causes  the  Wind  to  blow  from  East  to  West,  whilst  the  cold  air  rushing  m  from 
the  North  and  South  towards  the  heated  air  in  the  Tropics,  produces  the  N.  E.  and  S.  E.  Trade  Winds,  ana 
which  blow  continually  in  those  directions  Their  limits  extend  to  about  30*  on  each  side  of  the  Equator, 
but  near  to  the  coasts  of  America  and  Africa  they  extend  to  34°  sometimes.  The  limits  of  the  Trade 
Winds  are  very  variable,  even  in  the  same  months  of  the  year.  When  the  Sun  has  great  North  Declina- 
tion, their  limits  are  considerably  to  the  Northward  of  where  they  are  found  when  the  Sun  has  great  South 
Deelination.  In  the  month  of  June,  for  instance,  the  Northern  limit  of  the  N.  E.  Trade  may  be  found  in 
about  30°  North  Latitude,  and  the  Southern  limit  of  the  same  in  about  10°  North  of  the  Equator.  A 
space  of  calms  and  rain-squalls  intervene.  Until  the  Northern  limit  of  the  S.  E.  Trade  is  reached  in 
about  4°  North  of  the  Equator,  its  Southern  limit  at  this  season  extends  only  to  about  20*  South  of  thej 
Eqaator. 

In  the  month  of  December,  when  the  Sun  has  great  South  Declination,  the  Northern  limit  of  the  N.  L. 
Trade  Wind  may  be  expected  in  about  20°  North  Latitude,  and  its  Southern  limit  in  about  4°  North  of  thej 
Equator.     A  space  of  calms  and  rain-squalls  intervene,  and  the  Northern  limits  of  the  S.  E.  Trade  will  ba 
found  in  about  2'  North  of  the  Equator,  and  the   Southern  limit   about  30°  South   Latitude,     It  appears, 
then,  that  the  limits  vary  to  the  extent  of  10°  in  6  months,  and  that  the  Northern  limit  of  the  S.  E.  Trade] 
Wind  is  always  found  to  the  Northward  of  the  Equator. 

Ships  cross  the  region  of  calms,  &c.,  between  the  Trades,  quicker  bound  North,  than  they  do  when  bound  | 
South,  by  reason  of  the  airs  of  wind  being  more  favorable. 

Ships  on  approaching  the  limits  of  the  Trade  Wind,  fall  in  with  squally  weather  and  heavy  rains,  a  sure ' 
indication  of  a  change.     On  entering  the  Northern  limit  of  the  N.  E.  Trade,  the  wind  will  be  found  far  tOj 
the  Northward  :  but  as  you  advance  South,  the  Wind  will  draw  more  to  the  Eastward.     And  in  like  man- 
ner,  the  S.  E.  Trade  is  found  far  to  the  Southward,  and  draws  more  to  the  Eastward  as  you  advance. 

Ships  bound  to  the  Southward  should  endeavor  to  cross  the  Equator  in  about  Long.  25°  W.,  because  they^ 
will  meet  the  S.  E.  Trade  sooner  than  they  would  if  farther  to  the  Eastward.  They  must,  however,  bej 
careful  not  to  go  too  far  to  the  Westward  before  crossing  the  Equator,  on  account  of  meeting  tiie  S.  E. 
Trade  Wind  far  to  the  Southward,  which  heads  them  off  to  the  Westward,  and  because  of  the  Equatorial  | 
Current,  which  sets  in  towards  the  coast  of  Brazil.  But  in  a  fast  sailing  Ship  this  may  be  much  modified. 
When  the  vessel  is  caught  in  the  variable  weather  which  exists  between  the  N.  E.  and  S.  E.  Trade  Winds,] 
the  rule  is  to  keep  on  that  tack  in  which  she  makes  the  most  Southing  on,  so  as  to  get  out  of  it  as  quickly  j 
as  possible. 

Far  to  the  Eastward,  along  the  coast  of  Africa,  the   S,   E.  Trade   is  changed  to   a  S.  W.  Wind,  which 
blows   with   little    variation    throughout    the    year   in  that  direction,    interrupted   at    times   by   violent  j 
tornadoes,  and  the  Harmattan  or  East  Wind,  close  to  the  coast. 

A  ship  taking  this  Eastern  passage  to  the  Cape  of  Good  Hope,  vrould  certainly  have  to  beat  the  wholol 
way,  though  an  advantageous  slant  is  sometimes  obtained  when  the  Wind  veers   at  the  quarterly  changes 
»f  the  Moon. 

After  losing  the  S.  E.  Trade,  the  usual  variable  Winds  are   met  with,  but   the   most   prevailing  one  is 
from  the  S.  W.     When  a  Ship  is  bound  to  the  East   Indies  or  Australia,  the  best  parallel  of  Latitude  for 
running  down  her  Longitude  to  the   East  is  39°  0'  S.,  because  there  the  Westerly  Winds  prevail,  and  the; 
weather  is  not  so  tempestuous  as  it  is  farther  South.     (See  remarks  on  Great  Circle  Sailing.  Page  6.) 

If  bound  to  India,  and  having  reached  70°  0'  E.  Longitude,  they  steer  more  to  the  North,  and  fall  in  with  I 
the  Southern  limit  of  the  S.  E.  Trade  in  about  90°  E.  The  limits  of  the  Trade  Winds  here  are  governed  by 
the  same  laws  as  they  are  in  the  Atlaniic  Ocean,  but  do  not  blow  so  steadily.  The  space,  between  the 
Northern  limits  of  the  S.  E.  Trade  and  the  Equator  is  occupied  by  a  Wind  which  blows  6  months,  that  is, 
from  May  to  October,  from  the  Eastward  and  called  the  Easterly  Monsoon,  and  the  other  6  months  of  th« 
fax  in  an  opposite  direction,  and  then  called  the  Westerly  Monsoon. 


CURRENTS.  89 

After  crossing  the  Equator  and  bound  up  the  Bay  of  Bengal,  the  region  of  the  r»g,alarMonjoons  is  reached 
The  S.  W.  Monsoon  commences  in  May,  and  brings  rain  and  squally  weather,  which  continues  6  months 
«r  until  October.  The  N.  E.  Monsoon  then  commences,  and  durmg  its  continuance,  from  October  to  May 
(the  other  six  months  of  the  year),  fine  dry  weather  prevails  on  all  the  coasts  of  India.  The  Monsoons  varj 
their  direction  according  to  the  locality  of  the  place  at  which  they  blow.  This  includes  the  China  and 
Arabian  Seas.     At  the  changes  of  the  Monsoons,  terrific  hurricanes  frequently  occur  in  all  these  localities. 

In  the  Pacific  Ocean,  the  South  East  Trade  Wind  is  found  to  blow  very  steadily,  with  fine  serene 
weather,  and  its  limits  are  about  the  same  as  in  the  Atlantic  Ocean.  Not  so,  however,  with  the  North 
East  Trade  ;  it  is  generally  found  light  and  variable,  and  hangs  far  to  the  Northward,  especially  when 
the  Sun  has  great  North  Declination. 

Ship's  bound  to  California  generally  cross  the  Equator  in  about  112°  West  Longitude;  but  they 
seldom  find  the  North  East  Trade  blow  with  the  same, force  as  it  does  in  the  Atlantic. 

These  are  the  principal  winds  which  blow  with  any  degree  of  certainty  ;  but  where  there  are  larg* 
Islands  or  Contments  within  the  limits  of  the  Trade  Winds,  the  surfaces  of  which  becoming  violently 
heated  by  the  tropical  Sun,  causes  the  regular  wind  to  diverge  into  a  local  Trade. 

THE  CURRENTS  OF  THE  OCEAN. 

The  Trade  Wind  blowmg  continually  in  one  direction,  causes  the  water  on  which  they  act  to  acquire 
a.  movement  in  the  same  direction.  This  is  called  a  Current;  but  as  neither  the  direction  nor  the 
velocity  of  a  Current  continues  uniform,  it  becomes  one  of  the  most  perplexing  problems  in  Navigation, 
in  making  the  proper  allowance  for  the  effect  it  may  have  had  on  the  vessel's  course.  The  only  true  method 
i.s  to  keep  a  careful  account  of  the  Ship's  way  by  Dead  Reckoning,  and  compare  this  frequently  with  the 
place  of  the  Ship  by  Celestial  observations.  The  Set  and  Drift  of  the  Current  may  thus  be  ascertained, 
and  proper  allowance  made  until  next  observations.     (See  Current  Sailing,  page  29.) 

There  are  several  Currents  known  to  exist  in  various  parts  of  the  world.  The  one  known  as  the 
Florida  Stream,  originates  in  the  Trade  Winds  which  force  the  Water  in  towards  the  West  India 
Islands,  and  between  which  it  passes  into  the  Gulf  of  Mexico  ;  but  not  finding  an  outlet  there,  it 
rushes  out  between  Cape  Florida  shore  and  the  Islands  of  Cuba  and  Bahama,  pursuing  its  course 
to  the  North,  nearly  parallel  with  the  coast  of  the  United  States  ;  it  then  diverges  to  the  Eastward  and 
crosses  the  Atlantic.  One  part  of  it  is  supposed  to  enter  the  Straits  of  Gibraltar,  and  the  other  to 
proceed  along  the  Coast  of  Africa.  Passing  the  Cape  Verde  Islands,  it  rushes  along  the  S.  E.  Coast 
into  the  Gulf  of  Guinea. 

It  is  then  called  the  Guinea  Current,  and  which  runs  to  the  Eastward,  between  this  Coast  and  the 
Equator,  until  it  strikes  the  South  Coast  of  Africa,  by  which  cause  and  the  prevailing  winds  together 
it  is  forced  in  and  blended  with  the  great  Equatorial    Current    which  sets  West  to  the  South  of   tL 
Equator.       The  author  of  this  work   has  frequently  seen   the    extraordinary  phenomena   of   these    two 
great  Ocean  Rivers  brushing  past  each  other,  side    by  side,  the  dividing  line  marked  by  a  streak    of 
foam,  exactly  on  the  Equator.* 

It  will  be  perceived  that  what  is  called  the  Florida  Stream  makes  a  complete  circuit  of  the  Ocean.  For 
by  joining  this  Current,  which  is  formed  by  the  South  East  Trade  Wind,  it  is  again  precipitated  into  the 
Gulf  of  Mexico. 

The  Velocity  of  the  Florida  Stream  is  governed  by  the  force  of  the  Trade  Winds  and  the  obstruction  it 
meets  with  from  local  causes.  About  4  knots  an  hour  is  the  usual  rate  of"  the  Bahamas  ;  but  as  it  proceeds 
to  the  North  and  East  it  becomes  less. 

But  the  most  interesting  fact  of  its  retaining  its  heat  acquired  in  the  tropics,  and  preserving  its  borders 
from  mixing  with  the  surrounding  Sea,  is  very  extraordinary. 

This  is  of  great  use  to  Seamen;  because  by  ascertaining  the  temperature  of  the  Sea  water  by  the  Ther- 
mometer, he  knows  whether  he  is  within  the  influence  of  the  Stream  or  not. 

The  Sea- weed  floating  about,  usually  called  the  Gulf  weed,  which  although  brought  down  by  the  Stream, 
js  not  always  an  indication  of  being  in  it. 

The  Polar  Current  is  supposed  to  have  its  origin  in  Behring's  Straits,  in  the  North  Pacific  Ocean,  and 
ruuH  South  through  Davis'  Straits  into  the  North  Atlantic. 

Rennels'  Current  runs  across  the  mouth  of  the  British  Channel  towards  the  North  West,  and  is  caused 
by  the  water  escaping  out  of  the  Bay  of  Biscay,  which  had  been  forced  in  by  continued  gales  of  wind  from 
the  West. 

The  action  of  the  Trade  Winds  in  the  Indian  Ocean  produce  a  Current  which  sets  North  West  into  the 
Arabian  Sea,  and  having  no  outlet,  the  waters  make  their  escape  out  again  in  two  divisions,  one  runs  to 
Jhe  South  East  along  the  Malabar  Coast  and  past  the  Island  of  Ceylon,  and  again  joins  the  Equatorial 
Current  running  to  the  Westward.  The  other  division  runs  out  along  the  East  Coast  of  Africa,  between 
Ihat  Coast  and  the  Island  of  Madagascar.  Pursuing  its  course  to  the  South  West,  it  passes  along  the  edge 
jf  the  AguJhas  Bank  and  round  the  Cape  of  Good  Hope  ;  it  then  runs  to  Northward  and  joins  the  Equato- 
.•ial  Current  which  runs  to  the  Westward  in  the  Atlantic  Ocean.  Tliat  part  of  the  Current  which  sets 
round  the  Cape  of  Good  Hope  i.«  called  the  Agulhas  Current,  and  its  velocity  varies  from  5  knots  to  0, 
and  a  Current  has  been  found  someti  >ries  to  run  in  the  opposite  direction. 

A  Ship  bound  to  the  Eastward  should  keep  in  about  the  Latitude  of  40°  South  when  rounding  the  Cape 
By  that  means  they  will  avoid  the  Current  setting  to  the  Westward.  On  the  other  hand,  a  Ship  bound  to 
the  Westward  should  endeavor  to  get   into   this    Current  by  steering  for  the  coast  to  the  Eastward  of  the 

*  Ships  on  leaving  the  Gulf  of  Gniiiea,  or  the  Bi^lit  of  BiatVa,  bound  to  the  Westward,  consequently  have  to  Veat  to 
w^indward  between  tlie  Princes  Islands  and  tlie  mainland  of  Africa,  where  they  find  a  favorable  current  running  to 
ihe  Southward,  until  tiiey  have  crossed  tlie  Equator,  when,  by  then  standing  to  the  Westward,  they  fall  in  with  the 
regular  Eqn&toriai  Current  running  Wast.  Thereby  avoiding  the  Guinea  Cuirent  whijh  runs  in  a  contrary  direction  to 
Ml*  Northwfijd  of  the  Eouator. 


40  WINDS   AND   CURRENTS. 

Gape.  In  Westerly  gales  the  Current  running  against  the  wind  makes  the  Sea  run  heary  and  dangeroo* 
But  a  Ship  may  find  smoother  water  by  standing  in  for  the  Agulhas  Bank  and  keeping  on  it  until  the  gaU 
n»derate»  in  the  ofBug.  Two  Ships  becalmed  near  each  other,  one  may  be  in  the  Agttlhas  Current  and 
the  other  on  its  Bank,  and  it  frequently  happens  that  in  the  course  of  two  or  three  hours  the  one  in  th© 
Current  is  swept  away  to  the  Westward,  out  of  sight  of  the  other,  without  any  visible  cause  ;  and  befor« 
the  nature  and  effect  of  this  Current  was  understood  by  Navigators,  it  gave  rise  to  the  superstitious  story 
of  the  Flying  Dutchman. 

The  Trade  Winds  in  the  Pacific  Ocean  also  form  a  Current  which  runs  to  the  Westward,  and  thei 
between  the  North  and  West,  until   it  strikes  the  Coast  of  China.      One  division  then  running   throug 
the   Indian    Archipelago  joins  the  Westerly  Current    in  the   Indian   Ocean,  and   the  other  sets   toward 
Berhing's  Straits.     Ships  bound  to  California  cross  the  Equator  in  about  112°  West,  which  is  too  far  to  th« 
Eastward,  because  the  effect  of  the  North  East  Trade  Wind  is  deadened  by  its  proximity  to  the  Continent  of 
Nori  k  America,  which  has  exactly  the  same  effect  on  the  North  East  Trade  here  (that  is,  of  causing  light 
wines  from  the  North  and  baffling  weather)  as  there  is  found   in  the  South  East  Trade  in  the  proximity  t» 
the  (Continent  of  Africa,  where  light  Southerly  winds  are  found  to  prevail,  and  baffling  weather ;    but  on 
getting  further  to  the  Eastward  they  have  the  regular  Trade.     Consequently,  if  Ships  were  to  cross   the 
Equator  in  the  Pacific  Ocean  in  about  130°  West  Longitude,  they  would  find  a  steady  fresh  North  East 
Trade,  be  enabled  to  cross  it  quickly,  and   then  afterwards  run  down  their  Easting  in  a  high  Latitude, 
where  both  wind  and  current  would  be  found  more  favorable. 

In  the  Mediterranean  Sea,  there  exists  the  curious  phenomena  of  its  receiving  the  Currents  from  the 
Black  Sea,  and  large  rivers  running  into  it,  besides  the  regular  Current  from  the  Atlantic  Ocean,  which 
flows  in  through  the  Straits  of  Gibraltar.  Those  waters  have  no  visible  outlet ;  but  they  are  known  U> 
make  their  escape  out  into  the  Atlantic  Ocean  through  the  Straits  of  Gibraltar,  underneath  the  Current 
which  runs  in  on  the  surface.  This  has  been  proved  by  vessels  which  have  been  sunk  at  eome  distance 
inside  of  the  Straits,  the  wrecks  of  which  were  afterwards  cast  on  shore  to  the  Westward,  or  outsj-ie  of  the 
entrance. 

The  submarine  mountains  rising  from  the  bottom  of  the  Sea,  the  tops  of  which  are  /.j'/jo«  visible  in  the 
form  of  Shoals  or  Rocks,  are  no  doubt  the  fertile  cause  of  many  of  the  extraordinary  Coirenta  whi<* 
are  met  with  at  Sea.  Because  a  body  of  water  striking  these  elevations  at  right  a-igJ<5?  would  be  tume<i 
out  of  its  original  course,  and  rising  to  the  surface,  pursue  one  which  would  be  par».ilei  ^.tli  the  Mountai* 
range. 

Thif  is  a  subject,  however,  of  which  very  little  knowledge  can  ever  be  obtainci ;  at  least  to  be  of  am: 
benefit  fc  Navigators.     Becaun  the  effc  at  produced  by  the  surface  Current  which  icts  on  the  Ship  w 
ke  jurt  v  uncertain  m  ever. 


41 


HURRICANES 


Hurricanes  are  caused  by  a  po.-iion  of  the  Atmosphere  becoming  violently  heated,  ana  thereby  aoqairing 
«  circular  motion  around  a  center  or  focus,  (at  which  the  air  is  stationary,)  and  around  this  Focus  the  wind 
rushes  with  great  violence.  The  Meteor  has  also  a  progTssive  motion  to  the  Westward,  at  a  rate  varying 
from  12  to  30  miles  an  hour. 

The  diameter  of  these  Meteors  vary  from  100  to  300  miles.  The  wind  blows  with  the  greatest  fmy 
near  the  centre  or  Focus,  and  there  also  the  Shifts  of  wind  are  most  rapid.  Towards  the  circumference 
the  wind  has  less  force  and  the  shifts  of  wind  are  longer.  The  places  most  subject  to  Hurricanes  are 
the  Northern  limits  of  the  North  East  Trade  Wind,  to  the  Eastward  of  the  meridian  of  the  West  India 
Islands  in  the  North  Atlantic  Ocean,  and  the  Southern  limits  of  the  South  East  Trade,  to  the  Eastward  of 
the  meridian  of  the  Island  of  Mauritius,  in  the  South  Atlantic.  Hurricanes  also  occur  in  the  Bay 
of  Bengal  and  its  vicinity,  at  the  change  of  the  Monsoons  in  May  and  October. 

Those  in  the  China  Seas  are  called  Ty-foongs,  and  are  produced  from  the  same  cause.  These  Hurricanes, 
«r  Meteors,  are  governed  by  certain  Laws,  and  which  are  of  the  greatest  importance  to  Seamen  to  have  a 
knowledge  of.  Thanks  to  Colonel  Reed,  Mr.  Peddington,  and  other  scientific  men,  who  have,  by  patient 
investigation,  traced  out  and  explained  the  nature  of  those  destructive  Meteors,  and  given  rules  whereby 
they  may  be  avoided  :  or,  at  least,  by  which  a  vessel  may  suffer  the  least  from  their  effects. 

The  following  Remarks,  which  are  derived  from  the  experience  of  Hurricanes  in  both  Hemispheres,  in 
which  the  theory  and  practice  are  combined,  may  be  of  Bom«»  service,  when  the  more  regular  Book  on  Storma 
^a  not  at  hand. 

HURRICANES  IN  NORTH  LATITUDE. 

These  commence  on  the  Northern  limits  of  the  North  East  Trade  wind,  in  August  and  September,  and 
travelling  to  the  Westward,  visit  the  West  India  Islands,  and  thence  pursue  a  North  East  course  parallel 
with  the  Gulf  Stream,  along  the  Coast  of  the  United  States  of  North  America.  The  diameter  of  thiB 
Meteor  varies  from  100  to  200  miles,  and  its  progress  at  the  rate  of  about  17  miles  an  hour.  But  the  most 
distinctive  feature  of  this  Hurricane  is,  that  the  wind  blows  in  a  Circle  from  Right  to  Left,  (or,  as  Seamen 
would  say,  the  Left-handed  way.)  around  a  Focus  or  Centre,  the  centre  itself  being  a  calm  space.  The 
changes  of  wind  near  the  Focus  are  very  rapid  and  blow  with  destructive  violence  ;  hence  our  chief  care 
is  to  avoid  this  Focus.  The  Focus  of  t'^ese  Meteors  can  be  easily  ascertained  from  the  direction  in  which 
the  Hurricane  Wind  is  blowing  at  thr  time,  and  also  points  out  on  which  side  of  the  Storm  Circle  the  Ship 
is.  Suppose  the  Ship  to  have  entered  the  Storm,  and  has  the  wind  at  East,  Barometer  29,  and  falling. 
The  Rule  is.  Turn  your  back  to  the  Wind,  and  the  Left  hand  will  point  to  the  Focus,  bearing  South,  and 
by  referring  to  the  Diagram  on  the  next  page,  it  will  be  perceived  that  the  Ship  is  on  the  Northern  verge. 
Now,  if  a  Ship  is  to  the  Eastward  of  the  West  India  Islands,  by  standing  to  the  Northward  she  will 
get  out  of  its  range ;  or  by  heaving  to  on  the  Port  Tack,  with  her  head  to  the  Southward,  (in  the  direction 
of  the  Focus,)  the  wind  as  it  veers  from  right  to  left  will  be  found  to  draw  aft,  and  the  Ship  will  luff  up., 
and  Bow  the  Sea  with  safety.  But  heaving  to  on  the  opposite  tack  would  ensure  her  destruction.  Because 
the  wind  veering  would  head  the  Ship  off,  and  she  would  be  laid  in  the  trough  of  the  Sea ;  and  in  such 
cases  the  violence  of  the  wind  is  so  great  that  to  woai  round  on  the  other  tack  would  be  found  to  b« 
impossible.  The  effect  on  a  Ship  standing  to  the  Southward  with  this  Easterly  wind,  would  be  a  fall  of 
the  Barometer  and  an  increase  of  the  Storm  ;  and  as  long  as  she  carries  sail  she  is  rushing  towards  the 
Focus,  and  almost  certain  destruction.  The  most  dangerous  part  of  this  Storm  Circle  is  Us  Weatem 
aide.  You  will  then  have  the  wind  at  North.  By  turning  your  back  to  the  Wind,  your  left  hand  pointa 
to  the  East,  and  which  is  the  bearing  of  the  Focus.  Now,  as  the  Meteor  in  this  locality  is  travelling 
to  the  Westward,  it  is  evident  it  will  overtake  the  Ship  in  its  course,  unless  she  gets  out  of  its  path. 
The  Rule  in  this  case  is,  to  bear  away  under  what  sail  the  vessel  can  carry  towards  the  South  East, 
and  then  to  heave  to  on  the  Port  Tack,  allowing  the  Meteor  to  pass  to  the  North  West  of  her. 

As  before  mentioned,  the  path  of  these  Hurricanes,  after  leaving  the  limits  of  the  North  East  Trade 
Wind,  is  towards  the  North  East,  and  a  Ship  having  the  wind  at  East,  the  Focus  would  bear  South 
as  before,  and  the  Ship  is  ihen  on  the  Northern  verge  af  the  advancing  Storm.  Now,  by  steering 
about  50  miles  to  the  North  West,  and  then  heaving  to  on  the  Port  Tack  aa  before,  the  Meteor  will 
pesa  to  the  Eastward  of    her,  and  when    the  wind    has  veered  to  the  North    East   ahe    will  hare  tbe 


12 


HURRICANES  IN  NORTH  LATITUDE. 


Focus  bearing  South  East,  and  be  at  right  angles  lo  Us  path.  But  if  this  cannot  be  done  on  account  of 
her  proximity  lo  the  land,  heave  to  on  the  Port,  Tack.  Advantage  of  gaining  an  offiing  at  the  com- 
mencement  of  the  Storm,  when  the  wind  is  at  South  or  South  East,  may  be  done  by  running  off  to 
the  Eastward  as  long  as  sail  can  be  carried,  and  then  Wearing  Ship,  heave  to  on  the  Port  Tack,  and 
by  that  means  the  Focus  will  pass  to  the  Westward  of  her  position.  But  crossing  in  front  of  the  advancing 
Storm  is  always  attended  with  danger  because  the  Ship  may  be  taken  aback  before  she  gets  to  the 
Eastward  of  its  path. 

The  Barometer  should  be  carefully  watched  when  in  the  vicinity  of  those  Latitudes  where  Hurricanes 
may  be  expected,  and  when  it  falls  rapidly  to  29.50,  the  weather  threatening,  and  the  clouds  of  a  bluish, 
gloomy  appearance,  the  Ship  is  then  on  the  verge  of  the  Storm  Circle,  and  the  Focus  may  be  at  least 
150  miles  distant.  As  the  Focus  is  approached  the  Barometer  will  fall  to  29.20  inches  at  100  milog 
distant;  to  28.40  at  about  50  miles  distant,  and  to  28.00  at  about  30  miles  distant.  At  or  near  tlkt 
FocuB  itself  it  falls  as  low  as  27.00  inches  sometimes 


DIAGRAM  17  THE  STORM  ClR^Tic  ^^  NORTH  LATITUDE. 

Fig.  1&. 


RULES  TO  AVOID  THE  FOCUS 
Turn  your  back  to  the  Wind,  and  your  Left  hand  will  point  to  the  Focus. 


ifncrioaji*  Wind. 


V¥"ind  at  East 
"       N.  E. 

North. 

N.  W. 

West. 

S.  W. 
"       South. 
"       S.  E. 


Bearing  of  the  Focus. 


Focus  South. 
"       S.  E. 

East. 
"       N.  E. 

North. 
"       N.  W. 

West. 
"       R.  W. 


When  the  Path  is  to  the  W.N.  W. 


Heave  to  on  the  Port  Tack. 

do.  do. 

Run  50  m's  to  the  S'd,  and  heave  to 

Heave  to  on  the  Port  Tack. 

do.  do.  do. 

do.  do.  do. 

do.  do.  do. 

do.  (In.  do. 


When  the  Path  is  to  the  N.  E. 


See  the  remarks  above. 
Heave  to  on  the  Port  Tack. 

do.  do.  do. 

do.  do.  do. 

do.  do.  do. 

do.  do.  do. 

Get  a  little  to  the  E'd  if  possible.^  heave  to 

Run  50  miles  to  the  N.  W.,    aud  heave  to 


nURRI  CANES. 


4» 


HURRICANES  TN  SOUTH  LATITUDE 

The  Harricanes  in  the  South  Atlamio  Ocean  commence  near  the  Southern  Jimits  of  the  S.  E.  Trade 
W^ind,  to  the  Eastward  of  the  Island  of  Mauritius,  and  pursue  a  course  to  the  Westward.  They  are  gen- 
trally  expected  in  the  months  of  February  or  March.  The  diameter  of  these  Meteors  vary  from  150  to 
300  miles,  and  their  rate  of  progression  is  from  12  to  30  miles  an  hour.  The  distinctive  features  of  these 
Hurricanes  are,  that  the  wind  blows  in  a  circle,  around  a  focus,  from  left  to  right  (or  the  right-handed  way 
at!  seamen  call  it),  consequently  the  Rule  for  finding  the  focus  of  the  Hurricane  in  South  Latitude  is  to 
urn  your  back  to  the  Wind,  and  the  right  hand  will  point  to  the  centre.  Those  in  the  Bay  of  Bengal  and 
Ohina  Seas  being  in  North  Latitude,  revolve  the  left-handed  way,  sam«  as  in  the  North  Atlantic.  So  that 
in  meeting  one  of  these  Hurricanes,  it  must  be  considered,  in  the  first  place  whether  the  Ship  is  in  North 
01  South  Latitude,  and  then  to  act  accordingly.  If  the  Ship  is  in  South  Latitude,  the  rule  is  to  heave  to 
on  the  Starboard  Tack,  with  her  head  towards  the  Focus ;  and  supposing  the  Wind  at  East,  the  right  hand 
will  point  to  the  Focus  bearing  North.  The  Ship  would  then  be  on  the  Southern  verge  of  the  Storm  Circle, 
and  as  the  Vind  veers  to  the  Southward  she  will  luff  up  and  bow  the  sea.  The  Barometer  acta  in  a  aim> 
iiar  manner  as  before  stated. 

DIAGRAM  OF  THE  STORM  CIRCLE  IN  SOUTH  LATITUDE. 

Fig.   19. 


RULES  TO  AVOID  THE  FOCUS. 
Dim  your  back  to  the  Wind,  and  your  Right  hand  will  point  to  the  Focus. 


HaiTioun*  Wind. 


Wbd  at  "West. 

N.  W. 

North.. 

N.  E. 
•  East 

&E. 
"  South. 

S.  W. 


Bearing  of  the  Focus. 

Focus  bears 

South. 

t(          II 

S.  W. 

II                   u 

West 

II              II 

N.  W. 

11                   u 

North. 

U                      41 

N.  E. 

U                      II 

East 

U                     M 

S.  E. 

When  th«  Path  is  to  the  W.  S.  W. 


Heave  to  on  the  Starboard  Tack, 
do  do 

do  do 

do  do 

de  do 

Run  50  miles  to  N.  W.  and  heave  to. 

Heave  to  on  the  Starboard  Tack, 
do  do 


When  the  Path  i»  to  the  5.  B 


Heave  to  on  the  Starboard  Tack. 

do  do 

do  do 

Run  50  miles  to  the  S.  W.  and  heave  to, 

Heave  to  on  the  Starboard  Tack, 
do  do 

do  do 

do  do 


Jk"'    a^  Hurricanes  in  the  Sonlh  Atlantic,  after  leaving  the  Latitude  of  80*  S.  recurve  to  the  S.  E. 

■g  these  Horncanes  in  a  higher  Latitude  would  be  in  their  direct  path,  when  she  has  the  Wind  at  N.  E.,  becaose  o» 
■iraine  your  back  to  the  Wind,  the  right  hand  will  point  to  the  Focus  bearing  N.  W.,  and  ita  path  being  8. 1  ~- 
•▼•ruke  her  unless  she  gets  out  of  its  way  by  running  off  50  mile»  to  the  S.  W. 


A  Ship  mevW 
>o» 

wir 


44  HURRICANES. 

REMARKS  ON  HURRICANES.  • 

The  following  remarks  on  handling  a  Ship  in  a  Hurricane,  may  be  found  useful :  When  a  Ship  iaj 
approaching  the  locality  of  Hurricanes,  the  Barometer  should  be  carefully  watched,  and  when  it  ha«  fallen] 
rapidly  from  about  30  inches  to  29  20,  the  Ship  is  then  on  the  verge  of  a  Storm  Circle  At  the  same  time! 
■the  weather  will  appear  threatening,  with  heavy,  bluish-looking  clouds  in  the  sky.  At  other  times,  it  sett] 
in  with  small  rain,  and  the  Wind  increases  gradually.  Now  is  the  time  to  consider  which  side  of  the] 
Storm  Circle  the  Ship  is  on,  from  the  direction  in  which  the  Wind  is  theu  blowing,  by  the  rules  already] 
.given  for  that  purpose. 

The  most  severe  Hurricanes,  especially  those  in  the  Indian  Ocean  and  China  Seas,  generally  give  notic«] 
«f  their  approach  by  the  rapid  falling  of  the  Barometer  about  an  inch,  when  no  other  indications  in  the] 
••ky  are  visible,  at  from  12  hours  to  48  hours  before  the  verge  of  the  Storm  reaches  the  Ship.  And  in  this} 
«ase  no  time  should  be  lost  in  preparing  the  Ship  to  encounter  it,  by  sending  down  on  deck  all  the  light] 
spars  and  rigging,  and  the  studdmg-sails  out  of  the  tops,  rigging  in  the  flying-jib  and  standing-jib  booms,] 
securing  the  boats  and  hatchways,  and  the  sails  (which  are  furled  to  the  yards)  with  double  gaskets,] 
•because  after  the  Hurricane  sets  in,  the  violence  of  the  Wind  is  so  great  that  it  will  be  found  impossible] 
for  men  to  go  aloft  or  to  do  any  work  whatever.  Upon  the  same  principle  the  Ship's  place  in  the  Storm  j 
•Circle  should  be  ascertained  as  soon  as  possible,  and  arrangements  made  for  her  safety  by  running  out  of 
its  path,  if  necessary,  before  the  wind  has  increased  to  that  degree  that  no  sail  can  withstand,  or  to  heave] 
•to  on  the  proper  tack. 

Instances  have  been  known  of  Ships  getting  into  the  Storm  Circle,  and  been  obliged  to  scud  before  the] 
Wind  under  bare  poles,  and  changing  their  Course  as  the  Wind  veered,  and  have  been  kept  scudding  round] 
4he  Focus  tor  several  days  together,  and  only  got  liberated  after  the  Meteor  had  spent  itself,  and  found  them- 
selves several  hundreds  of  miles  to  the  Westward  of  where  they  had  entered  it. 

A  Transport  Ship,  with  troops  on  board,  from  Ceylon,  bound  to  the  Island  of  Mauritius,  fell  in  with  one  ] 
^of  those  Hurricanes  on  the  26th  of  March.     At  midnight  the  Barometer  had  fallen  to  28.90.     Wind  blow 
ing  hard  at  West.     And  the  captain,  not  being  acquainted  with  the  theory  of  storms,  the  Ship  was  kept] 
on  her  course  to  the  S.  S.  W.  50  miles,  and  next  day  the  centre  of  the  Hurricane  burst  upon  her,  and  threw 
ter  completely  on  her  beam  ends.     All  three  masts  went  by  the  board,  and  she  righted  a  little.     The 
wreck  of  the  masts  alongside  knocked  off  her  rudder,  and  caused  her  also  to  leak  badly ;  and  so  severe  was 
the  Hurricane  and  sea  that  the  men  were  frequently  washed  from  the  pumps,  the  Ship  laying  all  the  time 
m  the  trough  of  the  sea,  and  her  decks  were  continually  swept.     For  three  days  this  Hurricane  continued, 
jind  during  all  that  time  the  hatches  had  to  be  kept  carefully  closed  to  prevent  her  going  down.     And  when) 
the  storm  abated  so  that  the  hatches  could  be  raised  a  little,  14  of  the  soldiers  were  found  dead  by  suftoca- 
Uon  from  the  want  of  fresh  air  in  the  hold. 

Now  there  is  not  a  shadow  of  a  doubt  but  this  was  caused  by  the  ignorance  of  the  captain,  in  allowing] 
the  Ship  to  stand  on  to  the  S.  S.  W.  50  miles,  after  the  Barometer  had  fallen  to  28.90,  and  which  placed 
<hei  rigiit  in  the  centre  of  the  Hurricane. 

By  referring  to  the  Diagram  for  South  Latitude,  it  will  be  seen  that  with  the  Wind  at  West,  the  Ship] 
would  be  on  the  Northern  verge  of  the  Storm  Circle,  and  the  rule  applied,  of  turn  your  back  to  the  Wind] 
*nd  the  right  hand  points  to  the  centre.  The  right  hand  in  this  case  points  to  the  South,  and  which  was  I 
the  course  the  vessel  steered  for  50  miles,  which  brought  her  into  the  centre  of  the  Hurr^.'ane.  Now  it  may] 
be  pointed  out  how  she  not  only  could  have  escaped  all  this  disaster,  but  actually  to  La.  ye  made  a  fair  wind 
•out  of  part  of  this  Hurricane,  as  follows  :  Suppose  her  to  have  run  off  E.  N.  E.  or  East  with  her  Westerly  I 
Wind^  until  she  raised  her  Barometer  to  29.20,  which  she  would  have  quickly  done.  She  might  then  havaj 
hauled  gradually  to  the  Southward  as  the  Wind  veered  to  the  North  and  N.  E.,  and  thus  pass  round  behind 
or  to  the  Eastward  of  the  storm,  and  as  the  Meteor  was  advancing  at  the  rate  of  perhaps  30  miles  an  hour] 
to  the  W.  S.  W.  it  would  have  soon  passed  her  locality. 

At  all  events,  by  sacrificing  say  150  miles,  by  running  out  of  her   course  to  the   Eastward,  she  would  i 
^lave  sooner  got  clear  of  it  and  without  damage.     Or  by  heaving  to  at  once  with  her  head  to  the  Southward] 
on  the  starboard  tack,  when  the  Barometer  had  fallen  to  29.30,  she  would  then  have  been  on  the  outer 
•verge  of  the  Storm  Circle,  and  allowed  the  storm  to  pass  by  her. 

The  path  of  the  Hurricanes  in  the  N.  Atlantic  Ocean  being  near  the  coast  of  America,  the  same  advan- 
tage (that  is,  to  get  behind  the  storm;  is  not  always  practical  for  the  want  of  sea  room  to  perform  the 
•necessary  evolu;  ons  in.  But  supposing  a  case  of  a  Ship  falling  in  with  a  Hurricane  to  the  Eastward  of 
the  West  India  Islands,  when  bound  to  the  Northward.  The  Barometer  has  fallen  rapidly  to  29  inches. 
Wind  at  West  Under  close  reefs.  Apply  the  rule,  turn  your  back  to  the  Wind,  and  the  left  hand  will 
point  to  the  focus  bearing  North,  in  the  very  direction  the  vessel  is  steering. 

On  referring  to  the  Diagram  for  North  Latitude,  it  will  be  perceived  that  the  Ship  is  on  the  Southern 
verge  of  the  Storm  Circle,  and  the  barometer  at  29  inches  would  place  her  within  60  miles  of  its  centre. 
Now,  as  before  observed,  if  she  has  sea-room,  she  may  not  only  escape  the  effects  of  the  storm,  but  make  a 
fair  Wind  out  of  part  of  this  Hurricane  by  running  off  to  the  Eastward  with  her  Westerly  Wind,  until  the 
Barometer  rises,  which  it  will  soon  do,  to  29.20.  She  may  then  haul  gradually  to  the  Northward  as  the 
Wind  veers  to  the  S.  W.  and  South,  and  thus  continue  on  her  course. 

\  Ship  falling  in  with  a  Hurricane  off  the  coast  of  the  United  States,  its  path  being  then  to  the  N.  E., 
4he  same  difficulty  occurs  again,  that  is,  the  want  of  sea-room.  But  suppose  a  case.  A  Ship  bound  to  the 
S.  E.  has  the  Barometer  fallen  rapidly  to  29  inches.  Wind  at  N.  E.  Under  close  reefs.  Now  turn  your 
back  to  the  Wind,  and  the  left  hand  will  point  to  the  Focus  bearing  S.  E.,  distant  about  60  miles,  and  in 
the  very  direction  the  Ship  is  steering,  and  60  miles  more  of  a  run,  will  plunge  her  right  into  its  centre. 

On  referring  again  to  the  Diagram  for  North  Latitude,  it  will  be  perceived  that  the  Ship  is  on  the  North- 
western verge  of  the  Storm  Circle,  and  to  escape  its  effects  and  turn  part  of  it  into  a  fair  Wind,  run  off  to 
the  S.  W.  with  this  N.  E.  Wind,  until  the  Barometer  rises  to  29.20,  which  it  will  soon  do,  and  theu  haul 
^•dually  to  the  S  E.  as  the  Wind  veers  to  N.  and  N  W.,  thus  passing  round  behind  the  Meteor 


MUIUt.j  ANLS.  4j 

The  disxance  which  a  Ship  ■ift-ould  require  to  run  lat  right  angles  to  her  course)  befor*  sns  raised  tlM 
Barometer  to  29.20,  would  probably  be  about  100  miles,  and  which  would  take  her  10  hours  to  perform,  at 
the  rate  of  10  knots  an  houi.  But  she  would  soon  make  up  the  lost  time  when  the  wind  reers  so  iti*t  sbe 
•an  ie.f;*in  her  pi  one.  u>iirN«. 

i»oo  sne  been  hove  to  in  the  first  case  when  the  Barometer  fell  to  29  inches,  with  her  head  to  the  North- 
ward, on  the  Port  tack,  the  Meteor  would  have  passed  to  the  Northward  of  the  Ship  on  its  path  toward* 
the  W.  N.  W.,  and  the  Wind  as  usual  would  have  veered  to  the  S.  W.  and  South,  and  she  would  then  laff 
up  and  bow  the  sea,  but  would  be  kept  perhaps  two  or  three  days  in  the  storm. 

And  in  the  second  case,  by  heaving  to  under  the  same  circumstances,  the  storm  would  pass  to  the  Soath- 
•Mtward  of  the  ship,  on  its  path  towards  the  N.  E. ;  and  the  Wind  veering  to  thn  North  and  N.  W.,  *h» 
would  luif  up  as  before,  but  would  also  be  kept  2  or  3  days  in  the  storm  laiH  *o 


4« 


THE  CONSTRUCTION  AND  USE  OF  MERCATOR'S  CHART. 


A»  the  surface  of  the  Globe  is  round,  while  that  of  the  paper  is  flat,  every  chart  exhibiting  any  extent 
af  surface  is  necessarily  an  artificial  construction,  or,  as  it  is  called,  projection  of  the  real  state  of  things. 

The  Charts  used  in  navigation  are  those  on  Mercator's  Projection,  because  on  this  alone  the  track  of  » 
Ship  always  steering  the  same  course  appears  a  straight  line  ;  and  thus  all  calculations  respecting  the  Lati. 
tude  and  Longitude  of  a  Ship  steering  a  course  which  cuts  all  the  Meridians  at  the  same  angle,  are  reduced 
to  the  utmost  simplicity. 

On  Mercator's  Chart  all  the  Meridians  are  parallel  and  the  degrees  of  Longitude  are  all  equal,  and  of 
the  same  length  throughout,  as  a  degree  of  Latitude  is  on  the  Equator.  The  degrees  of  Latitude  ar* 
unequal,  being  extended  at  each  Latitude  beyond  their  proper  lengths,  in  the  same  proportion  as  the  degree» 
of  Longitude  are  diminished  on  the  Globe  towards  the  Poles. 

The  miles  of  Lati*Tide  are  consequently  increased  towards  the  Poles,  so  that  in  the  Latitude  of  60*  » 
degree  of  Longitude  will  measure  30  of  these  miles  only,  and  near  the  Poles  1  mile  of  Latitude  is  equal !» 
a  degree  of  Longitude. 

TO  CONSTRUCT  A  CHART  ON  MERCATOR'S  PROJECTION. 

Having  first  determined  the  limits  of  the  proposed  Chart,  that  is,  the  number  of  degrees  of  Latitude  and 
Longitude  it  is  to  contain,  and  the  degree  of  each  it  is  to  commence  from,  take  out  the  Meridional  part* 
fi»m  Table  III,  corresponding  to  each  degree  of  Latitude  within  the  intended  limits,  and  find  the  difference 
between  the  Meridional  parts  of  each  succeeding  degree,  or  every  fifth  degree  (if  the  scale  is  small.) 
Reduce  the  difference  of  the  Meridional  parts  into  degrees  by  dividing  them  by  60.  Draw  a  line  at  tb» 
bottom  margin  of  the  paper,  to  represent  the  parallel  of  the  least  Latitude,  on  which  lay  off  the  proposed 
•Bmber  of  Degrees  of  Longitude,  taken  from  a  scale  of  equal  parts,  or  the  space  to  be  occupied  by  the  Lon- 
gitude can  be  divided  into  equal  parts.  Draw  another  line  at  the  top  margin  parallel  to  the  bottom  one, 
and  divide  it  also  into  the  like  number  of  equal  parts.  This  top  line  or  parallel  of  Latitude  must  bedraw» 
at  a  distance  from  the  bottom  one  equal  to  the  Meridional  Difference  of  Latitude  between  the  extreme  Lat- 
itude!, taken  from  the  scale  of  Longitude,  which  must  previously  be  graduated  to  Degrees  and  Minutes. 

Take  the  Meridional  Difference  of  Latitude  between  the  least  Latitude  and  the  next  fifth  degree,  froni> 
.he  graduated  scale  of  Longitude,  and  lay  it  oflf  on  both  sides  from  the  parallel  of  least  Latitude  upwards, 
and  draw  the  parallel  of  Latitude  line  for  that  degree.  In  like  manner  lay  off  the  next  fifth  degree,  and 
draw  its  parallel  of  Latitude,  and  draw  the  Meridians  through  every  fifth  degree  of  Longitude  at  top  and 
bottom. 

Draw  Compasses,  showing  the  Rhumb-lines  at  convenient  places  on  the  Chart,  and  the  principal  point* 
•f  the  coasts  are  then  laid  down  according  to  their  Latitude  and  Longitude,  and  the  coast-line  filled  in  by 
hand.     The  variation  of  the  Compass,  and  other  matters  that  are  usually  inserted,  are  then  introduced. 

EXAMPLE. 

Required  to  construct  a  Chart,  extending  from  29  degrees  West  Longitude  to  60  degrees  West  Longitude  fio» 
<*reenwich,  and  from  the  Equator  to  50  degrees  North  Latitude. 

Take  out  the  Meridional  parts  for  every  fifth  degree  with  their  Difference  as  follows : 
Latitudes.         Merid.  Parts.         Differences. 

5*  300  300  — 

10  603  SOS  — 

15  '  910  307  — 

20  1226  316  — 

25  1650  325  — 

80  1886  338  — 

36  2244  S66  — 

40  2623  379  — 

46  3030  407  — 

60  S474  444  — 

Divide  the  bottom  line  into  40  equal  parts,  which  will  represent  the  Degrees  of  Longitude  on  the  Equat<v.  F«rm« 
«  Saale  of  miles  00  to  the  Degree;  take  the  first  Difference  5°  O'  in  the  Compasses,  and  lay  it  off  from  the  Eqoato* 
•m  both  sides,  and  draw  the  parallel  of  5*  ;  from  this  parallel  lay  off  the  next  Difference  6*  3'.  and  so  on 


5' 

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6 

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6 

7 

6 

16 

5 

25 

6 

88 

6 

66 

6 

19 

6 

47 

7 

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CONSTRUCTION  Ot  MEftCATOR'S  CHART.  49 

TO  CONSTRUCT  A  PARTICULAR  CHART  ON  A  LARGE  SCALE. 

When  the  Chart  does  not  oommenoe  at  the  Equator,  bat  is  to  serve  for  a  portion  of  a  coast  contained 
between  two  parallels  of  Latitude  on  the  same  side  of  the  Equator,  draw  a  line  at  the  bottom  margin  of  th« 
caper,  to  represent  the  least  parallel  of  Latitude. 

Divide  the  given  inches  to  the  Degree,  (according  to  the  scale  required,)  into  60  equal  parts,  -which  yriV 
wpresent  miles  of  Latitude. 

Now  enter  the  Traverse  Table  with  the  least  Latitude  as  a  Course,  and  find  the  length  of  a  Degree  of 
Longitude  in  that  parallel ;  that  is,  take  60  minutes  of  Longitude  in  the  Distance  Column,  and  in  th** 
Latitude  Column  wU  be  found  the  length  of  the  Degree  of  Longitude,  in  miles. 

Take  this  length  of  the  Degree  of  Longitude  in  the  dividars  from  the  scale  of  miles  of  Latitude,  and  la> 
■off  on  the  bottom  margin  line  as  many  Degrees  of  Longitude  as  required  in  the  Chart,  and  divide  each  into 
•60  equal  parts,  and  draw  Meridians  at  each  side. 

Enter  Table  III.,  and  take  out  the  Meridional  parts  for  each  Latitude,  beginning  with  the  least  Latitude^ 
and  take  the  Differ,  between  that  and  the  next  greater.  Take  this  Meridional  Difference  of  Latitude  in  the 
-dividers  from  the  graduated  Scale  of  Longitude,  and  lay  it  off  on  each  Meridian  from  the  bottom  margin 
line,  or  least  parallel  of  Latitude,  and  draw  the  next  greater  parallel  of  Latitude.  From  this  last  parallel 
of  Latitude  lay  off  the  Meridional  Difference  of  Latitude  between  that  and  the  next,  and  draw  the  next 
parallel  of  Latitude,  and  so  on,  to  the  extent  required.  Divide  the  greatest  parallel  of  Latitude,  at  the 
top,  into  the  same  number  of  Degrees  and  Minutes  of  Longitude  as  at  the  bottom  margin,  and  draw  Merid- 
ians through  each  Degree  of  Longitude,  and  number  the  Degrees  of  Longitude  (whenever  the  Latitude  ie 
North  of  the  Equator,  and  the  Longitude  West  from  Greenwich,)  from  Right  to  Left,  and  vice  versa. 

When  the  Chart  is  to  be  bounded  by  Parallels  of  Latitude  on  different  sides  of  the  Equator,  to  the  extent 
of  a  feif  Degrees  only,  the  Degrees  of  Latitude  and  Longitude  being  of  the  same  length,  we  first  draw  the 
Equator  and  lay  off  the  Degrees  of  Latitude  (according  to  the  scale  required)  North  and  South  of  it,  and 
draw  the  Parallels  of  Latitude.  The  Degrees  of  Longitude  on  the  Equator  are  then  made  of  the  same 
length,  and  the  Meridians  drawn  as  before.  This  is  called  a  Plane  Chart,  and  can  only  be  thus  constructed 
oear  the  Equator.  Having  thus  drawn  and  graduated  the  Parallels  of  Latitude  and  the  Meridians  of  Lon- 
gitude, the  Latitudes  and  Longitudes  of  places  are  laid  down,  and  the  coast-lines  sketched  by  hand.  Rocks 
and  shoals  are  then  inserted,  with  the  depth  of  water  at  low  water,  spring  tides,  the  setting  of  the  tides, 
the  tmies  of  high  water,  full  and  change,  variation  of  the  compass,  &o. ;  and  one  or  more  Compasses  are 
uis<«rted  in  the  most  convenient  parts  of  the  Chart. 

EXAM?L3. 

Required  to  eoDBtruet  a  Chart  between  the  Latitudes  of  40*  and  43*  North  and  the  Lozgitude  of  69*  and  li 
West 'from  Greenwich,  on  a  Scale  of  2  inches  to  the  Degree  of  Latitude.    (See  P^.  21.) 

Draw  a  line  at  the  bottom  margin  of  the  paper  to  represent  the  parallel  of  40' ,  take  2  inches  from  the 
Plane  Scale  and  divide  it  into  60  equal  parts,  representing  miles  of  Latitude.  Enter  the  Traverse  Table 
with  Latitude  40*  as  a  Course,  and  60  miles  of  Longitude  in  the  Distance  Column.  Then  in  the  Latitude 
Column  opposite  will  be  found  46  miles,  the  required  length  of  a  Degree  of  Longitude  in  that  parallel  of 
Latitude.  Now  take  this  46  miles  in  the  dividers,  from  the  two  inch  scale,  and  lay  off  3°  of  Longitude, 
divide  them  into  60  miles  each,  and  draw  a  Meridian  line  at  each  side.  Enter  Table  III.,  and  take  oat 
the  Meridional  parts  for  each  Latitude,  beginning  with  the  least,  as  follows  : 

Lat. 

Diff. 7»'— 1*  19' 


40' 

Merid.  Parts . . . . 

do 

do 

do 

2628 

41 

2702 

42 

2782 

•  •  • 

.      ..43 

2863 

.80—1    20 
.81—1    21 


Now  take  1*  19'  in  the  dividers,  from  the  Scale  of  Longitude,  and  lay  it  off  on  the  Meridian  lines  from 
the  narallel  of  least  Latitude,  40*,  and  draw  the  parallel  of  41°.  In  like  manner,  from  tne  parallel  of  41* 
iay  off  1*  20',  and  draw  the  parallel  of  42*,  and  1*  21'  laid  off  will  give  the  parallel  of  44*.  Divide  this 
last  parallel  of  Latitude  into  Degrees  and  Minutes  of  Longitude,  the  same  as  the  parallel  of  40*  at  the 
bottom  margin,  and  draw  the  Merid'an  lines.  Divide  the  Degrees  of  Latitude  into  60  miles  each,  and 
number  the  Degrees  of  Longitude  from  Right  to  Left,  because  the  Longitude  is  West  from  Greenwich. 

Lay  )ff  the  Latitudes  and  Longitudes  of  the  most  prominent  parts  of  the  ComI,  and  fill  in  the  Co««i 
Une  by  hand,  to. 


48 


THE  USE  OF  MEKCATOR'S  CHART. 


TO  PRICK  OFF  THE  SHIP'S  PLACE  ON  THE  CHART. 

Lay  the  edge  of  the  parallel  ruler  along  the  nearest  parallel  of  Latitude  line,  and  move  one  ;f  its  sidot 
ttntilitc  edge  is  over  the  Degree  and  Minute  of  Latitude  required,  and  as  near  as  possible  to  t:.e  required 
Longitude.  Draw  a  pencil  line,  which  will  represent  the  Ship's  parallel  of  Latitude.  Take  the  Longitude 
with  a  pair  of  dividers  from  the  scale,  one  foot  being  on  the  nearest  less  Meridian,  and  the  other  at  the 
Degiee  and  Minute  required.  Then  with  one  foot  on  that  Meridian,  extend  the  other  along  the  Ship's  par- 
allel of  Latitude,  and  mark  the  spot,  which  is  the  Ship's  place  required. 

Or  lay  the  edge  of  the  parallel  ruler  along  the  nearest  less  Meridian  line,  and  move  one  of  its  sides 
until  the  edge  is  over  the  Degree  and  Minute  of  Longitude  required,  and  transfer  the  same  to  the  Ship'* 
parallel  of  Latitude.  Draw  a  pencil  line,  and  at  the  intersection  of  these  two  lines  will  be  the  Slap'* 
place.     (See  Chart,  Fig.  20,  page  46.) 

EXAMPLE. 
Lay  oflf  the  Ship's  position  on  the  Chart,  Latitude  19°  30'  N.  and  Longitude  42°  W. 
The  nearest  less  parallel  of  Latitude  is  15°  ;  a  ruler  on  this,  and   moved  up  to  Latitude  19°  30'  on  th« 
Graduated  Scale,  gives  the  Ship's  parallel  of  Latitude.     Then  with  one  foot  of  the  dividers  on  the  neares 
less  Meridian  of  40*  on  the  Scale  of  Longitude,  and  the  other  extended  to  42°,  transferred  to  the  Ship's  par 
allel  of  Latitude,  points  out  the  Ship's  place. 

This  is  done  at  least  once  every  day  at  noon,  and  being  connected  together  ■vrith  a  pencil  line,  shows  the 
Riip's  track  on  the  Chart  from  day  to  day. 

TO  SHAPE  A  COURSE  ON  THE  CHART. 

Lay  the  edge  of  the  parallel  ruler  over  the  Ship's  place  and  the  place  she  is  bound  to.  Move  the  ruler 
«Ter  the  Chart  until  its  edge  is  placed  over  the  centre  of  the  nearest  Compass,  which  will  give  the  True 
Course.  Then,  if  the  variation  of  the  Compass  is  Westerly,  it  must  be  allowed  to  the  Right  hand  of  this 
True  Course,  but  if  Easterly,  to  the  Left  hand  of  the  True  Course,  will  give  the  Course  required  to  steer  b> 
Compass. 

EXAMPLE  1. 

A  Ship  in  Latitude  19°  SO'  and  Longitude  42*  W.,  is  required  to  shape  a  Course  by  Compass  to  St  Antonio,  one 
•r  the  Cape  Verde  Islands.     (See  Chart,  Fig.  20,  page  46.) 

Lay  the  Ruler  over  the  Ship's  place  and  that  of  the  Island,  and  move  the  edge  of  it  over  the  centre  of 
the  nearest  Compass,  gives  the  True  Course  E.  i  S.  The  variation  of  the  Compass  being  H  points  West- 
erly, which,  allowed  to  the  Right  hand,  gives  the  Compass  Course  required  E.  S.  E. 

EXAMPLE  i. 

Required  the  Course  to  the  mouth  of  the  River  Amazon  from  the  same  positioa 
Lay  the  ruler  over  the  Ship's  place  and  that  of  the  River  Amazon,  and  refer  it  to  the  centre  of  the  Com- 
paas  as  before,  will  give  the  True  Course  S.  S.  W.     The  Variation  being  i  point  Easterly,  which  allowed 
to  the  Left  hand  gives  the  Compass  Course  required  S.  by  W.  i  W. 

TO  MEASURE  THE  DISTANCE  BETWEEN  TWO  PLACES  ON  THE  CHART. 

When  the  places  lie  nearly  North  or  South  of  each  other,  their  Difference  of  Latitude  is  the  Distance 
required.  Extend  the  feet  of  the  dividers  to  the  places,  and  refer  this  extent  to  the  Scale  of  Latitude 
between  the  parallels,  and  count  the  number  of  Degrees  and  Minutes  contained,  which  multiplied  by  60  (and 
taking  in  tJie  odd  Minutes'  will  be  the  Distance  required. 

EXAMPLE  1. 

Required  the  Bearing  and  Distance  of  St.  Mary,  one  of  the  Western  Islands,  from  St  Antonio,  one  of  the  Cape 
?^erde  Islands,  both  Islands  being  on  the  same  Meridians. 

Answer. — The  True  Bearing  is  North,  and  2  points  Westerly  variation  allowed  to  the  Right  hand  givee 
the  Bearing  by  Compass  N.  N.  E.  The  extent  of  their  Distance  in  the  dividers,  and  applied  to  the  Scale 
•f  Latitude  from  the  parallel  of  17*  12'  N.  to  36*  59'  N.,  contains  19*  47',  which  multiplied  by  60  gives 
tb«  True  Distance  1187  miles. 


USK  OF  MEIfCATOR'S  CHAFtT.  4y 

When  the  places  lie  nearly  Easi  or  West,  or  on  the  same  parallel  of  Latitude,  extend  j^t  feet  of  tha 
dividers  betweei?  the  placets,  and  refer  tins  extent  to  tlie  Scale  of  Latitude,  holding  the  centre  or  joint  of 
the  dividers  directly  over  their  parallel  of  Latitude,  so  that  each  foot  may  reach  to  equal  distances  from  it 
Count  the  number  of  Degrees  and  Minutes  contained  between  the  feet  of  the  dividers,  which  multiply  by 
60,  (and  taking  in  the  odd  Minutes)  will  be  the  Distance  required.  But  if  the  Distance  is  too  great  for  the 
dividers,  take,  say  10°  from  the  scale  (5°  on  each  side  of  the  parallel  of  Latitude)  find  how  many  times 
this  extent  of  10°  can  be  obtained  between  the  places.  Then  contract  the  dividers  and  measure  tha 
remainder,  holding  the  centre  of  the  dividers  over  the  parallel  of  Latitude  as  before,  a«d  count  the  number 
of  Degrees  and  Minutes  they  contain.  Add  this  to  the  number  of  tens  of  degrees  already  measured,  which 
multiplied  by  60  (and  taking  in  the  odd  Minutes)  will  give  the  Distance  required. 

EXAMPLE  2.    , 

Required  the  Bearing  and  Distance  of  the  Island  of  Barbadoes  from  the  Isle  of  Brara,  one  of  the  Cape  Verda 
blands,  in  nearly  the  same  parallel  of  Latitude. 

Answer. — The  True  Bearing  is  W.  i  S.,  and  i^  a  point  Westerly  variation  allowed  to  the  Right  hand, 
gives  the  Compass  bearing  W.  i  N.  The  distance  being  too  great  to  be  measured  at  one  time,  take  10°  in 
the  dividers,  5  on  each  side  of  the  parallel  of  Latitude,  and  with  one  foot  of  the  dividers  on  Brava,  it  will 
take  3  times  this  extent,  or  30°,  to  reach  near  to  Barbadoes.  Then  the  remainder  of  the  distance  taken  in 
the  dividers,  will  be  found  to  measure  4°.  Total  34° ;  which  multiplied  by  60,  gives  the  Distance,  2040 
miles.  ' 

When  the  places  lie  obliquely,  neither  being  in  the  same  Latitude  or  Longitude. 

Find  the  Middle  Latitude  between  the  places.  Take  the  distance  between  them  in  the  dividers,  and 
refer  it  to  the  graduated  Scale  of  Latitude,  holding  the  centre  or  joint  of  the  dividers  directly  over  the 
Middle  Parallel  of  Latitude,  so  that  each  foot  may  reach  to  an  equal  distance  from  it,  and  count  tha 
Degrees  and  Minutes  contained  in  the  dividers,  and  proceed  as  before.  But  if  the  Distance  be  too  great  to 
be  taken  in  the  dividers,  take  an  equal  number  of  degrees  on  each  side  of  the  Middle  Parallel  of  Latitude, 
and  proceed  as  in  the  last  Example. 

EXAMPLE  8. 

Required  the  Bearing  and  Distance  of  St  John's,  Newfoundland,  from  St  Antonio,  one  of  the  Cape  Verde  Islands 

Answer. — The  True  Bearing  is  N.W.  i  N.,  and  2  points  of  Westerly  variation  allowed  to  the  Right  hand, 
gives  the  Compass  bearing  N.  by  W.  i  W.  The  Middle  Parallel  of  Latitude  is  32°.  Take  10°  in  the 
dividers,  that  is,  5  on  each  side  of  32°,  from  the  Scale  of  Latitude,  and  with  one  foot  on  St.  Antonio,  3 
times  this  extent,  or  30°,  will  reach  short  of  St.  John's.  The  remainder  of  the  Distance  taken  in  tha 
dividers,  middled  again  at  32°,  will  give  9°  more,  or  39°,  which  multiplied  by  60,  gives  the  Distance 
required,  2340  miles.     (See  Chart,  Fig.  20,  page  47.) 

THE  COURSE  AND  DISTANCE  GIVEN,  TO  FIND  THE  LATITUDE  AND  LONGITUDE  IN. 

Allow  the  variation  on  the  Compass  Course  steered  to  the  Left  hand,  if  the  variation  is  Westerly,  but 
to  the  Right  hand  if  Easterly,  will  give  the  True  Course.  Lay  the  edge  of  the  parallel  ruler  over  the 
centre  of  the  nearest  Compass  on  this  Course,  and  transfer  it  to  the  Ship's  place  of  departure,  and  draw 
a  pencil  track.  Take  the  Distance  run  from  the  Scale  of  Latitude,  middled  on  the  Middle  Parallel  of 
Latitude  the  Ship  has  sailed  in.  and  lay  it  off  on  the  track,  which  will  be  the  Ship's  place.  Take  the 
Distance  in  the  dividers  between  it  and  the  nearest  less  Parallel  of  Latitude  line,  and  refer  it  to  the  Scale 
of  Latitude,  will  give  her  Latitude  in.  In  like  manner,  take  the  Ehstance  between  the  Ship's  place  and 
Jhe  nearest  less  Meridian  line,  and  refer  it  to  the  Scale  of  Longitude,  will  give  her  Longitude  in. 

EXAMPLE. 

A  Ship  from  Barbadoes  sails  N.  K  by  Compass  300  miles.  Variation  of  the  Compass  J  a  point  Easterly 
Required  her  Latitude  and  Longitude  ia 

Answer. — The  True  Course  is  N.  E.  i  E. ;  the  variation  being  allowed  to  the  Right  hand,  because  it  la 
Easterly,  and  the  Distance,  300  miles,  or  5°,  taken  in  the  dividers,  from  the  Scale  of  Latitude,  to  the  North- 
ward of  the  Parallel  of  Barbadoes,  and  laid  off  on  this  N.  E.  i  E.  Track,  will  give  the  Ship^s  place.  The 
learest  less  Parallel  of  Latitude  line  is  15°.  A  parallel  ruler  laid  on  this  line,  and  moved  up  to  the  Ship'a 
place,  and  then  referred  to  the  Sale  of  Latitude,  will  give  her  Latitude  in,  16*  20'  N.  The  nearest  less 
Meridian  line  is  55°,  and  the  Difference  in  like  manner  referred  to  the  Scale  of  Longitude,  gives  her  Lon. 
gitude  in,  55°40'  West.  Or  the  Latitude  may  be  ascertained  by  taking  the  Difference  between  the  Ship's 
place  and  the  nearest  less  parallel  of  Latitude,  15°,  in  the  dividers,  and  applying  it  to  the  Scale  of  Latitude, 
gives  her  Latitude  in,  16°  20'.  And  in  like  manner  the  Longitude  is  found  by  taking  the  Difference 
between  the  Ship's  place  and  the  nearest  less  Meridian  line,  15°,  in  the  dividers,  and  applying  it  to  the  Sealt 
•1  Longitude,  gives  the  Longitude  in,  55'  40'  W. 


50 


USE  OF  THE  COASTING  CHART 


To  fina  the  Ship's  Position  from  the  Latitude  Observed  and  the  Bearing  of  the  Land  by  Compass 

Roi.K. — Place  the  edge  of  the  ruler  along  the  nearest  less  Parallel  of  Latitude  line,  and  moTe  it  up  to  the  requii  < 
«»ne  on  the  Scale  of  Latitude,  and  draw  a  pencil  line,  which  will  be  the  Ship's  Parallel  of  Latitude.  Correct  thJ 
''Compass  bearing  by  allowing  the  Variation  as  before  directed,  whieh  will  give  the  True  Bearing  of  the  object  PlaoJ 
'th«  edg«  of  the  ruler  over  the  centre  of  the  nearest  Compass,  and  transfer  this  True  Bearing  to  the  object  by  moviug 
•the  ruler  until  its  edge  is  placed  over  it,  and  draw  a  pencil  line,  and  where  this  line  cuts  the  Ship's  Parallel  of 
liEtitude  is  the  Ship's  place.     By  this  means  her  Longitude  in  and  Distance  off  the  object  is  ascertained. 

EXAMPLK 

A  Ship  obeerred  her  Latitude  to  be  40°  45'  N.  At  the  same  time  Moutauk  Point  Light  House  bore  by  Conipiu 
F.  W.  J  N.  Variation  J  point  Westerly.  Required  her  Distance  off  the  Point  and  her  Longitude  in.  (See  Chart 
Fig.  21,  page  47.) 

Answer. — Having  drawn  the  Parallel   of  Latitude  line  of  40*  43'  N.,    allowing  the  variation  on   tlr 
Compass  bearing,  gives  the  true  bearing  N.  W.     A  line  drawn  in  that  direction  from  Montauk  Point  inter-] 
•^scts  the    Parallel  of  Latitude    and   gives  the  Ship's  place.       Her  Distance  off  being    30  .-nilei.  and  he 
Longitude  in  71°  22'  W. 

To  find  the  Ship^s  Position  from  the  Cross  Bearing  of  two  Objects  on  the  Land. 

RaiA — Take  the  Bearings  by  the  Compass,  and  correct  them  for  the  Variation,  as  before  directed,  which  will  giv« 
<<th«  True  Bearings.     Place  the  edge  of  the  ruler  over  the  centre  of  the  nearest  Compass,  and  transfer  thi*  Tt 
Bearing  to  the  objects.     Draw  pencil  lines  from  each,,  and  where  they  cross  each  other  is  the  Ship's  place. 

EXAMPLE. 

Montauk  Point  bore  N.  W.  J  N,  and  the  East  end  of  Block   Island  N.  N.  E.  f  E.      Variation  i  point  We«t«rlyJ 
Required  the  Distance  off  each  object,  and  the  Latitude  and  Longitude  ia 

Answer. — The  True  Bearing  of  Montauk  Point  is  N.  W.  and  Block  Island  N.  N.  E.      The  former  is  1  ll 
<miles,  and  the  latter  14  miles  distant  from  the  Ship.     Latitude  in  40°  56'  N.  and  Longitude  in  71*  40'  W.I 

Having  the  Ship^s  Correct  Position  from  Cross  Bearings,  to  Shape  a  Course  along  Shore,  or  to  clear  a  ShoalA 

or  other  Danger.     (See  Chart.  Fig.  21,  page  47.) 

Rdli. — Place  the  edge  of  the  ruler  over  the  Ship's  place,  and  in  a  direction  which  will  lead  the  Ship  clear  of 
danger,  move  the  ruler  along  and  place  its  edge  over  the  centre  of  a  Compass,  which  will  give  the  True  Course. 
Then,  if  the  variation  is  Westerly,  allow  it  to  the  Right  hand  of  this  True  Course,  will  give  the  Compass  Courss 
'  required  to  steer ;  but  if  the  variation  is  Easterly,  allow  it  to  the  Left  hand  of  the  True  Course. 

EXAMPLR  , 

Required  to  shape  a  Course  from  the  position  found   by  Cross  Bearing  in  the  last  Example,  so  as  to  pass  clear 
iirough  midway  between  Nantucket  and  its  Shoals,  and  the  Distance  to  run  until  abreast  of  the  New  8outh  Sht*! 

Answer. — The  True  Course  to  pass  midway  is  E.  J  N.  The  variation  5-  of  a  point  to  the  Right  £;ive» 
•thft  Compass  Course,  East.  The  Distance  to  the  South  Shoal  in  the  dividers,  and  middled  on  ihe  i'arallel 
•of  Latitude,  41*^  gives  the  Distance  off,  80  miles. 

The  Latitude  by  Observation  and  Soundings  given,  to  find  the  Ship's  Position. 

Ruts. —  Place  the  ruler  on  the  nearest  Parallel  of  Latitude  line,  and  move  it  up  to  the  required  Lautude,  aad 
•draw  a  pencil  hue,  which  will  represent  the  Ship's  Parallel  of  Latitude.  Then  where  the  Soundings  <>ht>ihi«  J  are 
<fciind  to  agree  with  that  laid  down  in  the  Chart,  is  the  Ship's  place 

EXAMPLE. 

A  Ship,  In  the  Parallel  of  Latitude  of  Neverwnk  by  observatioo,  40*  it'  K.,  Sounded  in  «0  fathoms  crater 
^fUquirea  her  Lon^tude  in  and  DistanM  off 

Answer. — Her  Longitude  in  at  the  time  of  Sounding  was  7i*  20'  W.,  and  her  Distance  otf  the  Hiijh 
Itimd  of  Noversink  was  16  miles. 


USE  OF  THE  COASTING  CHART  5l 

Ftjinii  the  Distante  by  two  Bearings  of  the  same  Objert  having  the  Course  ana  Distance  Run  between  th*m, 

RoLK.  Take  the  Beariug  by  the  Compass,  and  note  the  time  by  wateh,  and  after  the  first  Bearing  haa  been  altered 
•t  least  8  f)oint8,  take  a  second  Beariug  and  iote  the  time  by  watch.  Asceitiiin  the  True  Course  tlie  vessel  haj 
made,  and  tlie  Distance  run  in  the  interval  between  the  Bearings.  Allow  the  variatiou  on  the  Compaj^s  Bearings, 
•nd  fiud  the  True  Bearings,  which  lay  oft'  on  the  Chart  as  in  the  former  examples,  mid  draw  pencil  liues.  Lay  th« 
ruler  over  the  Course  mude  good,  and  take  the  Distance  run  in  tlie  dividers.  Move  the  edge  of  the  ruler  up  on  th« 
♦wo  lines,  jutil  the  points  of  the  dividers  reach  to  both  lines  at  the  edge  of  the  ruler,  and  draw  a  pencil  line,  and 
ihe  result  is  the  Ship's  Distance  off  the  object  at  the  time  of  each  Beariug,  and  also  her  Latitude  and  Longituda  io 
at  those  times. 

EXAMPLE  L 

At  8  A.  M.,  Cape  Cod  bore  by  Compass  S.  S.  W.  f  W.,  and  at,  10  A.  M.  it  bore  W.  by  S.  i  S.  Course  steered 
E.  by  S.  i  S.  Rate  of  Sailing  10  knots  an  hour  Variation  J  of  a  point  Westerly.  Required  the  Ship's  Distano* 
of[  at  the  time  of  both  Bearings 

Answer. — The  first  Bearing  S.  S.  W.  }  V.  Corrected  for  variation  is  S.  S.  W.  The  second  Bearing  W 
■fcy  S.  i  S ,  corrected  is  W.  S.  W.,  and  laid  off  on  the  Chart ;  then  the  Course  steered  E.  by  S.  i  S.,  corrected 
for  variation  is  E.  i  S.,  and  the  Distance  run  in  the  interval,  20  miles,  applied  to  the  Ship's  track  drawn 
across  the  two  lines  of  Bearings,  gives  her  Distance  off  at  8  A.  M.,  13  miles,  and  her  Distance  off  at 
10  A.  M.  27  miles.     (See  Cliart,  Fig.  21,  page  47.) 

EXAMPLE  2. 

At  6  P.  M.  Barnegat  Light  came  in  sight,  bearing  by  Compass  S.  W.  by  W.  Ship  sailed  on  a  S.  by  W.  ^  W 
<Jour8e,  at  the  rate  of  8  knots  an  hour,  with  a  two  knot  tide  in  her  favor  until  7  30  P.  M.,  when  the  same  Light 
was  observed  to  bear  N.  W.  by  W.  Variation  ^  a  point  Westerly.  Required  her  distance  oflf  at  the  time  of  both 
Bearings. 

Answer.— The  Bearings  corrected  are  S  W.  i  W.  and  N.  W.  by  W.  i  W.  The  True  Course  S.  by  W., 
and  the  Distance  run  in  the  interval  of  li  hours  is  12,  to  which  add  3  for  the  effect  of  the  Tide,  making 
li  miles.  The  projection  of  this  case  on  the  Chart  by  the  above  rule  gives  her  Distance  off  Barnegat  at 
4  P.  M.  15i  miles  ;  and  at  7    «,  lOi  miles.      See  Fig.  17,  page  33.) 

EXAMPLE  3. 

At  6  A.  M.  Neversink  Light  Houses  bore  by  Compass  W.  by  S.  ^  S.  Ship  then  sailed  on  a  S.  4^  W.  Course,  at  ths 
rate  of  6|  knots  an  hour,  until  7  A.  M.,  when  the  same  object  bore  N.  W.  by  N.  Required  the  Ship's  Latitude  and 
Longitude  in  at  the  time  of  both  Bearings. 

Answer. — The  Variation  of  i  point  allowed,  gives  the  True  Bearings  W.  S.  W.,  and  N.  W.  i  N.  Tht 
True  Course  South,  and  the  Distance  run  in  the  interval  of  2  hours,  is  11  miles.  This  projected  on  the 
Chart  in  like  manner  as  the  last  example,  gives  the  position  of  the  Ship  at  6  A.  M.,  Lat.  40*  26'  N.,  Lon. 
"3°  51'  W  ;  and  al  7  A.  M.,  Lat.  40°  15'  N.,  and  Lon.  7?'  51'  W. 

EXAMPLI  4. 

At  noon  the  N.  W.  end  of  St.  Anthony  (one  of  the  Cape  Vc^de  Islands)  bore  S.  E.  by  E.  by  Compass.  Ship  then 
•ailed  on  a  South  Course  by  Compass  at  the  rate  of  10  knots  ac  hour,  until  4  P.  M.,  at  which  time  it  bore  N.  K  by 
E.  The  Variation  here  being  1^  points  Westerly.  Required  the  latitude  and  Longitude  of  the  Ship  at  the  time 
of  both  Bearinga 

Answer.— The  True  Bearings  are  E.  by  S.  i  S.  andN.E.^N.  The  True  Course  S  by  E.  i  E.,  and  the  Dis- 
tance  run  in  the  interval  of  4  hours  is  40  miles.  This  projected  on  the  Chart  in  like  manner  as  the  last, 
fives  the  Ship's  positun  at  noon.  Latitude  17*  23'  N.,  Longitude  25*  59'  Vf  ;  and  at  4  P.  M.  Latitud* 
16*  45'  N.,  Longitude  25*  46'  40"  W. 

NoTK. — These  two  last  examples  are  very  useful  when  it  is*  required  to  find  the  Ship's  exact  ^•osition  when  altitadss 
Aie  taken  for  the  purj)ose  of  verifying  the  Chronometer  froni  time  to  time  during  the  voyage,  and  in  ssctirtwmng  its 
•fror  on  Gr»«iwicn  Mean  Time  and  daily  rati,  snd  which  wil)  he  P>und  fully  explained  at  page  156. 


54 


SOUNDINGS 


The  Soundings  marked  on  the  Chart  are  those  at  low  -water  spring  tides,  and  the  depth  is  noted  u. 
fiithoms  (or  in  feet  in  some  of  the  harbor  plans),  and  the  nature  of  the  bottom  inserted. 

As  the  Ship's  place  on  the  Chart  can  be  determined  by  the  Latitude  observed  and  the  Soundings  laid 
down  in  that  parallel  of  Latitude,  it  may  also  be  determined  within  certain  limits  by  a  systematic  manner 
of  Sounding  on  approaching  the  land  in  foggy  weather  or  in  dark  stormy  nights,  which  is  always  a  proper 
precaution,  however  correctly  the  reckoning  may  have  been  kept,  because  near  the  shore  the  Ship  is  under 
the  influence  of  either  Tides  or  Currents,  which  may^  in  the  course  of  a  few  hours,  set  her  considerably  out 
of  her  proper  course. 

To  obviate  this,  take  Soundings  early  (when  Soundings  can  be  obtained),  say  at  noon.  The  Ship's  position 
by  observation  being  then  marked  on  the  Chart,  the  Soundings  as  laid  down  at  the  Ship's  place  may  be 
compared  with  the  depth  obtained  from  Sounding.  This  may  be  taken  as  a  point  of  Departure.  Then  the 
Course  and  Distance  sailed,  say  every  4  hours,  projected  on  the  Chart,  may  be  verified  by  the  Soundings  at 
the  end  of  every  4  hours,  and  in  the  event  of  thick  weather  setting  in  (as  is  often  the  case  in  making  the 
land)  any  deviation  from  the  proper  Course  and  Distance  allowed,  may  be  at  once  detected.  Even  although 
ne  vessel  retains  her  proper  Course,  it  gives  greater  confidence  in  the  Reckoning,  and  does  away  with  all 
doubt  and  anxiety  on  the  subject. 

But,  as  before  observed,  this  system  of  Sounding  must  be  commenced  early,  so  that  the  various  Soundings 
obtained  may  be  compared  with  each  other,  and  also  with  those  laid  down  on  the  Chart,  from  which  a 
judgment  may  be  formed  of  the  Ship's  pla»e  from  the  track  of  Soundings  she  has  passed  over. 

Single  Soundings  taken  without  any  reference  to  each  other,  are  seldom  of  any  use,  and  only  tend  to 
perplex  the  subject,  except  when  the  Latitude  is  known,  or  when  ihe  Ship  comes  suddenly  into  shoal  water 

REMARKS  ON  SOUNDING  WITH  THE  LEAD. 

There  are  two  Leads  used  for  Sounding,  the  Hand  Lead,  weighing  14  pounds,  and  attached  to  about  ib 
fathoms  of  line,  and  the  Deep-Sea  Lead,  weighing  28  or  30  pounds,  and  attached  to  100  fathoms  or  more  of 
line  wound  on  a  reel,  and  a  small  Lead  of  5  or  6  pounds  is  sometimes  used  in  shoal  water.  The  lower 
end  of  these  Leads  have  a  hole  in  which  a  lump  of  tallow  is  inserted,  for  the  purpose  of  adhering  to  the 
bottom  of  the  sea  and  bringing  up  a  portion  of  it  for  examination.  This  is  called  Arming  'the 
Lead. 

The  Hand  Lead  is  only  used  in  shallow  water,  and  the  Leadsman  standing  in  the  main  channels,  throws 
it  as  far  forward  as  he  can,  swingmg  it  once  or  twice  over  his  head  if  necessary,  to  give  it  increased  force, 
and  endeavoring  to  draw  the  line  tight  from  the  Lead  at  the  instant  the  Ship,  by  her  progress,  places  him 
directly  over  it.  The  hand  Lead  descends  about  10  fathoms  in  the  first  6  seconds,  hence  when  the  vessel  is 
going  fast  it  is  often  difficult  to  get  Soundings,  unless  her  way  is  deadened. 

The  line  is  marked  as  follows  :  Blue  at  3,  White  at  5,  Red  at  7,  Leather  at  10,  Blue  at  13,  White  at  15, 
Red  at  17,  and  2  knots  at  20  fathoms.  These  numbers  are  called  Marks,  and  the  intermediate  ones  Deeps. 
For  example :  In  obtaining  7  fathoms,  the  Leadsman  calls  out,  "  By  the  Mark  seven."  In  8  fathoms,  "  By 
the  Deep  eight."  Tlie  fathom  is  divided  into  a  half  and  quarters.  7i  fathoms  are  called  "  and  a  quartet 
seven,"  7i  fR*,homs  "  and  a  half  seven."  7J  fathoms  "  a  quarter  less  eight." 

Id  heaving  the  Deep-Sea  Lead,  it  is  carried  forward  to  the  weather  cat-head,  (and  sometimes  to  tho 
lee  cat-head  if  the  Ship  is  making  much  leeway.)  The  line  being  passed  forward  to  windward  an 
jutside  of  all,  the  Ship's  way  is  then  reduced,  if  necessary,  and  the  Lead  dropped,  and  as  soon  as  i 
is  felt  to  strike  the  bottom  the  line  is  hauled  in  a  little  and  the  bottom  struck  again.  The  mark  a.1 
the  surface  of  the  water  is  then  examined  and  the  depth  of  water  ascertained,  allowing  for  the  streaming 
of  the  line,  caused  by  the  vessel's  drift  when  hove  to,  and  which  sometimes  amounts  to  10  fathoms  to 
the  100  of  line  run  out. 

li.  Sounding  in  deep  water  in  small  vessels,  wnich  drift  to  leeward  rapidly  upon  losing  their  way, 
it  is  best  to  drop  the  Lead  before  the  headway  ceases,  and  to  cause  the  vessel  to  gather  stern- way,  so 
as  to  pass  over  the  Lead,  which  will  thus  have  descended  through  a  considerable  depth  perpendicularly. 

The  deep-sea  line  is  maiKed  at  each  10  fathoms  by  the  corresponding  number  of  knots,  and  with  2 
single  knot  at  each  five  fathoms.  The  error  in  Sounding  is  generally  in  excess,  because  the  line  can 
r^  ely  be  stretched  straight  from  the  Lead. 


SOUNDINGS.  i9 

A  I^ead-line  should  be  well  stretched  and  thoroughly  wetted  before  it  is  measured  and  marked ,  be«&uufl 
It  has  a  tendency  to  shrink  up  on  being  used ;  and  it  should  afterwards  be  verified  from  time  to  time, 
to  ascertain  whether  the  marks  remain  correct. 

Soundings  on  board  of  Steam  vessels  may  be  made  with  more  accuracy  than  on  board  of  Sailing 
vessels ;  because  they  can  be   kept  stationary  while  the  line  is   running  out  by  the  aid  of  their  wheela. 

Many  inventions  have  been  tried  from  time  to  time  to  obviate  the  inconvenience  of  rounding  the  Ship 
to  when  under  a  press  of  sail  for  the  purpose  of  Sounding.  And  amongst  them  may  be  mentioned  as  th« 
best,  Massey's  Lead,  Burt's  Buoy  and  Nipper,  and  Enccson's  Le^. 

Massey's  Lead  registers  the  depth  of  water  descended  through,  by  wheel-work,   set  in  motion  by  a  fl 
*cted  on  by  the  water  as  it  descends.     But  in  great  depths  this  fly  is  liable  to  be  crushed. 

In  Burt's  Buoy  and  Nipper,  the  line  being  rove  through  a  spring-catch  in  the  buoy,  the  Lead  is  dropped 
(and  the  buoy  afterwards)  into  the  water.  The  line  then  cbntinues  to  run  through  the  catch  till  the  Lead 
reaches  the  bottom,  or  is  checked  by  a  pull,  when  the  catch  firmly  seizes  the  line  attaching  the  buoy  to  H 
mt  the  depth  descended  through  it  by  the  Lead. 

Ericcson's  Lead  measures  the  depth  of  water  by  the  space  into  which  the  air,  (contained  in  a  giaaa 
tube  and  reservoir  within  the  Lead,)  is  condensed  by  the  pressure  of  the  water.  The  depth  is  indicated  on 
a  graduated  scale  by  the  height  to  which  the  water  rises  in  the  tube. 

These  instruments  require  a  great  deal  of  care  and  circumspection  in  their  management.  For  instance, 
by  raising  and  lowering  them  alternately,  they  will  be  made  to  show  the  depth  in  excess,  and  they  m^ut 
be  lowered  gradually  to  the  surface  of  the  water.  Moreover,  they  are  all  liable  to  get  »ut  of  order  in 
stormy  weather,  which  is  the  very  time  they  are  most  wanted.  From  these  considerations,  they  have  not 
come  much  into  use  amongst  merchant  vessels,  the  commanders  of  which  preferring  the  old  and  safe 
method  of  sounding  by  the  Deep-Sea  Lead  and  Line,  and  which  is  more  to  be  relied  on  in  t»a«©8  of 
emergency. 

In  thick  blowing  weather,  when  a  Ship  is  approaching  the  Coast,  common  prudence  would  dictakb  iUM 
she  should  be  under  easy  sail ;  and  by  the  exercise  of  a  little  seamanship,  Soundings  can  always  b« 
obtained  sufficiently  accurate  to  eusure  the  voM'.Pa  safety,  from  the  use  of  their  old  and  frjoiliar  frieaii 
the  Dcep-Ssa  Lead  and  Lui<> 


M 


NAUTICAL     ASTKONOMY. 


DIAGRAM  OF  THE  SOLAR  SYSTEM,  SHOWING  THE  PLANETARY  ORBITS  ROUND 

THE   SUN. 

Fio.  A. 


EXPLANATION  OF  THE  FIGURE. 
'^  Arrows  show  the  direction  in  which  they  revolve  roirwi  the  Hun  tn  the  centre 


No.  1 .  Orbit  of  Mercury. 

No  4.  ( 

Orbit  of  Mars. 

«    2.       "     of  Venus. 

"   5. 

"     of  Jupiter. 

"   3.       "    of  The  Earth  and  her  Moon. 

"    6. 

"     of  Saturn. 

The  Solar  System  is  that  in  which  our  Earth  is  placed,  and  in  which  the  Sun  is  supposed  to  bo  fixed  in 
the  wntre,  with  several  bodies,  called  Planets,  similar  to  our  Earth,  revolving  round  him  at  different  dis- 
tances from  him  and  from  each  other,  and  which  shine  by  the  light  borrowed  from  the  Sun. 

The  fixed  Stars  are  supposed  to  be  Suns  which  shine  by  their  own  light,  and  situated  in  the  heavene  at 


DESCRIPTION  OF  THE  PLANETS  55- 

nioh  an  immense  distance  from  our  system  that  it  is  found  impossible  io  measure,  or  th«  human  miix)' 
to  conceive  it. 

While  the  Earth  and  Planets  are  thus  revolying  r«und  the  Sun,  from  West  to  East,  they  hare  also 
a  motion  round  their  own  axis  in  thA  same  direction,  and  which,  in  the  case  of  the  Earth,  produoei( 
our  day  and  night. 

Although  to  a  spectator  placed  in  the  Sun,  the  Planets  would  appear  to  move  in  due  order  about- 
him  from  West  to  East,  yet  to  a  spectator  on  the  Earth  their  apparent  motions  appear  to  be  very 
irregular.  Sometimes  they  appear  to  move  from  West  to  East,  and  then  to  stand  still.  Then  they  seena 
to  move  from  East  to  West,  and  after  standing  some  time  they  again  move  from  West  to  East,  and  so  on 
continually.  This  is  easily  detected  by  noticing  the  relative  positions  of  a  Planet  and  a  fixed  Star  in  the 
heavens  on  a  certain  night,  and  then  again  at  an  interval  of  a  few  nights  after.  This  is  caused  oy  the 
Earth  not  being  iu  the  centre  of  the  system.  » 

That  is  the  real  state  of  the  case.  But  in  conformity  with  the  impression  on  the  mind  of  the  specta- 
tor, that  the  heavenly  bodies  appear  to  rise  in  the  East  and  set  in  the  West,  (which  in  reality  is  caused  by 
the  Eanh's  motion  on  its  axis  in  a  contrary  direction,)  and  in  treating  of  Nautical  Astronomy  as  applied  U» 
the  purpoi^es  of  Navigation,  we  suppose  the  Earth  to  be  placed  in  the  centre  of  the  Universe,  (See  Fig.  1, 
page  56,)  and  that  the  Sun  and  all  the  other  heavenly  bodies  revolve  round  it.  This  supposition  accords 
with  the  senses  of  the  spectator,  which  greoily  simplifies  the  whole  matter,  and  the  conclusions  arrived  at 
come  to  the  same  thing. 

DESCRIPTION  OF  THE  PLANETS:    THEIR  MAGNITUDE  AND  DISTANCE  FROM  THE  SUN 

The  Sun  is  the  great  centre  of  our  System,  and  is  890,000  English  miles  in  diameter,  and  he  turns  onc«- 
round  on  his  axis  from  West  to  East  in  25  days  10  hours. 

There  ai©  upwards  of  17  Planets  which  revolve  around  the  Sun  as  a  centre,  but  many  of  these  ar» 
invisible  lo  the  naked  eye.  Some  of  them  have  satellites  or  moons,  which  revolve  round  them,  and  being 
kttraotea  to  it,  they  are  carried  round  the  Sun  along  with  the  Planet,  as  in  the  case  of  our  Earth  and' 
Moon. 

Out  of  all  this  number  of  Planets  and  Moons^  only  5  can  be  made  serviceable  in  the  Practice  of  Naviga- 
Vton  at  Sea,  viz :  Venus,  Mars,  Jupiter,  Saturn,  and  the  Moon.  Mercury  being  always  too  near  the  Sun  is> 
ield(  m  seen  on  account  of  the  sunlight,  and  the  others  are  too  small  or  too  remote,  and  shine  with  such  t^ 
feeble  light  that  they  can  only  be  seen  and  distinguished  by  using  good  telescopes  on  shore. 

I'Ke  path  which  the  Planets  describe  round  the  Sun  is  called  their  Orbits.     Mercury  and  Venus  aro 
•ftlled  Inferior  Planets,  because  their  orbits  are  within  that  of  the  Earth,  while  the  Earth,  Mars,  Jupiter, 
oA  Saturn  are  called  Superior  Planets,  because  their  orbits  include  that  of  the  Earth. 

Mercury  is  a  small  Planet ;  his  diameter  being  only  3.200  miles.  His  distance  from  the  Sun  37  million* 
o'"  miles,  and  he  performs  his  revolution  in  his  orbit  in  87  days  23  hours. 

Venus  is  the  brightest  of  all  the  Planets.  Her  diameter  is  7,687  miles.  Her  distance  from  the  Sun  6* 
uiillions  of  miles,  and  she  performs  her  revolution  in  her  orbit  in  224  days  17  hours.  On  being  viewed 
through  a  telescope  she  appears  horned  sometimes,  like  our  Moon.  When  this  Planet  is  in  the  Western* 
)i&Tt  of  her  orbit  she  rises  before  the  Sun,  and  is  then  called  the  Morning  Star.  When  in  the  Eastern,  she 
iftmes  after  sunset,  as  the  Evening  Star. 

The  Earth  is  the  next  Planet  in  the  system,  the  mean  diameter  of  which  is  about  7,913  miles      (See 
»>escription  of  the  Earth  at  page  2d.)     Its  distance  from  the  Sun  is  95  millions  of  miles,  and  its  period  of 
rjvolution  in  its  orbit,  365  days  6  hours  nearly,  or  one  year,  which  produces  the  change  in  our  seasons,  and 
(Mining  on  its  axis  in  23  hours  and  56  minutes,  produces  our  day  and  night. 

The  Earth  is  attended  by  a  satellite  or  moon,  whose  diameter  is  2,161  miles,  and  her  distance  from  tht 
*entre  of  the  Earth  is  240,000  miles.  She  goes  round  her  orbit  in  27  days  8  hours ;  but  reckoning  from 
change  to  change,  in  29i  days,  and  she  turns  round  on  her  axis  in  the  same  time,  but  always  presents  th© 
same  side  to  the  Earth.  And  els  she  shines  by  the  reflected  light  of  the  Sun,  she  appears  diflerently 
according  as  she  is  situated  with  regard  to  him.  When  she  is  on  the  same  side,  her  dark  side  is  turned 
towards  the  Earth  and  is  then  invisible.  This  is  called  New  Moon.  When  she  is  on  the  opposite  side,  her 
Ught  side  is  turned  towards  the  Earth.     It  is  then  said  to  be  Full  Moon. 

Mars  is  the  next  Planet  to  the  Earth.  His  Diameter  is  4,189  miles.  His  d  stance  from  the  Sun  is  144- 
millions  of  miles.  He  performs  his  revolution  in  his  orbit  in  about  687  days,  and  turns  on  his  axis  once  in. 
24  hours  40  minutes.  Mars  may  he  easily  distinguished  from  the  other  Planets,  by  his  red  appearance, 
which  is  supposed  to  be  caused  by  his  dense  atmosphere. 

Eleven  small  Planets  revolve  between  the  orbits  of  Mars  and  Jupiter,  but  as  they  are  of  no  »^erTice  to 
Navigation,  it  is  useless  to  describe  them. 

Jupiter  is  the  next  and  largest  of  all  the  Planets,  and  is  easily  distinguished  by  his  peculiar  magnitude 
and  light.  His  diameter  is  89,170  miles.  His  distance  from  the  Sun  494  millions  of  miles  He  performs 
his  revolution  in  bis  orbit  in  4, 3321  days,  or  12  years  nearly,  and  he  turns  on  his  axis  once  in  9  hours  and 
66  minutes.  This  Planet  is  attended  by  4  satellites  or  moons,  but  is  invisible  to  the  naked  eye.  In  viewmj 
Jupiter  through  a  telescope,  these  "loons  make  a  beautiful  appearance,  together  with  the  belt  over  hi*- 
equator,  supposed  to  be  caused  by  the  swiftness  of  his  diurnal  motion,  in  drawing  his  clouds  and  vapors 
into  that  form. 

Saturn  is  the  remotest  of  all  the  Planets  which  are  useful  in  Navigation,  and  may  be  distinguished  by 
his  pale  and  feeble  light.  His  diameter  is  79,042  miles.  His  distance  from  the  Sun  is  about  900  millions  of 
miles.  He  performs  his  revolution  in  his  orbit  in  29  years  167  days,  and  turns  on  his  axis  once  in  10- 
hours  16  minutes,  and  is  attended  by  7  moons.  Thi.s  Planet  is  different  from  all  the  others  when  viewed 
tlirough  a  telescope,  being  furnished  with  a  broad  double  luminous  ring,  which  appears  intended  to  increaj» 
the  quantity  of  light  received  from  the  Sun,  and  which,  on  account  of  his  vast  distance  from  that  body 
must  b#  verv  feeble. 


m 


NAUTICAL  ASTRONOMY. 


DIAGRAM  O?  -^HF.  SPHERE, 


Drawn  on  the  Plane  of  the  Meridian  in  45°  NoriJ-  Latttu^ 


Fig.  1. 


Tkt  9p»€taior  is  supposed  to  be  situated  at  a  great  distance  East  of  the  Earth,  and  lookwg  towa^  th*  Wed. 

having  North  on  the  Right  and  South  on  the  Left. 

TO  CONSTRUCT  THE  FIGURE. 

Tak.  60-  from  the  line  of  Chords  on  the  Plane  Scale,  ind  describe  a  circle,  which  ^»  /•P;!'?: 
•ent  the  Circular  Dome  of  the  Heavens,  and  from  the  centre  draw  a  l«'««\«;':*'i«' J^^'^'^J^J^ 
represent  the  Earth  in  the  centre  of  the  Sphere.  Draw  a  horizontal  hne  through  he  ««°^'  ^^^ 
will  cut  the  Earth  in  two  halves,  and  represents  the  Rational  Horizon  Draw  another  line  P«JP«°f  ^J";" 
to  it,  which  will  divide  the  Heavens  into  four  equal  parts  of  90*  each.  This  line  or  ^irde  is  calledth* 
Prime  Vertical,  and  passes  through  the  East  and  West  points  in  the  centre.  The  top  or  point  overhead  i. 
wiled  the  Zenith,  which  i.  90"  from  the  Rational  Horizon;  and  the  bottom  or  point  under  foot  is  called 
the  Nadir,  also  90*  from  the  Rational  Horizon.  .,..-:,  ..     d-  v.*  Ko^^  «f  th*  Horizon 

Take  45-  from  the  line  of  Chords,  and  with  one  foot  of  the  dividers  on  the  Right  hand  <>/  f «  f  °"/°^' 
iay  it  off  upwards,  and  draw  a  line  from  thence  through  the  centre,  will  represent  the  Elevated  Pole  ot  tM 
Hlavens  and  the  Earth's  Polar  Axis.  At  90'  from  the  Pole  drawthe  Celestial  Equator  through  the  cen^. 
al«o,  and  it  will  be  perceived  that  the  Poles  of  the  Heavens  coincide  with  the  Poles  of  the  Earth,  ana  me 
Celestial  Equator  coincides  with  the  Equator  of  the  Earth.  Horizon. 

Take  2ir  from  the  line  of  Chords,  and  with  one  foot  of  the  dividers  on  the  Left  hand  of  the  Horizoi^ 
lay  it  oflT  upwards,  will  be  the  Sun's  place  on  the  Meridian  to  the  South  of  the  spectator  Th^s  is  oal led 
thl  Celestial  Meridian,  and  passes  through  the  Poles  of  the  Heavens.  Lay  2U-  off  in  ^^ke  manner  to  th. 
Right;  .hen  take  2U- from  the  line  of  semi-tangents  on  the  Plane  Scale  and  l^J '\«f  ff7,.\^X°^ 
•pwards,  and  through  these  three  points  describe  a  circle,  which  is  called  a  P*^^"«l  "^  ^^*''"f«;  "^J 
which  in  this  ca^/is  the  Parallel  of  the  Run's  Meridian  Altitude,  and  i.  always  measured  from  th. 
<iational  Horizon       Parallels  of   Altitudes  ar-  parallel  witl.  tho  horizon. 


NAVIGATION  AT  SEA  BY  ASTRONOMICAL  OBSERYATIONS.  57 

DEFINITIONS. 

Th»  relates  to  finding  the  place  of  the  Ship  on  the  surface  of  the  Earth  from  observations  of  the 
heaveiiiy  bodies. 

To  the  spectator  at  the  suriace  of  the  Earth  the  heavens  appear  to  form  a  vault,  or  the  upper  half  of  a 
hollow  hphere,  of  ■vrhich  he  is  the  centre.  The  Earth  itself,  or  the  ground  or  Sea  on  which  he  stands, 
occupying  the  lower  half.  And  supposing  the  North  Pole  Star  to  represent  the  Elevated  Pole  of  the 
heavens,  or  the  polar  axis  of  the  Earth  extended  to  the  heaven.s,  that  part  of  it  which  is  lituated  90* 
from  the  Polar  Star  will  be  the  Celestial  Equator,  or  the  Great  Circle  which  passes  round  the  heaveiM 
from  East  to  West,  the  half  of  which  only  is  above  the  horizon  of  the  spectator,  unless  he  is  stand- 
ing on  the  North  Pole  of  the  Earth  ;  then  the  Celestial  *  Equator  would  extend  around  and  coincide 
with  his  horizon,  and  the  North  Pole  Star  would  then  be  seen  directly  over  head.  At  the  South  Pole, 
the  Ceftstial  Equator  would  also  be  in  the  horizon,  and  the  North  Polar  Star  under  his  feet.  From 
which  it  is  easy  to  imagine  circles  drawn  in  the  heavens  corresponding  to  those  drawn  on  a  terrestrial 
globe. 

A  spectator  conceives  himself  standing  on  the  surface  of  the  globe,  with  his  feet  toward  the  centre. 
,  Now,  suppose  he  were  to  descend  to  the  centre,  and  the  upper  half  of  the  Earth,  or  globe,  to  bo  cut 
off  horizontally,  that  is,  parallel  with  the  horizon,  the  surface  of  the  lower  half  globe  so  exposed,  and 
being  produced  on  all  sides  to  meet  the  concave  Celestial  sphere,  is  called  the  Rational  Horizon.  Every 
point  of  the  Earth's  surface  has,  therefore,  a  different  rational  horizon.  But  all  these  horizons  meet  in 
the  centre  of  the  Earth.     (See  Fig.   1.) 

Celestial  observations  taken  at  the  surface,  are  reduced  to  the  centre  of  the  Earth;  therefore  the 
observer  is  supposed  to  be  at  the  centre  of  the  Earth.  This  is  necessary  in  the  case  of  the  Moon, 
because  she  is  near  the  Earth,  and  the  Sun,  and  some  others.  But  the  fixed  Stars  being  at  such  an  im- 
oiense  distance  from  the  Earth,  its  magnitude  is  nothing  in  comparison,  so  that  the  space  oetween  the 
oentre,  and  the  surface,  or  the  Earth's  semi-diameter,  would  produce  no  change  whatov^er  in  the  places  of 
the  Stars  in  the  heavens.  Therefore,  in  drawing  figures  for  general  purposes,  the  Earth  is  considered  as 
A  mere  speck  in  the  centre  of  the  Sphere,  and  its  magnitude  entirely  neglected. 

The  Zenith  is  the  point  vertically  over  the  spectator's  head,  and  distaai  99*  from  the  rational  boriaon  at 
«rnry  point. 

The  point  opposite  the  Zenith,  or  under  the  spectator's  feet  ou  tho  other  side  of  the  centre,  is  called  uu 
Nadir. 

The  Pole  of  the  heavens  is  the  point  which  remains  fijced,  while  the  rest  of  the  Celestial  surtaoe  soet. 
Above  ths  horizon  appear  to  revolve.     That  Pole  which  is  above  the  horizon,  is  called  the  EleTatod  Pole. 

The  Celestial  Equator  is  a  great  circle  passing  round  the  heavens,  at  90'  distance  from  the  Polea,  in 
the  same  plane  as  the  Earth's  Equator. 

The  Celestial  Meridian  is  a  circle  passing  through  the  Poles  of  the  heavens,  in  tLe  larae  plane  as  the 

Terrestrial  Meridia*. 

Circles  of  Altitude  are  circles  passing  through  the  Zenith,  and  vertical  at  the  place  of  the  obeenror,  ani 
are  measured  from  the  Horizon  towards  the  Zenith. 

The  Prime  Vertical  is  the  vertical  circle  passing  through  the  East  and  West  points  in  the  centre,  and 
appears  a^  a  straight  line. 

Zenith  Distance  is  the  distance  of  any  heavenly  body  from  the  Zenith.  The  Zenith  Distance  is  therefore 
Che  Difference  between  the  Altitude  and  90*. 


53 


NAUTICAL    ASTRONOMY. 


DIAGRAM    OF    IHE   SPHERE. 
Drawn  on  the  Plane  of  the  Meridian  in  45*  North  Latitudt. 

Fig.  2. 


hk  this  Figure  the  Earth  ts  supposed  to  be  a  mere  Point  in  the  Centre,  and  the  Spectator  situated  at  a 

distance  to  the  Eastward  of  it. 


g" 


TO  CONSTRUCT  THE  FIGURE. 

Construct  this  figure  in  the  same  manner  as  in  the  preceding  one.  Then  take  23°  28'  (the  extent  of  the 
Sun's  Declination  North  or  South  of  the  Equator)  from  the  line  of  Chords,  and  lay  it  off  on  both  sides  of 
the  Celestial  Equator  on  the  Meridian  Circle,  and  take  the  same  quantity,  23°  28',  from  the  line  of  Semi- 
tangents,  and  lay  it  off  on  both  sides  of  the  Equator  on  the  Earth's  axis.  Then  through  these  three  points 
on  each  side  of  the  Equator  describe  a  Circle,  which  will  be  the  Sun's  Parallels  of  Declination  North  and 
South  of  the  Equator.  Suppose  the  Sun  on  the  Prime  Vertical,  in  the  one  case,  having  North  Declination, 
and  in  the  Horizon,  in  the  other  case,  having  South  Declination.  A  Circle  drawn  from  the  Poles  through 
these  two  points,  will  be  the  Time  Circle,  and  which  will  cut  the  Equator  at  right  angles.  Take  the 
Distance  between  it  and  the  Meridian  Circle,  will  give  the  measurement  of  the  hour  angle  from  Noon  on  the 
line  of  semi-tangents  backwards  67°,  or  4  hours  28  mmutes.  The  Sun  being  on  the  Prime  Vertical  in  the 
one  case,  and  rising  or  setting  in  the  other. 

The  Sun  being  on  the  Prime  Vertical  Circle,  which  in  this  case  is  also  his  Azimuth  Circle,  and  which 
outs  the  horizon  at  right  angles,  is  measured  on  the  horizon,  towards  the  Polar  side  of  the  Meridian  Circle, 
and  in  this  case  measures  90*.  on  the  line  of  semi-tangents. 

k  Circle  drawn  from  the  Zenith  to  the  N.adir,  through  the  Sun's  place  in  the  horizon,  is  called  the 
Amplitude  Circle,  and  which  cuts  the  horizon  at  right  angles.  The  Distance  between  it  and  the  centre, 
or  the  East  and  West  points,  measured  on  the  line  of  semi-tangents,  gives  the  Amplitude,  34*,  North,  in 
the  one  case,  because  the  Declination  is  North,  and  South  in  the  other  case,  because  the  Declination  ^« 
South. 


DEFINITIONS  tiF  NAIITIUAL  ASTRONOMY  M 


DEFINITIONS. 

The  Declination  of  a  Heavenly  Body  is  the  portion  of  the  Meridian  contained  letween  the  Equator  and 
the  body.     It  is  reckoned  from  the  Equator,  and  is  therefore  either  North  or  South.     (See  Fig.  2.) 

Parallels  of  Declination  are  circles  parallel  to  the  Equator.  Thus  Declination  is  reckoned  from  th« 
Celestial  Equator,  as  Latitude  on  the  surface  of  the  Earth  is  reckoned  from  the  Terrestrial  Equator, 
and  as  both  these  circles  are  in  one  and  the  same  plane,  Declination  and  Terrestrial  Latitude  correspond. 

Polar  Distance  is  an  Arc  of  the  Meridian  contained  between  a  Celestial  body  and  the  Pole,  or  the  Angular 
Distance  of  a  body  from  the  P^le.  When  the  Latitude  and  Declination  are  of  the  same  name,  the  Polar  Dis- 
tance is  the  difference  between  the  Declination  and  90°,  because  the  distance  from  the  Pole  to  the  Equator  ii 
90*.  When  the  Latitude  and  Declination  are  of  contrary  names,  the  Polar  Distance  is  the  sum  of  the  Decli- 
nation and  90°. 

The  Azimuth  of  a  Celestial  body  is  an  Angle  at  the  Zenith  contained  between  the  Meridian  Circle  of  the 
place  of  the  spectator  and  the  Circle  of  Altitude  passing  through  the  body.  It  is  reckoned  to  begin  from 
that  part  of  the  Meridian  Circle  which  is  on  the  Polar  side  of  the  Zenith,  that  is,  from  the  North  in  North 
Latitud'..  anH  from  the  South  in  South  Latitude.  The  Supplement  or  Difference  between  it  and  180*  is  fre- 
quenily  used  i)r  convenience,  and  reckoned  from  the  opposite  point.  The  Azimuth  is  measured  by  an  Are 
of  'he  Horizon  contained  between  the  Meridian  Circle  of  the  place  and  the  Circle  of  Altitude  of  the  body, 
tiiwards  the  East  in  the  Mornins  and  the  West  in  the  Afternoon.  The  Ship's  Course  is  the  Azimuth  of  the 
Ship's  head,  and  reckoned  from  the  North  or  South.     So  also  is  the  bearing  of  an  object  its  Azimuth. 

When  a  body  is  on  the  Prime  Vertical  its  Azimuth  is  90°. 

The  Amplitude  of  a  body  is  an  Arc  of  the  Horizon  contained  between  a  Celestial  body  at  rising  or  set- 
ting, and  the  Prime  Vertical  Circle,  or  the  East  and  West  points.  Amplitude  is  reckoned  from  the  East  or 
West  towards  the  North  when  the  Declination  of  the  body  is  North,  and  towards  the  South  when  the 
Declination  is  South. 

The  Latitude,  or  Distance  of  the  observer  from  the  Terrestrial  Equator,  is  measured  on  the  Celestial 
Sphere  and  is  the  Distance  of  his  Zenith  from  the  Celestial  Equator.  When  the  object  is  to  the  South  of  th« 
observer,  his  Zenith  is  to  the  North  of  the  body,  and  is  called  North  Zenith  Distance.  When  the  object  is 
North  of  the  observer,  his  Zenith  is  to  the  South  of  the  body,  and  is  called  South  Zenith  Distance.  There- 
fore, when  the  Declination  and  Zenith  distance  are  of  the  same  name,  their  sum  is  the  Latitude  of  that 
name  ;  and  when  of  contrary  names  their  differenc*  is  the  Latitude  of  the  same  name  as  the  greater  of  the 
two. 

The  Elevation  of  the  Pole  above  the  Horizon  is  equal  to  the  Latitude  of  the  place,  and  the  Altitude  of 
the  ujipermost  point  of  the  Equator  on  the  Meridian  is  equal  to  the  Co-Latitude,  or  the  difference  betweeu 
the  Latitude  and  90°.  By  noting  this,  and  also  that  the  Equator  passes  through  the  East  and  West  points, 
it  is  easy,  in  looking  towards  the  Heavens,  to  figure  in  the  mind,  roughly,  the  position  of  this  circle.  Thii 
it  often  found  useful  in  identifying  a  Star  by  means  of  its  Declination,  which  is  measured  from  the  Equator. 

Tne  Hour  Angle  of  a  Celestial  body  is  an  Angle  at  the  Pole  contained  between  the  Meridian  Circle  of 
the  place  and  the  Celestial  Meridian  or  Time  Circle,  which  passes  through  the  body,  and  cuts  the  Equator 
at  right  angles,  and  is  measured  by  an  Arc  of  the  Equator  contained  between  the  Meridian  Circle  of  the 
place  and  the  Time  Circle  which  passes  through  the  body,  and  in  the  case  of  the  Sun  gives  the  apparent 
time  from  noon,  or  his  distance  from  the  Meridian,  reckoned  at  the  rate  of  15'  to  the  hour. 

Thus  in  figure  2d  we  have  the  Co-Altitude,  Co-Latitude,  and  Polar  Distance  ;  three  sides  of  a  SphencaJ 
Triangle  given  to  find  the  Angle  at  the  Pole,  which  is  measured  on  the  Equator. 

The  Hour  Angle  is  thus  measured  on  the  Celestial  Equator,  io  the  same  way  as  Longitude  is  measvireJ 
•n  the  Terrestrial  Equator. 

\ 


60 


DEFINITIONS.  81 


DLFINITJONS 

Tli9  path  on  which  the  Sun  appears  to  move,  or  the  great  Circle  which  he  seems  to  describe  in  th« 
Heavens,  is  called  the  Ecliptic. 

The  Eclipti*  is  divided  into  twelve  Signs,  or  portions  of  30'  each,  called  t'.ie  Signs  of  the  Zodiac,  which 
term  means  a  space  or  belt  of  8*  wide  on  each  side  of  the  Ecliptic,  in  which  the  older  discovered  Planets 
and  the  Moon  appeared  to  move,  and  to  which  they  were  odnfined.  The  Signs,  taken  in  the  order  in  which 
the  Sun  moves  through  them,  that  is,  in  the  contrary  direction  to  the  apparent  diurual  motion,  are  as 
follows: 


nn   Aries,   (The  Ram.) 
«    Taurus,  (The  Bull.) 
n   Gemini,  (The  Twins.) 
25   Cancer,   (The  Crabs.) 
^  Leo,  (The  Lion.) 
W  Virgo,  (The  Virgin.) 


d:^  Libra,  (The  Balance.) 

T^l  Scorpio,   (The  Scorpion.) 

t  Sagittarius,   (The  Archer.) 

y?  Capricornus,   (The  Goat.) 

■XC  Aquarius.  (The  Water  Bearer.) 

K  Pisces,   (The  Fishes.) 


Besides  this  perpetual  motion  from  West  to  East,  the  Sun  is  always  changing  his  Declination,  whi  jh 
raries  between  23'  28'  N.,  and  23*  28'  S.,  and  he  crosses  the  Equator  twice  in  ono  year,  namely  :  about 
the  21st  of  March,  he  is  then  entering  the  first  point  of  Aries,  and  commences  the  Astronomical  Year,  and 
proceeds  into  North  Declination.  He  crosses  again  about  the  22d  of  September,  and  is  th6n  said  to  be  in 
Libra,  and  proceeds  into  South  Declination. 

When  the  Sun  crosses  the  Equator,  he  rises  and  sets  at  6  o'clock  in  all  parts  of  the  world.  At  tl^ese 
times,  therefore,  the  days  and  nights  are  everywhere  equal. 

The  Sun  attains  his  greatest  North  Declination  about  the  21st  of  June ;  he  is  then  in  the  Tropic  of 
Cancer ;  and  his  greatest  South  Declination  about  the  22d  of  December ;  ho  is  then  in  the  Tropic  of 
Capricorn. 

Since  it  is  Summer  on  that  side  of  the  Equator  on  which  the  Sun  is,  and  Winter  on  that  side  on  which 
fce  is  not,  the  Seas>)ns  in  South  Latitude  are  reversed. 


•) 


The  Common  or  Civil  Year,  sjs  most  convenient  for  the  affairs  of  life,  includes  the  succession  of  th« 
seasons.  It  is  therefore  the  interval  in  which  the  Sun  leaves  any  Parallel  of  Declination,  and  returns  to  it 
again,  and  is  called  a  Tropical  Year.  Its  length,  that  is,  the  average  length  of  a  number  of  such  years,  is 
365  days  5  hours  48  minutes  6  seconds  of  Common  or  Mean  Time.  The  beginning  of  this  Tropical  Year 
eoinmences  on  the  1st  of  January. 

Declination  being  the  Distance  of  any  Heavenly  Body,  North  or  South,  of  the  Celestial  Equator,  it  is  used 
in  determining  the  position  of  the  Fixed  Stars,  exactly  as  Latitude  is  used  in  determining  places  on  the 
Earth's  surface. 

Right  Ascension  of  a  Celestial  Body  is  an  Arc  of  the  Celestial  Equator  included  between  the  first  point 
of  Arie«  and  the  Celestial  Meridian  of  the  body,  ana  is  reckoned  from  West  to  East.  Circles  of  Right 
Asceui.:on  are  drawn  from  the  Poles  through  the  body;  and  cutting  the  Celestial  Equator  at  right 
angles. 

The  Celestial  Equator  is  divided  into  360*  of  Right  Ascension,  which,  at  the  rate  of  15*  to  the  hour 
make  also  24  hours  of  time.  Thus  Right  Ascension  is  reckoned  on  the  Celestial  Equator,  exactly  as  Lon 
gitude  of  places  on  the  Earth  is  reckoned  on  the  Terrestrial  Equator.  The  first  point  of  Aries  being  used 
as  a  first  Meridian,  and  from  which  the  Right  Ascension  of  all  the  Heavenly  Bo^'les  are  reckoned  in  hours 
and  minutes,  the  same  as  the  first  Meridian  of  Greenwich  is  used  to  reckon  the  Longitude  from,  in  Degrees 
and  Minutes. 

Right  Ascension  is  therefore  used  in  determining  the  places  of  the  Heavenly  Bodies,  and  is  their  distance 
in  time  from  the  first  point  of  Aries. 

Sidereal  Time  begins  when  the  first  point  of  Aries  is  on  the  Meridian,  and  is  counted  through  the  84 
hours,  till  the  same  point  returns  again,  which  is  called  a  Sidereal  Day,  and  consists  of  23  hours  56  mm- 
Btes  4  seconds  of  Common  or  Mean  Time. 

The  Hour  Angle  of  the  first  point  of  Aries  is  the  Right  Ascension  of  the  Meridian. 


ft? 


NAUTICAL   ASTRONOMY. 


DIAGRAM, 
Sktnnng  the  Motion  of  the  Heavenly  Bodies  round  the  Pole,  drawn  on  the  Plane  of  tht  Celestial   Equal** 

Fig.  4. 


tK  th%*  Figure  the  Spectator  ts  supposed  to  be  standing  on  the  North  Pole,  facing  toward  tht  South,  havinr 

East  on  the  Right  hand  and  West  on  the  Left. 

TO  CONSTRUCT  THE  FIGURE. 

Take  60*  from  the  Chords  and  describe  a  circle  which  will  represent  the  Celestial  Equator.  Draw  a 
perpendicular  line  to  represent  the  Meridian.  Make  HP  the  first  point  of  Aries,  and  mark  the  Hours  of 
Riaht  Ascension  round  the  Equator  from  Right  to  Left,  according  to  the  progression  of  the  Heavenly 
Bodies,  which  is,  from  East  to  West.  Mark  the  Sun,  whose  Right  Ascension  from  the  first  point  of  Aries  is 
VII  h.     Then  the  Sun's  Hour  Angle  West  of  the  Meridian  at  M  is  3  hours. 

The  first  point  of  Aries  having  passed  the  Meridian  7  hours  before  the  Sun,  the  Sun's  Hour  Angle  added 
to  it  gires  X  h.  as  the  Right  Ascension  of  the  Meridian,  or,  as  it  is  called,  the  Sidereal  Time,  which  com 
mences  when  the  first  point  of  Aries  is  on  the  Meridian,  and  is  counted  through  the  24  hours,  until  it  again 
comes  to  the  same  Meridian. 

Suppose  a  Star,  whose  Right  Ascension  is  XIX  h.,  which  has  passed  the  opposite  Meridian  at  N.,  its  Hour 
Angle  is  15  h.,  counted  from  the  Meridian  round  by  the  West,  which,  together  make  34  h.,  from  which  sub- 
tract 24  h.,  gives  Xh.  for  the  Right  Ascension  of  the  Meridian  ;  or,  if  counted  to  the  Eastward,  its  Hour 
Angle  from  the  Meridian  is  9  h.     Subtracted  from  XIX  (its  Right  Ascension)  gives  the  same. 

Suppose  the  Moon's  Right  Ascension  to  be  XIII,  and  her  Hour  Angle  21  h.,  which  together  make  34,  frorn 
which  subtract  24  hours,  gives  the  Right  Ascension  of  the  Meridian  as  before,  X  h.  Or  the  Moon's  dis- 
tance from  the  Meridian  to  the  East  being  3  h.,  subtracted  from  her  Right  A.scen.sion,  gives  the  same. 

From  the  above  figure  it  will  be  perceived  that  the  Cele.«;tial  bodies  in  their  diurnal  motion  in  the 
Heavens  are  continually  forming  Angles  with  the  Meridian  around  the  Pole  from  West  to  East,  caused  by 
Uie  -otatory  motion  of  the  Earth  on  its  ax  s,  contrary  to  their  motion  in  Right  Ascension,  which  is  from  East 
u»  We«t.  and  which  is  caused  bv  the  Earth  revolving  round  the  Sun. 


DEFINITIONS.  83 

AD  Hour  Angles,  which  are  difTerenccs  of  Higi.t  Ascension  of  the  Meridian  and  that  of  a  Celch.ial  body, 
{nay  oe  considered  as  portions  of  Sidereal  Time.  Tlie  interval  of  time  in  which  a  body  describes  a«  Hour 
Angle,  depends  on  the  rate  at  which  its  Right  ascension  changes. 

The  Earth's  motion  round  its  axis  being  perfectly  uniform,  becomes  the  real  standard  of  a  uniform 
measure  of  time.  But  as  any  Star  passes  the  Meridian  nearly  4  minutes  earlier  every  night,  the  beginning 
«f  the  Sidereal  Day  has  no  connexion  with  that  of  the  common,  or  Civil  Day,  as  determined  by  light  and 
darkness 

The  Hour  Angle  of  the  Sun,  reckoned  always  Westward  from  the  Meridian,  is  Apparent  Time.  Thu 
when  the  Sun's  Meridian  has  passed  over  45°  of  the  Celestial  Equator  to  the  Westward  of  the  meridian  ot 
the  place,  it  is  said  to  be  3  hours  Apparent  Time. 

The  interval  between  the  Sun's  passing  the  Meridian  on  one  day  and  the  next,  or  the  apparent  Solar 
Day,  is  not  always  of  the  same  length,  the  difference  being  sometimes  half  a  minute  between  one  day  and 
the  next.  But  the  time  for  general  use  must  unite  the  two  advantages  of  being  regulated  by  the  San  and  of 
V)eing  perfectly  uniform.  The  mean,  or  average  day  of  24  hours,  must  thereiore  be  an  average  taken  of 
all  the  days  in  the  year.  That  is,  such  a  day  as  the  Sun  would  regulate  if  he  moved  uniformly  in  Right 
Ascension,  or  the  time  a  Solar  Clock  would  show,  when  set  at  0  hours,  0  minutes,  0  seconds,  at  the  instant 
the  Sun  was  on  the  first  point  of  Aries,  and  keeping  uniform  time  until  his  return  to  the  same  point, 
would  again  show  0  hours,  0  minutes,  0  seconds. 

This  average  day  ic  called  the  Mean  Solar  Day,  and  the  time  thus  regulated,  is  calle4  the  Mean  Time. 

The  Sun  being  generally  either  behind  or  in  advance  of  the  position  which  he  would  have  occupied  if  ha 
had  moved  uniformly.  Apparent  Time  is  in  general  either  fast  or  slow  of  Mean  Time.  The  correction  for  this 
irregularity,  that  is,  the  Difference  between  the  Sun-Dial  and  the  Solar  Clock,  is  called  the  Equation  of 
Time.  Mean  Time  is,  therefore,  deduced  from  Apparent  Time,  by  applying  the  correction  for  the  Equa- 
tion of  Time  taken  from  the  Nautical  Almanac. 

Suppose  O  to  be  the  place  of  the  Sun,  in  Fig.  4,  at  3  P.  M.  Apparent  Time,  and  m  the  place  he  would 
«e  if  he  moved  uniformly.  Then  the  space  between  O  ^^^  "»)  is  the  Equation  of  Time,  and  M  m,  the 
Mean  Time  from  Noon.  The  Equation  is  here  additive  to  Apparent  Time,  as  is  the  case  f^om  January  to 
March,  and  from  July  to  August. 

Referring  to  Fig.  4  again.  While  the  Sun  and  Aries  revolve,  the  Sun  moves  contrary  to  the  diuma 
rotation,  or  is  always  increasing  his  Right  Ascension  by  nearly  1*  a  day.  The  complete  revolution  of  V 
«onstitutes  a  Sidereal  Day,  that  of  O  an  Apparent  Solar  Day,  and  that  of  m  a  Mean  Solar  Day. 

After  24  Sidereal  hours,  the  Sun  has  still  to  describe  about  1*,  or  one  360th  of  24  Sidereal  hours,  or  4 
AiJereal  minutes.  Thus  the  Solar  Day  is  longer  than  the  Sidereal  Day  by  about  4  minutes.  The  Mean 
Solar  day  being  divided  into  24  hours,  the  Sidereal  Day  is  23  hours,  56  minutes,  4  seconds  of  such  a  day. 

Since  the  Sun  passes  over  15*  of  the  Circle  in  one  Mean  hour,  he  arrives  at  the  Meridian  of  a  place  15* 
West  of  M  one  hour  after  h«  has  passed  M,  that  is,  at  one  o'clock  of  the  time  at  any  place,  or  all  places 
«f  which  N  M  i&  the  Meridian.  In  like  maimer,  he  passes  a  Meridian  15*  East  of  M  one  hour  before  h« 
arrives  at  M,  that  is,  when  the  time  at  3f  is  1 1  o'clock  in  the  forenoon,  or  23  hours  after  the  nooa  of  th« 
•day  before. 

Thus  the  beginning  of  the  day,  and  therefore  the  hour  of  the  day  at  one  place  differs  from  that  of  another 
place  by  the  difference  of  Longitude  of  the  places.  The  time  at  the  Easternmost  of  the  two  being  m 
advance  of,  that  is,  greater  than  the  time  at  the  other.  Hence,  when  the  Mean  Time  at  two  places  at  th« 
«ame  instant  are  known,  their  Difference  of  Longitude  is  determined,  and  also  the  relative  positions  of  their 
Meridians. 

The  Civil  Day  is  dated  from  Midnight,  and  the  12  hours  are  computed  twice  over.  The  Astronomies. 
Day  is  dated  from  Noon,  and  runs  through  the  24  hours.  Civil  Time  is  converted  into  Astrenomieal  Tims 
*rj  diminishing  it  bv  13  hours. 


g4  NAUTICAL    ASTRONOMt 

DIAGRAM, 
Shoreing  the  method  of  finding  the  Stars  in  the  Heavens  from  their  Meridian  Altitudes, 

FWD   THB    MkRIDIAM    ALTITUDE   OF    THK    StaR    AlDKBARAN  IN  THK    LaTITODE   OT    45*    NORTW 

Fxo.  5. 
Drawn  on  the  Plane  of  the  Meridian. 


,//?c^ 


•V    V 


o     Nr^ 


RATIONAL 


HORIZON 


E.^W.    POINTS 


TO  CONSTUCT  THE  FIGURE. 
With  the  Chord  of  60  describe  a  semi-circle,  and  draw  the  Horizontal  and  Prime  Vertical  lines  at  Right 
Angles  to  each  other.  Elevate  the  Polar  Axis  equal  to  the  Latitude  of  45*  N.,  and  draw  the  Equator  at 
Right  Angles  to  it.  Lay  off  the  Star's  Declination,  16°  13',  on  the  Meridian  to  the  North  of  the  Equator, 
which  will  be  the  place  of  the  Star,  and  its  Distance  measured  from  the  Horizon,  is  the  Altitude  required. 
Now,  as  the  Elevation  of  the  upper  end  of  the  Equator  above  the  Horizon,  is  equal  to  the  Co-Latitude  of 
the  place,  which  is  North,  and  the  Declination  of  the  Star  being  also  North,  their  Sum  is  the  Meridiaa 
Ititude  of  the  Star,  61*  13',  South  of  the  observer,  because  his  Latitude  is  North. 

Find  th«  Mxridiam  Altitude  er  the  Star  Antarei  in  the  Latitodk  or  30*  North. 

Fig.  6. 
Drawn  on  the  Plane  of  the  Prime  VertieaL 


TO  CONSTRUCT  THE  FIGURE. 

With  the  Chord  of  60*,  describe  a  semi-circle  as  before,  which  will  represent  the  Prime  Vertioal  Cirele 
Draw  the  Rational  Horizon  line,  and  at  right  angles  to  it  from  the  centre,  draw  the  Meridan  line  or  Circle. 
The  Spectator  is  now  facing  the  South.  The  Prime  Vertical  Circle  passes  through  the  East  point  of  th« 
Horizon  on  the  Left,  and  through  the  West  point  of  the  Horizon  on  the  Right. 

The  Elevation  of  the  Celestial  Equator  above  the  Horizon  being  equal  to  the  Co-Latitude,  take  bO*  the 
Co-Latitude)  from  the  lino  of  semi-tangents,  and  lay  it  off  on  ihe  Meridian  line.  Then  through  thia 
point,  and  the  East  and  West  points  of  the  Horizon,  draw  the  Celestial  Equator.  From  the  line  of  semi- 
tangents  take  the  Star's  Declination,  26*  6'  South,  (measured  from  60*  backwards,)  and  lay  it  off  from  th« 
Equator  towards  the  South  point  of  the  Horizon  on  the  Meridian  line,  and  draw  the  Parallel  of  Declination 
parallel  to  the  Equator.  Then  where  it  crosses  the  Meridian  line  is  the  Star's  place,  and  its  Altitude  abore 
the  Horizon  is  33*  54'  South,  measured  on  the  line  of  semi-tangents ;  and  where  the  Parallel  of  Declinatior 
•uts  the  Horizon  shows  the  places  of  the  Star's  rising  and  setting. 


DEFINITIONS 

PiMS   THK    MXRIDIAN    ALTITUDE    Or    CaNOPUS,    IR    THE    LaTITUDB   Or    13*    SOOTI 

Fig.  7. 


TO  CONSTRUCT  THE  FIGURE. 

Hanng  drairn  this  Figure  as  in  Figure  5,  elevate  the  Polar  Axis  equal  to  the  Latitude  of  30*  South,  and 
iimyr  the  Equator  at  Right  Angles  to  it.  From  the  Equator,  lay  off  the  Star's  Declination,  52*  27',  on  thm 
Meridian  towards  the  South,  which  will  be  the  place  of  the  Star,  and  its  distance  from  the  nearest  Horizo» 
ia  its  Meridian  Altitude  South. 

In  this  case,  the  elevation  of  the  upper  end  of  the  Equator  above  the  Horizon  being  equal  to  the  Co-Lat- 
itude of  60*  South,  and  the  Declination  of  the  Star  52*  27'  South,  both  of  the  same  name,  their  Sum  111* 
17'  exceeds  90*,  must  be  subtracted  from  180*,  gives  the  Meridian  Altitude  of  the  Star  67*  33',  reckontd 
from  the  South  point  of  the  Horizon. 

Find  the  Meridian  Altitude  or  Castor  in  thk  Latitude  or  10*  North 

Fig.    8. 


TO  CONSTRUCT  THK  FIGURK. 

Elevate  th»  Polar  Axis  equal  to  the  Latitude  of  10*  North,  and  draw  the  Equator  at  right  angles  to  It 
rom  the  Equator  lay  off  the  Declination  of  the  Star,  32°  18',  on  the  Meridian  towards  the  North,  whieb 
*all  be  the  Star's  place.     Then  its  distance  from  the"  nearest  Horizon  is  its  Meridian  Altitude. 

In  this  case,  the  Sum  of  the  Co-Latitude  80°  North,  and  the  Star's  Declination  32'  18'  North,  is  111*  8', 
which  exceeds  90*,  must  be  subtracted  from  180*,  gives  the  Altitude  67*  42'  North. 

Thus  having  the  computed  Altitude  of  any  Star  on  the  Meridian,  the  Star  itself  is  found  by  setting  the 
index  of  the  instrument  to  this  Altitude  and  facing  towards  the  South  or  the  North,  as  the  case  may  be, 
and  the  Star  vrill  be  seen  on  the  Horizon. 

On  referring  to  Figure  4,  the  time  at  which  the  Stars  pass  the  Meridian  is  easily  computed  by  subtrael* 
ing  the  Sun's  R.  Ascension  from  the  Star's  R.  Aso«n.<«ion,  (increasing  the  latter  by  24  hours,  if  necessary), 
will  be  the  apparent  time  of  its  Meridian  passage.     For  example  :  Suppose  a  Star,  whose  R.  A.  is  XIX  k 
In  ¥^g.  4;  the  Sun's  R.  A.  same  time  is  V[I  h  '  the  differ«nr«  '•h    or  M'dn'sb*   '•  th*»  ^rv  th« 
oaKUHi  the  ^endiaii  iii  N 


«6 


NAUTICAL  ASTRONOMY. 
Fig.  •. 


DEFINITIONS.  r>T 

CORRECTIONS  OF  THE  ALTITUDES  OF  THE  HEAVENLY  BODIES  ORSER\ED  AT    SEA 

Dip  of  the  Horizon  is  the  Angle  through  which  the  Sea  Horizon  appears  depressed,  in  consequence  oJ  the 
elevation  of  the  spectator's  eye  above  the  Sea  level. 

Suppose  the  observer's  eye  to  be  at  e  (in  the  figure  for  Dip  of  the  Horizon)  and  a  perpeudicukr  line 
drawn  to  his  zenith.  Then  a  line  drawn  at  right  angles  to  it  will  be  the  True  Horizontal  Line.  But  hii- 
eye  being  elevated  above  the  Sea,  his  vision  extends  over  tlie  curvature  of  the  Earth's  surface,  in  tlie 
direction  of  the  Visible  Horizon,  or  the  dividing  line  between  the  Sea  and  Sky.  And  as  the  Altitudes  ol  aU 
Heavenly  Bodies  are  measured  to  this  line,  it  is  evident  that  the  Altitudes  so  obtained  are  too  great  bv  ihe 
amount  of  the  angle  of  the  Dip  of  the  Horizon  contained  between  the  True  and  the  Visible  Horizons.  The 
distance  of  the  Sea  Horizon  from  the  observer  is  about  6  miles  when  the  eye  is  elevated  30  feet  above  ihe 
Sea ;  and  if  it  were  possible  to  observe  an  Altitude  with  the  eye  at  the  surface  of  the  Sea.  as  at  S.  there 
would  be  no  correction  required  for  Dip  because  the  True  and  the  Visible  Horizons  are  in  the  same  liiif 
*nd  the  Rational  Horizon  is  considered  r  bp  also  on  the  same  line. 

The  Dip  of  the  Horizon  at  different  -  «»'  au^np  is  given  in  Table  V  for  that  purpose,  and  is  always  sub 
Iractive  from  the  observed  Altitude. 

Ke/ruction. 

The  rays  of  light  proceeding  fipr  r»  Heavenly  Body  when  not  in  the  zenith,  in  traversing  th« 
Earth's  atmosphere,  become  bent  or  .-etracted  more  and  more,  on  approaching  the  surface  of  the  Earth 
towards  the  perpendicular,  which  causes  all  the  bodies  to  be  seen  above  their  true  places  in  the  Heavens 
•onsequently  the  observed  Altitudes  are  too  great  by  the  amount  of  the  Refraction.  The  rays  of  ligkt  pro- 
eeeding  from  the  Sun  at  L  (in  the  figure  for  Refraction),  entering  the  atmosphere  at  A,  becoming  ^ent 
upwards  as  it  proceeds,  the  spectator  sees  the  object  at  U,  and  the  difference  between  the  True  and  the 
Apparent  places  of  the  Sun  is  the  amount  of  Refraction.  The  Refraction  is  0  at  the  zenith,  because  tin 
rays  of  light  penetrate  directly  downwards,  and  are  not  bent  out  of  their  course.  At  the  Horizon  th« 
Refraction  is  about  34',  because  the  rays  of  light  enter  the  atmosphere  obliquely,  so  that  all  bodies,  (except 
the  Moon),  when  on  the  Horizon,  are  raised  that  much  above  their  true  place.  In  the  figure  the  lower  0 
appears  in  his  true  place  below  the  Horizon,  but  the  rays  of  light  entering  the  atmosphere  at  m  are  oem 
■pwards  or  refracted,  and  the  ©  is  seen  above  his  true  place  in  the  Horizon.  Refraction  diminishes  aa 
the  Altitudes  increase  from  the  Horizon  to  the  Zenith,  and  the  correction  for  Refraction  is  g'van  m  Tabic 
IV  for  that  purpose,  and  is  always  subtractive  from  the  observed  Altitude. 

Parallax. 

As  before  observed,  ths  Earth  is  considered  as  a  mere  point  in  the  centre  of  the  Sphere,  as 
regards  the  Stars,  which  are  situated  a  great  distance  from  it,  but  with  respect  to  the  S^cn.  Moon,  and 
Planets,  the  Earth's  semi-diameter  musi  be  taken  into  consideration  in  measuring  the  Altitudes  of  these 
bodies,  especially  the  Moon,  which  is  the  nearest  to  the  Earth.  Parallax,  therefore,  is  the  depression  of  a 
Heavenly  body,  inconsequence  of  its  being  seen  from  the  surface  instead  of  from  the  centre  of  the  Earth  , 
and  the  nearer  any  Heavenly  body  is  to  the  Earth,  the  greater  is  the  Angle  of  Depression 

The  Moon,  to  an  observer  at  the  surface,  would  appear  to  be  situated  in  the  Heavens  at  A,  (in  the  figure 
for  Parallax),  but  to  an  observer  at  the  centre,  her  place  would  be  at  T,  her  true  place  in  the  heavens  ;  and 
the  difference  between  the  two  places  is  called  her  Horizontal  Parallax,  and  which  ir  always  greatest  at 
the  Horizon.  Again,  to  an  observer  at  the  surface,  the  Moon  would  appear  at  a,  but  to  an  observer  at  the 
centre  of  the  Earth  she  would  be  at  t.  b«r  true  place  in  the  Heavens.  The  difference  between  these  two 
places  is  called  her  Parallax  in  Altitude.  The  Sun  and  Planets  being  at  a  greater  distance  from  the  Earth 
hare  only  a  very  small  parallax.  S  and  P  represent  the  Parallax  of  the  Sun  and  Planet.  When  a  body 
u  in  the  Horizon  its  Parallax  is  greatest  The  Sun's  Parallax  is  only  9",  while  the  Moon's  Parallax  is 
above  1*  sometimes.  But  when  a  body  is  in  the  Zf-nitb  Mh  Parallax  is  0,  because  it  is  seen  in  the  same 
line  from  the  centre  as  from  the  surface  as  at  Z.     The  Sun's  Parallax  in  Altitude  is  given  in  Tabls  VI. 

The  Moon's  Horizontal  Parallax,  which  is  in  perpetual  change,  and  the  Parallax  of  the  Planet*,  ar* 
fiven  in  the  Nautical  Almanac. 


M 


NAUTICAL  ASTRONOMY 
DIAGRAM, 


Showing  the  Manner  of  Measuring  the  Altitudes  of  the  Heavenly  Bodies  ai   Sea,  and  the  Correction  ftp 

Semi-diameter. 

Fio.  10. 


This  figure  repreient*  the  different  methods  of  observing  th^  Altitudes  of  the  Sun  and  Moon  by  bringinf 
Iheir  upper  or  lower  limbs  in  contact  with  the  Horizon. 

No.  1  is  an  Altitude  of  the  Sun's  lower  limb  brought  in  contact  with  the  Horizon.  This  it  the  usual 
method  practised  at  Sea,  being  the  most  simple  and  correct  mode  of  doing  it.  His  semi-diameter  added 
giTea  his  observed  Central  Altitude. 

No.  S  ii  an  Altitude  of  the  Sun's  upper  limb  brought  in  contact  with  the  Horizon.  This  is  only  resorted 
to  in  the  event  of  the  lower  limb  being  hidden  by  clouds.  His  semi-diameter  subtracted  gives  hia  observea 
Central  Altitude. 

No.  3  is  an  Altitude  of  the  middle  of  the  Sun  brought  down  to  the  Horizon.  This  kind  of  observation 
u  only  used  when  his  limbs  are  so  ill-defined,  in  consequence  of  the  sky  being  overcast,  as  in  the  case  when 
he  shines  through  a  rain-cloud,  that  no  observation  can  be  made  with  them  j  the  body  of  the  Sun,  however, 
may  be  visible.  By  a  little  practice  this  method  may  be  turned  to  a  good  account  in  finding  the  Latitude  of 
the  Ship,  in  the  room  of  a  better.  At  all  events,  it  is  more  to  be  trusted  to  than  the  Latitude  by  Dead  Reck- 
oning.    In  this  case  no  semi-diameter  is  allowed,  because  the  Central  Altitude  is  observed. 

No.  4  i«  an  Altitude  of  the  Moon's  lower  limb  brought  in  contact  with  the  horizon.  In  this  case  the 
Moon'a  semi-diameter  added,  gives  her  observed  Central  Altitude. 

No.  5  is  an  Altitude  of  the  Moon's  upper  limb  brought  m  contact  with  the  Horizon.  This  is  necessary 
when  her  horns  are  turned  downwards,  and  in  this  case,  her  semi-diameter  subtracted  gives  her  observed 
Central  Altitude. 

No.  6  IS  an  Altitude  of  a  Star  or  Planet  bisected  on  the  Horizon.  This  gives  its  observed  Central 
Altitude. 

Tne  semi-diameter  of  the  Sun  is  given  in  the  Nautical  Almanac  throughout  the  year.  His  greatest 
semi-diameter  is  16'  18",  at  the  time  the  Earth  is  nearest  to  the  Sun,  in  December;  and  his  least  is  15'  45", 
at  the  time  the  Earth  is  farthest  from  the  Sun,  in  June.  But  in  dealing  with  Altitudes,  we  generally  allow 
16'  as  his  mean  semi-diameter  throughout  the  year. 

The  Moon's  semi-diameter  is  also  given  in  the  Nautical  Almanac  for  the  nearest  noon  and  midnight  at 
Greenwich,  because  it  changes  very  rapidly,  her  greatest  being  about  16'  48",  and  her  least  about  14'  4^\ 
■o  that  it  is  necessary  to  take  it  from  the  Almanac  when  great  accuracy  is  required.  But  in  general  ttM 
lean  of  the  extremes,  which  is  about  16',  is  taken  as  the  Moon's  seihi-diameter. 

The  Stars  and  Planets  require  no  eorrection  of  the  Altitude  for  semi-diameter. 


69 


INSTRUIVtENTS  OF  NAUTICAL  ASTRONOMY. 


DESCRIPTION,  ADJUSTMENTS,  AND  USE  OF  THE  QUADRANT  AND  SEXTANT. 

These  are  instruments  for  measuring  angles  between  two  objects,  by  bringing  the  reflected  image  of  one 
•f  them  in  contact  with  that  of  the  other  seen  direct.  They  are  also  necessary  for  observing  Altitudes 
•f  the  heavenly  bodies  at  Sea,  where  the  spectator  has  no  fixed  point  of  reference  except  the  horizon. 
<See  Fig.  10.) 

On  Shore  this  fixed  point  is  obtained  by  means  of  the  Artificial  horizon,  when  the  Sea  hori«on  U 
oDstructed  by  the  land. 

The  Quadrant  contains  an  Arc  of  more  than  45**,  or  the  eighth  part  of  a  Circle  ;  but  on  account  of  the 
double  reflection  it  measures  a  few  degrees  more  than  90*.  The  Arch,  or  Limb,  is  divided  into  degreea,  and 
numbered  from  Right  to  Left.  These  are  subdivided  into  3  parts  of  20  mmutes  each,  which  are  agaio 
subdivided  into  single  minutes,  by  means  of  a  scale  at  the  end  of  the  Index.  The  Index  is  a  flat  brass  bar 
that  turns  on  the  centre  of  the  instrument.  When  moved  forward  in  measuring  Altitudes  the  icrew  behind 
ilamps  it  to  the  limb,  and  the  tangent  screw  is  then  used  to  make  the  contact. 

The  Nonius  is  a  scale  fixed  to  the  lower  part  of  the  Index  bar,  and  is  sometimes  called  a  Vernier.  Thi» 
is  a  portion  of  an  Arc  having  the  same  centre,  and  divided  into  one  part  more  than  an  equal  portion  of 
the  Arc  itself,  and  is  used  for  making  more  minute  divisions  on  the  Arch,  which  may  be  be»t  explained  by 
the  following 

EXAMPLE. 

Suppose  a  division  on  the  Arch  to  be  one-third  of  1*.  or  20',  and  the  Vernier  to  be  equal  in  length  to  19  divisions, 
or  880  ,  and  divided  into  20  equal  parts,  then  each  of  the  divisions  on  the  Vernier  is  one-twentieth  of  880',  that  k 
19',  and  therefort  the  diflference  between  one  division  on  the  Arch,  or  20',  and  one  on  the  Vernier,  it  1'. 

Now,  suppose  the  beginning  of  the  Vernier  at  0  to  coincide  with  the  beginning  of  the  Arch  at  0,  then 
the  first  of  tl  "  dividing  lines  of  the  Vernier  falls  short  of  the  first  dividing  line  of  the  Arch  by  1'.  There- 
fore, if  tl  »•  -es  are  made  to  coincide,  the  Vernier  must  be  advanced  1',  and  to  make  the  next  dividing 
line  or  2  on  tne  Vernier,  coincide  it  mu.'it  be  advanced  again,  and  so  on  until  the  division  of  20'  on  the 
Arch  is  all  gone  through.  Hence,  for  an  angle  on  the  Arch,  the  number  of  divisions  counted  on  the  Vernier 
before  the  coincidence  is  arrived  at,  is  the  number  of  minutes  to  be  added  to  the  division  of  the  Arch  next 
behind  the  0  on  the  Vernier.  For  an  angle  off  the  Arch,  it  must  be  read  from  the  opposite  end  of  th« 
Vernier 

"      TO  READ  OFF  AN  ALTITUDE. 

Look  at  the  0,  or  begmnmg  of  the  Vernier,  and  ascertain  how  many  degreea  and  divisions  it  has  passed 
on  the  Arch,  counting  the  first  division  20',  the  second  40',  and  then  look  along  the  divisions,  or  linei,  on 
the  Vernier  until  one  of  them  is  found  to  coincide  with  a  division,  or  line,  on  the  Arch,  which  being  counted 
from  the  0,  or  beginning  of  the  Vernier,  towards  the  left,  is  ciie  number  of  minutes  to  be  added  to  thai 
iirision  on  the  Arch  which  is  the  nearest  to  the  right  of  the  0  on  the  Vernier,  and  which  will  be  the  Altitude 
required. 

In  some  Quadrants  the  Vernier  ia  divided  into  40  equal  parts,  and  the  Angles  can  then  be  read  off  to 
half  minutes,  or  io" 


-yo 


l^sTRU^^K^•TS  of  nautical  astronomy. 


TO  ADJUST  A  QUADRANT. 


To  Set  the  Index  Glass  Perpendicular  to  the  Plane  of  the  Instrument. 

Move  the  Index  to  about  45°  on  the  Arch,  and  holding  the  instrument  in  a  horizontal  position,  face 
upwards,  look  obliquely  into  the  Index  Glass,  and  ascertain  if  the  true  and  reflected  images  of  the  Arch 
are  in  the  same  straight  line  ;  if  so,  the  Glass  is  adjust.  But  if  the  reflection  seems  to  droop  from  the 
Arch  itself,  the  Glass  leans  back  ;  if  it  rise  upwards,  the  Glass  leans  forward.  The  position  is  rectified 
by  the  screws  on  the  back. 

To  Set  the  Horizon  Glass  Parallel  to  the  Index  Glass. 

Set  the  0  on  the  Vernier  at  0  on  the  Arch,  and  clamp  the  Index;  hold  the  instrument  vertically,  and 
look  through  the  sight-vane  at  the  horizon,  or  any  other  well-defined  and  distant  object.  Then,  if  the 
reflected  and  the  true  horizons  appear  in  the  same  straight  line,  the  Glass  is  adjust.  But  if  the  horizona 
do  not  coincide,  use  the  lever  on  the  under  side  of  the  instrument  until  they  are  made  to  do  so.  This 
adjustment  ought  to  be  tried  before  and  after  every  observation. 

To  Set  the  Horizon  Glass  Perpendicular  to  the  Plane  of  the  Instrument. 

Having  previously  made  the  above  adjustment,  incline  the  instrument  on  one  side  as  much  as  poBsibl 
Then,  if  the  horizon  seen  through  the  sight-vane  continues  to  form  one  unbroken  line,  the  Glass  is  adjust. 
But  if  the  reflected  horizon  appears  to  separate  from  that  seen  direct,  then  the  Glass  wants  rectifying.  If 
the  face  of  the  instrument  is  upwards,  and  the  reflected  Sea  appears  higher  than  the  real  Sea,  you  must 
slacken  the  screw  before  the  Horizon  Glass  and  tighten  that  behind  it.  But  if  the  reflected  Sea  appears 
lower,  the  opposite  screws  must  be  used.  Care  must  be  taken  in  this  adjustment  to  loosen  one  screw  before 
tiie  other  is  screwed  up,  and  to  leave  the  adjusting  screws  tight.  Some  instruments  have  their  adjusting 
■crews  differently  constructed,  but  a  little  practice  will  soon  enable  a  person  to  adjust  them. 

The  graduation  of  the  Arch  should  commence  at  a  certain  point.  When  this  is  not  the  case,  the  Index 
Error,  as  it  is  called,  must  be  measured. 

The  point  at  which  the  graduation  of  the  Arch  is  supposed  to  begin,  is  that  at  which  the  Index  stands 
when  the  mirrors,  or  glasses,  are  parallel,  as  is  the  case  when  the  image  of  a  distant  object  is  seen  to  coin* 
cide  with  the  object  itself.  The  Index  Error,  therefore,  is  merely  the  error  of  the  place  of  the  beginninf 
of  the  divisions,  and  affects  all  angles  alike. 


TO  FIND  THE  INDEX  ERROR 


By  the  Horizon. 

Hold  ihe  iii.'^irutiieni  vertically,  and  make  the  image  of  the  horizon  comcide  with  the  horizon  itself,  a* 
iccurately  as  [lossible 

Then,  it  ilie  '>  on  the  Vernier  stands  at  the  0  on  the  Arch,  there  is  no  Index  Error.  Suppose  it  stood 
at  2  on  the  Arch,  that  is,  to  the  Left  of  the  0  on  the  Arch,  then  the  Index  Error  is  that  much  subtract) ve , 
but  if  it  siaiidi^  at  2'  otT  the  Arch,  that  is,  to  the  Right  of  the  0  on  the  Arch,  then  it  is  that  much  additive 
to  all  allsle^  liiken  hy.the  instrument. 

By  the    Sun. 

If  the  iii>iniMiiiii  has  no  Shade  for  the  Horizon  Glass,  take  the  opportunity  when  the  Sun  is  veiled  over 
by  thin  cloutls.  and  u^e  them  as  a  substitute  for  Shades.  Hold  the  instrument  vertically,  and  look  through 
the  sight-vane  diret'tly  at  the  Sun,  and  make  the  reflected  sun  cover  the  one  seen  direct.  Then  if  the  0 
on  tlie  Vernier  siands  at  0  on  the  Arch,  there  is  no  Index  Error.     Otherwise  it  is  found  as  before  explained. 

For  the  |)urposes  of  adiusting  an  instrurnenl,  objects  should  be  used  which  are  at  least  1  mile  distant; 
because  at  a  nearer  object  the  distance  between  the  glasses  produce  a  sensible  parallax,  and  the  ooincidenec 
doeft  not  take  place 


MANNER  OF  MEASURING  ALTITUDES  WITH    THE  UUADRANT  Tl 


MANNEH  OF  MEASURING  ALTITUDES  WITH  THE  QUADRANT 


To  Observe  the  Sun's  Altitude  at  Sea. 

Set  'fle  index  at  0,  and  put  do-WTi  a  screen  or  shade  before  the  Index  Glass.  Hold  the  instrument  m  a 
TerlicnJ  position,  and  direct  the  sight  through  the  sight-vane  and  Horizon-Glass  to  that  part  of  the  horizoB 
which  is  directly  under  the  Sun.  Now  move  the  Index  onwards  with  the  left  hand,  and  the  image  of  the 
Sun  will  appear  to  descend  towards  the  horizon.  Give  the  instrument  a  slow  motion  from  side  to  side^ 
round  the  line  of  sight,  and  the  Sun  will  appear  to  sweep  the  horizon,  and  it  must  be  made  just  to  touch  it  at 
the  lowest  part  of  the  arch.  This  gives  the  Observed  Altitude  of  his  lower  limb.  It  is  best  to  commence 
the  pbs'jrvation  some  time  before  the  Meridian  Altitude  is  expected,  and  to  continue  observing  until  his 
greatest  Altitude  is  obtained,  unless  the  watch  has  been  previously  regulated  and  the  apparent  time  at  the 
ship  known. 

This  last  Altitude  is  sometimes  near  enough,  but  for  accuracy,  having  made  a  rough  contact  as  above, 
put  in  the  telescope,  previously  set  to  distinct  vision  by  looking  through  it  at  the  horizon,  and  the  tube  may 
be  marked  at  the  proper  focus  of  the  observer's  eye.  The  image  being  now  magnified,  the  contact  is  made 
more  correctly.  Clamp  the  Index,  and  make  the  contact  perfect  by  turning  the  Tangent  Screw.  This  L» 
the  method  generally  used  in  taking  Altitudes  for  time. 

The  Tangent  Screw  should  be  kept  nearly  middled  when  not  in  use,  and  the  contact  should  be  made  in 
the  centre  of  the  field  of  view  of  the  telescope. 

To  Observe  the  Altitude  of  a  Star. 

Turn  up  the  sight-vane  or  unship  the  telescope.  Set  the  Index  at  0,  and  direct  the  sight  to  the  star,  antf 
look  with  both  eyes,  as  close  to  the  sight-vane  or  color  of  the  telescope  as  possible,  and  move  the  Indei 
onwards,  when  the  reflected  star  will  be  seen  to  descend,  and  which  must  be  followed  by  the  eye  until  i\ 
finally  reaches  the  horizon.  Now  give  the  instrument  a  slow  motion  from  side  to  side,  round  the  line  of 
sight,  and  the  Star  will  appear  to  sweep  the  horizon,  which  it  must  be  made  to  touch  at  the  lowest  part  of 
the  arch 

To  find  any  particular  star  on  the  Meridian,  the  readiest  way  is  to  compute  the  Meridian  Altitude,  (Se* 
pages  64  and  106)  and  set  the  Index  to  it.  Then  with  both  eyes,  as  before  observed,  look  towards  that  part 
of  the  horizon  indicated,  and  the  proper  star  will  be  seen  on  or  near  it.     Continue   to  observe   it,  until  il 

tains  its  greatest  Altitude.  By  this  means  it  is  impossible  to  mistake  the  star,  because  no  other  can  be 
on  the  Meridian  at  that  time. 

The  Altitude  of  Planets 

May  be  observed  in  the  day  time,  even  when  the  Sun  is  considerably  above  the  horizon,  for  though  they 
are  invisible  to  the  naked  eye,  they  may  readily  be  found  by  computing  their  Meridian  Altitude,  (see  page 
104),  and  set  the  Index  to  it.  Screw  in  the  telescope,  and  direct  the  sight  to  the  true  North  or  South  pointc 
nf  the  horizon  at  the  time  it  passes  the  Meridian,  and  the  Planet  will  be  plainly  seen  on  or  near  it. 

To  Observe  an  Altitude  of  the  Moon. 

The  same  directions  may  be  followed  as  given  for  the  stars,  to  bring  her  down  to  the  horizon,  an4  the 
telescope  afterwards  used  in  making  the  contact.  But  sometimes,  when  she  is  faintly  seen,  it  is  better  te 
use  both  eyes  without  the  telescope.  Her  upper  limb  must  be  observed  when  her  horns  are  downwards^ 
and  care  must  be  taken,  in  making  the  sweep  for  the  horizon,  that  her  limb  just  touches  it  at  the  lowest 
part  of  the  arch. 

The  best  time  for  making  observations  of  the  Moon  and  Stars  is  at  twilight,  for  then  the  horizon  is  di»- 
tinctly  visible ;  but  in  cloudy  weather  at  night  long  dark  shadows  are  sometimes  projected  on  the  sea, 
which,  in  the  case  of  the  Moon,  renders  it  difficult  to  ascertain  the  real  horizon  under  her. 


72  INSTRUMENTS  OF  N-4.UTICAL  ASTRONOMl 


THE  SEXTANT 


The  Sextant  is  constructed  upon  the  same  principle  as  the  Quadrant,  and  contains  an  Arc  of  more  thaa 
€0'  of  a  circle,  but  on  account  of  the  Double  Reflection,  it  measures  Angular  Distances  of  more  than  120*. 
The  Arch  or  limb  is  divided  into  degrees,  and  the  degrees  into  6  equal  parts  of  10'  each.  The  Vernier  is  gen- 
•crally  cut  to  10",  for  the  purpose  of  minute  readings,  which  is  thus  explained  :  Suppose  a  division  on  the 
Arch  to  be  J  of  1°  or  10',  and  the  Vernier  to  be  equal  in  length  to  590  of  such  divisions,  or  9*  50',  bu/ 
■divided  into  600  equal  parts.  Then  each  of  the  divisions  on  the  Vernier  is  ^^  part  less  than  the  591 
■divisions  on  the  Arch.  Therefore  the  difference  between  one  division  on  the  Arch  and  one  on  the  \ermei 
is  10".  As  the  Vernier  contains  600",  it  is  divided  into  10  equal  parts  or  minutes,  and  the  minute  into 
■6  equal  parts  of  10"  each. 

Now  suppose  the^  or  beginning  of  the  Vernier,  and  the  0  or  beginning  of  the  Arch  to  coincide;  then 
ihe  first  of  the  dividing  lines  of  the  Vernier  fall  short  of  the  first  dividing  line  of  the  Arcfc  by  10". 
If  we  make  these  lines  coincide,  we  advance  the  Index  and  Vernier  10".  Again,  to  make  the  second  divid- 
ing line  of  each  to  coincide,  we  must  move  the  Vernier  to  20",  and  so  on  to  30",  40",  50",  and  then  to  1'. 
Therefore  to  make  l'  on  the  Vernier  coincide  with  1'  on  the  Arch,  we  must  advance  the  Index  or  Vernier  1'. 
Hence  for  an  angle  on  the  Arch  the  number  of  divisions  counted  on  the  Vernier  before  we  arriTe  at  a 
coincidence  is  10",  20",  &c.,  to  be  added  to  the  division  of  the  Arch  next  behind  the  ^  or  to  the  right  of  the 
beginning  of  the  Vernier.  For  an  angle  off  the  Arch  we  must  read  from  the  opposite  end  of  the  Vernier 
And  from  left  to  right. 

The  scale  on  which  these  divisions  are  marked  is  generally  made  of  silver,  and  in  consequence  of  their 
minuteness  a  magnifying  glass  must  be  used  in  reading  them  off",  which  is  fixed  to  the  Index  bar  for  that 
purpose. 

The  Adjustment  of  the  Sextant  is  done  in  exactly  the  same  manner  as  that  described  of  the  Quadrant 
The  only   addition  is   the   following: 

To  set  the  Line  of  Sight  of  the  Telescope  parallel  to  the  Plane  of  the  Instrument. 

Thi»  is  »  very  important  matter,  beoaose  when  the  Inverting  Telescope  is  used,  as  in  the  case  of  mearar- 
ing  the  Lunar  Distance,  any  defect  in  this  adjustment  causes  a  considerable  error  in  the  measurement  of  the 
«ngle,  and  always  makes  it  too  great. 

Place  the  two  wires  of  the  Inverting  Telescope  parallel  to  the  plane  of  the  instrument.  Select  two  dis- 
tant objects  about  120°  apart  from  each  other,  such  as  two  stars,  or  the  Sun  and  Moon,  and  make  an  exact 
contact  at  the  lower  wire,  or  that  nearest  the  instrument.  Now  move  the  instrument  so  as  to  throw  the 
image  in  contact  upon  the  upper  wire.  If  the  contact  is  still  perfect,  (the  images  continuing  the  surae  in  the 
middle  of  the  field),  the  adjustment  is  perfect ;  but  if  they  have  separated,  the  object  end  of  the  telescope 
^oops  towards  the  plane  of  the  instrument ;  if  they  overlap,  it  rises  from  the  plane  of  the  instrument. 
The  position  of  the  telescope  is  rectified  by  the  screws  in  the  collar. 

The  adjusting  screws  are  never  to  be  touched,  except  from  necessity,  and  then  with  the  greatest  ponible 
■caution. 

When  two  screws  work  against  each  other,  care  must  be  taken  in  tightening  one  to  loosen  the  other 
if  necessary. 

The  sides  of  the  colored  glasses  are  sometimes  not  exactly  parallel,  and  the  shades  may  cause  an  error  in 
Ihe  angle.  It  is^  therefore,  prudent  to  find  the  error  of  each  shade  or  combination  of  shades  from  actual 
4ri«L 


ro  FIND  THE  INDEX  ERROR  OF  THE  SEXTANT. 


T9 


TO  FIND  THE  INDEX  ERROR  BY  MEASURING  THE  SUN'S  DIAMETER. 


Ihe  Index  Error  of  an  instrument  being  merely  the  error  of  the  place  of  the  Beginning  of  the  divisioa*, 
^hen  all  the  Mirrors  or  Glasses  are  pexiectly  adjusted,  and  it  aifects  all  angles  alike.     >. 

To  Measure  the  Sun's  Diameter. 

Screw  in  the  Inverting  Telescope  and  adjust  it  to  direct  vision;  turn  up  the  proper  Shades,  place  the    t 
on  the  Vernier,  about  40'  to  the  Right  of  0,  on  the  Arch,  and  clamp  the  Index.      Then,  holding  the  instru- 
ment horizontally,  bring  the  direct  and  reflected  Suns  in  exact  contact  by  the  use  of  the  tangent  screw,  and 
read  off  the  minutes  and  seconds,  counting  from  the  opposite  or  Left  end  of  the  Vernier,  which  call   off  tlie 
Arch. 

Next  place  the  f  of  the  Vernier  about  40'  to  the  Left  of  0,  on  the  Arch,  and  make  the  contact  of  the 
two  Sun's  as  before,  and  read  off  the  minutes  and  seconds  in  the  usual  way,  which  call  on  the  At«k,  and 
set  it  under  the  first  reading ;  then  half  the  difference  of  the  two  readings  will  be  the  Index  Error,  which 
is  additive  to  all  angles  taken  with  the  Sextant,  when  the  Reading  to  the  Right  of  0  is  greater  than  the 
Reading  to  the  Left  of  0,  but  subtractive  when  the  reading  to  the  Left  is  the  greatest.  If  the  two  reading? 
are  equal  there  is  no  Index  Error  to  the  instrument.  The  direct  and  reflected  Suns  will  appear  through 
the  Inverting  Telescope  thus  : 


iVhen  the  Vernier  is  to  the  Right  of  0  on  the  Arch. 


Keflected  Sun.     Direct  Siin. 


When  the  Vernier  is  to  the  Left  of  0  on  the  Arch. 

Direct  Sun.    Reflected  Sun. 


Suppose  the  following  Observations  were  taken  to  determine  the  Index  Error  : 

EXAMPLE  1.  EXAMPLE  2. 


let  Jan.,  1854. 


Reading off  31'  65" 

do on  33  15 

)1   20 


Index  Error O'  40"  Sub. 

Because  the  reading  on  the  Arch  is  greater  than  the 
feading  off. 


31st  Jan.,  1854. 


Index  Error. 


Reading off  S3'  40" 

do on  31   20 

)2  20 


1'  10"  Add. 


Because  the  reading  off  the  Arch  is  greater  ♦ban  th« 
reading  on. 


When  both  Readings  are  on  the  Arch,  (which  can  only  happen  when  the  Index  Error  exceeds  half  a 
degree,)  the  Index  Error  is  the  Mean  of  the  two,  and  subtractive,  but  when  both  Readings  are  off  tlie  Arch, 
the  Index  Error  is  the  mean  of  the  two  additive. 

To  prove  that  the  contacts  were  made  correctly,  add  the  Readings  together  and  divide  their  Sum  by  4, 
find  the  quotient  should  be  equal  to  the  Sun's  semi-diameter  as  given  in  the  Nautical  Almanac  for  the 
cbove  days  of  the  month. 


In  Example  1,  the  Sum  of  the  Readings  is  65'  10" 
WhicJi  divided  by  4  gives  the  Semi .1,6'  17".5. 


In  Example  2,  the  Sum  of  the  Readings  is   65'  00" 
Which  divided  by  4  gives  the  Semi 16'  16" 


These  agree  nearly  with  that  given  in  the  Almanac,  namely,  16'  18"  on  the  1st,  and  16'  15".7  on  the 
31st.     It  may,  therefore,  be  presumed  that  the  contacts  were  correctly  made. 

In  this  manner  the  error  of  each  colored  glass,  or  Shade,  may  be  found  by  first  measuring  the  Sun'« 
diameter  at  the  time  when  there  is  a  thin  veil  of  clouds  over  his  disc,  (which  will  answer  the  purpose  of 
Shades,)  and  as^certain  the  Index  Error  as  in  the  above  Examples  (without  using  any  Shade.)  'Then  to 
measure  it  again,  using,  say,  the  Green  Shades.  If  these  two  measured  diameters  agree,  the  GrcQn  Shades 
are  correct.  If  they  do  not,  then  their  difference  is  the  error  of  the  Green  Shades,  which  must  be  applied  to 
the  Index  Error,  when  they  are  n.«ed.  In  like  manner,  the  Red  Shades,  or  any  combination  of  Red  and 
Green,  may  be  proved  by  using  them  in  measuring  the  diameter,  and  afterwards  comparing  them  with  that 
'vhich  was  measured  without  the  Shados. 


74  INSTRUMENTS  OF  NAUTICAL  ASTRONOMY. 


USE  OF  THE  SEXTANT. 

To  Observe  the  Angular  Distance  between  the  Sun  and  Moon. 

When  the  Distance  between  them  is  considerable,  lind  their  approximate  distance  in  the  Nautical 
Almanac,  corresponding  to  the  Greenwich  Time  of  the  observation,  (by  simply  turning  the  Ship's  Longitude 
Lnto  Time,  by  Table  XXVI.,  and  adding  it  to  the  Time  at  the  Ship  in  West,  or  subtracting  it  in  East  Lon- 
gitude.) Now  set  this  approximate  distance  on  the  Sextant,  turn  up  one  or  more  of  the  Shades  before  the 
Index  Glass,  according  to  the  brightness  of  the  Sun.  Screw  in  the  Plane  Tube  into  its  collar.  Then,  hold- 
ing the  Sextant  (with  its  face  upward  when  the  Sun  is  to  the  Right  hand  of  the  Moon,  or  downward  wherv 
the  Sun  is  to  the  Left,)  with  its  Plane  in  the  line  of  Sight  of  the  two  objects,  and  direct  the  Sight  to  the 
Moon,  and  the  Sun's  image  will  be  seen  near  to  it.  Make  the  contact  roughly.  Take  out  the  Tube  and 
screw  in  the  Inverting  Telescope,  and  adjust  it  to  distinct  vision,  placing  the  wires  parallel  to  the  Plane  of 
the  instrument.  Raise  the  Telescope  (by  the  screw  behind)  to  the  transparent  part  of  the  Horizon  Glass. 
Then,  directing  the  Sight  through  the  Telescope  to  the  Moon,  holding  the  instrument  as  before  directed, 
make  the  contact  perfect  by  means  of  the  tangent  screw,  at  the  same  time  moving  the  Sextant  round  the 
axis  of  the  Telescope,  by  which  means  the  Sun  will  appear  to  pass  slowly  by  the  Moon,  and  the  contact  be 
more  accurately  made.  Observing  always  that  the  point  of  contact  of  the  limbs  should  be  as  near  the 
centre  of  the  field  of  the  Telescope  (that  is,  in  the  middle  between  the  four  wires)  as  possible. 

Reading  off  the  Angle. 

Ascertain  the  nearest  degree  on  the  Arch  to  the  Right  of  the  f  ,  or  the  beginning  of  the  Vernier,  then 
the  nearest  division  of  the  degree  on  the  Arch.  Then  look  along  the  Vernier,  and  ascertain  whicl  line 
coincides  with  the  line  on  the  Arch,  then  the  minutes  to  the  Right  of  where  the  coincidence  takes  place 
must  be  added  to  the  division  of  the  degree,  and  the  seconds  are  counted  to  the  Left  of  the  nearest  m:nut« 
on  the  Vernier  up  to  the  place  of  coincidence.  1 

EXAMPLE, 

Of  finding  the  Approximate  Central  Distance  between  the  Sun  and  Moon.  • 

February  7th,  1854.  At  8  hours  20  minutes  A.  M.,  Sea  Time,  in  Longitude  of  70*  0'  West  Required  the  Ap 
proximate  Central  Distance  of  the  Sun  and  Moon. 

■nme  of  Observation 8h  20m.  A.M     The  Distance  in  N.  A.  at  Noon  is 117'  47'  61"  West 

A.dd 12h  Acdatlllh. 119     8  28 

From  the  preceding  Noon  20h.  20m.  The  Moon's  Motion  in  3b.  is 1°  20'  87"    Increaaiiig. 

Long.  70*  in  Time .4h  40m.  q  t.  being  Ih.  from  Noon,  or  equal  to  i  of  it  . ,.    26' 52" 

26h.  00m.  Which  added  to  the  Distance  at  Noon 1 1 7  °  47 '  6 1 " 

Subtract 24h.  qj^^  th^  required  Distance  at  8h.  20m,  A-M-llS"  14'  48" 

Greenwich  Time,  Feb.  7th    Ih.  00m. 

Now  put  this  on  the  Arch  of  the  Sextant  as  follows :  Advance  the  Index  until  the  f  on  the  Vernier  has 
passed  the  stroke  of  118°,  and  also  the  first  division,  or  10',  of  the  adjoining  degree  on  the  Arch.  Then 
look  along  the  Vernier,  and  make  the  5'  on  it  coincide  with  one  of  the  divisions  on  the  Arch.  The  instru- 
ment will  then  have  on  it  118°  15',  or  even  118°  is  near  enough  for  the  purpose  of  bringing  the  objects 
into  the  field  of  view.  Accuracy  is  not,  therefore,  required  when  the  Sun  is  used.  After  bringing  the 
nearest  limbs  "n  contact,  screw  in  the  Telescope,  and  proceed  as  directed.  In  this  case,  the  Sun  being  to 
the  Right  of  the  Moon,  (in  North  Latitude.)  the  instrument  is  held  with  its  face  upwards,  in  the  line  of 
Sight,  and  the  Telescope  directed  to  the  Moon,  when  the  Sun  will  appear  inverted,  or  on  the  Left  of  the 
Moon. 

In  South  Latitude,  by  direct  view,  the  Sun  will  be  on  the  Left  of  the  Moon,  and  the  Sextant  roust  be 
\eld  face  downwards,  and  the  Sight  directed  to  the  Moon. 


TO  OBSERVE  THE  DISTANCE  BETWEEN  THE  MJON  AND  A  STAE.  Ti 


TO  OBSERVE  THE  DISTANCE  BETWEEN  THE  MOON  AND  A  STAR. 


Turn  the  Ship's  Longitude  into  time  by  Table  XXVI,  and  add  it  lo  the  time  at  the  Ship  in  West  Longi- 
tude, or  subtract  it  in  East,  will  give  the  approximate  time  at  Greenwich.  Look  into  the  Nautical  Almana* 
amongst  tlie  Lunar  Distances,  agamst  the  day  of  the  month,  and  find  the  given  Star's  distance  from  the 
Moon  corresponding  to  this  Greenwich  time.  Put  this  distance  on  the  Arch  of  the  Sextant.  Turn  up  one 
of  the  green  shades  before  the  Index-glass  ;  then  holding  the  plane  of  the  instrument  in  the  line  of  sight 
between  the  Moon  and  Star,  with  its  face  upwards  when  the  Moon  is  to  the  Right  of  the  Star,  or  downward* 
when  the  Moon  is  to  the  Left  of  the  Star.  Direct  the  sight  through  the  ring  of  the  collar  towards  the  Star, 
(without  using  the  Telescope),  and  the  Moon's  image  will  be  seen  near  the  Star.  Move  the  Index  so  as  to 
bisect  the  Star  on  the  bright  limb  of  the  Moon  Now  screw  in  the  Inverting  Telescope,  and  adjust  it  to 
distinct  vision,  and  make  the  contact  perfect  by  means  of  the  tangent  screw,  at  the  same  time  moving  the 
Arch  of  the  Sextant  slowly  up  and  down,  by  which  motion  the  bright  limb  of  the  Moon  will  appear  to 
pa«s  the  Star,  and  the  contact  be  more  accurately  made,  and  "which  should  always  be  done  as  nearly  at 
possible  in  the  centre  of  the  field  of  the  telescope.  The  angle  being  read  off  will  give  the  observed  dis- 
tance between  the  Star  and  the  Moon's  bright  limb. 

In  the  Nautical  Almanac,  headed  Lunar  Distance,  the  Sun,  Stars,  and  Planets  are  marked  according  ar 

they  are  East  or  West  of  the  Moon.     By  attending  to  this  and  having  the  approximate  distance  on  the 

Arch  of  the  Sextant  corresponding  to  the  Greenwich  time,  any  Lunar  Star  may  be  easily  found  by  a  person 

otherwise  unacquainted  with  the  stars  in  the  heavens,  because  no  other  one  in  that  direction  will  correspond 

%  it  in  distance. 

EXAMPLE 

Of  Finding  a  Lunar  Star. 

January  3l8t,  1854,  at  lOh.  25m.  P.  It,  Sea  Time,  in  Longitude  60*  0'  W.  Required  th«  Bpprozimato  distitvM 
between  the  Moon  and  the  Star  Aldebaran 

Time  of  Observation. . .  .lOh  25m         Distance  of  Aldebaran  at  Midnight  86*  88'  38"  East  of  the  Moob. 

Long.  60*  W.  in  time _4 Do.  do.  XVh....83    63    69 

Greenwich  time  Jan.  30th  14h  26m  Moon's  motion  in  3  hours 1*  44'  89"      Pro.  Loir.,   2855 

\^ G.  Time  past  Midniglit 2h  25m     Pro.  Log..  098» 

Past  Midnight 2h  26m         pp^.  of  Dist.  to  be  subtracted 1*  24'~18^     Pro.  Log..  829r 

From  the  Dist  at  Midnight 85    88   28 

Which  gives  the  Star's  Distance  from  the  Moon 84"  14'  10"  at  lOh  26m  P.  M. 

It  18  necessary  to  be  as  exact  as  possible  in  finding  the  approximate  distance  between  the  Moon  ard  a 
Star,  for  very  often  it  is  the  only  security  we  have  for  employing  the  right  star.  Now  put  84*  14'  on  the 
Arch,  as  follows  :  Advance  the  Index  until  the  f  on  the  Vernier  has  passed  the  Stroke  for  84°,  and  also 
that  of  the  first  division  or  10'  of  the  adjoining  degree.  Then  look  along  the  Vernier  and  make  4'  on  it 
coincide  with  .some  line  on  the  Arch,  which  will  be  the  required  distance.  The  Star  bein^  East  or  to  tho 
left  of  the  M8on  (in  North  Latitude),  the  Sextant  must  be  held  with  its  face  upwards  in  the  proper  line  of 
sight,  and  the  sight  directed  through  the  collar  in  the  direction  of  the  Star.  Then  if  it  be  the  right  Star 
it  will  appear  on  ihe  face  of  the  Moon.  Bring  it  in  contact  with  her  bright  limb,  screw  in  the  Inverting 
Telescope,  and  the  contact  is  then  made  perfect  by  the  tangent  screw  as  before  directed. 

In  South  Latitude  the  same  Star  w^ill  be  to  the  right  of  the  Moon,  and  the   Sextant   must   be   held  fact 
downwards,  and  as  a  general  rule  the  sight  must  be  directed  to  th«  dimmest  object,  and  the    orightest  or 
•rought  to  it 


T«  INSTRUMENTS  OF  NAUTICAL  ASTRONOMY. 


REMARKS  ON  MEASURING  THE  LUNAR  DISTANCE. 

Of  the  Inverting  Telescope. 

(jn  ftcootirt  of  all  the  objects  seen  through  this  Telescope  being  inverted,  and  the  difficulty  of  keeping 
them  in  th<^  tleld  of  view  in  consequence  of  the  motion  of  the  Ship  at  Sea,  which  is  extremely  puzzling 
for  a  lear»irf,  because  when  the  instrument  is  not  held  steady  they  always  appear  to  go  out  of  view  on  the 
WT'ng  Bid,.  This  however  can  only  be  remedied  by  practice  and  by  shifting  the  instrument  in  the  opposite 
divectic.7  to  what  he  would  do  if  they  were  seen  direct.  We  are  obliged  to  submit  to  this  »-.nnnyance, 
becauH«»  of  the  superior  power  derived  from  the  Inverting,  to  what  could  be  obtained  trom  a  Direct  Telescope, 
of  tM  same  length.  Besides,  the  cross  parallel  wires,  which  are  so  useful  in  the  Inverting  Telescope,  could 
not  b«  used  in  a  common  one. 

Of  the  Common  Telescope. 

Those  who  find  a  difficulty  in  observing  with  the  Inverting  Telescope  may  find  a  good  substitute  in  tht 
Common  one.  For  although  its  power  is  not  so  great,  if  the  contact  is  made  as  near  as  possible  in  the 
eentre  of  the  field,  by  a  little  practice  a  very  fair  result  may  be  obtained,  if  distances  are  observed  East  and 
West  of  the  Moon,  and  the  mean  of  the  Longitudes  taken. 

TTie  Proper  Place  of  the  Ship  for  taking  the  Observation, 

Is  as  near  as  possible  to  the  midships  of  the  vessel,  because  there  her  motic  .  is  the  least  felt,  and  when 
•he  rolls  heavy  going  before  the  wind,  if  the  yards  were  braced  forward  a  litl'  ^  it  would  help  to  keep  her 
■teady  until  the  observation  is  completed. 

The  observer  should  place  himself  firmly  in  a  corner,  and  sit  or  lie  down  on  the  deck,  whichever  is  most 
convenient,  so  that  the  least  bodily  effort  may  be  required  to  steady  himself.  The  following  method  I  have 
found  of  great  utility,  which  does  not  require  the  tangent  screw  to  be  touched  at  all,  v/hen  the  contact 
takes  place,  consequently  both  hands  can  be  used  to  hold  and  steady  the  instrument,  and  the  whole  atten 
tion  is  directed  to  the  time  of  the  contact.  It  also  does  away  with  what  is  called  the  springing  of  th» 
Index  Bar,  (after  the  contact  is  made  with  the  tangent  screw),  which  is  the  case  even  in  the  best  instru- 
tnenta : 

NEW  METHOD  OF  MEASURING  THE  LUNAR  DISTANCE. 

When  the  Distarut  is  Increasing  (which  may  be  known  by  inspecting  the  N.  A.),  and  the  Near  Limbs  to  b« 

Observed, 

Set  the  Index  rf  the  Sextant  so  that  the  objects  may  overlap  each  other  a  little,  and  watch  for  the  instant 
when  the  Moon,  by  her  motion  in  the  heavens,  brings  the  limbs  in  contact.  Note  the  time  and  read  off"  the 
ansle.  Advance  the  Index  1',  and  then  watch  as  before  for  the  contact.  Now,  as  the  Moon  advances  to 
the  Eastward  in  the  heavens  at  the  rate  of  about  1'  in  two  minutes  of  time,  this  will  give  time  to  read  off 
the  angles  and  to  note  down  the  observation.  Then  having  advanced  the  Index  another  1',  proceed  a« 
before,  until  the  required  number  of  distances  are  observed. 

Distance  Increasing,  and  the  Far  Limb  of  the  Moon  to  be  Observed. 

By  advancing  the  Index  1',  the  Star  will  appear  separated  from  the  Moon's  Limb.  The  contact  is  then 
watched  for,  and  the  observation  made  in  the  same  manner  as  the  above. 

Distance  Decreasing,  and  the  Near  Limbs  to  be  Observed. 

Set  the  Index  so  that  the  limbs  may  appear  a  little  separated,  and  watch  for  the  contact  taking  place. 
Mote  the  time  and  read  off.  Then  set  back  the  Index  l',  and  watch  the  contact  as  before.  Note  the  time 
and  read  off,  and  so  on. 

Distance -Decreasing,  and  the  Far  Limb  to  be  Observed. 

By  setting  back  the  Index  1',  the  Star  will  appear  to  overlap  the  Moon's  Limb.  Watch  for  the  contact 
a.s  before,  and  in  the  same  manner  as  the  last.  By  this  means  the  Moon  is  made  to  measure  her  own  di». 
taiice,  and  all  that  is  required  to  be  done  is  to  note  the  time  of  the  contact 

For  further  remarks  on  measuring  the  Lunar  Distance,  see  page  163 


THE  ARTIFICIAL  HORIZON  tT 


THE  ARTIFICIAL  HORIZON. 

Whsn  an  observer  has  not  the  advantage  of  a  Sea  Horizon  for  the  purpose  of  measuring  Altitudes  of  the 
neavenly  bodies,  or  when,  for  instance,  the  Ship  is  in  port  and  the  Sea  Horizon  obstructed  by  the  land 
around,  he  is  obliged  to  use  an  Artificial  one,  and  which  is  used  for  finding  the  Latitude  of  the  place,  and 
also  for  rating  the  Chronometer,  &c.     (See  Fig.  11,  page  78.) 

An  Artificial  Horizon  is  variously  constructed,  but  the  general  principle,  is  to  produce  a  perfectly  level 
surface.  The  most  simple  is  that  of  a  pool  of  water  on  a  calm  day,  or  a  basin  containing  water.  But  the 
most  common  in  use  is  a  trough  filled  with  quicksilver,  and  protected  from  the  wind  by  a  roof,  in  which  are 
fixed  two  glasses,  ground  perfectly  plane  and  parallel. 

Another  kind  has  a  plate  of  glass  in  the  trough,  which,  when  the  quicksilver  is  poured  in,  floats  on  the 
surface,  and  a  roof  is  not  required.  But  these  kind  of  instruments  are  troublesome,  in  having  to  pour  in 
and  out  the  quicksilver  every  time  they  are  used.  Besides,  there  is  a  scum  or  film  gathers  on  the  surface 
of  the  fluid.  This,  however,  may  be  prevented  from  running  into  the  trough,  by  holding  the  bottle  bottom 
op,  while  it  is  poured  out. 

Tar,  Treacle,  and  Oil  have  been  tried  for  this  purpose,  but  they  do  not  give  satisfaction  j  especially  when 
exposed  to  the  strong  heat  of  the  Sun,  because  the  fluidity  varies  from  unequal  expansion. 

The  best  and  cleanest  kind  of  Horizon  is  a  brass  circular  box,  of  about  5  inches  in  diameter,  supported  on 
three  screw  legs,  having  a  thick  plate  of  glass  glazed  into  its  rim.  The  under  surface  of  this  glass  is  unpol- 
ished, and  a  space  left  between  it  and  the  bottom,  this  space  being  nearly  filled  with  spirits  of  wine,  leaving 
a  small  portion  vacant,  so  as  to  produce  an  air  bubble,  and  which  bubble,  by  the  use  of  the  screws  is 
brought  under  the  centre  of  the  glass.  This  centre  must  be  ascertained  from  actual  trial,  and  marked,  so 
that  the  bubble  can  always  be  placed  under  it.  The  strong  heat  of  the  Sun  will  cause  the  spirits  to  expand, 
but  a  screw  plug  is  fixed  at  the  side,  which  can  be  taken  out,  and  a  small  bell-shaped  funnel  put  in  its 
place  to  receive  the  surplus  spirits  caused  by  expansion.  This  instrument,  together  with  a  pocket  Sextant, 
will  form  a  portable  Observatory,  valuable  to  those  who  may  have  occasion  to  travel  much  inland. 

When  one  of  these  instruments  is  used,  it  must  be  placed  on  firm  ground,  and  the  observer,  facing 
towards  the  Sun,  walks  backwards  until  he  sees  the  direct  image  of  the  Sun  reflected  on  the  surface  of  the 
Artificial  Horizon.  Then,  turning  down  the  Shades  over  both  the  Index  and  Horizon  Glasses  of  the 
Sextant,  he  directs  his  sight  through  the  Collar  of  the  Telescope  at  the  reflected  image  in  the  Artificial 
Horizon,  at  the  same  time  advancing  the  Index  Bar,  when  the  reflected  image  from  the  Sextant  will  appear 
to  descend.  He  now  brings  the  lower  limb  of  this  Sun  in  contact  with  the  upper  limb  of  the  direct 
Sun  already  seen.  The  Telescope  is  then  screwed  in  and  the  observation  made.  It  is  thus  necessary 
to  bring  the  limbs  in  contact,  before  using  the  Inverting  Telescope,  as  a  security  against  using  the 
wrong  limbs. 

The  Image  of  a  heavenly  body  reflected  from  the  surface  of  a  fluid  at  rest,  appears  as  much  below  the 
true  horizonal  line  as  the  object  itself  appears  above  it.  The  Angular  Distance,  measured  between 
the  object  and  its  image,  is,  therefore,  Double  the  Altitude.  And  in  halving  the  Angle  shown  by  tho 
iDitrument.  we  halve  at  the  same  time  all  the  errors  of  the  observation. 


b 


78 


INSTRUMENTS  OF  NAUTICAL  ASTRONOMV. 


DESCRIPTION  AND  USE  OF  THE  ARTIFICIAL  HORIZON. 

Tki  foLowing  Diagram  will  illustrate  the  Method  of  Observing  Altitudes  with  an  Artificial  Horizon 

Fig.  11 


^^x-<C* 


^nyle  ^^°A 


^y'Wl^ 


,^'%^ 


JicrtT-onlal      C-t 


as  seen   I'rt   tke  J/oriZo?v 


Hefleiled 

frcm  i/ie       I 

Sextant 


i-n.    the 


onzoii 


In  taking  Altitudes  for  Time,  the  Sun  will  appear  to  rise  or  fall  with  double  the  velocity  he  would  other 
arise  do,  when  observed  with  the  natural  horizon. 

AVhen  the  Sun  is  rising,  the  observer  is  obliged  to  approach  nearer  to  the  Artificial  Horizon,  according 
as  the  Altitude  increases.  On  the  other  hand,  when  the  Sun  is  falling,  he  is  obliged  to  increase  hts  distanc* 
from  it,  according  as  the  Altitude  decreases.  And  when  the  Sun's  Altitude  is  at  12°,  or  14°,  it  becomes 
difficult  to  .eep  sight  of  the  imases  reflected  in  the  Horizon,  and  with  Altitudes  below  this,  it  is  generally 
»npractic-  ole,  on  account  of  the  slanting  direction  of  the  Sun's  rays. 

An  Altitude  of  the  Sun,  or  other  heavenly  body,  may  be  obtained  by  this  instrument  to  the  extent  of 
60";  that  is,  to  120°  by  reflection,  this  being  generally  the  limits  of  the  Scale  on  the  Arch  of  the  Sextant. 
In  Low  Latitudes,  therefore,  it  is  often  impossible  to  observe  with  the  Artificial  Horizon  any  heavenly  body 
whose  Altitude  exceeds  60°,  unless  we  use  a  Sextant  of  superior  power. 

The  Latitude  may.  however,  be  obtained  near  the  Equator,  by  choosing  a  Star  of  the  first  magnitude, 
which  has  great  North  or  South  Declination,  and  whose  Meridian  Altitude  is  less  than  60°.  In  computing 
the  Meridian  Altitude  of  a  Star,  for  the  purpose  of  observing  with  the  Artificial  Horizon,  we  have  only  to 
double  the  computed  Altitude  found  by  the  Rule  at  page  66,  and  place  it  on  the  Arch  of  the  Sextant.  Face 
towards  the  Star,  and  walk  backwards  until  the  Star's  image  appears  reflected  in  the  Horizon.  Then  direct 
Jhe  sight  through  the  Collar  of  the  Telescope  of  the  Sextant  at  the  Horizon,  and,  holding  the  instrument 
rertically,  the  two  Star?  will  be  seen  in  contact  with  or  near  to  each  other,  (at  the  time  of  its  Meridian 
passage.)  They  are  now  brought  in  contact,  and  kept  so  until  the  greatest  Altitude  is  obtained.  This 
gives  security  that  the  right  Star  has  been  observed. 

In  observations  taken  with  this  instrument,  it  mu.st  be   remembered  that  no  Dip  is  to  be  allowed  for,  aa 
2  the  case  of  usma  the  Sea  Horizon.      (See  Da^es  92.  131,  and  159.  for  Ob.servations  with  this  Instrument.) 


THK  CHRONOMETER.  /         19 


THE  CHRONOMETER. 


The  Chroiiomt  tcr  is  a  superior  kind  of  Watch,  constructed  so  as  to  keep  as  near  as  possible  a  Uniform  or 
Mean  Time.  It  is  set  generally  to  the  Mean  Time  at  Greenwich,  and  its  Daily  Rate  ascertained,  that  is,  what 
it  is  gaining  or  losing  on  this  Uniform  or  Mean  Time.  This  instrument  is  of  great  value  to  the  Navigator, 
principally  in  determining  the  Longitude  at  Sea,  and  other  useful  purposes  in  Navigation,  because  if  the 
Mean  Time  at  Greenwich  (where  the  Longitude  is  reckoned  from)  be  known  from  consulting  the  Chronom- 
eter, and  the  Mean  Time  at  the  Ship  be  known  from  observation  at  the  same  instant  of  time,  this  difference 
of  time  turned  into  degrees  and  minutes  at  the  rate  of  15°  to  the  hour  of  Time,  is  the  Longitude  of  the 
Ship. 

The  following  .omarks  will  be  found  useful  in  managing  this  instrument: 

When  a  Cb'onometer  is  received  on  board,  it  should  be  screwed  down  in  a  safe  and  proper  place,  at  a 
distance  fron.  all  iron  substances,  and  where  it  is  not  likely  to  receive  any  sudden  shock  or  jerk,  and  there 
it  must  remain  during  the  voyage,  and  wound  up  regularly  every  morning  before  breakfast. 

In  winding,  the  key  should  be  turned  steadily,  and  about  half  a  turn  taken  each  time,  and  it  should  be 
wound  close  up.  After  winding,  it  should  be  examined,  and  if  close  up,  the  Index  Hand  on  the  face  of  it 
will  stand  at  0.     Ascertain,  also,  that  it  has  not  stopped  after  being  wound  up. 

When  a  Chronometer  is  wound  up  after  running  down^  it  is  set  agoing  by  giving  it  a  small  horizontal 
circular  motion. 

When  a  Chronometer  stops  it  generally  alters  its  Rate. 

The  hands  of  a  Chronometer  must  not  on  any  account  be  touched,  either  before  or  after  it  is  set  agoing 
The  proper  way  to  set  it  to  Greenwich  Time  is  as  follows  :  Look  at  what  hour,  minute  and  second  the 
hands  of  the  Chronometer  has  stopped  at,  and  note  it  down.  Turn  the  Ship's  Longitude  into  Time,  and 
subtract  it  from  that  Time  if  the  Longitude  is  West,  or  add  it  to  that  Time  if  the  Longitude  be  East,  and 
the  result  is  the  computed  Mean  Time  at  the  Ship.  Now  have  your  Watch  previously  regulated  to  the 
exact  Mean  Time  a*  the  Ship  found  by  observation,  and  when  the  hands  of  the  Watch  arrive  exactly  at  this 
computed  Mean  Time  at  the  Ship,  set  the  Chronometer  instantly  agoing.  If  the  Longitude  of  the  Ship  be 
correct,  then  the  Chronometer  will  show  the  same  Greenwich  Mean  Time  as  before  it  stopped 

For  example  •  Suppose  the  Chronometer  to  have  stopped  atlOh.  20  in.  10  sec.  Ship's  Longitude  by 
account  being  65°  W.,  or  4  h.  20  m.,  subtracted  from  10  h.  20  m.  10  sec,  leaves  6  h.  0  m.  10  sec.  Now, 
having  had  the  Watch  regulated  in  the  afternoon  to  the  mean  time  at  Ship,  I  wait  until  the  hands  of  the 
Watcl   show  6  h.  Om.  lb  sec,  and  then  set  the  Chronometer  instantly  agoing. 

Again;  Suppose  the  Chronometer  to  have  stopped  at  5  h.  40  m.  20  sec.  The  Ship's  Longitude 
by  account  being  110'  20'  East,  or  7  h.  21  m.  20  sec.  This  added  to  5  h.  40  m.  20  sec ,  produces  13  h.  Im. 
40  sec,  or  1  h,  1  m.  40  sec.  past  Noon  for  the  computed  Mean  Time  at  the  Ship.  Now,  having  had  the 
Watch  previously  regulated  in  the  morning  to  Mean  Time  at  the  Ship,  I  wait  until  the  hands  of  the  Watch 
eome  to  1  h.   1  m.  40  sec.  and  then  set  the  Chronometer  instantly  agoing. 

In  taking  the  time  from  the  face  of  the  Chronometer,  the  Second  Hand  is  first  noted,  then  the  Minute 
Hand,  and  lastly  the  Hour  Hand. 

Any  common  Watch  which  has  a  Second  Hand  will  do  for  taking  the  time  when  making  observations, 
but  it  must  be  compared  with  the  Chronometer,  both  before  and  after  the  Observations  are  made,  and  its 
Rate,  if  any,  allowed  for. 

EXAMPLE. 

Supj-ote  the  CbroDometer  showed lib.  20m.  lOsec.         Again  the  Chronometer  showed. .  .llh.  30m.  15se« 

And  at  the  same  time  the  Watch  showed.  •  6     10        0  Watch  showed 8      20        5 

rhe  Difference  is  called  the  Comparison. .     8h.  10m.  lOsec.         Comparison 3h.  10m.  lOse* 

Ir  this  case  the  comparison  must  be  added  to  the  Mean  of  the  Times  shown  by  the  Watch  when  th« 
Altitudes  were  observed,  which  will  give  the  time  by  Chronometer  when  the  Altitudes  were  observed,  just 
the  same  as  if  the  time  of  each  Altitude  had  been  noted  from  the  face  of  the  Chronometer.  In  comparing 
the  Watch  with  the  Chronometer,  the  best  metl  od  is  to  wait  until  the  Second  Hand  of  the  Watch  comes  to 
60  seconds,  wliich  completes  the  minute,  and  at  tliat  instant  note  the  number  of  seconds  which  the  Hand 
•f  the  Chronometer  shows,  and  then  the  minute  and  the  hour. 

It  will  also  save  some  trouble  if  the  Altitudes  are  taken  at  the  instant  the  Second  Hand  of  the  watch 
tas  completed  the  full  minute.  This  serves  as  a  check  on  the  measured  change  of  the  Sun's  Altitude  is 
on*  minute  of  time,  and  which  is  uni.' >rm      (See  the  Table  on  page  100.) 


j,^  rNSTRUMENTS- OF  NAUTICAL   ASTRONOMY. 


REMARKS  ON  THE  CHRONOMETER. 


Chronometers,  when  sent  on  board  of  Ships,  are  provided  with  a  Certifica.te  of  their  Error  ;  that  i* 
what  they  are  fast  or  slow  of  Greenwich  Mean  Time  on  a  certain  day  of  the  month,  and  also  their  Dail^ 
Rate,  that  is,  what  they  are  gaining  or  losing  on  Mean  Uniform  Time.  Consequently,  the  Greenwich 
Time  can  easily  be  computed  for  any  subsequent  period  of  time,  by  multiplying  the  Daily  Rate  by  the 
number  of  days  elapsed,  and  applying  it  to  the  original  Error.  And  if  Chronometers  always  kept  a  uniform 
steady  Rate  they  Avould  answer  every  purpose  required  of  them.  But  unfortunately,  they  do  not  always 
keep  a  steady  Rate,  at  least  not  the  Rate  given  in  the  Certificate,  or  the  Shore  Rate,  as  we  call  it.  For  it  is 
found  by  experience  that  after  Chronometers  have  been  placed  on  board  Ships  their  Rates  change,  caused. 
no  doubt,  by  the  magnetic  action  of  the  iron  on  board  the  vessel  on  the  steel  work  of  the  Watch,  and  also  by 
the  change  of  temperature  in  the  weather  during  the  voyage.  And  as  this  is  difficult  to  remedy  on  board  a 
merchant  vessel,  it  becomes  necessary  to  find  the  Sea  Rate  at  the  earliest  convenient  opportunity,  and  to 
rerify  it  from  time  to  time  during  the  voyage.  The  method  of  doing  this  will  be  found  in  its  proper  place 
under  the  head  of  Rating  the  Chronometer  at  Sea.  (See  page  155.) 

This  method  is  simply  to  ascertain  the  Error  of  the  Chronometer  on  Greenwich  Mean  Time  when  the 
Ship  is  in  sight  of  land,  the  position  of  which  is  well  laid  down.  And  the  difference  in  the  Error  ascer- 
tained at  one  place  and  the  next,  divided  by  the  number  of  days  elapsed  between  the  observations,  is  the 
Sea  Rate.  Or,  when  the  Ship  is  in  port,  and  the  Sea  Horizon  visible,  the  Rate  may  be  found  by  comparing 
it  with  M.  Time.  Or  the  Artificial  Horizon  may  be  used  on  shore,  the  times  of  the  Altitudes  being  taken 
by  a  Watch,  which,  as  before  explained,  must  be  compared  with  the  Chronometer,  both  before  and  after 
the  observations  are  made,  and  its  Rate  (if  any)  allowed.  Rating  Chronometers  by  the  Artifical  Horizon 
is  a  more  correct  method  than  by  the  Sea  Horizon,  because  of  the  haze  and  change  of  Dip,  which  some- 
times effects  the  latter. 

When  there  are  several  Chronometers  on  board  a  vessel,  the  one  which  keeps  the  most  uniform  Rate  is 
taken  as  a  standard  one,  and  with  which  all   the   others  are  compared.     The  cause  which  alters  the  Rate 
of  one  Chronometer  may  likewise  alter  the  Rate  of  another,  so  that  the  agreement  of  any  number  of 
Chronometers  cannot  be  admitted  as  e\'idenee  of  the  truth  of  the  time  which  they  show.     One  good  Chro 
Bometer,  in  the  hands  of  a  competent  person  to  manage  it,  is  sufficient  for  almost  any  voyage. 

THE  AZIMUTH   COMPASS.  "* 

The  Azimuth  Compass  is  of  a  superior  construction  to  the  Steering  Compass,  and  is  particularly  adapted' 
for  observing  Bearings. 

It  is  fitted  with  vertical  Sight  Vanes  for  the  purpose  of  observing  objecta  elevated  above  the  horizon,  la 
one  of  these  Vanes  there  is  a  long  and  very  narrow  slit,  and  in  the  other  is  an  opening  of  the  same  kind, 
out  wider,  and  having  a  wire  up  and  down  the  middle  of  it  exactly  opposite  to  the  slit. 

The  Card  is  similar  to  those  of  the  Steering  Compass,  with  this  difference  only,  that  a  circular  ring  of 
silvered  brass,  divided  into  four  times  90°,  or  360°,  circumscribes  the  card. 

To  Observe  the  Sun^s  Amplitude. 

Turn  the  Compass  Box,  until  the  Vane  containing  the  magnifying-glass  is  directed  towards  the  Sun,  and 
antil  the  bright  speck  or  rays  of  the  Sun  (collected  by  the  magnifying-glass)  falls  upon  the  slit  in  the  other 
Vane.  If  the  Card  vibrates  considerably  at  the  time  of  observation,  take  the  middle  between  the  extrem* 
vibrations  for  the  Observed  Amplitude. 

Or  the  sight  may  be  directed  through  the  dark  glass  towards  the  Sun,  which  must  be  bisected  by  th* 
wire  in  the  other  Vane. 

A  common  spare  Steering  Compass  may  be  made  a  very  good  substitute  when  a  Ship  is  not  furnished 
with  an  Amplitude  Compass,  (and  which  is  frequently  the  case),  as  follows  :  Place  the  Compass  Box  as 
near  the  Binnacle  as  possible,  and  in  such  a  position  that  the  Sun  at  Rising  or  Setting  may  be  seen  over  it. 
Now  take  a  Plane  Scale  or  a  thin  straight-edge,  and  place  it  over  the  centre  of  the  Card  in  the  direction 
of  the  Sun.  Look  along  the  edge  of  the  Scale  and  see  that  the  far  end  of  it  points  to  the  Sun's  centre. 
Then  the  point,  or  fraction  of  a  point  of  the  Compass,  which  is  under  the  edge  of  the  Scale,  will  be  the 
Observed  Amplitude,  which  must  always  be  reckoned  from  the  East  or  West  points  towards  the  North  or 
South 

The  observation  should  be  made  when  the  Sun's   lower  limb  appears  somewhat  more  than  his  semi 
diameter  above  the  horizon,  because,  on  account  of  the  Refraction  of  the   atmosphere  his  centre  is  then 
really  in  the  horizon. 


THE  AZIMT'TH  COMPASS.  ;^V 

To  Observe  the  Sun^s  Azimuth. 

In  observing  the  Azimuth  of  the  Sun  his  Altitude  is  required  to  be  taken  at  the  same    nstant  of  tim 
with  a  Quadrant,  in  order  to  obtain  his  True  Azimuth. 

Raise  the  magnifying-glass  to  the  upper  part  of  the  Vane,  and  move  the  box,  with  the  nagnifying-glass^ 
to  the  Sun,  until  the  bright  speck  falls  on  the  other  Vane,  or  on  the  line  on  the  horizontal  bar.  The 
divisions  being  then  read  off  ■will  be  the  Sun's  Magnetic  Azimuth. 

If  the  Card  vibrates  considerably  at  the  time  of  observation,  take  the  middle  between  the  extreme 
vibrations. 

The  Azimuth  is  counted  generally  from  the  North  point  of  the  Compass  in  North  Latitude,  and  from 
the  South  point  of  the  Compass  in  South  Latitude.  Towaiids  the  East  in  the  morning,  and  towards  the 
West  in  the  afternoon. 

But  sometimes,  for  convenience  sake,  it  is  counted  from  the  South  in  North  Latitude,  and  from  the  North 
in  South  Latitude. 

In  high  Latitudes,  the  Sun's  Azimuth  may  be  observed  at  Noon  at  the  instant  he  is  on  the  Meridian , 
that  is,  when  he  is  true  South  or  North,  and  the  difference  between  that  and  the  Azimuth  bearing  by  Com- 
pass gives  the  magnetic  variation  at  once. 

But  to  do  this  it  is  r.eceefary  to  have  the  Watch  previously  regulated  to  Apparent  Time  at  the  Ship,  so 
that  the  Sun's  Azimuth  may  be  observed  at  the  instant  the  Watch  shows  1 2  o'clock  ,  because  the  Sun  then 
is  True  South  in  North  Latitude,  and  True  North  in  South  Latitude.  And  supposing  the  Bearing  by  the 
Azimuth  Compass  to  have  been  South  also,  there  would,  in  that  case,  be  no  variation.  On  the  other 
hand,  if  *.he  Bearing  by  the  Azimuth  Compass  was  S.  22°  30'  W.,  then  there  would  be  that  amount  of 
Magnetic  Variation  Westerly,  But  if  the  Bearing  of  the  Azimuth  Compass  had  been  S.  B2°  30'  E.,  ther* 
would  be  that  amount  of  Magnetic  Variation  Easterlv, 


INSTRUMENTS  USED  IN  NAVIGATION, 


DESCRIPTION  AND  USE  OF  THE  THERMOMETER. 


Fahrenh  jit's  Thermometer  is  used  on  board  of  Ships  for  the  purpose  of  registeriiier  the  temperature  of  th« 
Oecan  at  the  surface,  and  also  the  temperature  of  the  Air  on  the  "'pen  Sea.  The  Zero,  or  commencement 
•f  the  Scale,  begins  at  32°,  or  the  Freezing-point,  and  is  counted  upwards  and  downwards,  according  as  the 
«olumn  of  mercury  expands  or  contracts.  When  the  temperature  or  heat  increases  it  rises ,  but  when  the 
temperature  decreases,  or,  (which  is  the  same  thing),  the  cold  increases,  it  falls,  and  the  degree  opposite  th 
top  of  the  mercury  is  the  reading  required.  When  it  is  below  32°  it  is  said  to  stand  so  many  degree* 
below  tne  Freezing-point;  and  during  the  Winters  in  the  Arctic  or  Polar  regions,  the  mercury  itself  freezes 
from  the  intense  cold. 

The  Thermometer  is  a  most  useful  instrument  in  giving  warning  of  the  Ship's  approach  to  Ice  in  thick 
foggy  weather.  This  is  simply  done  by  drawing  a  bucket  of  water  from  alongside  and  plunging  the  Ther- 
tnometer  into  it  at  regular  intervals  in  the  day,  during  the  voyage,  and  the  readings  noted  down.  And, 
when  it  is  found  that  the  temperature  of  the  water  has  fallen,  on  approaching  a  locality  where  Ice  may  be 
«xpevjted  to  be  fallen  in  with,  the  observations  should  be  repeated  every  few  minutes.  And  should  the 
mercury  in  the  tube  keep  sinking,  you  may  conclude  that  the  Ship  is  approaching  Ice,  and  the  precaution 
should  be  taken  at  once  to  shorten  sail.  For  if  it  be  in  the  Winler  season,  and  the  Thermometer  has  fallen 
to  34°,  she  will  then  be  only  half  a  mile  off  the  Ice.  If  in  the  Sum  ner  season,  and  the  Thermometer  has  fallen 
to  42°,  she  will  then  be  about  the  same  distance  off,  and  on  a  nearer  approach  the  glass  will  fall  still  lower. 
But  when  the  Ship  has  passed  the  Ice,  the  Thermometer  will  gradually  rise  again. 

In  the  month  of  June,  near  the  Bank  of  Newfoundland,  the  Thermometer  had  fallen  suddenly  from  48* 
to  42°.  Ship  was  then  running  with  Studding-sails  set  on  both  sides,  in  very  thick  weather.  They  were 
immediately  taken  in  and  the  Courses  hauled  up,  when  the  white  glare  of  an  immense  Iceberg  was  seen 
Tight  ahead,  and  she  had  to  be  hauled  to  the  wind  in  order  to  pass  clear  to  the  windward  of  it  at  less  than  a 
■quarter  of  a  mile  distant;  so  that  by  a  timely  reference  to  this  useful  instrument  the  Ship  was  rescued 
from  imminent  danger. 

The  temperature  of  the  Ocean  is  higher  in  deep  water,  than  it  is  in  shoal  water  near  the  land,  or  on  banks. 
Hence,  a  Ship  on  approaching  land,  or  on  Soundings,  the  Thermometer  falls  from  2°  to  6°,  except  on  a  high 
bold  shore  with  deep  water  close  to  it,  when  it  is  not  so  apparent.  The  difference  of  temperature  on  and 
off  the  Banks  of  Newfoundland  is  5°. 

Currents  in  the  Ocean  coming  from  high  Latitudes  have  their  water  colder  than  those  which  come  from 
low  Latitudes,  which  accounts  for  the  variation  in  the  temperature  of  the  surface  water,  out  on  the  open 
Sea 

On  a  Ship  entering  the  Eastern  edge  of  the  Florida  stream,  the  water  will  be  found  to  be  from  5*  to 
■8°  warmer,  and  after  crossing  it  and  leaving  its  Western  edge,  the  adjoining  Sea  will  be  found  that  much 
eolder.  and  when  she  gets  on  soundings,  several  degrees  colder  still.  So  that  a  careful  observer  will  always 
be  warned  of  his  approach  to  the  coast  of  the  United  Stales  of  America,  by  consulting  this  useful  instru- 
ment m  thick  we?.ther,  when  no  Celestial  observations  can  be  obtained. 

The  Plate  of  the  Thermometer  should  be  made  of  Ivory  or  Metal,  .so  that  the  tube  will  be  less  liable  to 
break,  and  it  should  be  fixed  in  a  square  metal  box,  the  bottom  of  which,  as  high  as  the  mark  30°,  should 
be  water-tight,  so  that  in  examining  the  degree  of  temperature,  the  bulb  may  be  kept  immersed  in  the  water 
The  remainder  of  the  length  should  be  open  in  front,  with  only  two  or  three  cross  bars  to  ward  off  any 
accidental  blow.  It  would  be  better  to  have  a  spare  one  also,  fixed  up  in  some  safe  part  of  the  ship,  in  the 
•hade,  out  of  the  wind,  and  in  as  dry  a  place  as  possible,  ♦'  -egister  the  temperature  of  the  air,  while  the 
.«tber  may  be  used  for  the  water. 


THE   JSE  OF  THE  BA.tOMETER. 


DESCRIPTION  AND  USE  OF  THE  BAROMETER. 

iTi*  Barometer  is  used  on  board  of  Ships  for  the  purpose  of  foretelling  the  state  of  the  weather.  By  th« 
^oBsure  of  the  Atmosphere  acting  on  a  column  of  Mercury,  contained  in  a  glass  Tube,  which  has  aScala 
iv. ached  to  it,  marked  in  inches,  and  a  sliding  Vernier,  the  top  of  which  being  set  at  the  height  of  th« 
Mercurial  column,  gives  the  measurement  in  inches,  and  hundredth  parts  of  an  inch.  In  North  Latitude  it 
■itaads  highest  with  N.  E.  winds,  and  lowest  with  S.  W.  In  South  Latitude  it  stands  highest  with  S.  E. 
wiuds,  and  lowest  with  N.  W. 

\bout  the  commencement  of  a  Storm,  in  North  Latitude,  from  the  S.  W.,  with  rain,  the  Barometer 
oe^ins  to  fall,  and  continues  to  fall  as  the  Storm  increases  j  and  when  it  stops  and  begins  to  rise,  the  rain 
w.ll  80on  cease,  and  a  shift  of  wind  to  the  Northward  maybe  expected;  but  it  may  continue  to  blow 
hard  until  the  Barometer  rises  to  30  inches. 

In  South  Latitude,  N.  W.  winds  bring  rain,  with  a  falling  Barometer;  but  it  rises  with  Southerly 
winds.  If  it  rises  slowly  and  gradually,  good  weather  may  be  expected  to  follow;  but  if  it  rises  rapidly, 
the  weather  will  continue  unsettled  and  stormy. 

In  general,  before  a  heavy  fall  of  snow  or  sleet,  the  Barometer  falls  very  low,  and  the  wind  commences 
to  biOW  from  the  quarter  in  which  it  generally  stands  the  highest  in  fine  weather,  and  after  the  fall  of  snow 
it  riocs  rapidly. 

Rat  there  are  many  curious  exceptions  to  these  general  rules ;  for  I  have  seen  the  Barometer  steady  at 
30  inches,  with  the  wind  blowing  hard  at  S.  W.,  with  heavy  rain  falling  for  several  days  together,  Ship 
being  then  in  a  high  Northern  Latitude.  But  the  secret  of  this  turned  out  to  be,  that  an  Easterly  wind 
waj.  at  hand,  which  followed  the  S.  W.  wind,  and  continued  blowing  for  several  weeks  afterwards. 

riie  never-failing  sign  of  bad  weather  is,  when  daylight  breaks  high  over  head,  and  the  clouds  to  lee- 
ward look  heavy  and  near  ;  also,  when  the  Sun  rises  or  sets  with  a  lurid  red  glare.  These  appearances 
should  be  taken  in  connexion  with  the  action  of  the  Barometer,  before  a  proper  opinion  can  be  formed  of 
the  kind  of  weather  that  may  be  expected  to  follow. 

The  Barometer  generally  stands  about  30  inches  in  the  fine  serene  weather  experienced  in  the  Tropics, 
except  between  the  Trade  Winds,  when  it  falls  a  little  during  the  rainy  weather  which  prevails  there. 
but,  if  it  falls  rapidly  near  the  Northern  or  Southern  limits  of  the  Trade  Winds,  (that  is,  between  the  Lati- 
tudes of  20°  and  30°,)  down  to  29.50,  there  is  a  Hurricane  at  hand,  and  by  referring  to  the  Diagrams  of  the 
Slorra  Circle,  at  pages  43  and  44.  measures  must  be  taken  at  once  for  the  safety  of  the  Ship,  where  it  will  be 
perceived  thaj".  with  the  Barometer  at  29.50,  the  Ship  will  be  about  150  miles  distant  from  the  Focus  ,  when  it 
falls  to  29.20,  100  miles  ofl";  to  28.40.  50  miles  off;  and  at  the  Focus  itself  it  will  stand  at  27  inches. 
When  the  Ship  increases  her  distance  from  the  Focus  the  Barometer  will  rise ;  so  that  it  is  a  most  valuable 
instrument  in  the  locality  of  HurriAnes. 

THE  ANEROID  BAROMETER. 

This  instrument  is  constructed  so  that  the  pressure  of  the  Atmosphere  acts  upon  a  metalic  spring,  con- 
A'ected  with  a  vacuum,  and  turns  a  band  to  the  Right,  answering  to  the  rising  of  the  Barometer,  and  to  the 
l^eTt  wh^n  it  is  falling.  It  has  a  round  face,  similar  to  a  Chronometer,  and  the  Inches  are  marked  on  it 
and  counted  in  the  same  manner  as  tlie  Mercurial  one.  This  instrument  is  very  sensitive  and  exact,  very 
superior  to  the  old  ones,  which  are  sorneiiines  difficult  to  read  ofi",  on  account  of  the  Mercury  plunging  up 
ajid  down  in  the  tube,  when  the  Ship  has  violent  motion. 

I  have  used  this  instrument  myself  for  some  years,  and  in  a  great  many  instances  it  has  given  me  warning 
of  a  coming  Hurricane  more  than  24  hours  in  advance.  It  is  also  more  portable,  and  can  be  hung  up,  or 
f  laced  any  where  about  a  Ship's  cabin,  or  in  a  place  where  it  would  be  inconvenient  to  swing  a  Mercurial 
Hie. 


AA 


NAUTICAL    ASTRONOMY. 


Having  thus  given  a  short  description  of  the  principal  instruments  used  in  Nav  eating  a  Ship,  we  now 
proceed  to  find  the  Ship's  place  on  the  Ocean  from  Astronomical  Observations,  and  commence  with  finding 
the  Latitude  from  the  Meridian  Altitude  of  the  Sun.  The  Correct  Declination  of  the  Sun  must  be  found 
at  the  time  of  Observation,  as  follows  : 

The  Sun's  Declination,  found  in  Table  X,  to  the  nearest  minute,  is  calculated  for  every  Noon  at 
Greenwich,  for  several  years  in  advance,  and  which  will  answer  for  every  fourth  year  afterwards,  by 
applying  a  small  correction  found  in  the  adjoining  Table ;  or  it  may  be  taken  from  the  Nautical  Almanac. 

When  the  Ship  is  on  the  Meridian  of  Greenwich,  no  correction  is  required,  and  the  Declination  standing 
asainst  the  day  of  the  month  may  be  taken  out  and  applied  at  once,  because  it  is  Noon  at  the  Ship  and 
Noon  at  Greenwich  at  the  same  instant  of  time.  But  when  a  Ship  is  on  a  Meridian  to  the  Eastward  or 
Westward  of  Greenwich,  that  is,  when  her  Longitude  is  East  or  West  from  Greenwich,  the  Declination 
must  be  corrected  for  the  Change  of  Declination  corresponding  to  the  Longitude  in  time  ;  because  when  it 
is  Noon  at  the  Ship,  in  15°  East  Longitude,  it  wants  1  hour  of  being  Noon  at  Greenwich,  and  when  it  is 
Noon  at  the  Ship,  in  15°  West  Longitude,  it  would  be  1  hour  past  Noon  at  Greenwich.  This  correction 
amounts  to  a  considerable  quantity  when  the  Longitude  is  great,  and  when  the  Sun  changes  his  Declinatior 
rapidly  in  the  months  adjoining  March  and  September. 

RULE 

For  Correcting  the  Sun's  Declination  at  Noon. 

Enter  Table  XI  with  the  Longitude  at  the  side  column  and  the  Declination  at  the  top,  and  the  angle  of  meetinf^ 
loints  out  the  correctaon  to  be  applied,  according  to  the  precepts  at  the  bottom  of  the  Table. 

EXAMPLE  1. 

Required  the  Sun's  Correct  Declination  on  the  Ist  of  March,  1854,  at  the  Ad  ot  the  Sea  Day,  in  the  Longitude  of 
80*  West 
The  Sun'i  Declination,  March  Ist,  at  Greenwich,  at  the  end  of  the  Sea  Day,  or  the  beginning  of  the 

day  in  the  Nautical  Almanac,  by  Table  X,  is 7'  85'  S. 

Conection  for  the  Declination  in  Table  XI,  for  Longitude  80°  "West,  is Sulx 6 

(Because  the  Long,  is  West  and  Declination  Decreasing,)  Gives  the  Correct  Declination .7°  80'  S. 

EXAMPLE  2. 

Required  the  Sun's  Correct  Declination  on  the  1st  of  April,  1854,  at  the  end  of  the  Sea  Day,  in  the  Longitude  of 
90°  East 

The  Sun's  Declination,  April  1st,  at  Greenwich,  by  Table  X,  is ■#*  32'  N 

The  Correction  for  the  Declination  in  Table  XI,  for  Long.  90°  East,  is  6'.8 Sub^ 6 

Because  the  Long,  is  East  and  Declination  Increasing,)  Gives  the  Correct  Declination 4°  26' 

jjjyj5_ 'Phe  Corrections  in  Table  XI,  are  expressed  in   minutes  and  tenths  of  minutes,  and  it  is  usual  in  practice  that 

when  the  tenths  exceed  5,  we  call  the  minutes  one  more,  but  when  the  tenths  are  less  than  5,  they  are  not  used  at  alL 
But  when  jrreater  accuracy  is  required,  multiply  the  tenths  by  6,  which  will  give  seconds  of  Declination. 

It  may  also  be  remarked  here,  that  the  Declinations,  or  any  other  quantity  found  in  the  Nautical  Almanac,  are  all 
calculated  for  Astronomical  Time  at  Greenwich  ;  and  that  the  Astronomical  Day  begins  24  hours  after  the  Sea  Day,  and 
12  hours  after  the  Civil  Day,  and  is  counted  through  the  24  hours.  ,  .    ,  ^    ,     -,,     •     •         ,  .u      .   . 

Hence  the  Noon  of  the  Civil  Day,  (or  that  used  by  the  generality  of  mankuid,)  the  Begmmng  of  the  Astronomical 
Day  and  the  End  of  the  Nautical  Day,  take  place  at  the  same  period  of  time. 

There  is  no  reason  why  this  absurd  system  of  keeping  Sea  Time  should  be  continued ;  because  it  is  just  as  easy  Ic 
keep  Civil  Time  commencing  the  day  at  Midnight,  and  the  Day's  Work  could  still  be  reckoned  from  Noon  to  Ndoh, 
as  before  The  only  difference  would  be,  that  one  half  of  it  would  appear  in  the  preceding  day's  Log,  (where  it  roallT 
belongs  )'  »nd  the  other  half  in  the  following.     Many  Logs  ar;  now  kept  on  this  principle.    (See  page  195.) 


4 


FINDING  THE  SUN'S  CORRECT  DECLINATION'  gft 


To  Correct  the  Sun's  Declination  to  any  Time  of  the  Day. 

When  the  Declination  is  required  at  any  other  time  than  at  the  Noon  of  the  Ship,  a  farther  conection  is 
necessary  :  because,  for  instance,  an  observation  of  the  Sun  made  at  4  hours,  either  before  or  after  the 
Noon  of  tile  Ship,  his  Declination  must  be  corrected  for  the  change  of  Declination  in  that  time. 

RULK 

Correct  the  Declinaliou  for  Noon  as  in  the  foregoing  Examples.  'Then  enter  Table  XI  again,  with  the  time  from 
Noon  at  the  Ship  in  the  side  column,  and  the  Declination  at  the  top,  and  the  angle  of  meeting  points  out  the  correc- 
tion in  mimites  and  tenths,  to  be  applied  according  to  the  precept  at  the  bottom  of  the  Table. 

EXAMPLE.  ?,. 

Required  to  find  the  Sun's  correct  Declination  on  the  Istof  March,  1854,  at  8h  10m  in  the  forenoon,  Sea  AcrouLu 
jD  the  Longitude  of  80°  West 

The  Sun's  Declination,  March  1st,  at  Greenwich  Noon,  by  Table  X,  is V  35'  S.  Decreasing 

Correction  for  Declination,  in  Table  XI,  for  Longitude  80°  West, Sub.  6 

(Because  the  Long,  is  West,  and  the  Declination  Decreasing),  gives  theDeel.  at  Noon  7°  30'  S. 
Correction  for  3h  50m,  or  the  time  from  Noon,  Table  XI,  is  3'  8"  = Add  4 

(Because  the  Time  was  before  Noon  and  Decl.  Decreasing.)    Correct  Decl.  at  8h  10m  7°  34'  S. 

EXAMPLE  4. 

Required  to  find  the  Sun's  correct  Declination  on  the  1st  of  Anril,  1854,  at  7h  20m  in  the  forenoon,  Sea  Account 
in  the  Longitude  of  90°  East 

The  Sun's  Declination,  April  1st  at  Greenwich  Noon,  by  Table  X,  is 4°  82'  N.  Increasing. 

Correction  for  the  Declination,  in  Table  XI,  for  Long.  90°  East  is  5'  8" Sub.  6 

(Because  the  Long,  is  East  and  the  Decl.  Increasing),  gives  the  Decl.  at  Noon 4°  26'  N. 

Correction  for  4h  40m,  or  Time  from  Noon,  in  Table  XI,  is  4'  5'' Sub.  5 

(Because  the  Time  was  before  Noon  and  the  Decl.  Increasing.)    Cor  Decl.  at  7h  20m  4°  21'  N. 

EXAMPLE  5. 

Required  to  find  the  Sun's  Declination  on  the  21st  of  March,  1854.  at  5h  20m  in  the  afternoon,  Sea  Account  id 
the  Long,  of  120°  West 


21st,  Sea  Account,  is  March  20th.  Declination  at  Greenwich  Noon,  Table  X,  is  0°  10'  S.  Decreasing, 
tion  for  the  DecHuation,  in  Table  XI,  for  Long.  120°  W.  is  7'  8" Sub.  8 


March 
Correction 

(Because  the  Long,  is  West,  and  the  Decl.  Decreasing),  gives  Decl.  at  Noon 0°    2'  S. 

Correction  for  5h  20m,  or  the  time  from  Noon,  in  Table  XI,  is  5'  2" Sub.  6 

Here  the  Decl.  has  changed  from  S.  to  N.,  and  the  Diff.  is  the  Decl.  at  5h  20m.  P.  M.  "o°    3^N. 


Hence,  the  rule  in  this  case  is,  that  when  the  Correction  Subtract! ve,  exceeds  the  Declination,  the  differ 
•nee  is  the  Declination  of  a  contrary  name. 

EXAMPLE  6. 

Required  to  find  the  Sun's  correct  Declination  on  the  23d  of  September,  1854,  at  lOh  Om,  in  the  forenoon,  ic 
Long.  15°  0'  East 

The  Sun's  Declination  on  the  23d  September,  at  Greenwich  Noon,  is 0*    8'  S.  Increasing. 

Correction  for  the  Declination  in  Table  XI,  for  Long  15°  East, Sub.  1 

(Because  the  Long,  is  East  and  the  Declination  Increasing.)  Declination  at  Noon ....  0°    2'  S. 
Correction  for  2h  Om,  or  the  time  from  Noon,  Table  XI Sub.  2 

(Because  the  Time  was  before  Noon  and  the  Decl.  Increasing.)    Correct  Decl.  at  lOh.  0*    0'  Sun  on  the  Eqna 
To  Correct  the  Sun's  Declination  to  the  Greenwich  Time  of  Observation. 

RULE 

Turn  the  Ship's  Long,  into  Time  by  Table  XXVI,  and  add  it  to  the  time  at  the  Ship,  in  West  Longitude,  oi 
•ubtract  in  East  The  lesult  will  be  the  Greenwich  Time  of  the  observation.  If  it  is  before  Noon  at  Greenwicli, 
subtract  it  from  12h;  if  afternoon,  it  is  the  required  Time.  Take  f)ut  the  Declination  against  the  day  of  the  month, 
from  Table  X.  Then  enter  Table  XI  with  this  time  from  Greenwich  Noon,  in  the  side  column,  and  the  Declination 
at  the  top,  and  at  the  angle  of  meeting  will  be  the  required  correction,  to  be  applied  according  to  the  precept  at 
the  bottom  of  the  Table /or  Time. 

Suppose,  as  in  Example  3d.  the  time  at  Ship  to  be  8h  10m  A  M.  Long.  80*  W.,  in  time,  is  5h  20m, 
which,  added,  makes  13h  30m,  less  12h^  gives  Ih  30m,  the  Greenwich  time  past  Noon,  which,  with  the 
Declination  7'  35',  gives  the  Correction  1'  subtractive.  and  the  cor-ect  Declination  is  7*  34'  S 


M  NAUTICAL  ASTRONOMY 


LATITUDE  BY  THE  MERiDIAN  ALTITUDE  OF  THE  SUN. 


Latitude  is  the  Distance  of  a  place  from  the  Equator  either  North  or  South,  and  is  measured  by  an  Are 
91  the  Meridian  contained  between  the  Zenith  of  the  observer  and  the  Celestial  Equator.  Hence,  if  the 
distance  of  any  heavenly  body  from  the  Zenith,  when  on  the  Meridian,  be  known,  and  its  Declination 
found  in  Table  X,  that  is,  the  number  of  degrees  and  minutes  it  is  to  the  Northward  and  Southward  of 
the  Celestial  Equator,  the  Latitude  may  thence  be  found. 

As  the  Pole  round  which  the  Celestial  Bodies  appear  to  revolve,  remains  always  in  the  same  fixed  place 
m  the  heavens,  from  whatever  point  of  the  Earth's  surface  it  is  viewed,  its  elevation  at  any  particular 
place  is  always  the  same,  and  the  Celestial  Equator  is  90°  from  it.  When  the  observer  changes  his  Lati- 
tude he  changes  the  distance  between  his  Zenith  (which  moves  with  him)  and  the  Pole.  He  therefore 
changes  the  Altitude  of  the  Pole  above  the  Horizon,  and  which  is  always  equal  to  the  Latitude  of  the 
place.     The  position  of  the  Celestial  Equator  is  changed  in  like  manner.     (See  Figure  12th,  next  page.) 

The  simplest  and  most  efficient  manner  of  determining  the  Latitude  is  by  measuring  the  Meridian  Alti 
tude  of  the  Sun  with  a  Quadrant,  at  the  time  he  attains  his  greatest  Altitude.     It  is  then  Apparent  Noo» 
at  tWe  Ship. 

To  Find  the  Latitude  from  the  Meridian  Altitude  of  the  Sun. 

RULE. 

RmuI  off  the  Observed  Altitude  from  the  Quadrant,  and  write  it  down.  In  practice,  three  Correctioni  only  ar^ 
reauired  to  be  applied  to  the  Sun's  Observed  Altitude,  viz :  The  Semi-diameter,  taken  at  16',  the  Dip  found  in 
Table  V,  and  the  Refraction  found  in  Table  IV.     The  Sun's  Parallax,  being  small,  is  omitted. 

If  the  lower  limb  be  observed,  we  find  his  central  Altitude  by  adding  the  Semi-diameter  16',  and  sub- 
tracting the  Dip  and  Refraction  ;  or  by  subtracting  the  Dip  and  Refraction  from  16',  and  adding  the  bal- 
ance, which  comes  to  the  same  thing. 

In  Table  IX,  the  balance  of  all  the  corrections  may  be  taken  out  at  once  by  inspection,  as  follows 
Enter  the  Table,  with  the  Observed  Altitude,  at  the  side,  and  the  height  of  the  eye  above  the  Sea,  in  feet, 
at  the  top,  and  at  the  angle  of  meeting  will  be  the  Correctien  required  in  minutes  and  tenths,  and  whicb 
is  always  additive  when  the  lower  limb  is  observed.  When  the  tenths  amount  to  more  than  .5,  we  call  the 
minutes  1'  more,  but  if  less  than  .5,  we  throw  them  away,  and  the  result  is  the  True  Central  Altitude. 
But  if  greater  accuracy  be  required,  multiply  the  tenths  by  6,  will  give  seconds  of  Altitude. 

If  the  Sun's  upper  limb  be  observed,  the  whole  of  the  Corrections  are  to  be  subtracted,  which  will  give 
the  True  Central  Altitude. 

(f  the  Sun's  centre  itself  be  observed,  as  in  figure  10.  No.  3,  the  Semi-diameter  is  not  required  to  be 
allowed  for.  In  that  case,  the  Dip  and  Refraction  together,  subtracted,  will  give  the  True  Central 
Altitude. 

Subtract  the  Sun's  True  Central  Altitude  from  90°,  will  give  the  Zenith  Distance.  Then  if  the  Sun 
bear  South  when  on  the  Meridian,  mark  his  Zenith  Distance  North,  and  if  he  bear  North,  mark  his  Zenith 
Distance  South. 

Take  out  the  Sun's  Declination  from  Table  X,  and  correct  it  for  the  Longitude  of  the  Ship  by  Table  XI 
Write  it  down  under  the  Zenith  Distance,  and  mark  it  North  or  South,  as  named  in  Table  X  ,:  or,  if  taken 
from  the  Almanac,  in  the  page  containing  the  day  of  the  month. 

Then  if  the  Zenith  Distance  and  Declination  be  both  North  or  both  South,  their  sum  is  the  Latitude  of 
that  name.  But  if  one  be  North  and  the  other  South,  their  difference  is  the  Latitude  of  the  same  name  a* 
the  greater  of  the  two. 

Non.  When  the  horizon  under  the  Sun  is  obstructed  by  land,  the  Correctioa  for  Dip  must  bo  taken  from  Table  Vlll,. 
when  at  less  distance  from  the  Shore  than  6  miles. 

EXAMPLE  1, 

Jannary  Ist,  1864.  In  the  Longitude  of  80*  West,  the  Meridian  Altitude  of  the  Sun's  Lo^er  Limb  was  observed 
lo  be  26*  62',  bearing  South,  Index  Error  2',  subtractive  Height  of  the  eye  above  the  Sea,  18  feet  Required' 
rho  Latitude  in. 


FINDING  THE  LATITUDE  BY  MEKIDIAN  ALTITUDE. 


87 


Projection  of  the  Meridian  Altitude. 
Fig.  12. 


Rule.— With  the  Chord  of  60*  describe  a  semi-circle,  to  represent  the  concave  Arch  of  the  heavens,  and  draw  the 
Rational  Horizon.  Lay  off  the  Sun's  Altitude,  27°,  on  the  Left.  Take  the  Declination,  23°  S.,  in  the  diyiders,  (from 
th«  hne  of  Chords,)  and  with  one  foot  in  the  Sun's  place,  extend  the  other  towards  the  Zenith,  (because  the  Declina- 
tion 18  South  )  which  will  mark  the  place  of  the  upper  end  of  the  Equator  on  the  Meridian  Circle.  Now  draw  the 
Equator  through  the  centre  and  the  Polar  Axis  at  right  angles  to  it.  Mark  the  Zenith  at  gO"  from  the  horrzon,  and 
draw  a  line  from  it  through  the  centre,  and  where  it  cuts  the  Earth's  surface  is  the  place  of  the  Observer.  His 
Latitude  is  measured  on  the  Meridian,  and  is  the  Distance  of  his  Zenith  from  the  Celestial  Equator,  which,  on  the 
hne  of  Chords,  measures  40°,  and  the  Elevation  of  the  North  Pole,  40°  above  the  horizon,  is  equal  to  the  Latitude 
of  the  place.     Hence  the  Distance  of  the  Observer  from  the  Equator  of  the  Earth,  which  is  40°,  is  his  Latitude  North. 


By  Computation. 


Sun's  Declination,  Jan.  1st,  Table  X, 23' 

Correction  Table  XI,  Long.  80  W Sub. 


1' 
1 


Corr.  Declination  at  Noon  of  (he  Ship 23°  0  S. 


Sun's  Observed  Altitude,  Lower  Limb 26°  52'  S. 

Semi-diam,  add, 16'  Index  Error,  Sub.... 2_ 

Dip.  4,  Ref  2=Sub..^  26°  50' 

Balance  of  Corr 10', Add.^^ 10 

Sun's  true  Central  Altitude 27*    0' 

90     0 

Zenith  Distance .63°    0' N 

Correct  Declination. 23     0   S. 

Latitude  in 716°    0'  N. 

EXAMPLE   2. 

June  1st,  1854.     In  the  Long,  of  90°  E.,  the  Meridian  Altitude  of  the  Sun's  Lower  Limb  was  observed  to  b«  69* 
45',  bearing  S.,  Index  Errors',  additive.     Height  of  the  eye  above  the  Sea,  20  feet.     Required  the  Latitude  in. 

Projection  of  the  Meridian  Altitude. 
Fig.  13. 


R0LK.— Proceed,  as  in  the  last  Example,  to  draw  the  figure.  Then  lay  off  the  Sun's  correct  Altitude,  70*  on  the 
left.  Take  the  Declination,  22°  N.,  in  the  dividers,  and  with  one  foot  in  the  Sun's  place,  extend  the  other  downwards, 
(because  the  Declination  is  North,)  which  will  mark  the  upper  end  of  the  Equator.  Now  draw  the  Equator  and  the 
Polar  Axis  as  before.  A  line  drawn  from  the  Zenith,  let  fallen  the  Earth's  surface,  and  through  the  centre,  will  be 
the  piece  of  the  Observer,  and  his  Latitude  is  the  Distance  of  the  Celestial  Equator  from  his  Zenith,  which  measures 
42°  on  the  line  of  Chords,  and  the  Elevation  of  the  Pole  is  equal  to  th«  Latitude. 


m 


NAUTICAL  ASTRONOMY. 


Ftfviing  the  Latitude  by  the  Meridian  Altitude  of  the  Sun. 

BY  COMPUTATION.— (See  Examfk  S., 

Sun's  Observed  Altitude,  Lower  Limb 69°  45'  S.  Declination,  June  1st,  1854,  Table  X, . .    .  22'  8'  H 

Semi-diam. 16'     Index  Error, Add.. ._ 3  Corr.  in  Table  XI,  Long.  90°  E.—  . Sub.^ 2 

Dip.  4,  Ref.  0,  Sub^ 4  69°  48'  Sun's  Corr.  Dec,  Noon  of  Ship 22°  1  'N 

Balance  of  Corr 12  Add 12 

Sun's  true  Central  Altitude 70°  0' 

90   0 

Zenith  Distance 20°  0'  N. 

Sun's  Correct  Declination 2^   1   N. 

Latitudein 42°  1'  N. 


EXAMPLE  3. 

July  22d,  1854.  In  Long.  25°  "West,  the  Meridian  Alti- 
tude of  the  Sun's  Lower  Limb  waa  89°  1'  South.  Height 
of  the  eye,  18  feet  Required  the  Latitude  ia 

Obs.  Alt  Sun's  Lower  Limb 89°    1'  S. 

Corr.  found  in  Table  IX., Add. . . . 12 

True  Central  Altitude 89°  13' 

90     0 

Zenith  Distance ..0°47'N. 

Declij  ation.  Table  X,  22d  July,  20°  19'  N,  )  „^  ,0  vr 
Corr,  fable  XL  Long.  26°,  .  .Sub.. .  1        J       "  ^ 

Latitude  in 21°    5'  N. 


EXAMPLE  5. 

Aug.  7th,  1854.  In  Long.  112°  W.,  the  Meridian  Alti- 
tude of  the  Sun's  Lower  Limb  was  74°  27'  North.  Re- 
quired the  Latitude  ia 

Obs.  Alt  Sun's  Lower  Limb 74°  27'  N. 

Corr.  from  Table  IX, Add.  ._^ 12 

True  Central  Altitude 74°  39' 

Zenith  Distance ,15°  21'  S. 

Declination,  Table  X,  7th  Aug.,  16°  28'  N.  i      ,«  „„    vr 

Corr,  Table  XI,  Lon.  1 1 2°  W.,  Sub . .  5        f     ^^  ^  ^^ 

Latitudein 1"    2' N. 


EXAMPLE  7. 

March  20th,  1854,  In  Longitude  160°  W.,  the  Meridian 
Altitude  of  the  Sun's  Lower  Lunb  was  32°  58'  N.  Re- 
quired the  Latitude. 

Obs.  Alt  Sun's  Lower  Limb 32°  58'  N. 

Correction,  Table  IX, Add . .         10 

True  Central  Altitude 33°    8' 

Zenith  Distance 56°  52'  S. 

Jeclination,  Table  X,  March  20th,  0°  10'  S.  )     ^     .   ^^ 
Corr, Table  XL Lon.l60°W.,Sub.O    11        ^     0     1  JN. 

Latitude  in 56°  51'  S. 


EXAMPLE  4.      ' 

July  23d,  1854.  lu  Long.  27°  W.,  the  Meridian  Alti 
tude  of  the  Sun's  Lower  Limb  was  88°  4'  N.  Height  of 
the  eye,  18  feet.     Required  the  Latitude. 

Obs.  Alt  Sun's  Lower  Limb 88°    4'  N 

Correction,  in  Table  IX. Add.^ 12 

True  Central  Altitude 88'  16 

90     0 

Zenith  Distance 1*44    S 

Declination,  Table  X,  July  23d,  20*  7'  N.  )      9^     a   V 
Corr,  Table  IX,  Lon.  27°  W.,  Sub..  .1        f      ^"     "    " 

Latitude  in 18'  22'  N 


EXAMPLE  6. 

Aug.  8th,  1854.  In  Long.  140°  East  the  Meridian  Alti- 
tude of  the  Sun's  Lower  Limb  was  7  2°  46'  N.  Required 
the  Latitude. 

Obs.  Alt  Sun's  Lower  Limb 72°  46'  N. 

Correction,  Table  IX, Add. . 12 

True  Altitude 72°  58'  N 

Zenith  Distance 17"    2'  S. 

Declination,  Aug.  8th,  Table  X,         16°  11' )    ,  ^ 

Corr,  Table  XI,  for  Lon.  140°  E., .  .Add. 7  )_____ 

Latitude  in 0°  44'  S. 


EXAMPLE  8.  ' 

March  21st  1864.  In  Long.  1.75°  E.,  the  Meridian  Alti- 
tude of  the  Sun's  Lower  Limb  was  40°  20'  N.  Required 
the  Latitude. 

Obs.  Alt  Suu's  Lower  Limb  was 40°  20'  N 

Correction,  Table  IX Add. . H 

True  Altitude 40*  31' 

Zenith  Distance 49''  29'  S. 

Declination,  Table  X,  March  21st  0"  14'  N.  |  n"  9'  NT 
Corr.,  Table  XI,  Lon.  175°  E,    Suh.  12        [____ 

Latitude  in 4  9°  27'  S. 


In  the  above  Examples  the  height  of  the  eye  above  the  Sea  is  supposed  to  be  about  16  or  18  feet,  which 
answers  very  well  for  vessels  of  common  size ;  but  in  very  large  Ships  the  height  of  the  eye  will   be  con 
siderably  above  that.     On  the  other  hand,  in  small  vessels  the  height  of  the  eye  will  be  much   less  than  IS 
feet  above  the  Sea.     The  Dip,  found  in  'Table  V,  or  the  height  of  the  eye,  in  Table XI.  inusl  be  regulated 
fccoordingly 


TO  FIND  THE  LATITUDE  BY  THE  MERIDIAN  ALTITUL  E  OF  THE  SUN. 


89 


FINDING  THE  LATITUDE  BY  THE  MERIDIAN  ALTITUDE  OF  THE  SUN. 


When  the  Sun's  True  Central  Altitude  is  90',  he  is  in  the  Zenith,  and  the  correct  Lcclination  for  tk 
day  is  th«  Latitude  of  the  same  name  as  the  Declination. 

When  the  Declination  is  0°  0',  the  Zenith  Distance  is  the  ISatitude  of  a  contrary  name  to  the  Beariiig  of 
the  Sun  when  on  the  Meridian. 

When   the    Zenith    Distance  and  Declination  are  equal,  but  of   contrary  names,  the  Ship  is  on  th 
Equator. 

When  the  Sun  is  in  the  Zenith,  and  his  Declination  0°  0',  the  Ship  is  on  the  Equator,  which  the  follow- 
ing Diagram  will  show. 

Fig.  14. 


» 


I 


aH  thig  Figure,  the  Sun  appears  in  the  Zenith,  and  his  Declination  at  the  same  time  being  23°  28'  N. 
from  the  Equator,  is  the  Latitude  of  that  name,  and  which  is  equal  to  the  elevation  of  the  Pole  above  the 
Horizon.  Now  suppose  the  Sun  to  be  on  the  Equator,  then  his  Zenith  Distance  would  be  23°  28'  N.,  which 
is  also  the  Latitude.  Again :  Suppose  the  Equator  to  coincide  with  the  Zenith ;  then  both  North  and 
South  Poles  would  appear  in  the  Horizon,  and  which  is  the  case  when  the  Ship  is  on  the  Equator.  Again  : 
if  the  Sun  has,  say  23°  28'  S.  Declination,  his  Zenith  Distance  in  this  case  would  be  23°  28'  N.,  which 
being  equal  and  of  contrary  names,  the  Ship  would  be  also  on  the  Equator. 

When  the  Sun  is  in  the  vicinity  of  the  Zenith,  it  is  often  difficult  to  observe  his  Altitude,  in  consequence 
of  not  knowing  on  which  side  of  it  he  will  pass  the  Meridian.  But  if  the  Watch  be  previously  regulated 
to  Apparent  Time  it  will  be  found  of  great  service  in  indicating  the  exact  time,  that  is,  12  o'clock,  when 
the  Sun  will  be  on  the  Meridian,  because  his  motion  is  then  very  quick,  and  he  requires  to  be  carefully 
watched  to  obtain  his  proper  Altitude.  It  may,  however,  be  obtained  to  nearly  90°  in  this  way,  by  th« 
exercise  of  a  little  care. 

It  is  nevertheless  advisable  to  verify  the  Latitude  so  obtained,  by  an  observation  of  a  Planet  or  a  Star 
taken  at  twilight,  when  the  Horizon  is  distinctly  seen,  and  for  which  there  are  good  opportunities  to  be 
found  during  the  fine  serene  weather  in  the  tropics. 

To  Find  the  Latitude  by  Observing  the  Sun's  Centre. 

When  the  Sun  shines  through  watery  clouds  his  limbs  may  not  be  distinctly  visible,  but  a  good  observa- 
tion may  still  be  obtained  by  bringing  his  middle  down  to  the  Horizon.  (See  page  68,  Fig  10.)  The 
observation  is  then  worked  as  follows  : 


EXAMPLE   9, 

Observed  Meridian  AIL  of  the  Sun's  Centre.  ..10°  10'  N 

Dip  4,  Refraction  6 Sub.         9 

Sue's  True  Central  Altitude 10°    1' 

Zenith  Distance 79°  59'  S. 

DecUnation,  June  21st 23    27    N. 

Ship  ofif  Gape  Horn,  Latitude  in 56^  32'   S 


EXAMPLE  10. 

Observed  Merid.  Altitude  of  the  Son's  Centre.  60'  14'  & 
Dip  4,  Refraction  1 Sub.         6 

Sun's  True  Central  Altitude 60^    9* 

Zenith  Distance 29°  51'  N. 

Declination,  December  2l8t 23    27    S 

Latitude  in , 6°  24'  N 


M 


NAUTICAL  ASTRONOMY. 


TO  FIND  THE  LATITUDE  FROM  A  BACK  OBSERVATION  WITH  A  SEXTANl 

RULE. 

Bring  the  Lower  Limb  of  the  Sun  in  contact  with  the  Back  Horizon,  and  subtract  the  Angle  so  obtained  fr«nii 
180°  0  ,  which  will  give  the  Meridian  Altitude  of  the  Upper  Limb  Subtract  the  difference  between  the  Dip  and 
the  Semi  diameter,  (usually  taken  as  12'),  and  the  result  is  the  True  Central  Altitude.  In  thia  case,  no  Correction  fo» 
Refraction  is  required,  because  the  Sextant  can  only  measure  about  120°  of  an  Angle,  the  supplement  of  which  i» 
60*  of  an  Altitude,  (for  which  no  Correction  for  Refraction  is  required  in  Praottoe  at  Sea.)  This  method  is  useful  ia 
kw  Latitudes  when  the  Horizon  uuder  the  Sun  is  obstructed  by  the  laud. 

DIAGRAM  OF  A  BACK  OBSERVATION. 
Fig.  15. 


•    ZENITH 


D\ST     ,0F  THE 


<%:-. 


VISIBLEl 


HORIZON 


EXAMPLE  11 

xTie  Angle  of  the  Sim's  Lower  Limb  from  a  back  Ob- 
•ervation  with  a  Sextant,  was  119°  32'  on  the  Meridian, 
the  observer  facing  towards  the  North.  The  correct  De- 
clination at  the  same  time  was  20°  10'  N.  Required  the 
Latitude. 

Observed  Angle  Sun's  Lower  Limb 119°  32'  N. 

Subtract  from 180      0 

Sun's  Meridian  Altitude,  Upper  Limb 60°  28'  S. 

Semi-diameter  16'  and   Dip  4',  subtract  Corr.  12 

Sun's  True  Central  Altitude 60°  16' 


Subtracted  from  90°,  gives  the  Zenith  Distance  29°  44'  N. 
Correct  Declination 20    10   N. 

Latitude  in 49°  54'  N. 


EXAMPLE  12. 

The  Angle  of  the  Sun's  Lower  Limb  from  a  Back  Ob 
servation  with   a  Sextant  was  100°  25'  on  the  Meridian, 
the  observer  facing  towards  the  South.     The  Correct  De- 
clination at  the  same  time  was  22°  15'  N.     Required  the  : 
Latitude. 

Observed  Angle  Sun's  Lower  Limb 100°  26'  & 

Subtiact  from 180 

Sun's  Meridian  Altitude,  Upper  Limb 79°  36'  N 

Semi-diameter  16'  and   Dip  4',  subtract  Corr.  12 


Sun's  True  Central  Altitude 79°  23' 


Subtracted  from  90°,  gives  the  Zenith  Distance   10°  37'  S 
Correct  Declination 22°  16'  K 

Latitude  in 11°  38'  N 


To  Find  the  Latitude  from  an  Altitude  by  the  Shore  Horizon 

When  the  Ship  is  less  than  6  miles  from  the  Shore  under  the  Sun,  when  on  the  Meridian,  his  Lower 
Limb  is  brought  down  to  the  line  which  divides  the  Sea  and  Land,  and  a  Correction  for  Dip  taken  from 
Table  VIII,  to  be  used  in  the  room  of  the  Dip  usually  taken  from  Table  V. 


EXAMPLE  13, 

"With  the  Bearing  of  the  Land  find  the  Distance  off,  by 
•ome  one  of  the  Rules  given  at  pages  32  and  33,  or  by  the 
Soundings  on  the  Chart. 

Suppose  the  Distauce  off  shore  to  be  1  mile,  and  the 
Observed  Altitude  to  be  60°  11'  S ;  height  of  the  eye  18 
feet:  Correct  Declination  20°  10'  N.  Required  the  Lati- 
tude. 

Observed  Alt  Lower  Limb  to  the  Sea  Line 60°  11'  S. 

8emid.l6',  Dip  at  1  mile.  Tab.  VIII,  is  11',  Add  Diff.  5' 

Sun's  True  Central  Altitude 6'o°~T6"^ 

Subtracted  from  90°,  gives  Zenith  Distance..  ..29°  44'  N. 
Correct  Declination 20    10    N. 

Ijititude  in 49°  54'  N. 


EXAMPLE  14. 

Find  the  Distance  off  shore  from  the  Bearing  of  th» 
Land,  as  before  directed,  and  the  correct  height  of  th* 
eye  above  the  Sea  level. 

Suppose  the  distance  off  shore  to  be  -J-  a  mile,  and  th» 
Observed  Altitude  to  be  79*  35' ;  height  of  the  eye  2& 
feet ;  Correct  Declination  22°  15'  N.  Reqaired  the  Lati- 
tude. 

Observed  Alt.  Lower  Limb  to  the  Sea  Line. .  .79°  35'  N 
Semid.  16',  Dip  at -J  m.,  in  Tab  VIII,  is  28'  Sub.  Diff.  12 
Sun's  True  Central  Altitude 79°  23' 

Subtracted  fiom  90°,  gives  the  Zenith  Dist lO"  37'  S' 

Coirect  Declination 22    15    N 

Latitude  in .11°  38'  I» 


FINDING    THE  LATITUDE    BY  MERIDIAN  ALTITUDE. 


91 


TO  FINJ  THE  LATITUDE  FROM  A  MERIDIAN  ALTITUDE  BELOW  THE  POLE 

When  the  difference  between  the  Declination  of  a  body  and  90°,  or  the  Polar  Distance,  is  less  than  Um 
Latitude  of  the  place,  and  they  are  both  of  the  same  name,  the  object  comes  to  the  opposite  Meridian  with- 
out setting,  and  passes  that  Meridian  below  the  Pole.  If  the  Altitude  be  then  observed,  the  Latitude  may 
oe  found  as  follows  : 

RoLK. — Correct  the  Observed  Altitude  as  usual,  and  tc  the  true  Central  Altitude,  add  the  DiflFerence  between  U»« 
D<K:linatioD  and  90°,  or  the  Polar  Distance.     The  Sum  will  be  the  Latitude  of  the  same  name  as  the  Decliuatioa 

In  High  Latitudes,  in  the  Summer  time,  the  Sun  does  not  set  for  many  days,  and  the  Latitude  iray  be 
retained  from  hie  Meridian  Altitude  twice  in  the  24  hours  ;   that  is,  at  N»on  and  Midnight. 

DIAGRAM 

Of  the  Meridian  Altitude  Below  the  Pole. 

Fio.  16. 


In  tins  Figure  the  true  Meridian  Altitude  of  the  Sun  at  Noon  is  33*  28'  South,  and  which,  worked  ou. 
m  the  usual  manner,  gives  Latitude  80*  0'  North,  (on  the  coast  of  Spitzbergen,)  and  the  Latitude  from  th« 

Meridian  Altitude  at  Midnight,  is  found  as  follows  • 


EXAMPLE  16. 

June  21m,  1854.  Sea  Time  at  Midnight  ou  the  coast 
of  Spitzer.beiLceii,  the  Merid.  Altitude  of  the  Sun's  Lower 
Limb  was  ol).^etved  to  be  13°  17'  N.  Height  of  the  eye, 
<J  feet;  Long,  iu,  17°  East.     Required  the  Latitude  in. 

Obs.  Alt.  Sun  8  Lower  Limb 1H°  17'  N. 

Correction,  Table  IX,  to  be  added 10 

True  Central  Altitude 13°  27' 

Dedination,  June  2utl 23°  27'  N. 

Corp.  for  Long.  ]  7  °  East 0 

Corr.  1 2h.  past  Noon 0 

Correct  Deeliuation .23°  27'  )        ^^.  „„,  .. 

Scbtract  fi'om 90     0    f  "^  ^^    ^^   ^• 

Latitude  in 80°    o'  N. 


EXAMPLE  16. 

May  16th,  IBM.  Sea  Time  at  Midnight  the  observed 
Morid  Altitude  of  the  Sun's  Lower  Limb  was  8'  68' N 
Heiglit  of  the  eye,  15  feet.  Ship  off  Verlugen  Hook,  ii, 
Long.  16°  60'  East.     Required  the  Latitude  in. 

Obs.  All.  bun  s  1...WC,   Limb. , 8°  63'  N 

Correction,  Table  IX,  to  be  added 6 

True  Ceutral  Altitude 8°  6»' 

Declination,  Mav  15tli 18*  51'  N. 

Corr.  for  Long.  16°  60'  East,. Sub..  1 

Corr.  for  12h.  past  Noon  .  . .  .Add.  7 

Correct  Deliuation 18°  67'  )      „-,»    m' v 

Subtract  from »()     0    ) 

Latitude  in 80*    8'  ^ 


NoTK.—Thi8  Rul^  applies  likewise  to  the  Polar  and  other  Stars,  which  have  great  North  Declination,  examples  of 
which  will  be  found  at  page  109  ;  and  it  must  be  understood  that  although  the  foregoing  Examples  and  Diagrams  of 
Nautical  Astronomy  are  generaHy  constructed  for  North  Latitude,  and  the  North  Pole  elevated  above  the  horizon,  hy 
^'ereing  the  figure,  that  is,  by  elevating  the  Soutn  Pole,  the  Rules  are  the  same,  cnly  substituting  South  for  Ncrth. 
rhe  Spectator  i.s  then  supposed  to  be  situated  at  a  great  dis'jiuce  to  the  Westward  ot  the  Earth  and  facing  towards  tb* 
«wt,  having  South  on  his  Right  and  North  on  his  Lett. 


M 


NAUTICAL    ASTRONOMY 


FINDING  THE  LATITUDE  ON  SHORE  BY  THE  ARTIFICIAL  HORIZON. 

When  the  Sea  Horizon  is  obstructed  by  the  Land^  the  Latitude  may  be  found  by  an  Artificial  Honzor 
on  shore,  (a  description  of  which  is  given  at  pages  78  and  79,)  in  places  where  the  Sun's  Meridian  \ltituao 
does  not  exceed  60°;  because  in  observing  with  this  instrument,  the  angle  is  doubled,  that  is.  60*  of  Alti- 
tude would  require  an  angle  of  120'  on  the  Arch  of  the  Sextant,  and  the  Arch  of  common  Sextanta  dc 
not  extend  much  beyond  120°. 


RULE. 

Bring  the  Limbs  of  the  Sun  in  contact,  and  when  he  has  attained  his  greatest  Altitude  read  off  the  angle,  to  -whict 
apply  the  Index  Error  of  the  Sextant,  and  take  half  the  angle  for  the  Meridian  Altitude  of  his  Lower  Limb,  to 
•which  add  the  Sun's  semi-diameter,  and  subtract  the  Refraction,  will  give  his  true  Central  Altitude. 
ie  tlien  found  in  the  usual  manner. 


The  Latitu  le 


EXAMPLE  17. 

Jan.  20th,  1854.  At  New  York  the  observed  Angle  of 
the  Sun's  Lower  Limb  in  the  Artificial  Horizon,  ou  the 
Meridian,  was  57°  57'  20"  S.,  the  Index  Error  of  the  Sex- 
tant being  2'  subtractive.     Required  the  Latitude 

Ohs  Angle  Sun's  Lower  Limb 57°  57'  20"  S. 

Index  Error Sub..  2      0 

Apparent  Angle 57°  55'  20" 

Half  the  Angle  is  the  Sun's  Mer.  Alt. . .    28°  57'  40"  S. 
Sun's  semid,  N.  A..  .Add.  16  17 

App.  Central  Altitude  ...     29°  13'  67" 
Refraction,  Table  IV,  Sub.  1  41 

Sun's  True  Central  Alit.  . .    29°  12'  16" 

Sub.  from  90°,  gives  the  Zen.  Distance. .  60°  47' 44"  N. 

Sun's  Dec,  Jan.  20th,  N.A.,  20°  7'  38  '  S. ) 

•  Cor.  for  LoD.  74°  W,  in  5.20     5     2    S. 

Table  XL Sub.    2  6=2  36        ) 

Latitude  of  New  York. . . ,  40°  42'  42"  N. 


EXAMPLE  19. 

June  21st,  1864.  At  the  North  Cape  of  Europe  the 
observed  Angle  of  the  Sun's  Lower  Limb  in  the  Artificial 
Horizon,  on  the  Merid;<in,  was  84°  5'  36"  S.  No  ladex 
Error  in  the  Sextant.     Required  the  Latitude. 

Obs.  Angle  Sun's  Lower  Limb   84^    6'  36"  S. 

Half  the  Sum  is  the  Sun's  Mer.  Alt 42°    2' 48" 

Sun's  semi-diam.,  N.  A 15  46 

Sun's  App.  Altitude   42°  18'  34" 

Refraction,  Table  IV 1     2 

Sun's  True  Central  Alt.. . .  42°  17' 32"S. 

90    00    00 

Zenith  Distance 47°  42'  28"N. 

Declination,  June  2 Ist.    No  Corr.  required .  23    27  32  N. 
Latitude  of  the  North  Cape,~7T°  10'    0"N. 


EXAMPLE  18. 

March  30tb,  1864.  At  Valparaiso  Fort  the  observed 
Angle  of  the  Sun's  Lower  Limb  in  the  Artificial  Horizon, 
on  the  Meridan,  was  105°  44'  10"  N.,  Index  Error  of  the 
Sextant  being  1'  30",  additive.     Required  the  Latitude. 

Obs.  Angle  Sun's  Lower  Limb 105°  44'  10"  N 

Index  Error Add  1    30 

Apparent  Angle 105°  45'  40" 

Half  the  Angle  is  the  Sun's  Mer.  Alt.  .      52°  62'  50" 
Sun's  semid.,  N.  A..  .Add    J16 2_ 

Apparent  Central  Alt. ...      53°  '~8^52' ' 
Refraction,  Table  IV,  Sub. 43 

True  Central  All     53°    8'    9"  N. 

Sub.  from  90°,  Gives  the  Zenith  Dist. .     36°  51'  51"  S 
Sun's  Dec,  March  30th. .  ,3°  45'  22"  N. ) 
Corr.  for  Lon.  72°  W.,  in                          }•     3   49    62    N 
Table  XI,  Add  4'.5,  or        4   30        ) 

Latitude  of  Valparaiso  Fort,  "33°"  1'  59"  S 

EXAMPLE  20. 

Sept.  1st,  1854.  At  Antipodes  Island,  in  Lat.  49°  35' 
S.,  Lon.  179'^  2'  E..  the  obseived  Angle  of  the  Sou's  Lowei 
Limb,  on  the  Meridian,  in  the  Aititieial  Hoiizou,  was  63* 
21'  10"  N.     N<    Index  Error.     Required  the  Latitude. 

Obs.  Angle  Sui.    Lower  Limb 63°  21'  lO"  N 

Half  the  Angle  is  che  Sun's  Mer.  Alt. . .  31°  40'  35" 
Sun's  semid.,  N.  A Add.  16    63 

Sun's  App.  Altitude 31°  66'  28" 

Refraction,  Table  IV,  Sub  1    33 

Sun's  True  Central  At 31°  54'  55"  N 

Sub.  from  90°,  Gives  the  Zenith  Dist £8°    6'    5"  3 

Sun's  Dec,  Septlst  N.A.  8°  19'  18"  N.)       q   or^    la  k! 
Cor.Long.l79°E.,Ta.XI.Addll  \      "  ^"    ^"  ^ 

Latitude  of  Antipodes  Island.  .49°  34'  47"  S. 


NoTK. — In  correcting  the  Declination,  the  Civil  Time  is  used  in  the  above  Exiimples  ;  that  is,  the  Noon  of  the  Civil 
day  oorrespondinjr  to  the  Beginning  of  the  Astronomical  day.  The  Latitude  found  in  this  mannei'  is  more  correctly 
©btained  than  by  the  Sea  Horizou. 


•  The  Correction  for  the  Declination  in  Table  XI  being:  in  minutes  and  tenths  of  a  minute,  by  multiplying  the  tenth* 
Wy  •  wi  get  seconds  of  Declination 


FINDING  THE  LATITUDE  OUT  OF  THE  MERIDIAN.  08 


I 


By  one  Altitude  of  the  Sun  and  the  Time  from  Noon. 

It  frequently  happens  that  the  Meridian  Altitude  of  the  Sun  is  lost,  in  consequence  of  cloudy  weainer 
•oming  on,  and  that  he  may  he  visible  both  before  and  after  he  passes  the  Meridian.  In  either  case,  if  an 
Altitude  be  then  obsei-ved,  and  the  Apparent  Time  at  the  Ship  known,  the  Latitude  may  still  be  found 
M  correct  as  at  Noon. 

To  facilitate  this  computation,  a  Table  has  been  constructed  so  that  the  required  Logarithms  can  be  taken 
out  by  inspection,  for  the  purpose  of  finding  the  number  of  Minutes  of  Altitude  which  the  Sun  has  to  rise, 
when  the  observation  is  made  before  Noon,  or  what  he  has  fallen,  when  made  in  the  Afternoon.  In  both 
eases  this  Correction  is  additive  to  the  Sun's  Observed  Altitude,  which  will  give  his  Meridian  Altitude,  or 
what  it  would  have  been  if  observed  at  that  place. 

Table  XV,  in  Five  parts,  is  given  for  this  purpose,  and  explained  as  follows  : 

PART  I 

Contains  the  Logarithm  of  the  Hour  Angle,  or  the  time  from  Noon,  and  extends  to  64  m.  30  sec.  1  his 
%eing  sufficient  for  the  common  purposes  of  Navigation,  and  within  which  the  observation  must  be  made 
according  to  the  limits  given  in  Part  V,  (except  in  a  very  high  Latitude  in  the  Winter  months,  and  where 
few  Ships  frequent.)  This  part  is  entered,  with  the  minutes  and  the  nearest  seconds,  from  Noon,  and  oppo- 
site to  it  stands  the  Logarithm,  to  which  annex  the  Index  found  at  the  top  of  the  table. 

PART  II 

Contains  the  Logarithm  of  the  Latitude  by  the  Dead  Reckoning,  and  the  Sun's  Declination  when  they 
are  of  the  same  name.  The  Latitude  extends  to  60°,  and  the  Declination  to  23°.  This  part  is  entered  with 
ihe  Latitude  by  Dead  Reckoning  at  the  side,  and  the  Declination  at  the  top.  The  Angle  of  meeting  points 
•at  the  required  Logarithm.  When  the  minutes  of  the  Latitude  and  Declination  amount  to  nearly  half  a 
degree,  tak*)  out  the  nearest  Logarithm  preceding  and  the  nearest  Logarithm  following  it,  add  them 
t^ether   and  take  their  half  sum  for  the  required  Logarithm. 

PART  III 

Contains  the  Logarithm  of  the  Latitude  and  the  Declination,  when  they  are  of  contrary  names,  and  la 
entered  in  the  same  manner  as  the  other. 

PART  IV 

Contains  the  Sura  of  the  Logarithms  of  the  time  from  Noon,  and  that  of  the  Latitude  and  Declination, 
opposite  to  which  stands  the  required  correction,  to  be  added  to  the  observed  Altitude. 

PART  V 

Contains  the  limits  of  the  Time  from  Noon,  at  which  the  Observation  can  be  relied  on.  It  is  entered 
with  the  Declination  at  the  top,  (according  as  it  is  of  the  same  or  of  contrary  names  to  the  Latitude),  and 
the  Latitude  at  the  side,  and  the  angle  of  meeting  points  out  the  time  from  Noon,  at  which  the  observation 
should  be  made,  and  it  must  not  greatly  exceed  this  time,  especially  near  the  Equator.  And  it  will  be  per- 
ceived by  this  Part,  that  in  low  Latitudes  the  Observation  must  be  made  nearer  to  Noon  than  in  high  Lati- 
tudes. This  table  is,  therefore,  of  the  greatest  utility  in  high  Latitudes;  and  where,  also,  it  is  oftenest 
required,  on  account  of  the  stormy  weather  which  generally  prevails  there,  when  the  Meridian  Altitude  can 
seldom  be  obtained. 

This  method  of  find.ng  the  Latitude  will,  therefore,  be  found  very  useful  when  an  Altitude  can  be 
jbtained  near  Noon,  (but  which  is  generally  considered  by  seamen  as  useless  after  their  Meridian  Altitudt 
has  been  lost),  and  although  a  Ship  at  Sea  is  almost  continually  changing  her  time,  if  the  time  of  the  Observa- 
tion be  noted  by  a  good  watch,  which  may  have  been  regulated  previously  to  Apparent  Time  at  the  Ship,  then 
the  difference  of  LouLntude  made  in  the  interval  since  it  was  last  regulated,  turned  into  time,  and  subtracted 
from  the  time  by  watch,  if  the  Ship  has  been  sailing  West,  or  added  to  it  when  sailing  East,  will  give 
the  Apparent  Time  of  the  Observation  ;  which,  if  before  Noon,  subtracted  from  12  hours,  will  give  the  time 
from  Noon,  A.  M. ;  otherwi.se  it  will  be  the  lime  from  Noon,  P.  M.  (See  Example  6,  page  95.)  Or  the 
watch  may  be  regulated  by  equal  Altitudes  near  Noon,  as  in  Example  5. 

But  the  most  correct  mode  ;  is,  to  find  the  Apparent  Time  at  Ship  from  the  Greenwich  Time  by  Chronom- 
Bter.  The  Ship's  Longitude  being  generally  known  within  a  feAV  minutes  of  the  truth,  which  turned  into 
tme  and  applied  to  the  Greenwich  Time,  furnishes  the  Apparent  Time  of  the  Observation  as  follows  • 


91 


NAUTICAL  ASTEONOMV. 


o  Fitid  the  Latitude  by  one  Altitude  of  the  Sun,  having  the   Apparent    Time  from  Noon  deduced  from  th» 

Greenwich  Time  by  Chronomeui . 


RULE  FOR  FINDING  THE  TIME. 

Note  the  Time  of  the  Observation  by  Chronometer,  and  find  the  Greenwich  Time  by  applying  its  error.  Turn 
the  Ship's  Lone^itude  in  (at  the  time  of  the  Obseivatiou)  into  Time,  and  subtract  it  from  the  Greenwich  Time  in 
West  Longitude,  or  add  it  to  the  Greenwich  Time  in  East  Longitude,  will  give  the  Mean  Time  of  the  Obserration 
et  the  Ship.  To  this  Mean  Time  apply  the  Equation  of  Time  tlie  contrary  way  to  what  is  directed  in  tlie  precept 
at  the  head  of  the  column  iu  the  Nautical  Almanac  fur  Apparent  Time,  and  the  result  is  the  Apparent  Time  of  the 
Observation  at  the  Ship,  which,  if  before  Noon,  must  be  subtracted  from  12h,  (or  from  24h  if  above  I2h,)  will  give 
the  time  from  Noon,  A.  M,  otherwise  it  is  the  required  Time  from  Noon,  P.  M. 

THE  OBSERVATION. 

Observe  an  Altitude  of  the  Sun  near  the  limits  of  the  time  from  Noon,  given  in  Part  5th,  Table  XV,  and  note 
the  Time  by  the  Watch  or  Chronometer,  and  find  the  time  from  Noon  as  previously  directed.  Find  the  Latitude  in 
by  Dead  Reckoning  to  the  nearest  half  degree,  and  correct  the  Sun's  Declination  to  the  time  of  the  Observation  ai 
usual,  but  to  the  ueare.et  half  degree  is  enough  for  the  tables. 

RULE  FOR  USING  TABLE  XV. 

Enter  Part  1st  with  the  Time  from  Noon,  and  take  out  its  Logarithm. 

Enter  Part  2d  when  the  Latitude  and  Declination  are  of  the  same  name,  or 

Enter  Part  3d  when  they  are  of  contrary  names,  and  take  out  the  Log.  as  explained  m  the  preceding  page.  Add 
together  these  two  Logarithms,  and  find  their  sum  in  Part  4th,  against  which  will  be  found  the  Correction  required 
ID  Minutes,  or  Degrees  and  Minutes,  and  which  must  a/«'ays  be  added  to  the  Sun's  Observed  Altitude,  and  the  result  is 
the  Sun's  Meridian  Altitude,  or,  what  it  would  have  been  if  observed  on  the  Meridian  at  the  place  at  which  the  observa 
tion  was  made. 

The  Latitude  is  now  found  in  the  usual  manner,  which  will  be  that  of  the  Ship  at  the  time  of  the  Observation 
and  may  be  brought  up  to  Noon  by  applying  the  Difference  of  Latitude  made  in  the  iutervaL 


EXAMPLE    \. 

Feb.  26th,  1854,  a  Ship  at  Sea  in  Latitude  by  Dead 
Reckoning  about  38°  N.,  and  Long.  7t)°  30'  W.,  by  Chro., 
an  Altitude  of  the  Sun's  L.  Limb  was  observed  to  be  41° 
44'  S.  P.  M..  and  the  Greenwich  Time  by  Chro.  6h  53m 
67see.  P.  M.  at  Greenwich.  Requn-ed  the  Latitude 
in.    - 


Green.  Time  by  Chro.  5  63  57  Deel.  Feb.  25. .  .9° 
Ln.  76°  30'  W.in  time  5     6     0  Corr.  Table  XL._ 

Mean  Time  at  Ship. . 
Equa.  of  Time . .  .  Sub. 


5' 
6 


S. 


47  67   Corr.  Deel 9°  0'  S. 

13   16  Equ.of  T.,N.A.,  13ml6s 

App.  Time  from  Noon       34  41  =  Log.  7.757  Part  1st. 
Lat.  38°  N.,  Deel.  9°  S Log.  0.328  Part  Sd. 

Oorr.  in  Part  4th. . 


Obs.  Alt.  L.  Limb... 

Meridian  Altitude.  . . 
Corr.  Table  IX... Add 

Sun's  Central  Alt. ,  . 


0' 
41 


42' 
44 


Log.  8.085  Table  XV. 


42' 


26' 
11 


42°  37' 
90      0 

Zenith  Distance 47°  23'  N. 

Correct   Declination..     9      0S. 


Latitude  in 38°  23'  N.  at  35  min.  past  Noon. 

D.  Lat  made  since  N  5  to  the  Ni  rtliward. 


Latitude  in. 


38°  18'  at  Noon. 


EXAMPLE   2 

March  15th,  1854,  a  Ship  at  Sea,  in  Latitude  44*  80' 
N.,  by  Dead  Reckoning,  and  Long.  60°  30'  W.  by  Chro, 
the  Sun's  obsei'ved  Altitude  was  42°  20'  S.,  A.  M  The 
Greenwich  Time  by  Chro.  was  3h  31m  Psec.  P.  M.  The 
course  to  Noon  was  S.  W.  true,  going  9  knots.  Required 
the  Latitude  iu  at  Noon. 

(  H.      M.      8. 

Green.  Time  by  Chro...   3  31   9  Deel.,  March  15.2*  9'  & 
Add  .12     0  0   Corr.  T.  X I .  Sub^ 4 

For  the  purpose  of  Sub.  1 5  31   9  Correct  Deel.    .2°  5'  S. 
Ln.  60°  30'  W.in  time.   4     2  0 

Mean  Time  at  Ship. . .  r]~29~9'  Equa.  Time  N.  A.  9m  96. 
Equa.  of  Time . . .  Sub.         9  9 
App.  Time  at  Ship. . .  rr20  0  A.  M. 
Sub.  from  .12     0  0 

Time  from  Noon 40  0       Log. '  SSI  Pvt  IsL 

Lat  44°  30'  N.,  Deel.  2°  S.  Log.  0.2'.'4  Part  3d. 

Corr.  in  Part  4th    0°  61'  Log.  8  175  Table  XV 

Obs.  Altitude   L.  Limb.  .   42    20    S. 

Meridian  Altitude '^°"TT' 

Corr.  Table  IX Add  11 

Sun's  Central  Altitude..    43°  22' 

Sub.  from  90"  =  Zen.  Dist^i°  38'  N. 
Correct  Declination 2      5     S. 

Latitude  in 44°  33'  N.  at  40m  before  Noo» 

Course  S.  W.  6  m.  gives  D.  Lat.    4    to  the  Southward 

Latitude  iu ~44°"1>9''  N.  at  Nooa 


FINDING  THE  LATITUDE  BY  THE  SUN. 


FINDING  THE  LATITUDE  OUT  OF  THE  MERIDIAN. 


EXAMPLE  8. 

Oet  20tlv  1854.  In  Latitude  by  Dead  Reckoning  about 
40"  0'  S.,  Long,  by  Chro.  62°  E.,  the  Suu'a  Obs.  Alt  waa 
69°  30'  N.,  P.  M.  The  Greenwich  Time  by  Chronometer 
waa  19h.  58m.  54a.  A.  M.  The  Couree  aince  Noon  waa 
S.  S.  K,  going  12  knota  an  hour.  Required  the  Latitude 
in  at  Noun. 

H.  M.     s. 

Green.Time  by  Chr.,  19  58  54  Dec,  Oct.  20. . .  10°  20'  S. 
Lou.  62°  E.  in  time..  4    8     0  Cor.,  Ta.  XL  Sub.         4 

24    6  54  Cor.  Dec 10°  Iti'  S. 

Subtract. . .  .24    0     0 

Ma  Time  at  Ship..         6  54  Equa.  Time.N.  A.  16'  6" 
Eq.  of  Time,. .  Add..  15     6 

Ap.  Time  from  Noon.   22m.08.Log  7.862  Part  1st 
Lat  40°  S.  and  Dec.  10*  S.        Log  0.480  Part  2d. 

Cor.  in  Part  4th,  Add  0°  24'=  Log777842  Table  XV. 
Oba.  Alt 59  30'  N. 

Mer.  Altitude 59°  64'  N. 

Corr.,  Table  IX,  Add 1_2 

True  Altitude 60°    6'  N. 

Zenith  Dist 29°  64'  S. 

Declination 10    16  S. 

Latitude  in 40°  10'  S.  at  22'  past  Noon. 

S.S.E.  4  m.  ■=D.Lat.         4  to  the  South'd  since  Noon. 

Latitude 40°    6'  S.  at  Noon. 

EXAMPLE.  5 

June  22d,  1854.     Ship  near  the  Equator,  equal  Alti- 
tudes were  taken  to  correct  the  Watch. 

Altitude  A.M.  66°  4'  N.     Time  by  Watch lib.  48m, 

do.      P.M.  66    4   N.  do.         do 12     18 

Watch  is  8  min.  fast  of  Apparent  Time )24       6 

"l2h.    3  m. 
Required  the  Latitude  in  at  the  time  of  the  P.M.  Altitude. 

Time  by  Watch,  P.M Oh.  18m. 

Watch  fast  of  App.  Time.         3 

App.Time  from  Noon  . .  .Oh.  15m.Log  7.029  Part  let 
Lat  0°  0',  Dec 23°  N.  Log  0.673    I'ait  2d. 

Corr.  Part  4th,  .  .Add  0    17'     =  Lug  7.702  Table  XV. 
Oba  Altitude 66     4  N. 

Merid.  Altitude 66"  21'  N. 

Cor.,  Table IX,   Add. Vl 

True  Altitude 66°  33'  N. 

Zenith  Distance 23°  27'  S. 

Declination 23    27    N. 

Latitude 0°    0' 


EXAMPLE  4. 

July  5th,  1864.     In  Lat  by  Dead  Reckonmg  about  50 
S.,  and  Long,  90°  36'  E„  by  Chro.,  the  Sun's  Oba.  Alt 
was»l5'  47'  N.,  A.M.     The  Greenwich  Time  by  Cro.  wm 
17h.  Im.  47s.  A.M.     The  Course  to  Noon  waa  N.E.,  going 
10  knots  an  hour.     Required  the  Latitude  at  Noon. 

H.   M.     8. 

Green.  T'e  by  Chr.,   17   1  47  Dec,  July  5 22'  49'  N. 

Lon.90°  36'  E.iu  time,  6  2  24  Cor.,  Ta.XI,  Add  2 

M.  Te  at  Ship,  A.M.    23  4  11   Cor.  Dec 22°  5]  N 

Equa.  of  tune. Sub.         4  11' 

Sub  fr.  24h.=Ap.T.  ^00  Equa.,  N.  A 4'  11" 

Log  8.231   Part  Ist. 


Ap.  T.  f  m  Noon . .  Ih.Om.Os. 
Lat  50°  S.,  and  Dec.  23°  N. 

Cor.,  Part  4th,.  Add   1°  13'== 

Obs.  Altitude 15    47'  N. 

Mer.  Altitude 17°    O'  N. 

Corr.,  Table  IX,  Add      9 

True  Altitude  . .  17°  9  N. 
Zenith  Distauce  . .  72°  61'  S. 
Declination 22    51  N. 

Latitude. 


Log  0.093  Part  3d. 
Log  8.324  Table  XV 

\ 


.60°    0'  S.  at  11  o'clock  A.M. 
Co.  N.E.  10  m.=D.Lat    7  to  the  Northward. 
Latitude 49°  53'  S.  at  Noon. 

♦ 
EXAMPLE  6. 

Nov.  15th,  1854.  In  Latitude  about  56*  5'  N.,  uua^. 
15°  W.,  an  Altitude  of  the  Sun  was  observed  in  the  after- 
noon to  be  14°  7'  S.  Time  shown  by  the  watch,  lh.8m.46s, 
which  had  been  regulated  in  the  morning,  since  which 
time  the  Ship  had  made  64'  of  Longitude  to  the  West- 
.ward.  Required  the  Latitude  in  at  the  time  of  the  Alti- 
tude. 

Time  of  Alt  by  Watch Ih.  8m.  468. 

*  D.Lon.  ma.  64'  W.  in  time.  Sub.  4      16 

App.  Time  at  Ship,  P.  M Ih.  4m.  SOs.Log.  8.294 

Lat  56°  N.,  and  Dec.  18^  S Log.  0.042 

Corr.  in  Part  4th. .  Add  1°  14'  -=  Log.  8.336 

Obs.  Altitude 14 7    S.  Table  XV. 

Merid.  Altitude 15°  21'  S.  Dec 18^30'  S. 

Corr.,  Table  IX . .  Add  8  Corr. . .  Add     1 

True  Altitude 1_6°  29'  S.  Cor.  Dec  18°  31  S. 

Zenith  Distance 74°~Tr  N. 

Decimation 18    31    S. 

Latitude  in  . . .  ^6°~b'  N.  at  Ih.  4m.  P.  M 


QUESTIONS  FOR  EXERCISE. 

ijuestian  1st.— Dec.  11th,  1854.     The  Latitude  by  Dead  Reckoning  was  about  50°  0'  N.,  and  the  Longi 
tude  by  Chronometer  41°  20'  W.     An  Altitude  of  the  Sun  was  observed  in  the  forenoon   to  be  15°  28'  S 
and  the  time  by  ChronometerlSh.  40m.  6.s,  P.  M.,  whicTi  was  fast  of  Greenwich  3m.  20s.     The  Course  untii 
Noon  was  S.  by  W.,  going  8  knots.     Required  the  Latitude  at  the  time  of  the  Altitude  and  at  Noon. 

Answer. — Latitude  at  lOh.  58m.,  or  tune  of  Altitude,  was  50°  4'  N.,  and  at  Noon,  49°  56'  N. 

Ques.  2d.— August  27th.  The  Latitude  by  Dead  Reckoning  was  35*  30'  N.,  and  Long.  75'  W.  An 
Altitude  of  the  Sun  was  observed  to  be  63°  59'  S.  at  20  minutes  past  Noon,  apparent  time  at  the  place 
Ship  running  to  the  Northward,  going  9  knots.     Required  the  Latitude  as  before. 

Ans — Latitude  at  20  minutes  past  Noon  was  35°  27'  N.     Latitude  at  Noon,  35'  24'  N. 


•  When  the  Differonc*  of  Lon^tude  made  in  time  is  Eaat,  it  muatbe  added  to  the  Time  by  Watch. 


»6 


NAUTICAL  ASTRONOMY. 


TO  FIND  THE  LATITUDE  BY  TWO  ALTITUDES  OF  THE  SUN,  (USUALLY  CALLED 

DOUBLE  ALTITUDES,) 

Having  the  Measured  Interval  of  Time  between  the  Observations  by  the  Watch. 

This  method  will  be  found  more  simple  and  useful  than  the  old  and  tedious  methods  of  Double  Altitudes 
usually  given  in  works  of  this  kind,  many  cases  of  which  are  of  very  doubtful  utility,  besides  the  time 
ipent  in  working  them  out. 

The  principle  of  this  method  is  simply  to  find  the  Sun's  Hour  Angle  at  the  time  the  Altitude  was 
observed,  which  was  farthest  from  the  Meridian,  and  to  measure  the  interval  of  time  elapsed  between  it 
and  another  Altitude  observed  near  the  Meridian,  by  a  good  Watch  or  Chronometer.  This  interval  of 
time  being  then  corrected  for  the  Ship's  change  of  Longitude  in  time,  and  applied  to  the  Outer  Hour  Angle, 
the  difference  between  them  is  the  Inner  Hour  Angle,  and  which  is  the  Apparent  Time  from  Noon.  The 
observation  then  becomes  the  same  as  if  only  one  Altitude  had  been  observed,  and  the  limits  are  the  same 
as  in  the  last  case. 

The  Time  so  found  is  only  an  approximation,  because  the  Latitude  la  not  known,  but  it  is  near  enough 
for  this  purpose.  And  as  every  Navigator,  now-a-days,  is  supposed  to  know  how  to  find  the  time  at  Sea, 
nothing  new  is  required  to  be  learned.     The  Rule  for  findiilg  the  time  at  Sea  is  given  at  page  124. 

When  both  Altitudes  are  Observed  in  the  Forenoon. 

RULE. 

"When  the  Sun  is  at  a  proper  distance  from  the  Meridian,  or  on  the  Prime  Vertical,  that  is,  when  he  bears  nearly 
true  East  or  West,  take  an  Altitude,  and  note  the  time  by  a  good-going  Watch,  or  the  Chronometer.  Take  another 
Altitude  nearer  Noon,  about  the  limits  given  in  Part  5th,  Table  XV,  and  note  the  time  by  the  same  Watch,  and 
find  the  Interval  of  Time  elapsed  between  the  observations. 

Correct  the  lesser  Altitude  by  Table  IX.  Compute  the  Latitude  in  by  the  Dead  Reckoning  at  the  tim 
ihe  lesser  Altitude  was  observed,  and  also  the  Sun's  Declination,  and  find  his  Polar  Distance.  Then,  with 
the  true  Altitude,  Latitude,  and  Polar  Distance,  find  the  Sun's  Outer  Hour  Angle.  If  the  Ship  has  been 
stationary  during  the  Interval,  or  been  sailing  due  North  or  South,  no  correction  of  the  Interval  is  neces- 
sary. But  if  she  has  made  Easting  or  Westing,  then  find  the  Departure  the  Ship  has  made  in  the  Interval, 
from  her  true  Course  and  Distance  >nade  good,  and  the  corresponding  Difference  of  Longitude.  Turn  this 
Difference  of  Longitude  made  into  Time,  by  Table' XXVI,  and  add  it  to  the  Interval  if  the  Ship  has  been 
sailing  East,  or  subtract  it  from  the  Interval  if  she  has  been  sailing  West,  will  give  the  correct  Interval  of 
Time  between  the  observations ;  then  the  Difference  between  this  corrected  Interval,  and  the  Sun's  Outer 
Hour  Angle,  will  give  the  Inner  Hour  Angle,  at  the  time  the  greater  Altitude  was  observed,  and  the 
result  is  the  Apparent  Time  from  Noon.  The  Latitude  is  thence  found  in  exactly  the  same  manner  as  if 
only  one  Altitude  had  been  observed  near  Noon. 

When  the  Lesser  Altitude  is  Observed  Before  and  the  Greater  Altitude  in  the  Afternoon. 

The  Interval  is  found  in  the  same  manner,  and  the  Outer  Hour  Angle  subtracted  from  it,  gives  the  Innet 
Hour  Angle,  whi®h  will  be  the  Apparent  T'ime  past  Noon  at  the  Ship, 


When  Both  Altitudes  are  Observed  in  the  Afternoon* 

Take  an  Altitude  near  Noon,  about  the  limits  in  Part  5th,  Table  XV,  and  another  when  the  Sun  is  at  a 
Distance  from  the  Meridian,  and  find  his  Hour  Angle  as  before,  from  which  subtract  the  Interval,  will  give 
the  Inner  Hour  Angle  past  Noon. 

When  the  Lesser  Altitude  ts  Observed  After  Noon,  and  the  Greater  Altitude  Before  Noon.* 

The  Interval  is  found  in  the  same  manner,  and  the  Outer  Hour  Angle  subtracted  from  it,  gives  the  Inner 
Hour  Angle,  which  will  be  the  Apparent  Time  from  Noon,  A.  M.,  at  the  Ship. 

Hence  it  is  easy  to  ascertain  at  once  whether  the  observations  have  been  made  on  the  same,  or  on  opposite 
•sides  of  the  Meridian,  by  comparing  the  Outer  Hour  Angle  with  the  Interval  of  time  between  the  obser- 
vations. If  the  Interval  bo  less,  they  must  have  been  taken  on  the  same  side,  that  is,  both  in  the  fore- 
noon or  both  in  the  afternoon.  If  greater,  they  must  have  been  taken  on  opposite  sides  of  the  Meridian,  that 
H,  one  Altitude  has  been  taken  in  the  forenoon  and  the  other  in  the  afternoon. 

*  When  both  Altitudes  are  observed  in  the  Afternoon,  or  the  Greater  Altitude  before  Noonj  and  the  Lesser  Alti- 
tude after  Noon,  the  difference  of  Long,  in  time  made  in  t,he  interval,  should  be  added  to  themterval,  if  the  course 
"lae  been  Westerly,  or  subtracted  from  the  interval,  if  the  uourse  has  been  Easterlv. 


FINDING  THE  LATITUDE  BY  TWO  ALTITUDES  OF  THE  SUN. 


»7 


ExampUs  of  Finding  the  Latitude  by  two  Altitudes  of  the  Sun, 
( Usually  called  Double  Altitudes.) 


EXAMPLE   1 


April  1st,  1854,  the  Latitude  Id  was  86*  48'  N.,  and  the  Long.  60*  W.  by  Dead  Reckoning.  In  the  morning,  at  7b 
I8ni  per  Watch,  the  Sun's  Observed  Altitude  was  20°  10'.  Ship*  then  sailed  on  a  True  S.  E.  course,  going  9  kaot* 
an  hour,  until  llh  SOm  per  Watch,  when  another  Altitude  of  the  Sun  was  observed  to  be  67°  28'  S.  Required  the 
Latitude  of  the  Ship  at  the  time  of  the  last  Altitude,  and  at  Noon. 


Observed  Altitude  L.  Limb  20  10 
Corr.  Table  IX Add  9 


Time  of  Lesser  Altitude 
rime  of  Greater  Alt. . . 


H.    H. 

7  28  Decl.  in  Table  X 4*32  N 

11  30  Cor.Ln.60°W.,T.XI,Add       4 

4    2  Corr.  Decl.  Noon 4  86 

4 


True  Altitude 20  19  Interval  of  T.  by  watch 

Latitude 36  48  Log.  0.09R61  Rate  of  Sailing 9  k's  Cor.4h32'beforeN.  Sub. 

P.  Distance 85  28  Log.  0.00136  Distance  SaUed 36  m.  Corr.  DecL  at  7h  28m,. .    "432  M 

Sum 142  85  90    0 

i  Sum -, 71  18  Log.  4.50598  .  Polar  Distance. 86°28' 

True  Altitude 20  19 

Difference 50  59  Log.  4.89040  Course  S.  E.  36  m.,  Dep.  26.5,  D.  Long.  32'  in  time. Oh  2m  88  Add 

Outer  HoiH-  Angle 4h  31m  41s  =  9.49425  Interval  of  Time  by  Watch 4    2      0 

Correct  Interval 4      4        8 

Inner  H.  Angle, 


Correct  Interval  of  Time.  ,< 4h  4m  Ss 


AM..        27m  338  Log.  7.555  Part  Ist 
Lat  36i*  N;  DecL  4^°  N Log.  0.481  Part  2d. 

Corr.  in  Pa^  4th Add     0°  37'=-  Log.  8.036  Table  XV. 

Greater  Altitude 57    28 

Meridian  Altitude 58°    6' S.  Coui-se  S.  E.,  Dist.  in  27  min.  4  miles  gives  D.  Lat  to  Noon    0*    8'  & 

Corr.  Table  IX 11  Latitude  at  27m  before  Noon 36    20   N 

True  Central  Altitude. . .   58°  16''S. 

Dist. . 


Latitude  at  Noon 86°  17'  N 


From  90'  Zen.  Dist 31    44'  N. 

Corr.  Decl.  Noor*  4    36  N. 


The  Watch  in  this  case  was  2m  278  fast  at  time  of  Greater  Altitude 


Latitude 36°  2u'  N.  at  27  minutes  before  Nooa 


EXAMPLE  2. 


16th  March,  1854,  In  Latitude  44*  42'  Ji,  and  Long.  50°  W.  by  Dead  Reckoning.  In  the  morning  at  9h  10m  pei 
Watch,  the  Sun's  Observed  Altitude  w.ns  25°  8'.  Ship  then  sailed  ©n  a  True  W.  S.  W.  course,  going  8  knots  aa 
hour,  until  Ih  11m,  per  Watch,  in  the  afternoon,  when  the  Sun's  Observed  Altitude  was  42°  SO'  S.  Required  tb« 
Latitude  in  at  the  time  of  the  P.  M.  Altitude,  and  also  at  Noou. 


Observed  Altitude  L.  Limb 
Corr.  Table  IX Add 


26    8 
10 


Time  of  Lesser  Altitude 
Time  of  Greater  Alt  Ih  ) 
lira  add  12h=. ) 


H.   H. 

9  10 
13  11 


Decl.  in  Table  X 2    9 

Corr.  Lon.  60°  W Sab.        3 


S. 


True  Altitude 25  18  

Latitude 44  42  Log.  014825  Interval  of  T.  by  watch  ..41 

Polar  Distance 92    9  Log.  0.00031   Rate  of  Sailing 8  ks.  Dg^L  at  9h  A.  M. "i 

Sum 162    9 

Sum 


Distance  Bailed. 82m. 


DecL  at  Noon 2    6 

Corr.  3h  before  Noon  Add.        3 

T 

0 


90 


i  Sum 81    5  Log.  4.19038 

Altitude 25  18 

Difference 66  47  Log.  4.91746 


Polar  Distance 92°  9' 


9.26635 


Course  W.  S.  W.  32  miles  — 
Dep.  80  =-  D.  Lon.  in  time. 
Interval  of  Time  by  watch . . 

Correct  Interval  of  Time 3h  58m  Ss 


I  Oh 
..4 


2m  62a  Sub 
1        0 


Outer  Hour  Angle 3h  21m  68 

Correct  Interval S    58      8 

Inner  Hour  Auu;le 37m  28  Log.  7.813  Part  Ist 

Latitude  44^°  N.  DecL  2°  S Log.  0.293  Part  8d. 

Corr.  Part  4th Add     0°  44'  Log.  8.106  Table  XV. 

Greatsr  Altitude 42    80 

Meridian  Altitude. 43°  14'  S 

Curr.  Table  IX Add  11 

True  Central  Altitude. 

Bub.  from  90°  Zenith  Dist. 
DecL  Noon  2°  6',  Corr.  for  | 
37m  Sub.    1 f      *      "   °'    The  W^tch  in  this  case  was  83m  588  fast  at  the  time  of  the  Greater  Altikod* 

Latitnde 44°  30'  N.  at  37  minutes  past  Nooa 

Note.  In  the  Ist  E.xample,  10  miles  of  an  error  in  the  Latitude,  in  working  the  Hour  Angle,  would  produce  an  error 
in  the  time  of  about  9  seconds,  and  which  does  not  affect  the  Corr.  for  Altitude. 

In  the  2d  Example,  10  miles  of  at  error  in  tlie  Latitude,  in  working  the  Hour  Angle,  would  pro^> '-«  •  5  error  cf  ii 
♦•conds  in  the  time  from  Noon,  and  ^n  error  of  only  1'  80"  in  the  Correction  for  Altitude 


48°  25'  S. 


Course  W.  S.  W.  5  miles  since  Noon  D.  Lat    0'    2' 

Latitude  at  87m  past  Noon 44   80 

Latitude  in  at  Noon 44°  82'  S 


46' 
2 


35' N. 
5   S. 


i'S  NAUTICAL  ASTRONOMY. 


FINDING  THE  LATITUDE  BY  TWO  ALTITUDES  OF  THE  SUN, 
(Usually  called  Double  Altitudes.) 

EXAMPLE  S. 

Nov.  80th,  1864,  Ship  oflf  Cape  Horn,  in  Latitude  66°  S.,  Long.  80°  W.,  by  the  Dead  Reckoning.  In  the  after 
noon,  at  Oh  36m  523,  per  Watch,  the  Observed  Altitude  of  the  Suu  was  54°  49'  N.  Ship  then  sailed  on  a  True  N 
W  by  W.  Course,  going  10  knots  an  hour,  until  4h  47m  41  sec,  by  the  same  Watch,  when  the  Sun's  Observed  Alti- 
tode  was  26°  38'.     Required  the  Latitude  at  the  time  of  the  Greater  Altitude,  and  at  Nooa 

•      /  H.  M.   a  , 

Lesser  Altitude  Observed..    26  88  Time  of  Lesser  Alt.  |    ^  d7  a.1  Sun's  Decl.  Nov.  30, 2140  8 

Corr.  Table  IX. Add 10  by  Watch J    4  4<  41  Cor.  Ln. 80°  W. Tab.  XI  Add 2 

True  Altitude 26  48  Time  of  Greater  Alt.  0  86  62  pgcl.  at  Noon 21  42  a 

Latitude  by  Dead  Reck 65  38  Log.  0.24835  Interval  Time  by  W.   4  10  49  Cor.  for  4h  47m  past  Noon  Add    2 

Polar  Distance _^i?  W-  0.03202  ^iij 4J  hours  Decl.  Time  of  Lesser  Alt.   2T~44  S 

Sum 150  42  Rate  of  Sailing 10  knots  90    0 

^  Sum Ts  21  Log.  4.40297  Distance  Sailed. . .    .42  miles.  Polar  Distance 68°16' 

Difference "48  33  Log.  4.87479 

•Outer  Hour  Angle 4h~55m4'l8  -=  9.55813  Course  N.  W.  by  W.  42  miles  )  .    ,.    ^    kaa  r.u    a      ,o 

Correct  Interval. 4     16        1  Dep.  35  =  D  Lon.  =  63. . .  f"  '"««•  Add  Oh    4m  128 

Time  past  Noon 40ra  40s  Log.  7.895  Part  1st  Inte'-^al  of  Time  by  Watch 4    10      49 

Lat.  56°  S.,  DeeL  22°  S Log.  0.268  Pait  2d.  Correct  Interval  of  Time. 4h  16m    Is 

Corr.  Part  4th Add     0°  50'  =  Log.  8.163  Table  XV. 

Greater  Alt  Observed. .   64    49 

Merid.  Alt 65°  39'  N.  Course  N.  W.  by  W.  7  miles,  since  Noon,  gives  =-  D.  Lat.  0*    4' 

Ccrr.  Table  IX- Add  11  Latitude  in  at  41m  past  Noon 56°  62  S. 

True  Altitude 55°  60'  N.  Latitude  in  at  Noon 55°  66'  S 

Zenith  Distance 34°  10'  S.     And  the  Watch  in  this  case  was  3m  488  slow,  at  the  time  of  the  Greater  Al* 

Decl.  at  Noon ._21    42    S. 

Latitude 65°  52'  S.  at  Oh  41m  past  Noon. 

EXAMPLE  4 

August  lOth,  1864,  Ship  off  the  Cape  of  Good  Hope,  in  Latitude  38°  20'  S.,  and  Long.  20°  10'  E.  by  the  Dead 
Reckoning.  At  lib  28m  in  the  forenoon,  the  Sun's  Observed  Altitude  was  36°  2'  N.  Ship  then  sailed  due  East, 
going  8  faiotj,  until  4h  21m  298  in  the  afternoon,  when  the  Sun's  Observed  Altitude  was  10°  8'.  Required  the 
Latitude  in  at  the  time  of  the  A.  M.  Altitude,  and  also  at  Noon. 

Lesser  Altitude  Observed...  10°  8  Timeof  Great  Alt  K ,  „„    ^  Decl  Aug.  10th 16'37'N 

Corr.  Table  IX Add 7_  by  Watch p i  /»    u  q^^^  20°  E.  Long..  ..Add  1 

True  Altitude 10  15  Tiraeof  Lesser  Alt  [  jg  .^^  ^g  Declination  Noon UsT 

Lat  Dead  Reckoning 38  20  Log.  0.10546  4h  21m  298  add  12h  ^        "  Corr.  for  4h  21m Sub.  8 

Polar  Distance  105  35  Log.  0.01627  Interval  Time  by  W.  4  53  29  Decl.  Time  of  Lesser  Alt.*   16  85 

Sum 154  IJO  Say 5  hours.  90     0 

\  Sum 77  "6  Log.  4.34934  ^^^e  of  Sailing.. . .  ^_8 p^lar  Distance lOe^S^ 

Altlude 10  15  Distance  sailed 40  miles. 

Difference 66  50  Log.  4.96349  Course  True  East  40  miles ■=  D.  Lon.  61' in  time  Oh    Sm  24a  Sut 

Outrtr  Hour  Angle 4h  11m  29s  =  9.434^  Interval  of  Time  by  Watch 4    68      29 

Cor  ect  Interval 4    50        5  Correct  Interval  of  Time 4h  fiOm    58 

Time  before  Noon 88m  36s  Log.  7.851  Part  Ist  )  rp  ui    vir 

Lat  38iS.,Decl.  16i  N Log.  0271^  Part  3d   \  ^'^'"'^^  ^^ • 

Corr.  Part  4th Add     0°  46'  Log.  8.122 

Greater  Altitude  Observed.    35      2  Ship's  Course  having  been  due  East  she  is  on  the  name  Parallsl 

Meridian  Altitude ~Z^'~^'  N.  of  Latitude  at  Noon,  38'  23 

Corr.  Table  IX Add 1 1 

True  Altitude 35°  59'  N 

Zenith  Distance 64°     IS.     In  this  case  the  Watch  was  6m  868  fast  at  the  time  of  the  Greater  Altituae 

Decl.  Noon 16    88   N. 

liatitude 38°  23^  S.  at  llh  21m  248  in  the  forenoon. 


Note. — In  Example  8d,  the  Lesser  Altitude  having  been  observed  on  the  Prime  Vertical,  an  error  in  the  Latitad# 
does  not  affect  the  Hour  Aiiirle. 

In  Example  4th,  an  error  of  10'  in  the  Latitude  would  produce  an  error  of  29  hpc.  in  working  tne  Hour  Auffle  bnl 
vhich  has  little  or  no  effect  on  the  correction  for  Altitude 


I 


FINDING  THE  LATITUDE  BY  THE  SUN  99 


FINDING  THE  LATITUDE  BY  TWO  ALTITUDES  OF  THE  SUN 

QUESTIONS  FOR  EXERCISE. 

Question  \st. — October  20th,  1854.  Ship  becalmed  in  Latitude  50*  9' N.,  and  Longitude  30*  W  by 
Dead  Reckoning.  In  the  afternoon  at  Oh.  34m.,  per  watch,  the  Sun's  observed  Altitude,  Lower  Limb,  was 
29°  5'  S.,  and  at  2h.  46m.  it  was  19°  54'.  Required  the  time  from  Noon,  when  the  greater  Altitude  waa 
observed,  and  the  Latitude  in. 

Answer. — The  time  from  Noon,  when  the  greater  Altitude  was  observed,  is  Oh.  28m.  46s.,  and  the 
Latitude  in  at  that  time  was  50°  3'  N. 

Ques.  2d. — February  25th,  1854.  In  Latitude  51°  2'  N.,  Longitude  45*  W.,  by  Dead  Reckoning.  In  the 
afternoon,  at  Oh.  33m.,  the  Altitude  of  the  Sun's  Lower  Limb  was  28°  53'  S.  Ship  then  sailed  to  the  East- 
ward 20  miles,  and  at  2h.  43m.  P.  M.,  it  was  19°  44'.  Required  the  error  of  the  Watch,  and  the  Latitude 
at  the  time  of  the  greater  Altitude. 

Ans. — The  time  from  Noon,  when  the  greater  Altitude  was  observed,  was  Oh.  40m.  lis  Watch  was 
tra.  lis.  slow,  and  the  Latitude  in  51°  17'  N. 

Ques.  3d. — January  6th,  1854.  In  Latitude  58°  25'  S.,  and  Longitude  138'  E.,  (at  Noon,  by  Dead  Reck- 
oning.) At  llh.  2m.,  A.  M.,  per  watch,  the  Altitude  of  the  Sun's  Lower  Limb  was  52°  13'  N.  Shipthsa 
sailed  on  a  S.  S.  W.  i  W.  Course,  (true,)  going  8  knots  an  hour  until  4h.  50m.  P.  M.,  when  his  Altitude 
was  28°  10'.  Required  the  correct  time  from  Noon,  when  the  greater  Altitude  was  observed,  the  Latitude 
in  at  tSiat  time,  and  the  Latitude  at  Noon,  brought  on  by  the  Dead  Reckoning. 

Ans. — The  time  from  Noon,  when  the  greater  Altitude  was  observed,  was  Ih.  Im.  58s.  A.  M.  Latitude 
in  at  that,  time  58°  30'  S.  The  Difference  of  Latitude  made  to  Noon  was  7'  S.,  and  the  Latitude  in  at  Noon 
was  58°  37'  S.     {In  this  case,  at  the  time  of  the  lesser  Altitudej  the  Sun  was  on  the  Prime  Vertical.) 

Ques.  4th. — August  30th,  1854.  In  Latitude  12°  43'  S.,  and  Longitude  93°  W.,  Dead  Reckoning,  at  llh. 
45m.  12s.,  A.  M.,  the  observed  Altitude  of  the  Sun's  Lower  Limb  was  67°  44'  N.  Ship  sailed  S.  W.  by  W., 
going  4  knots  an  hour,  until  Ih.  15m.  12s.,  P.  M.,  (both  times  being  noted  by  the  same  watch,)  when  the 
Altitude  was  62°  0'.  Required  the  time  from  Noon,  when  the  greater  Altitude  was  observed,  and  the 
Latitude  in. 

Atis. — The  time  from  Noon  was  Oh.  20m.  22s.,  A.  M.,  and  the  Latitude  observed  at  that  time  was 
12°  32'  S. 

Note. — In  Low  Latitudes,  the  Lesser  Altitude  may  be  taken  much  nearer  to  Noon  than  in  High  Latitudes;  because 
there  the  Sun's  motion  is  much  quicker,  and  the  Time  is  more  correctly  found  in  Low  Latitudes  •  but  in  all  cases  the 
Greater  Altitude  should  be  observed  as  near  to  Noon  as  the  limits  required  in  Part  6th,  Table  XV 

Should  there  happen  to  be  a  very  great  difference  between  the  Latitude  so  found,  and  that  by  the  Dead 
Reckoning  at  the  lime  of  the  greater  Altitude,  the  Latitude  used  in  finding  the  Outer  Hour  Angle  must  bo 
corrected  accordingly,  and  the  case  worked  over  again,  and  the  Inner  Hour  Angle  found  anew,  which  will 
.{ire  the  correct  Latitude. 

In  the  above  Examples  the  height  of  the  eye  is  taken  at  16  or  18  feet  above  the  Sea  Iflvei. 


100 


NAUTIUAL  ASTRONOMY. 


TO  FIND  THE  -.ATITUDE  FROM  THE  SUN'S  CHANGE  OF  >  LTITUUE. 

This  Table  contains  the  Sun's  Change  of  Altitude  in  One  Minute  of  Time  for  every  Degree  of  Lmtitud* 

When  on  the  Prime  Vertical, 


Lat. 

Change 
of  Alt. 

L.u. 

Change 
of  Alt. 

L..t. 

Change 
of  Alt. 

Lilt. 

Change 
of  Alt. 

Lat. 

Change 
of  Alt. 

Lat. 

Change 
of  Alt. 

Lat. 

Change 
of  Alt. 

Lat. 

Change 
of  All. 

Lat. 

Change 
of  Alt. 

O 

1 

/       // 

15.    0 

O 

11 

14.44 

O 

21 

14.   0 

o 

31 

/      // 

12.52 

o 

41 

11.20 

O 

51 

/      // 

9.27 

o 

61 

7.16 

O 

71 

1      II 

4.53 

0 

81 

/      II 

2  22 

2 

16.    0 

12 

14.41 

22 

13.54 

32 

12.44 

42 

11.10 

52 

9.15 

62 

7.    2 

72 

4.38 

82      2.    6| 

8 

14.68 

13 

14.37 

23 

13.48 

33 

12.35 

43 

10.59 

63 

9.    2 

63 

6.48 

73 

4.23 

83 

1.50 

4^ 

14.68 

14 

14.34 

24 

13.42 

34 

12.26 

44|  10.48 

64 

8.49 

64 

6.34 

74 

4.    8 

84 

1.34 

5 

14.57 

15 

14  80 

25 

13.36 

36 

12.17 

45    10.37 

55 

8.36 

66 

6.20 

76 

3.53 

85 

1.18 

6 

14.56 

16 

14.26 

26 

13.29 

36 

12.    8 

46 

10.26 

56 

8.23 

66 

6.    6 

76 

3.38 

86 

1.    2 

7 

14.64 

17 

14.21 

27 

13.22 

37 

11.59 

47 

10.15 

67 

8.10 

67 

5.52 

77 

3.23 

87 

0.46 

8 

14.51 

18 

14.16 

28 

13.15 

38 

11.60 

48 

10.    8 

58 

7.67 

68 

5.38 

78 

3.    8 

88 

0.30 

9 

14.4'.» 

19 

14.11 

29 

13.    8 

39 

11.40 

49 

9.51 

59 

7.44 

69 

6.24 

79 

2.52 

89 

0.15 

10 

14.46 

20 

14.    6 

30 

13.    0 

40 

11.30 

50 

9 .  39 

60 

7.30 

70 

5.    9 

80 

2.36 

90 

0.   0 

When  the  Sun,  or  any  other  heavenly  body,  is  on  the  Prime  Vertical,  that  is,  when  it  bears  true  East  or 
iVcst,  its  change  of  Altitude  is  then  greatest.  If  its  change  of  Altitude  in  one  minute  of  time  be  then 
measured  with  a  Sextant,  to  the  nearest  second,  the  Latitude  corresponding  to  it  will  be  found  in  the  abova 
Table  This  method  depends  entirely  upon  the  accuracy  with  which  the  change  of  Altitude  is  measured, 
and  cannot  be  much  depended  on,  even  in  High  Latitudes,  where  the  change  of  Altitude  in  one  minute  of 
time,  between  any  two  degrees,  differ  the  most. 

It  is  merely  given  here  to  illustrate  the  subject.  The  Table  itself,  however,  will  be  found  useful  when 
we  want  to  know  the  change  of  Altitude  of  any  heavenly  body  when  bearing  East  or  West ;  for  instance, 
in  observing  Altitudes  for  Time,  it  may  be  used  as  a  check  on  the  difference  of  the  observed  Altitudes  in  a 
given  time,  and  which  should  agree  with  the  change  of  Altitude  in  one  minute  of  time  given  in  the  abov© 
Table,  according  to  the  Latitude  of  the  place  of  observation. 

But  as  the  heavenly  bodies  only  pass  the  Prime  Vertical  above  the  horizon  when  the  Latitude  of  the 
place  and  the  Declination  of  the  body  are  of  the  same  name,  (as  in  the  case  of  the  Sun  in  the  Summer  time  | 
the  change  of  Altitude  will  be  slower  when  they  are  of  contrary  names,  and  in  this  case  the  quickest 
change  will  take  place  when  the  Altitude  is  from  5°  to  10°  above  the  horizon,  but  there  are  always  som* 
one  or  other  of  the  heavenly  bodies  on  the  Prime  VerticaL  which  may  be  observed. 


To  find  the  Latitude  from  the  Change  of  the  Sun^s  Altitude  tn  One  Minute  of  Time. 

RULE. 

Observe  with  a  Sextant  an  Altitude  of  the  Sun,  when  he  bears  true  East  or  West,  and  note  the  full  mmntc  oy  th» 
Watch.  Three  minutes  afterwards,  observe  another  Altitude,  at  that  exact  time  Divide  the  Difference  of  th» 
Observed  Altitudes  by  the  number  of  minutes  ehipsed,  will  give  the  Change  of  Altitude  in  1  minnte  of  time,  with 
^hich  enter  the  above  Table,  opposite  to  which  will  stand  the  Latitude  required. 


EXAMPLE  1. 

The  Sun's  Change  of  Altitude  in  1  minute,  and  his 
tearing  East  (passing  tlie  Meridian  to  the  Southward) 
given.  But  neither  the  Declination  nor  the  Latitude 
by  account  known.     Required  the  Latitude  in. 

T.by  Watch. .  5h  20m.     1st  Alt..  14°  17'  40" 
do.         do.   .  .  5    23 


2d  Alt..  14    52    10 


3  m. 


)34'  30"Diff.of  Alt. 


Bun's  Change  of  Alt  in  1  minute.         11'  30" 
Which  corresponds  to  Lat .  .  40°  0'  N.  in  the  Table. 


EXAMPLE  2. 

Required  to  find  the  Latitude  by  the  Sun's  Change  ot 
Altitude  in  1  minute   of  time,  when  on  the  Prime  Ver 
tical,  having  passed  the  Meridian   to  the  North  of  th» 
Obsei'ver. 

T.  by  Watch. .  5h.4m.     Ist  Alt.. 21*     6'  20' 
do.         do.  ..  5    7         2d  Alt. 20    37    23 

3m )28'  67"  Dilf.  of  Al»' 

Sun's  Change  of  Alt  in  1  minute.         9'  39" 
Which  corresponds  to  Lat.  .60"  O'  S.  b  the  Table. 


i 


FINDING  THE  LATITUDE  BY  THE  MERIDIAN  ALTITUDE 'CF- TUE  MOON'  101 


The  Latitude  may  be  found  from  the  Meridian  Altitude  of  the  Mooi>,  upon  the  same  pniclple  an  tbat  by 
the  Sun.  But  as  the  Moon's  Declination  changes  very  rapidly,  we  must  know  the  exact  Grvsehwich  data 
at  which  the  Observation  is  made,  in  order  to  correct  her  Declination  to  that  date. 

The  Moon's  Declination  is  given  in  the  large  Nautical  Almanacs  for  every  hour  of  the  day  at  Greenwich 
and  her  change  of  Declination  in  seconds  for  every  10  minutes  between  the  hours,  so  that  the  Correction 
can  easily  be  computed. 

In  the  small  Almanacs,  it  is  only  given  for  every  Noon  and  Midnight  at  Greenwich,  and  we  take  the 
proportional  part  of  hpr  change  iu  Declination,  corresponding  to  the  hours  and  minutes  past  the  nearest 
Noon  or  Midnight,  or  enter  Table  XXIII  with  the  Diff.  in  12h  at  the  side,  and  the  tiiHe  past  Noon  or  Mid- 
night at  the  top,  and  take  out  the  Correction. 

But  if  the  Longitude  of  the  Ship  be  not  known,  the  correct  peclination  cannot  be  computed,  consequently 
the  Latitude  cannot  be  found  by  tlie  Moon. 

Ships,  however,  which  carry  good  Chronometers,  have  their  Longitude  always  tolerably  correct ;  hence, 
the  Latitude  found  by  the  Moon,  in  that  case,  can  be  depended  on,  and  is  sufficiently  near  the  truth  for  all 
practical  purposes. 

The  Moon  being  nearer  the  Earth  than  any  other  heavenly  body,  her  place  in  the  heavens  is  greatly 
affected  by  Parallax ;  that  is,  she  always  appears  below  her  true  place  in  the  heavens,  by  the  amount  of 
her  Parallax  in  Altitude.  This  Correction  is  given  in  Table  XXV,  (and  which  includes  the  correction  for 
the  Refraction  of  the  Atmosphere),  and  is  always  additive  to  the  Apparent  Altitude. 

The  Moon's  Semi-diameter  and  Horizontal  Parallax  is  given  in  the  Nautical  Ainianac  tor  every  Noon 
and  Midnight  at  Greenwich,  and  are  generally  taken  out  for  the  nearest  Noon  or  Midnight  corresponding 
to  the  Greenwich  date  of  the  Observation. 

When  the  Moon  is  in  the  Zenith,  she  is  nearer  to  the  observer  than  when'm  the  Horizon,  by  the  amount 
of  the  Earth's  Semi-diameter;  hence,  her  Diameter  is  augmented,  or  appears  16"  larger  than  when  in  the 
Horizon.  This  Correction  is  given  in  Table  VII,  but  is  seldom  used  in  the  practice  of  finding  the  Latitude 
at  Sea. 

The  first  thing  ri*quired  to  be  done  is  to  find  at  what  time  the  Moon  passes  the  Meridian  of  Greenwich, 
in  the  Nautical  Almanac,  on  the  day  before  the  Sea  Date,  and  correct  it  to  the  time  she  passes  the  Merid- 
ian of  the  Ship  ;  because,  as  the  Moon  is  constantly  advancing  to  the  Eastward  in  the  Heavens,  she  will 
pass  any  Meridian  to  the  Eastward  of  Greenwich  sooner  in  the  day,  or  a  Meridian  to  the  Westward  later 
in  the  day,  by  a  certain  number  of  minutes.  Therefore,  in  West  Longitude  we  take  out  the  Meridian 
passage  on  that  and  the  following  day,  but  in  East  Longitude,  on  that  and  the  preceding  day,  and  take 
their  difference,  which  is  tne  daily  variation  of  the  Moon's  passing  the  Meridian.  Enter  Table  XXII  with 
the  daily  variation  at  the  top,  and  the  Longitude  of  the  Ship  in  the  side  column,  and  at  the  angle  of  meet- 
ing will  be  the  number  of  minutes  required,  which  must  be  added  to  the  time  of  her  Meridian  passage  on 
the  day  before  the  Sea  Date,  if  the  Longitude  be  West,  or  subtracted,  if  East,  will  give  the  Mean  Time  oi 
her  passing  the  Meridian  of  the  Ship. 

This  correction  may  also  be  found  by  adding  2  minutes  of  time  for  every  15°  of  Longitude  which  the 
Ship  is  to  the  Westward  of  Greenwich,  to  the  Mean  Time  of  her  passing  the  Meridian  of  Greenwich  (by  th<< 
Nautical  Almanac),  or  subtracting  the  same  when  the  Longitude  is  East,  will  give  the  Mean  Time  of  tier 
passage  at  the  Ship. 

Here  it  may  be  remarked,  that  as  the  Watch  is  generally  regulated  to  Apparent  Time  at  Ship,  and  is 
referred  to  in  ascertaining  the  time  to  begin  the  observation,  these  two  times  may  differ  as  much  as  16 
minutes  sometimes,  and  the  observation  is  frequently  lost ;  that  is,  the  Moon  has  passed  the  Meridian 
before  the  observation  has  been  begun.  To  prevent  this  happening,  take  out  the  Equation  of  Time  given 
in  the  Nautical  Almanac,  and  apply  it  to  the  Mean  Time  of  passing  the  Meridian  at  the  Ship  the  contrary 
way  to  what  is  directed  in  the  precept  at  the  head  of  the  column  for  Apparent  Time,  and  the  result  is  the 
Apparent  Time  of  her  passing  the  Meridian  at  the  Ship.  Then  if  the  Watch  be  regulated  to  Apparent 
'•'ime  at  the  Ship,  it  will  show  the  exact  time  at  which  the  Moon  will  pass  the  Meridian,  because  all  the 
ieavenly  bodies  pass  the  Meridian  at  Apparent  Time. 


i 


Having  thus  found  the  Mean  Time  of  the  Moon's  Meridian  passage  at  the  Ship,  as  directed  above ' 

2.  To  Find  the  Greenwich  Date, 


Turn  the  Ship's  Longitude  into  Time  by  Table  XXVI,  and  add  it  to  the  above  time,  if  the  Longitude  be 
West,  or  subtract  it  if  the  Longitude^ be  East.  The  Sum  or  Difference  will  be  the  time  at  Greenwich 
(usually  called  the  Greenwich  Date)  when  the  Moon  passes  the  Meridian  of  the  Ship.  But  should  the 
lum  exceed  24  hours,  subtract  24  hours  from  it,  and  add  one  day  to  the  Greenwich  Date.  On  the  other 
hand,  when  the  Longitude  is  subtractive,  and  greater  than  the  time  of  Passing  the  Meridian,  add  24  hours 
to  the  latter,  for  the  purpose  of  subtraction^  and  take  one  day  from  the  Greenwich  Date. 

3.  To  Correct  the  Semi-diameter  and  Horizontal  Parallax 

From  the  Nautical  Almanac  take  out  the  Moon's  Semi-diamSter  and  Horizontal  Parallax  for  the  nearest 
Noon  or  Midnight  corresponding  to  this  Greenwich  Date,  and  correct  them  if  required  by  Table  XXIV, 
and  to  the  Moon's  Semi-diameter  add  her  augmentation  found  in  Table  VII.  (But  this  is  seldom 
necessary.) 

4.  To  Find  the  Apparent  Altitude. 

Add  the  Difference  between  the  Moon's  Semi-diameter  and  the  Dip  of  the  Horizon  found  in  Table  V  to 
the  Observed  Altitude  of  her  Lower  Limb,  or  siil)tract  their  Sum  if  the  Upper  Limb  be  observed,  will  gire 
the  Moon's  Apparent  Central  Altitude.     (See  remarks  on  taking  A.ltitudes  at  page  71.) 


102 


NiUTICAL  ASTRONOMY. 


5,  To  Find  the  Moon^s  Tru*  Altitv.de. 

Enter  Table  XXV  with  the  Moon's  Horizontal  Parallax  at  the  top,  and  her  Apparent  Altitude  at  tb« 
•ide,  and  take  out  the  Correction  for  her  Parallax  in  Altitude,  and  which  ij  always  additive  to  her  Apparent 
Altitude. 

6.  To  Correct  the  Declination  by  the  Large  Nautical  Almanac 

To  correct  the  Moon's  Declination,  taken  from  the  large  Nautical  Almanac,  take  out  the  Declination  fo- 
the  day  and  hour  corresponding  to  the  Greenwich  Date.  And  when  there  are  odd  minutes,  take  out  th« 
Diff.  of  Declination  in  10  minutes,  found  in  the  side  column  opposite,  and  wnich  is  expressed  in  seconds 
and  hundred  parts  of  a  second  ;  and  when  the  hundredths  are  more  than  6u,  call  the  seconds  one  more, 
but  if  less,  throw  them  away.  Multiply  the  seconds  by  the  odd  minutes,  and  strike  off  the  right  hand 
figure  ;  then  divide  by  60,  will  give  the  Correction  in  minutes  and  seconds.  If  the  Declination  is  increasing, 
add  this  Correction,  but  if  it  be  decreasing,  subtract  it. 

7.  To  Correct  the  Declination  by  the  Small  Nautical  Almanac. 

To  Correct  the  Moon's  Declination  taken  from  the  small  Nautical  Almanac,  take  out  the  Declination  for 
the  nearest  Noon  or  Midnight,  if  the  Greenwich  Date   be  exactly  at  Noon  or  Midnight;  but  if  not,  take  it| 
out  for  the  nearest  Noon  or  Midnight  preceding,  and   the  nearest  Noon  or  Midnight  following,  the  Green- 
wich Date,  and  take  their  difference,  which  will  be  that  for  12  hours. 

Enter  Table  XXIII  with  the  difference  for  12  hours  at  the  side,  and  the  hour  from  Noon  or  Midnight  atj 
the  top,  and  take  out  the  Correction.  If  there  are  odd  minutes,  enter  the  right  hand  side  of  the  table  with  I 
the  odd  minutes  at  the  top  and  the  difference  for  12  hours  at  the  side,  and  take  out  the  Correction.  Add\ 
the  Sum  of  these  Corrections  to  the  Declination  at  the  preceding  Noon  or  Midnight,  if  the  Declination  ir] 
increasing,  but  subtract  it  if  decreasing,  will  give  the  Moon's  correct  Declination  at  the  time  of  the  obser 
vation. 

But  when  the  Declination,  taken  from  the  Nautical  Almanac,  for  the  preceding  Hour  or  the  Noon  or  Mid- 1 
night,  is  decreasing,  and  the  correction  subtractive  exceeds  it,  the  difference  is  the  Declination  of  a  contrarr^\ 
name 

ff 
8.  To  Find  the  Latitude 

Thus  having  the  Moon's  Correct  Altitude,  and  her  Correct   Declination,  the  Latitude  is  found  by  thai 
same  rule  as  for  the  Sun's  Meridian  Altitude.     That  is:  Subtract  the  True  Altitude  from  90°,  will  g\y^\ 
the  Zenith  Distance  of  a  contrary  name  to  the  Moon's  Bearing.     Place  the  Correct  Declination  under  it. 
Then  if  they  are  both  North  or  both  South,  their  Sum  is  the  Latitude  of  that  name ;  but  if  one   be  Nortbj 
and  the  other  South,  their  difference  is  the  Latitude  of  the  same  name  as  the  greater  of  the  two 


EXAMPLE  1 


Jul  J'  12th,  1854,  Sea  Time,  in  the  Longitude  of  75*  W.,  the  Meridian  Altitude  of  the  Moon's  Lower  Limb  wa«  j 
•bse'-ved  to  be  40°  85'  S.     Height  of  the  eye  18  feet     Required  the  Latitude  of  the  Ship. 


July  12th  is  July  11th,  Astronomical  Time. 

Moon's  Men  Passage,  July  11th, .13h  58m 

On  the  following  day,  July  I'ith 14    56 

Long.  75°  W.,  and  daily  variation 58m  b  Table  XXII. 

Gives  the  Correction  to  be  added Oh  12m 

To  the  Meridian  Passage,  July  11th .13    58 

Mean  Time  of  the  Men  Passage  at  Ship. .  .14h  10m 

Long.  75°  W.  in  time Add  5 0 

Greenwich  Date,  July  11th 19h  10m 

Less  12h,  gives  the  time  past  Midnight. . . .  7h  10m 

Moon's  Decliuatiou  at  Midnight,  July  Uth..   21*  21'  S. 
Moon's  Declination  at  Noon,  July  12th 19      9    S 


Diff.  of  DecUnation  in  12  hours 2 

Time  from    Midnight    7h  10m 
in  Table  XXIU-Corr. 


12'  and  the 


'  j- .Sub.    1"  18' 

Declination  at  Midnight  decreasitig 21    21    S. 

Correct  Declination  at  time  of  Observation  20°    3'  S 


Mean  Time  of  Mer.  Pass,  at  Ship. . .  .14h  10ra| 
Equa.  of  Time  N.  A.  applied  con.  way  Sub.   6 
App.  Time  by  Watch  of  Merid.  Pass..  14h    5n»| 
Or  at  2h  5m  in  the  morning. 

Moon's  Hor.  Pari,  at  Mid.  July  1 1th 60'  0" 

Observed  Altitude  Moon's  L.  Limb  40°  35'  &| 
Semid.  at  Midnight  16'  ) 
Dip  of  the  Horizon  4'  \ 

Moon's  Apparent  Altitude 40°  47' 

Co.T.  for  Alt.  in  Table  XXV..  Add  44 

Moon's  True  Central  Altitude 41°  31'  Sj 

90      0 

Zenith  Distance.^ 48°  29' N  I 

Correct  Declination 20      3    S  | 

Latitude  in '"8°  2«' S  i 


Add    Diff. 


12 


FINDI>  G  THE  LATITUDE  BY  THE  MERIDIAN  ALT  ITUDE  OF  THE  MOON.  \Q» 

EXAMPLE  2. 

April  26th,  1864,  Sea  Time,  in  the  Longitude  of  80*  East,  the  Meridian  Altitude  of  the  Moon't  Upper  Limb  wm 
•keerred  to  be  67*  36'  N.     Height  of  the  eye  21  feet     Required  the  Latitude  of  the  Ship. 

April  25th  is  April  24th,  Astronomical  Time.  Mean  Time  ot  passing  the  Mer.  at  Ship. .  22h  SSm 

Moon's  Mer.  Passage  April  24th, 22h  4Sm  Equa.  of  Time,  N.  A.,  applied  contr'y  way  -Add  2 

•  Long.  80*  E.,  which,  at  the  rate  of  )        ^^^         jq  App.  Time  of  the  Merid.  passage 22h  86m 

2m  to  every  1**  —  Corr )""      J Legs 12      0 

Mean  Time  of  the  Mer.  Pass,  at  Ship 22h  83m  ^pp.  time  by  Wat«h  of  the  Mer.  passage. .  lOh  36m  A.  M. 

Long.  80*  K  in  time Sub.  5    ao 

Greenwich  Date,  April  24th 17h  13m  -  Moon's  Por.  Pari  at  Midnight,  April  24th 6T  0" 

Lees 12h    0 

Time  past  Midnight  at  Greenwich "^13  Moon's  Obs.  Altitude  Upper  Limb 67*  86'  ». 

Semid  Midnight...  16   31       s^^^j^^g^^^^^        ^ 

Moon's  DecL  Midnight,  April  24th, 0°  61'  S.  ^'P  of  <^'^«  Horizon.  4  28    J  

Moon's  DecL  Noon,  April  25th _2 2'N.  App.  Altitude 67"  16' 

Diff  of  DecL  in  12  hours 2°  63'  ^orr.  for  Altitude,  Table  XXV Add 22_ 

And  time  fi-om  Midnight  6hl3m  in  Table  Un>,"T^      ^°"°''  "^'"^  ^^"*'^^  '^^'^'"*^* ol'  ^J  ^■ 

XXnLCorr. ^Suh.l    15  90^_0^ 

Declination  at  Midnight  decreasing 0    51  S.  Zenith  Distance   22"  22' S 

Correct  DecL  at  the  time  of  GUervation 0°  24'  N.  Correct  Declination •  <>   ^*  ^ 

Latitude  in 21"  68'  S 

•  This  Correction  is  found  by  adding'  2  minutes  of  Time  for  every  15*  of  Longitude  which  the  Ship  is  to  the  West- 
ward of  Greenwich,  to  the  time  of  her  passnge  in  the  Nautical  Almanac,  or  subtracting  the  same  in  East  Longituda, 
will  gfive  the  Mean  Time  of  her  passage  at  the  Ship. 

Correction  of  the  Declination  {used  in  the  above  Examples),  taken  from  thf  large  Nautical  Almanac 


EXAMPLE  1. 

Decl.,N.  A.,  July  11, 19h.20"  4'  44"  S.  Diflf:  10m  110".83 
DecL  Decreasing. .,  .Sub.       1    60  10m. 

Correct  Declination 20"  2'  64"  S.  60)110.0 

Correction  for  10  minutes 1'  50" 


EXAMPLE   2. 

DecL  April  24,  17h 0"  21'    8"  N.    Diff.  10m  144    60 

DecL  Increasing . . .  Add        8      8  13 

Correct  Declination 0°  24'  U"  N.  ~~60)188.5 

Correction  for  10  minutes 8'  8" 


QUESTIONS  FOR  EXERCISK 

Question  1. — April  6th,  1854,  Sea  Time,  in  Longitude  80°  44'  W.,  the  Meridian  Altitude  of  the  Moon's   Upp«r 
Limb  was  76°  15   S.     Height  of  the  eye  18  feet      Required  the  Latitude  of  the  Ship. 

iltwwer.— Latitude  in  40"  58'  N. 

Quextion  2. — April  2d,  1864,  Sea  Time,  the  Observed  Altitude  of  the  Moon's  Lower  Limb  was  64°  39'  S.  in  Lo» 
gitude  60"  W.     Required  the  Latitude  ia 

.4n«u»*r.— Latitude  b  54"  31'  N. 

Question  8.— April  13th,  1864,  Sea  Time,  the  Observed  Altitude  of  the  Moon's   Upper  Limb  wa«  80°  20'  &.  m 

Longitude  Po°  W,     Required  the  Latitude  ia. 

Antft^ — latitude  in  64°  18'  N. 


104  NAUTICAL  ASTRONOMY. 


TO  FIND  THE  LATITUDE  BY  THE  MERIDIAN  ALTITUDE  OF  A  PLANET. 


The  Latitude  may  be  found  from  the  Meridian  Altitude  of  the  Planets  upon  the  same  principle  as  that 
fcy  the  Sun  and  Moon. 

Their  Declinations  are  given  in  the  Nautical  Almanac  for  the  Noon  at  Greenwich,  for  every  day  of  th« 
month  throughout  the  year. 

When  their  Declinations  change  slowly,  they  may  be  taken  out  for  the  Noon  of  the  day  at  once  by  inspec- 
tion.  But  when  there  is  a  considerable  change  in  their  Declinations  between  the  Noon  of  one  day  and  the 
next,  we  must  correct  the  Declination  to  the  Greenwich  time  of  Observation,  in  a  similar  nianner  as  is  done 
in  the  case  of  the  Moon,  except  that  their  Meridian  Passage  is  taken  from  the  Nautical  Almanac  and  used 
without  being  corrected,  as  the  Mean  Time  of  their  passing  the  Meridian  at  Greenwich,  is  near  enough  for 
general  practice  at  Sea. 

But  to  find  the  Apparent  Time,  or  the  Actual  Time,  they  do  pass  the  Meridian  by  the  watch,  (regulated 
to  Apparent  Time  at  Ship),  the  Equation  of  Time  must  be  applied  to  the  time  of  passage  taken  from  the 
Nautical  Almanac,  the  contrary  way  to  what  is  directed  in  the  precept  at  the  head  of  the  column  for  Equa 
tion  of  Time,  in  the  same  manner  as  it  is  done  in  the  case  of  the  Moon,  so  as  the  Observation  may  not  be 
iost  in  consequence  of  being  too  late  in  beginning  it. 


To  Find  the  Planets  tn  the  Heavens  when  on  the  Meridian. 

RULE. 

1.  Fmd  at  what  time  a  Planet  will  pass  the  Meridian  in  the  Nautical  Almanac,  select  one  in  preference 
which  will  be  on  the  Meridian  at  twilight,  because  then  the  Horizon  is  distinctly  visible ;  or  even  when  the 
Sun  is  several  degrees  above  the  Horizon,  some  of  them  may  be  observed,  though  invisible  to  the  nakea 
eye,  and  they  are  found  as  follows  : 

Apply  the  Equation  of  Time,  as  before  directed,  to  the  Mean  Time  of  their  passage  in  the  N.  A.,  will 
ijive  the  Apparent  Time  of  their  passage  at  the  Ship,  and  the  Watch  must  be  previously  regulated  to 
Apparent  Time,  or  its  error  known. 

2.  Subtract  the  Latitude  by  Dead  Reckoning  from  90°,  and  the  remainder  will  be  the  Co-Latitude.  Take 
oat  the  Declination  oi  that  Planet  from  the  Nautical  Almanac,  which  passes  the  Meridian  at  the  proposed 
time.  Then  if  the  Co-Latitude  and  its  Declination  are  of  the  same  name,  take  their  sum,  but  if  of  con- 
trary names,  take  their  difference,  for  the  Meridian  Altitude  of  the  Planet. 

Now  put  this  Computed  Altitude  on  the  Arch  of  the  Sextant,  and  if  in  the  day  time,  screw  in  the  Inverting 
Telescope,  (otherwise  use  the  Direct  one),  and  look  towards  the  South  point  of  the  Horizon  when  the  Latitude 
is  North,  and  towards  the  North  point  of  the  Horizon  when  the  Latitude  is  South,  and  the  Planet  will  be 
distinctly  seen,  through  the  Telescope,  on  or  near  it. 

But  when  the  Sum  of  the  Co-Latitude  and  Declination  exceed  90°,  it  must  be  subtracted  from  180°,  and 
the  Planet  must  be  looked  for  in  the  North  point  of  Uie  Horizon,  in  North  Latitude,  and  in  the  South  point 
•f  the  Horizon  in  South  Latitude. 

Bring  the  Planet  in  contact  with  the  Horizon,  and  when  it  attains  its  greatest  Altitude,  read  off  the 
Arch,  and  find  the  Latitude  as  follows  : 


To  Compute  the  Latitude  from  the  Meridian  Altitude  of  a  Planet. 

RULE 

Subtract  the  Sum  of  the  Refraction  and  Dip,  found  in  Tables  IV  and  V,  from  the  Observed  Altituoe, 
will  give  the  True  Altitude,  which,  subtracted  from  90°,  gives  the  Zenith  Distance  of  the  contrary  name  to 
the  Planet's  Bearing.  Take  from  the  N.  A.  the  Declination,  and  correct  it  if  required.  Then,  if  th«» 
Zenith  Distance  and  Declination  are  of  the  same  name,  their  Sum,  but  if  of  contrary  names,  their  Differ' 
tnu.  u  the  Latitude  of  the  same  name  as  the    reatrr  of  the  two 


FINDING  THK  LATITUDE  BY  THK  PLANETS 


106 


TO  COMPUTE  THE  MERIDIAN  ALTITUDE  OF  THE  PLANETS. 


Pro.  for  2h...Sub.  2' 
Dec  Jan.  1st,  18°  6' 
Cor.  Dec...  T3^~~3'  S, 


EXAMPLE  1. 

January  2d,  1 864.  Sea  Time.  Required  the  Apparent 
Ttofl,  and  the  Altitude  at  which  the  planet  VeuuB  will 
pass  the  Meridian.  Ship  off  the  Cape  of  Good  Hope,  in 
Latitude  84°  0'  S,  and  Longitude  18°  O'  K 

II  Pas.  N.A.,  Jan.  l8t,Sh.  15m.  M.  Time  at  Greenwich. 

Eqa.  of  Time,.  .Sub.  4 

H.  Pass,  at  Ship 3h.llm.  App.  Time  P.  M. 

M.  Pas,  N.A..  Jan.l8t,  3h.  15m.  Dec.,  N'n,  Jan.lst,  13°  5'  S. 
Loii.l8°  E.  in  T,  Sub._l__12  do.  Jan.  2d^240    S. 

iQaeenwich  Date. . .    2h.  3m.  Change  in  24h..         25' 

Lat.  of  Ship.. . .  .34°T'X 
^   0 

Cor.  Lat 66^' S. 

Dec.  Venus 1£_3   S. 

€ompu.  Alt 69°  3'  of  Venus  at  8h.  11m.  P.  M. 

Put  this  Altitude  on  the  Sextant  and  look  towards  the 
North  point  of  the  horizon,  (the  Latitude  being  South.) 

\  EXAMPLE  3, 

April  14th,  1854.  Sea  Time.  Required  the  Apparent 
rime,  and  tiie  Altitude  at  which  the  planet  Jupiter  will 
pass  the  Meridian.  Ship  on  the  Equator,  in  Longitude 
■25°  West 

M.  Pas.N.A.,Ap.l3th,18L24ui.  M.Time  at  Greenwich. 

Equ.  of  Time.  .Sub.  1 

M.  Pass,  at  Ship, . .  'a8L23ra,  or  6L23m.  A.  M  by  "Watch. 

M.  Pass.  April  13. .  .18h.24m.  Dec,  April  13th,  21°  7'  S. 
Lon.25°W.  inT.,Add  J_40  do.  April  14th,  21  6  S. 
Greenwich  Date, . ,   20h.  4nx  Change  of  Dec.24h.—1 ' 

Pro.  for  20h .  Sub.—   1 
Lat  of  Ship  0°  0'  Co-Lat,    90°  0'     Dec,  Ap.13,  21°  T 

Add  Dec  of  Jupiter 21  6  S.  Cor.  Dec       21°  6' 

111°  6' 

Subtract  from 180   0 

Computed  Altitude 68  °54'  of  Jupiter  at6h.23'A3I, 

Put  this  Altitude  on  the  Sextant  and  look  towards  the 
South  point  of  the  horizon,  (because  the  Declination  is 
SouUl) 


EXAMPLE  2. 

June  1th,  1854.     Sea  Time.     Required  the  Apparent 
Time,  and  the  Altitude  at  which  tne  planet  Mars  wiD 
pass  the  Meridian.     In  Latitude  40°  20  N,  and  Lonir' 
tude  75°  West 

M.  Pas.  June 6th, N.A.,6h.  2m.  M.  Time  at  Greenwiob 
Equa.  of  Time....Add      2 

M.  Pass,  at  Ship 6h.  4m.  App.  Time,  P.  M. 

M.Pass.  N.A.,June  6th,  6h.  2m.  Dec,  June  6th, 7*  26'  N. 
Lon.  76°  W.  in  T,  Add  5  do.  June  7th,7    13 

Greenwich  Date. . .    llh.  2m.  Change  in  24h.. .  12' 

Lat  of  Ship 40 °~2b'  N,     Pro.  for  llh..  SubTT' 

_90 0  Dec,  June  6, . .  7  °  26'  N. 

Co-Latitude 49°  40'  N.     Cor  .Dec,. . . .    7°  20'  N 

Dec  of  Mars, ...    7     20  N. 

Computed  Alt. .    67°     0'  of  Mars  at  6h.4m.  P.  M. 

Put  this  Altitude  on  the  Sextant  and  look  towards  th« 
South  point  of  the  horizon,  (the  Latitude  being  North.) 

EXAMPLE  4. 

Feb.  2d,  1854.  Sea  Time  Required  the  Apparent 
Time,  and  the  Altitude  at  which  the  planet  Saturn  wiU 
pass  the  Meridian  in  Latitude  30°  20'  N-  and  Lomritude 
76°  30'  W.  ^ 

M.  Pass.  Feb.  1st. ,     6L  46m.  M.  Time  at  Greenwich. 

Equa.  of  Time..  Sub.        14 

Mer.  Pass,  at  Ship. . .  6h.  82m.  App.  Time,  P.  M. 

M.  Pass.  Feb.  1st 6h  46m.  DecNA.,  Fcl»t.  17°  4'  N 

Lon.  76°  30'  W.  in  T.J 6         do.         Feb.  2d.  17  4  N 

Greenwich  Date. . .  llh.  62m.  No  Cor.  for  Dec.  required 

Lat  of  Ship 30°  20'  N. 

90     0 


,59' 
.17 


40' N 
4   N, 


Co-Latitude . . . 
Dec  of  Saturn, 

Computed  Alt.  76°  44'  of  Saturn  at  6L  82m.  P  M. 

Put  this  Altitude  on  the  Sextant  and  look  towards  the 
South  point  of  the  horizon,  (because  the  Lat  is  North.) 


To  find  the  Latitude  from  the  Meridian  Altitude  of  the  Planets. 


EXAMPLE  1.     . 

Jaa  2d,  1864,  Sea  Time.  The  observed  Altitude 
•f  the  planet  Venus  was  69'  7'N.  in  Longitude  18°  East 
Required  the  Latitude. 

Observed  Altitude  of  Venus 69°    7'N. 

Dip  4.  Ref.  0 Sub . . 4 

IVue  Altitude 69°    3'  N. 

Zenith  Distance 20°  67'  S. 

Declination 13      3    S. 

LaUtude 34°    O'  S, 

EXAMPLE  3. 

April  14th,  1864.  Sea  Time.  The  observea  Altitude  of 
Jupiter  was  68°  68'  S.,  in  Longitude  26°  West  Required 
the  Latitude 

Observed  Altitude  of  Jupiter 68°  68'  S. 

Dip  4.  Ref.  0 Sub. 4 

True  Altitude 68°  64'  S. 

Zenith  Distance, .      21*    6"  N. 

Declii.ation ^      6   S. 

«hip  on  the  Equator "OO^^' 


EXAMPLE  2. 

June  7th,  1864.  Sea  Time  The  observea  Altitude  oi 
Mars  was  57°  4'  S,  b  Longitude  76°  West      Required 

the  Latitude. 

Observed  Altitude  of  Mars 67*    4'  S. 

Dip  4.  Ref.  1 Sub.  6 

True  Altitude 56°  69' 

Zenith  Distance ~83°    ]'  JJ 

Declination ^    20  N 

Latitude 40°  21'  N 

EXAMPLE  4. 

Februaiy  2d,  1854.  Sea  Time  The  observed  Altitud* 
of  Saturn  was  76*  48'  S.,  in  Longitude  76*  80'  West 
Required  the  Latitude. 

Observed  Altitude  of  Saturn 76°  48'  & 

Dip  4.  Ref.  0 Sub.  4 

True  Altitude 76°  44'  g 

Zenith  Distance 13°  jq'  jf 

Declination 17      4  N 

Latitude 80°  20'  5 


100  NAUTiLAL    ASTRONOMY. 


TO  FIND  THE  LATITUDE  BY  THE  MERIDIAN  ALTITUDE  OF  A  ST.Ul. 

The  Latitude  may  be  found  by  the  Meridian  Altitude  of  a  fixed  Star,  upon  the  same  principle  as  that 
hj  the  Sun. 

1.  Table  XIX  contains  the  Right  Ascensions  and  Declinations  of  24  of  the  principal  Fixed  Stars,  for  the 
year  1854,  and  the  annual  variation  or  change  of  the  same.  So  that  this  Table  may  serve  for  future 
years,  by  simply  multiplying  the  number  of  years  elapsed  by  the  amount  of  the  annual  variation,  and 
applying  it  according  to  the  sign  of  addition  (•+•),  or  subtraction  ( — ),  to  the  Sums  taken  from  the  Table. 

2.  To  Find  what  Star  will  Pass  the  Meridian  at  any  Given  Hour  of  the  Day, 

Enter  Table  XVIII,  with  the  Day  of  the  Month  at  the  top,  and  follow  down  the  column  until  we  comfr 
to  the  required  hour,  opposite  to  which  will  stand  the  name  of  the  Star.  But  as  the  Meridian  passages  in 
this  Table  are  only  given  for  every  third  day,  should  the  day  required  be  between  those  which  are  m.arked 
at  the  head  of  the  column,  take  it  out  for  the  nearest  day  preceding  the  required  day,  and  subtract  4 
minutes  for  each  intermediate  day. 

The  times  shown  in  this  Table  are  only  approximations,  but  are  sulBciently  near  enough  for  the  purpose 
of  finding  the  Latitude  by  the  Stars. 

By  the  assistance  of  this  Table,  the  method  of  finding  the  Latitude  by  the  Meridian  Altitude  of  a  Star 
will  be  greatly  facilitated  ;  for  when  we  know  at  what  time,  nearly,  a  Star  will  pass  the  Meridian,  and 
the  approximate  Altitude  at  that  time,  there  can  be  no  difficulty  in  making  the  requisite  observation  t* 
determine  the  Latitude.  These  opportunities  occur  frequently  in  the  course  of  a  clear  night,  and  may  Ui 
put  in  practice  by  any  person  otherwise  unacquainted  with  the  Stars  in  the  heavens,  by  reference  to  tLt 
Figures  at  pages  65  and  66,  and  the  following  Rules. 

3.    To  Compute  the  Meridian  Altitude  of  a  Star. 

Subtract  the  Latitude  by  Dead  Reckoning,  (at  the  proposed  time  of  observation,)  from  90',  will  ?ivp  thp  ion 
plement  of  the  Latitude,  or  Co-Latitude,  of  the  place  of  observation.  Take  out  the  Star's  Docl'.nation  fronr 
Table  XIX,  and  correct  it  for  the  years  elapsed  since  1854.  Then,  if  the  Co-Latitude  and  its  Derhnation  ar» 
•f  the  same  name,  take  their  Sum,  but  if  of  contrary  names,  take  their  Difference  for  the  Meridian  Altitude 
and  the  Star  will  be  found  in  the  South  part  of  the  heavens  when  the  Latitude  is  North,  and  in  th3  Nortu 
part  when  the  Latitude  is  South.  But  when  the  Sum  exceeds  90°,  subtract  it  from  180"" ;  the  remainde. 
will  be  the  Altitude,  and  the  Star  will  be  found  in  the  North  part  of  the  heavens  in  North  Laticude,  and 
m  the  South  part  in  South  Latitude.     (See  remarks  on  taking  Altitudes  of  the  Stars,  at  page  71.) 

4.  To  Find  the  Star  from  its  Computed  Altitude  and  Meridian  Passaf^e. 

Set  the  Index  of  the  Quadrant  to  the  Computed  Altitude,  and  at  a  few  minutes  before  the  time  of  its 
Meridian  passage,  direct  the  sight  towards  the  North  or  South  points  of  the  horizon,  as  shown  above,  and 
the  reflected  image  of  the  Star  will  be  perceived  in  the  Horizon  Glass,  upon  or  near  the  horizon,  which 
being  brought  in  contact  with  it,  and  kept  so  until  it  arrives  at  its  greatest,  or  Meridian  Altitude,  the 
angle  is  then  read  off  the  Quadrant. 

There  is  not  the  least  danger  of  mistaking  the  Star,  as  no  other  will  have  the  s^me  Meridian  Altitudt 
at  that  time.     (See  remarks  at  page  71.) 

The  best  time  for  observing  Altitudes  of  Stars  is  at  twilight,  for  then  the  horizon  is  distinctly  visible, 
and  the  Latitude  may  be  found  as  correctly  as  by  the  Sun.  But  in  dark  nights  an  error  of  from  6  to  id 
miles  in  the  Altitude  may  be  made,  in  consequence  of  the  obscurity  of  the  horizon.  To  obviate  ttds,  the 
Latitude  should  be  found  from  an  Altitude  of  a  Star  to  the  Southward,  and  anather  to  the  Northward, 
and  the  half  Sum  of  the  two  Latitudes  thus  found  will  be  the  correct  one  This  will  be  further 
explained  in  the  following  Examples. 


FINDING  THE  LATI'lUUE  BV  THE  STARS. 


107 


FINOING  THE  LATITUDE  BY  THE  MERIDIAN  ALTITUDE  OF  A  STAR 

The  Meridian  passages  of  the  Stars  shown  in  Table  XVIII,  being  for  Apparent  Astronomical  Time 
which  commencea  at  Noon,  one  day  before  the  Sea  Day  begins,  and  the  hours  are  counted  in  successioB 
throughout ;  so  that  when  Sea  Time  is  used,  the  Tables  must  be  entered  with  the  date  one  day  less  than 
Sea  Time. 

If  Civil  or  Common  Time  is  used,  the  hours  less  than  12  -w-ill  be  the  time  past  Noon  on  that  day  (and 
which  are  the  same  as  Astronomical  Time.)  But  when  the  hours  are  greater  than  12.  subtract  12  hours 
from  it,  and  it  will  be  the  time  on  the  morning  of  the  following  Civil  Day,  and  which  commences  at  Mid- 
night. Because  the  Noon  of  the  Civil  Day,  the  beginning  of  the  Astronomiaal  Day,  and  the  end  of  th* 
Sea  Day,  takes  place  at  the  same  period  of  time. 


To  Find  the  Stars  tn  the  Heavens  from  their  Computed  Altitude. 


EXAMPLE  1 

Feb.  28th,  1854,  Sea  Time,  in  Latitude  by  D.  R.  40°  10' 
N.  Required  what  Star  will  be  on  the  Meridian  at  twi- 
light in  the  evening,  and  its  Computed  Altitude. 

On  referring  to  Table  XVTII,  and  taking  the  date  one 
day  less,  or  Feb.  27  th,  I  find  the  Star  Aldebaran  will  pass 
at  6h  48m  P.  M. 

Latitude  by  Dead  Reck.. 40°  10'  N. 
Subtract  from ._90 0 

Co-Latitude 49^~50'  N. 

Declination  Table  XIX...  16    13   N. 

Computed  Altitude 66°    3'.     I   now  set  the  Index 

of  the  Quadrant  to  this  Altitude,  and  face  towards  the 
South,  because  the  Latitude  is  North.  Flatten  down  the 
Sight  Vane,  and  using  both  eyes,  the  Star  Aldebaran  will 
be  distinctly  seen  upon,  or  near  the  Horizon. 


EXAMPLE  3. 

March  2l8t,  1854,  Civil  Time,  in  Latitude  by  D.  R. 
0°  30'  S.  Required  to  find  a  Star  b  the  evening  at  twi- 
light. 

In  Table  XVIII,  I  find  that  the  Star  Sirius  passes 
the  Meridian  at  6h  34m  P.  M. 
Latitude  by  Dead  Reek- .     0°  30' S. 
Subtract  from 90      0 

Co- Latitude 89°  30'  S. 

Declination,  Table  XIX..  16    31   S. 

106°    1' 
Subtract  from 180      0 

Computed  Altitude 73°  59'   towards  the  South. 


EXAMPLE  6. 

May  2d,  1854,  Sea  Time,  in  Latitude  by  D.  R.  20°  0' 
N.  Required  at  what  Time  and  Altitude  the  Star  Vega 
will  pass  the  Meridian. 

On  the  Ist  of  May,  by  Table  XVIII,  Vega  passes  the 
Meridian  at  15h  59m,  or  time  by  Watch  at  8h  59m  A.  M. 
Latitude  by  Dead  Reck..   20°    0' N. 
Subtract  from 90     0 

Co-Latitude '70°    O'  N. 

Declination,  Table  XIX.   38    39  N. 

108°  39' 
Subtract  from 180      0 

Computed  Altitude 71°  21'    towards  the  North. 


EXAMPLE  2. 

March  1st,  1854,  Sea  Time,  in  Latitude  by  D.  R.  38* 
10'  N.  Required  what  Star  will  pass  the  Meridian  at 
twilight  in  the  morning,  and  its  Computed  Altitiide. 

On  referring  to  Table  XVIII,  and  taking  the  date  one 
day  less,  or  February  28th,  I  find  that  the  Star  Antares 
will  pass  on  the  27  tb,  at  17h  40m,  from  which  I  subtract 
4  minutes,  gives  17h  3fim,  and  less  12h  gives  6h  36tn,  th« 
time  it  passes  in  the  morning. 

Latitude  by  Dead  Reck 38°  10'  N. 

Subtract  from 90      0 

Co-Latitude 6T°~50'  N. 

Declination,  Table  XIX 26      6   S. 

Computed  Altitude 25°  44'.       Set  the  Index  ta 

this  Altitude,  and  face  towards  South  in  North  Latitudi^ 
and  the  Star  will  be  found  as  before. 


EXAMPLE  4. 

March  26th,  1854,  Civil  Time,  in  Latil^ido  by  D.  R 
30°  25'  S.  Required  to  find  a  Star  in  the  morninff  twi 
light 

In  Table  XVIH,  I  find  that  the  Star  Ve^-a  passes  the 
Meridian  at  18h  20m,  on  the  24th,  from  which  I  subtract 
8  minutes,  gives  18h  12m,  and  less  12h  gives  6h  12m,  ita 
passage  in  the  morning. 
Latitude  by  Dead  Reck..   80°  25'  S. 
Subtract  from 90      0_ 

Co-Latitude. 69°  35'  S  • 

Declination,  Table  XIX..  38    39   N. 

Computed  Altitude 20°  56'   towards  the  NortL 


EXAMPLE    6 

June  22d,  1854,  Sea  Time,  Ship  on  or  near  the  Equa- 
tor. Required  at  what  Time  and  Altitude  the  foot  Stai 
of  the  Southern  Cross  will  pass  the  Meridian. 

On  the  2 Ist  June,  by  Table  XVIII,  it  passes   the 
Meridian  at  6h  21m  in  the  evening. 
Latitude  by  Dead  Reck..     0°    0' 

Co- Latitude 90°    0' 

Declination,  Table  XIX..   62    17    S. 

Computed  Altitude 27°  43'     towards   the    South. 

because    the    Declination  is    South.     The    Crost  alvayt 
pasxes  the  Meridian  erect. 


Note. — When  the  Star's  Declination  Subtractive  is  ereater  than 
V  the  observer. 


ttie  Co-Latitude,  the  Star  is  not  above  the  flor 


108 


NAUTICAL  ASTRONOMY 


TO  FIND  THE  LATITUDE  BY  THE  MERIDIAN  ALTITUDE  OF  A  STAR. 


I 


RULE. 

FroK:  tie  Observed  Altitude  of  the  Star,  subtract  the  Dip  of  the  Horizon,  and  the  Refraction,  taken  from  Tablet 
IV  and  V ;  or  the  Sum  of  these  Corrections  may  be  taken  out  at  once  from  Table  XX,  by  entering  it  with  the  height 
of  the  eye  at  the  top,  and  the  Observed  Altitude  at  the  side,  and  tlie  Angle  of  meeting  is  the  required  CorreetioB, 
iJways  subtractive  from  the  Observed  Altitude,  will  give  the  Star's  True  Altitude,  which,  subtracted  from  90°,  gives 
the  Zenith  Distance.  Then,  if  the  Star  bears  South,  mark  the  Zenith  North,  and  if  the  Star  beai-s  North,  mark  the 
Zenith  Distance  South. 

Take  out  the  Star's  Declination  from  Table  XIX,  and  correct  it  for  the  years  elapsed  since  1854,  as  before  shown, 
and  mark  it  North  or  South. 

Then,  if  the  Zenith  Distance  and  Declination  are  of  the  same  name,  take  their  Sum,  but  if  they  are  of  contrarj 
Dames,  take  their  Difference,  for  the  Latitude,  of  the  same  name  as  the  greater  of  the  two. 


EXAMPLE   L 

Feb.  28th,  1854,  Sea  Time,  at  5h  48m  P.  M.,  the  Ob- 
served Altitude  of  the  Star  Aldebaran  was  66°  7'  S. 
Required  the  Latitude. 

#'8  Observed  Altitude 66°    7'  S. 

Corn,  Table  XX )  g^j^  ^ 

Height  of  the  eye  16  feet  j 

True  Altitude 66°     8' 

90      0 

Zenith  Distance 23°  67'  N. 

Declinatiou,  Table  XIX 16    1.3   N. 

Latitude  Observed 40°  10'  N.  at  5h  48m  P.  M. 


EXAMPLE   8. 

March  2l8t,  1854,  Civil  Time,  at  6h  34m  P.  M.,  the  Ob- 
served Altitude  of  the  Star  Sirius  was  74*  8'  S.  Height 
af  eye  18  feet     Required  the  Latitude. 

#'8  Observed  Altitude 74°    8'  S. 

Corr,  Table  XX. Suk 4_ 

True  Altitude .78°  59' 

Zenith  Distance 16*    1'  N. 

Declination,  Table  XIX 16  ^  S. 

Latitude  Observed ."o^  80'  S.  at  6h  84m  P.  M. 


EXAMPLE  8. 

Mar  2d.  1864,  Sea  Time,  at  3h  59m  A.  M.,  the  Ob- 
served Altitude  of  the  Star  Vega  was  7 1°  26'  N  Height 
of  the  eye  20  feet.     Required  the  Latitude. 

#'8  Observed  Altitude 71*  26'  N. 

Corr,  Table  XX 5 

True  Altitude .71°  21' 

Zenith  Distance '. .18°  39'  S. 

Declination,  Table  XIX 88    39  N. 

Latitude  Obeer^ed .2*^°    O'N.at  8h  6»m  A.  M. 


I  EXAMPLE  2. 

I 

March  Ist,  1854,  Sea  Time,  at  6h  36m  A.  M.,  the  Ob- 
served Altitude  of  the  Star  Antares  was  25°  60'  S.  Re- 
quired the  Latitude. 

#'s  Observed  Altitude 25°  50'  S. 

Corr.,  Table  XX  (16  feet)  Sub^ 6_ 

True  Altitude .26°  U' 

90      0 

Zeuith  Distance 64°  16'  N. 

Dechnation,  Table  XIX 26      6    S. 

Latitude  Observed .38°  10'  N.  at  5h  36m  A.  M 


EXAMPLE  4. 

March  26th,  1864,  Civil  Time,  at  6h  12m  A.  M.,  th« 
Observed  Altitude  of  the  Star  Vega  was  21°  2'  N. 
Height  of  the  eye  16  feet     Required  the  Latitude 

#'s  Observed  Altitude 21°    2' N 

Corr.,  Table  XX Sub.        _6 

True  Altitude 20°  66' 

Zenith  Distance 69°    4'  S. 

Declination,  Table  XIX ._88_  89   N. 

Latitude  Obsei-ved 80'  25^  S.  at  6h  l«m  A.  M. 


EXAMPLE  6. 

June  22d,  1864,  Sea  Time,  at  6b  21m  P.  M.,  the  Ob- 
served Alt.  of  the  foot  Star  of  the  Southern  Cross  was 
27°  50'  S.  Height  of  eye  25  feet  Required  the  Latitude. 

#'8  Observed  Altitude 27*  50'  S. 

Corr.,  Table  XX 7_ 

True  Altitude .27*  43' 

Zenith  Distance .62°  17'  N. 

Declination,  Table  XIX.. . .  .62°  17'  S 

Ship  on  the  Equator 0°    0'  at  6h  21m  P.  M. 


QUESTIONS  FOR  EXERCISE. 

Qitest.  lit. — April  2d,  1864,  Sea  Time,  what  Star,  and  at  what  Time  and  Altitude  will  it  pass  the  Meridian  aboot 
Twilight  in  the  evening,  in  Latitude  42°  25'  N 

Antieer. — The  Star  Castor,  April  1st,  at  6h  43m,  and  its  Meridian  Altitude  is  79°  47'  S. 


QiuKt.  2d. — April  2d,  1854,  Sea  Time,  the  Meridian  Altitude  of  the  Star  Castor  was  observed  to  be  79*  4»'  8,  »• 
lb  48m  in  the  evening.     Height  of  the  eye  16  feet     Required  the  Latitude. 

Anmctr. — Latitude  Observed  42°  27'  N. 


FlNDiNG  THh  LATITUDE  BY  THE  STARS. 


109 


TO  FIND  THE  LATITUDE  BY  THE  MERIDIAN  ALTITUDE  OF  THE  POLE  STAR 


RULE. 


Ck»rrect  the  Observed  Altitude  for  Dip  and  Refraction  by  Table  XX-  Take  out  the  Pole  Star's  Declination  from 
Table  XIX,  and  correct  it  for  the  years  elapsed  since  1854,  and  subtract  its  Declination  from  90°,  will  give  iti 
Polar  Distance  ;  then  the  Sum  of  the  true  Altitude  and  Polar  Distance  is  the  Latitude,  when  observed  below  tb« 
Pole,  but  the  Difference  between  them  is  the  Latitude  when  observed  above  it. 

To  find  when  the  Pole  Star  passes  the  Meridian  below  the  Pole,  we  add  half  the  interval  of  its  revolution,  which 
is  llh  58m.,  to  the  time  at  which  it  passes  the  Meridian  above  the  Pole,  found  in  Table  XVIII,  and  subtract  24 
hours  from  it,  if  it  exceeds  that  quantity 


EXAMPLE  1. 

July  2d,  1854,  Sea  Time.  At  6h.  20m.  in  the  even- 
ing the  Meridian  Altitude  of  the  Pole  Star  (below  the 
Pole)  was  oberved  to  be  43°  10'.  Height  of  the  eye,  20 
feet      Required  the  Latitude. 

Bv  Table  XVIII,  it  passes  the  Merid.  at  18h.  26m.  A.M. 
Obs.  Alt  Pole  m  .  43°  10'  Dec,  Table  XIX,  88°  32'  N. 
Cor., Tab. XX..  Sub.     5  90    00 


True  Alt . , . 

43°    5'      Polar  Dist 

..    1°  28' 

Polar  Dist. . 
liAtitude  iu. 

.Add.l    28 
44°  83'  N, 

EXAMPLE  2. 

July  2l8t,  1854.  Sea  Time.  At  5h.  9m.  in  the  morn- 
ing, the  Meridian  Altitude  of  the  Pole  Star  (above  th« 
Pole)  was  observed  to  be  32°  28'.  Height  of  the  eye,  16 
feet     Required  the  Latitude. 

By  Table  XVIII,  it  passes  the  Merid.  at  17h.  9m.  A.  M. 
Obs.  Alt  Pole  #. .  32°  28'       Dec,  Table  XIX,  88°  32'  N 


Cor.,  Tab.  XX,  Sub^ 6 

True  Alt 32°  23'      Polar  Dist. . , 

Polar  Dist. .  Sub.     1   28 

Latitude  in 30°  55'  N. 


90  00 
1°28' 


To  Find  the  Latitude  by  the  Pole  Star  at  any  Hour  in  the  Night. 

RULE. 

To  the  Sim's  Right  Ascension,  taken  from  Table  XIII,  add  the  time  since  Noon,  when  the  Altitude  was  observed 
Tlie  Sum  (rejecting  24  hours  if  it  exceeds  that  quantity)  will  be  the  Right  Ascension  of  the  Meridian,  with  which 
enter  Table  XXI,  and  take  out  the  correction,  to  be  applied  as  dire<{ted  in  that  Table,  and  the  Sum,  or  remainder, 
will  be  the  required  Latitude. 

Remarks  on  Finding  the  Latitude  by  the  North  Pole  Star. 

This  method  of  finding  the  Latitude  by  the  Pole  Star  is  only  an  approximation,  and  may  deviate  two  ot 
three  miles  from  the  truth ;  but  from  its  extreme  simplicity  it  is  well  adapted  to  the  practice  of  Seamen,  ii 
cases  where  an  error  of  a  mile  or  two  can  be  of  oo  material  consequence. 

If  the  time  at  the  Ship  is  not  known,  that  is,  if  the  Watch  has  not  been  previously  regulated  at  the  time 
of  the  Altitude,  the  Apparent  Time  at  Ship  may  be  deduced  from  the  Greenwich  Time  by  Chronometer, 
by  turning  the  Ship's  Longitude  into  time,  and  subtracting  it  in  ^Vest  Longitude,  or  adding  it  in  East,  will 
give  the  Mean  Time  at  Ship,  and  the  Equation  of  Time  applied  the  contrary  way  will  give  the  Apparent 
Time  at  Ship.     In  general,  a  few  minutes  error  in  the  time  will  not  affect  the  result. 

To  Find  the  North  Pole  Star  Itself 

The  North  Pole  Star  is  easily  found  in  the  heavens,  from  the  direction  of  the  two  lirgo  Stars  in  the  coulter 
of  the  Plough,  that  well-known  constellation,  which  is  perpetually  wheeling  round  the  Pole  of  the 
heavens,  so  that  these  two  Stars,  or  Pointers,  always  point  to  the  North  Pole  Star  a«  a  centre.  The  Pole 
Star  itself  is  only  a  dim  object,  of  the  second  or  third  magnitude,  and  it  requires  good  silvered  mirrors  in  the 
Quadrant  to  obtain  a  tolerable  observation,  and  the  glasses  should  be  wiped  clean  bo*ore.  the  observation  u 
•wimmenced.     (See  remarks  on  taking  Altitudes  of  the  Stars,  page  71.) 


EXAMPLE.  1, 

January  2l8t  1864.  Sea  Time.  At  8h.  25m.  P.  M. 
the  Altitude  of  the  Polar  Star  was  observed  to  be  38°  16'. 
Height  of  the  eye,  18  feet     Required  the  Latitude. 

#'8  Obs.  Alt 38°  15'     App.  Time  at  Ship.  .8h.  25m. 

Cor,  Tab.  XX,  Sub^       5      Sun's  R.A.  Jan.20th,  20      9 

True  Alt .38°  10'     R.  A.  Meridian 28h. 34m. 

Cor,  Ta.XXl,Sub.0    53      Less 24      0 

Latitude  in "^"7°  17'  N.  R.A.  of  Meridian. .    4h.  34m. 


EXAMPLE  2. 

February  11th,  1854.  Sea  Time.  The  Greenwich 
Time  by  Chronometer  being  21h.  30m.,  in  Longitude  60° 
0'  W.,  an  Altitude  of  the  Pole  Star  was  observed  to  1x8 
32°  45'.  Height  of  the  eye,  20  feet  Required  the  Lat- 
itude. 

#'s  Obs.  Alt... 32° 45' 
Cor.,  Tab.  XX,  Sub.     6 


True  Alt 32°  39' 

Cor.,Ta.XXI,Addl   18 

Latitude  in 


Gr.  T.  byChro 21  h.  30m. 

Lon.60°  W.  in  T.,Sub.  4       0 

M.  Time  at  Ship. . .  17h.  80m. 

Eq.  of  Time. .  Sub.         16 

.  83°  67'  1^.  App.  Time  at  Ship.l7h.  15m. 

Sun'a  RA.  Feb.l0tb.21     86 

38h.61m. 
Less 24h.    0 

R.  A  of  Meridian.  14h.  61m. 


no 


NAUTICAL  ASTRONOM\, 


FINDING  THE  LATITUDE  BY  THE  MERIDIAN  ALTITUDE  OF  TWO  STARfc 


In  the  Northern  Hemisphere. 

'in  the  night  time,  as  before  observed,  errors  in  the  observed  Altitudes  of  the  Stars  are  liable  to  be  made 
in  consequence  of  the  obscurity  of  the  horizon. 

But  if  we  observe  one  Altitude  of  a  Star  to  the  Southward  and  another  to  the  Northward,  (md  although 
they  may  both  be  in  error,  the  one  error  will  balance  the  other;  that  is,  the  Latitude  found  from  the  Alti- 
tude of  both  Stars  may  be  erroneous,  but  if  we  add  the  two  Latitudes  together,  their  half  Sum  will  be  th« 
correct  Latitude. 

EXAMPLE, 

March  I9th,  1854.  Sea  Time.  At  lOh.  10m.  P.  M.,  Apparent  Time  at  Ship,  the  Meridian  Altitude  of  the  Stai 
Regains  was  observed  to  be  64°  1'  South,  and  at  the  same  time  the  Altitude  of  the  Pole  Star  was  37°  67'  North 
Height  of  the  eye.  18  feet     Required  the  Latitude. 


Obs.  Alt.  of  the  #  Regulus.  64°    7'  S. 
Cor.,  Table  XX Sub.. 6 


True  Alt 64°    2' 


Zenith  Dist 25" 

Dec,  Table  XIX 12 


58' N. 
_41'N. 
"39'  N. 


Lat.  by  Regulus 38° 

The  Altitudes  were  ^\m.  too  great. 


Obs.  Alt.  Pole  * 37°  57' 

Cor.,  Table  XX Sub. 5 

True  Alt 37°  52' 

Cor.,  Table  XXI Add     1     2 

Lat.  by  Pole  Star 38° 


App.  Time  at  Ship lOh.  10m. 

Sun's  R.  A.,  March  18th,.  23L  51 


34h 
24 


Im 

0 


Lat.  by  Regulus 38 


54' 
39 


R.  A.  of  the  Meridian. , 


lOh.    Im. 


Sum )77°  33^ 

Correct  Latitude 38°  46'  30"  N,  at  10b.  10m.  P.  M 


In  the  Southern  Hemisphere. 

There  are  no  Stars  near  the  Pole  which  will  answer  the  same  purpose  as  the  North  Pole  Star.  Cons*  • 
quently,  we  have  to  observe~the  Meridian  Altitudes  of  two  Stars  in  opposite  directions,  but  which  do  not 
pass  the  Meridian  at  the  same  period  of  time.  (The  difference  of  their  Meridian  passages  is  shown  in  Table 
XVIII.)  So  that  the  Altitude  of  the  first  Star  observed  must  be  reduced  to  the  place  where  the  second  was 
observed,  by  applying  the  difference  of  Latitude  the  Ship  has  made  in  that  interval  of  time,  by  the  following 
simple  Rule,  and  which  is  founded  on  the  fact  that  when  a  Ship  sails  South  she  rises  all  the  Stars  in  that 
direction,  that  is,  their  Meridian  Altitudes  increase^  while  those  to  the  North  gradually  smk,  that  is,  their 
Meridian  Altitudes  decrease ;  and  in  sailing  North,  those  to  the  North  are  raised,  while  the  Stars  to  the 
South  decline,  by  a  quantity  equal  to  the  Difference  of  Latitude  she  has  made  in  a  given  time. 

RULE 


Enter  the  Traverse  Table  with  the  Course  and  Distance  made  good  in  the  interval  between  the  times  of  the  StAn 
passing  the  Meridian,  and  take  out  the  Difference  of  Latitude  made  in  that  mterval,  and  apply  it  as  follows  : 


Ship  saihng  South. 
Ship  sailing  NortL 


. ,  .     ,      r ,,     n    J.  c^.       i_  J  i  to  the  Southward,  Add  Difference  of  Latitude  to  it 

Altitude  of  the  first  Star  observed,  ^  ^  ^^^  Northward,  Sub.       do.  do.         from  it 

,  .     ,      ,    ,     ^    ,   ,        ,  J  i  to  the  Noithward,  Add       do.  do. 

Altitude  of  the  first  btar  observed,  -j  ^  ^j^^  Southward,  Sub 


do 


do. 


to  it 
from  it 


EXAMPLE, 

March  18th,  1854.  Sea  Time.  At  12h.  50m.  the  Meridian  Altitude  of  the  foot  Star  of  the  Southeru  Cross  Wiu 
observed  to  be  61°  47'  South.  Ship's  Course  S.  W.,  (true,)  going  10  knots  ;  and  at  Ih.  48m.  the  Meridian  Altitude 
of  Spica  was  66°  35'  North.     Required  the  Latitude. 

Mer  Pass,  of  the  Cross 12h.  50m.    First  Obs  Alt.  S.  Cross 61°  47'  S. 

do.       of  Spica 13     48ra.    Cor.  for  Diff  Lat Add.  7 


Interval  of  time Oh.  58m. 


Cor.,  Table  XX Sub 


61' 


54' 
5 


Couise  S.W.,  Dist  1  (^  gives  D.Lat  7'  S.  True  Alt 61°  49' 

Zenith  Dist 28°  11'  N. 

Dec,  Table  XIX 62    17    S. 

Latitude  by  the  S.  Cross. ,  34°    6'  S. 
do.     by  Spica 33    54  S. 


Ob.s.  Alt  of  Spica 66'  35'  N- 

Cor.,  Table  XX Sub. 5 

True  Alt 66°  30' 

Zenith  Dist 23°  30'  S 

Dec,  Table  XIX 10    24   S 

Latitude  by  Spica 83°  64'  S. 


Sum )68°    0' 

Correct  Latitude 34°    O'  S.    at  Ih.  48m.  or  time  of  the  last  Altituae 


The  Altitudes  in  this  case  have  been  too  great  by  6  minutes,  and  which  is  generally  the  case  in  observing 
Altitudes  of  Stars  in  the  night  time 


FINDING  THE  LATITUDE  BY  THE  STARS. 


Ill 


FINDING  THE  LATITUDE  BY  AN  ALTITUDE  OF  A  STAR  OUT  OP*  THE  MERIDIAN. 

• 

The  Latitude  may  be  found  by  an  Altitude  of  a  Star  out  of  the  Meridian,  upon  the  same  principle  bm 
the  method  given  at  page  94,  by  the  Sun,  using  the  Star's  Distance  from  the  Meridian  in  the  room  of  the 
time  from  Noon. 

And  it  is  necessary,  in  this  case,  (in  obtaining  a  correct  result),  to  compute  the  Star's  Meridian  passage, 
in  the  room  of  taking  it  from  Table  XVIII. 

,» 

RULK 

Turn  the  Ship's  Longitude  into  Time,  and  add  it  in  West  Longitude,  or  subtract  in  East,  to  or  from  the  Apparent 
Time  of  Observation,  reckoned  from  the  preceding  Noon,  -will  give  the  Greenwich  Time,  nearly.  Or  the  Greenwieb 
Time  may  be  found  at  once  from  the  Chronometer.  Take  out  the  Sun's  Right  Ascension  from  the  Nautical  Almanac; 
one  day  less  than  the  Sea  Date,  and  correct  it  to  the  Greenwich  Time  by  multiplying  the  difference  for  1  hour  by 
the  time  fmm  Greenwich  Noon,  and  add  it  to  the  Right  Ascension  at  tlae  preceding  Noon,  (because  it  is  always 
increasing.)  Take  out  the  Star's  Right  Ascension,  and  correct  it,  if  required.  Then  subtract  the  Sun's  Right  Ascen- 
aioD  from  the  Star's  Right  Ascension,  (increasing  the  latter  by  24  hours,  if  necessary,  for  the  purpose  of  subtraction), 
and  the  I'emaiuder  will  be  the  correct  Apparent  Time  of  the  Star's  Meridian  passage. 

The  limits  of  the  time  from  the  Meridian  passage  of  the  Star,  are  the  same  as  the  time  from  Noon  by 
the  Sun,  given  in  Part  5.  Table  XV,  and  the  rules  for  using  the  Tables  are  the  same  as  given  at  page  94. 

If  the  time  of  the  Altitude  of  the  Star  is  noted  by  the  Watch,  it  must  be  previously  regulated,  or  its 
error  on  Apparent  Time  knowTi. 

The  Chronometer  may  be  used  to  find  the  Apparent  Time  of  Observation,  as  at  page  94. 


EXAMPLE  1 

Feb,  28th,  1854,  Sea  Time,  in  Latitude  by  Dead  Reck- 
•ning,  about  40°  10'  N.,  and  Longitude  60°  W.,  at  6h  5m 
P.  M..  tlie  Oliserved  Altitude  of  the  Star  Aldebaran  was 
65°  43'  S. ;  height  of  the  eve  18  feet;  the  Watch  show- 
ing the  correct  Apparent  Time.     Required  the  Latitude. 


1      30 

.22h  42m  298 
28    27     32 


Feb.  27th,  the  Sun's  R.  A.,  N.  A.  Noon 22h  40m  598 

Time  of  Obs.    6h  6m  Change  of  R.  A.  in  ' 

Long.  60°  W._4_0         Ih  =  9s  X  10h  = 

Green. Date.  lOh  5m   0's  Correct  R.  A. 
#'8  R.  A.  4h  27 ra  328  ) 
Increased  by  24h J' 

#Aldebaran's  Mer.  Passage 5h  45m    38 

Apparent  Time  of  Observation 6       5        0 

Time  past  the  Meridian 

#  Past  the  Meridian  19m  57s 

Part  1st 

Lat  40°  N.,  #8  Decl.  16s 

Part  •2d..' 

Corr.  for  Altitude... Add  0°  24'  Log 

#'s  Ohs.  Altitude .65    43 

Meridian  Altitude "66^     7'  S. 

Corr..  Table  XX... Sub.  5 


J  Log. 
. . .'  f  ^°^- 


19m  578 


7.279 


0.559    }■  Table  XV. 

7.838 


True  Altitude 66°    2' 

Zenith  Distance .23°  58'  N. 

Declination 16    13   N. 


Latitude  in 40°  11'  N.  at  6h  5m  P.  M. 


EXAMPLE   2. 

March  22d  1864,  Sea  Time,  in  Latitude  by  Dead  Reck 
ouing  about  38°  N.,  aud  Longitude  46°  W.,  an  Altitude 
of  the  Star  Sirius  was  observed  to  be  34°  36'  S.,  when 
the  Greenwich  Time  by  Chro.  was  9h  3m  P.  M :  height 
of  the  eye  18  feet.     Required  the  Latitude. 

March  21st,  Sun's  R.  Ascen.,  N.  A.,  at  Noon    Oh    2m    58 
G.  Time  of  Obs.  9h    3m    Os    Corr.  for  G.  )    „      ,      „, 
Long.  45°  W.  )   3      ^       ^^      T. 9h  X  9s  f  __^_J^ 

^  ^^^^^-  •  •  ) ©'8  Cor.R.A.  Oh    3m  268 

Mer.  T.  at  Ship. 6h    3m    Os    #'8  R.  Ascen.   6    38     43   ' 
Equa  of  Time .  Sub.  7      15      ^-g  Mer.  Pas.  6h  35m  PTa 
App.  T.  at  Ship.5h  55m  458    or  T.  of  Obs.     5    55      45 

Time  before  passing  the  Meridian 39m  32i 

Time  before  Mer.  Pass.  39m328>T        /,n„^' 

Part  1st.. f  ^^-  ^-^^^ 

Lat.  38°  N.;  #'s  Deci  'iVr's.".*.'.  [  j  ).Tab.  XV 

Part  3d \  ^°^-  ^'-^^^ 

Corr.  for  Altitude Add  0°  47'  Log.  8.187. 

#'8  Observed  Altitude..  ..34   36 

Meridian  Altitude 35°  23'  S. 

Corr.,  Table  XX Sub 5^ 

True  Altitude 36°  18' 

Zenith  Distance 54°  42'  N. 

#'s  Decl.,  Table  XLX... 16    31    S. 

Latitude  in 38°  11'  N.  at  5h  56m  P.M. 


The  same  Examples  as  above,  worked  with  the  Star's  Meridian  Passage  taken  from  Table  XVIII. 


Mer.  Passage  of  Sirius,  March  21,  Table  XVIII. 6b  84m 
Time  of  Observation 5    66 

Time  before  passing  the  Meridian sg^i 

Time  before  Mer.  38m  Part  1st... Log.  7,8361 

Lat. 38°  N.,Decl.  16i°  S.  Part  Sd.Log.  0.266  ^ Table  XV 


Mer.  Passage  of  Aldebaran,  Feb.  27,  Tab.  XVIII  6h  48m 
Time  of  Observation 6       5 

Time  past  the  Meridian 17^ 

#  past  tiie  Mer.  17m  Part  1st..  .Log.  7.138^ 
Ut.  40°  N.,  #'s  Decl.  16°  N. .  K        .  , 

Part  2d \  ^"S-  0.5o9  iTable  XV. 

Corr.  for  Altitude  17' Log.  7.697  „ 

Hence  an  error  of  nearly  3  minutes  of  time  m  the  Meridian   Passage  of  Aldebaran  would   produM  m 
WTor  of  7'  in  tlie  Correction  for  Altitude. 

And  an  error  of  Im  32s  of  time  in  tlie  Meridian  Passage  of  Sirius  would  produce  an  error  of  3'  in  t^ 
•vorrectioD  '-^r  Altitude. 


Corr.  for  Altitude  44' 


.Log.  8.102 J 


112 


NAUTICAL  ASTRONOMY. 


FINDING  THE  LATITUDE  BY  AN  ALTITUDE  OF  A  STAR  OUT  OF  THE  MERIDIAN. 

As  the  Parts  2d  and  3d  of  Table  XV  are  only  calculated  for  objects  whose  Declinations  do  not  exceed 
8** :  therefore,  when  the  Declination  of  a  Star  exceeds  that  quantity,  the  Logarithm  of  the  Latitude  and 
Declination  must  be  computed  as  follows :  . 


I 


RULE. 

Compute  the  Meridian  Altitude  of  the  body  by  adding  ita  Declination  to  the  Co-Latitude,  when  they  .are  of  m 
mM  name,  or  taking  their  Difference  when  of  contrary  names.  Enter  Table  XXVIII  with  the  Latitude  and  th« 
Declination,  (as  if  they  were  Half  Sums),  and  take  out  three  figures  of  these  Logarithms  with  their  Indices.  Entei 
Table  XXVll,  with  the  Meridian  Altitude,  (as  a  Latitude),  and  take  out  its  Logarithm  in  like  manner,  and  write 
under  it  the  constant  Logarithm  0.301.  Add  these  four  Logarithms  together,  and  their  Sv,m  (rejecting  lO's  in  the 
Index),  will  be  the  Logarithm  of  the  Latitude  and  Declination  required. 


EXAMPLE   L 

Required  the  Logarithm  for  Lat  48°  80'  N,  and  the 
Decimation  of  the  Star  Castor  32°  12'  N. 


Latitude 48° 

Subtract  from,.. 90 

Co-Lat.'*ude....  AV 
#'8  DecL 32 

Mer.  Altitude 


30'  N.  as  a  half  Sum . 
_0    (Table  XXVIII.) 

80' N. 

12   N.  as  a  half  Sum. 


,  .Log.  4.821 


.Log.  4.927 
^Log.  0.552 


73°  42'  S.  as   a  Lat.,  Table 
XXVII. . 
Constant ,'.  Log.  0.301 

Required  Computed Log.  0.601 


EXAMPLE  3. 

March  81  st,  1854.  Sea  Time,  Latitude  by  Dead  Reck- 
oning 48'  30'  N.,  Long.  30°  W.,  the  Observed  Altitude  of 
the  Star  Castor  was  73°  1'  S.,  and  the  Greenwich  Time 
by  Chronometer  8h  28m  49^     Required  the  Latitude. 


Oh  34m  488 
1      16 

Oh  36m    48 

7    25 17 

6h  49m  13s 
6    24      IS 


March  30th.  Sun's  R  A.,  in  N.  A.,  Noon. . 
G.  T.  by  Chro.  8h  28m  49s  Cor.  for  G.  T.  ) 
Lon.  80°  W.  I   2      0       0        8ih  X  98...  f 

"°  *™«-  •  i ©'8  Cor.  R.  A.. 

M.  T.  at  Ship.  6h  28m  49s  #'s  R  Ascen.. . 

Equa...   iSub. ^_86_^-8Mer.  Pass... 

App.  Time. . .  6h  24m  138  App.  T.  of  Obs.. 

Time  before  the  Meridian  Passage 26m    Os 

#'s  Diet  fm.  the  Mer.  25m,  Part  1st,  Tab.  XV.  Log.  7.478 
Lat  48°  80'  N..  DecL  82*  12'  N.,  Computed.  .Log.  0.601 

Part  4th,  Corr.  for  Altitude Add  0°  41'  Log.  8.074 

♦'s  Observed  Altitude 78      1 

Meridian  Altitude 73°  42'  S. 

Corr,  Table  XX Sub^ ^ 

True  Altitude 78°  88' 

Zenith  Distance ..16°  22'  N. 

#'8  Declination 83    12    N. 

Latitude  Obs^-rved .48°  84'  N. 

At  6h  24m  ISs  P.  M. 


EXAMPLE  6. 

Required   the  Logarithm  for  Latitude  10'  O'  S,  and 
the  Declination  of  the  Star  Dubhe  62'  82'  N. 

Latitude  10°    0'  S.  as  a  half  Sum  Log.  4.998 

Sub.  fm.  90      0 

Co- Lat..  80°    0'  S. 

Decl 62    32   N.  as  a  half  Sum Log.  4.664 

Mflr.  Alt"T7'~28'  8.  as  a  Latitude Log.  0.021 

Constant Log.  0.301 

Required  Computed Log.  9.97  9 


EXAMPLE   2. 

Required  the  Log.  for  Lat  88°  25'  S.,  and  the  Decl 
of  the  foot  Star  of  the  Cross  62°  17'  S. 


Latitude 88°  26'  S.  as  a  half  Sum., 

Sub.  from, , . ,.     90     0    (Table  XXVII L) 

Co-Latitude....  51°  35'  S. 

DecL 62    17   S.  as  a  half  Sum. . 

"113°  62' 
Subtract  from.. .180     0 

Mer.  Altitude..  66° 


.Log.  4.894 
.Log.  4.661 


8'  S.  as  a  Lat,  Table  )  ^         -  „„. 
XXVII [Log.  0.39» 

Constant Log.  0.301 

Required  Computed Log.  0.25f» 

EXAMPLE   4. 

Jan.  2d,  1854,  Sea  Time,  in  Lat  by  Dead  Reckoning 
88°  25'  S.,  Long.  30°  E.,  the  Obs.  Alt  of  the  foot  Star  of 
the  Southern  Cross  was  65°  41'  S.,  and  the  Greenwich 
Time  by  Chro.  16h  2m  40s.     Required  the  Latitude. 


2     56h 


Jan.  1st,  Sun's  R.  A.,  in  N.  A.,  Noon 18h  47m    6> 

G.  T.  by  Chro..  16h    2m  408  Cor.  for  G.  T.  ) 

Long.  30°  E.  )    2      0       0    ^^^  >'  ll8=  f 

mtime....) ©'sCor.  R.  A..18h  50m    2a 

M.T.  at  Ship.  .18h    2m  408  #"8  R.  A.. ..  1 

--    -  -  61     r2hl8m3l8>86 


Equa.  of  T.Sub. 
App.  Time 


18      81 


17h  58m  498  +24h  -  . .  )  ^ 

#'8  Mer.  Pass..  17h  28m  2»« 
App.  T.  of  Obs.l7    68      49 

Time  past  the  Meridian 80m  20s 

#'s  Dist  from  the  Mer. 
80m  208,  Part  Ist 


/ 


Log.  7.641 

Lat  88°  26'  S.,  DecL  62'  )  Computed  Log.  0.265 

17   o )  . 

Corr.  for  Altitude Add  0'  27'  Log.  7.896 

#'8  Obs.  Altitude .66   41 

Meridian  Altitude 66*    8'  S. 

Corr.,  Table  XX Sub.         4 


Table 
XV. 


True  Altitude .66'    4' 

Zenith  Distance 23°  66'  N. 

Declination 62    17    8. 


Latitude  Observed 88°  21'  8. 

EXAMPLE  6. 

Required  the  Log.  tor  Latitude  40'  27'  8,  and  th« 
Declination  of  the  Star  Canopus  52°  37'  S. 

Latitude    40'  27'  S.  as  a  half  Sum Log.  4.881 

Sub.  fm..   90      0 

Co-Lat...."49°"¥3'  S. 

Decl 52   37   8.  as  a  half  Sum Log.  4.7 8« 

102°  10' 
Sub.  fm.,  180     0 


Mer.  Alt.   77°  50'  S.  as  a  Latitude Log.  0.676 

Constant Log.  0.301 

Reoiiired  Computed Log.  0.64) 


nNDING  THE  LATITUDE  BY  THE  STARS 


ll» 


FINDING  THE  LATITUDE  BY  TWO  STARS,  ONE  OF  THEM  OUT  OF  THE  MERIDIAN. 

As  before  observed,  a  single  Altitude  of  a  Star  for  Latitude,  on  a  dark  night  at  Sea.  is  always  of  a  doubt 
ful  character,  in  consequence  of  the  obscurity  of  the  horizon*  but  which  may  be  remedied  byob.servLng  twc 
Btars  on  opposite  sides  of  the  Meridian.  But  as  no  two  Stars  pass  the  opposite  Meridians  at  the  same  period 
of  time,  the  Ship  may  have  changed  her  place  in  the  interval  of  their  passing,  and  a  correction  must  be 
applied  to  the  first  Altitude,  to  reduce  it  to  the  place  where  the  second  was  observed,  (an  Example  of  which 
is  given  at  page  110.)  But  when  we  want  to  find  the  Latitude  at  once  from  the  Altitude  of  two  Stars  ott 
opposite  sides  of  the  Meridian,  we  observe  the  Meridian  Altitude  of  one,  and  directly  afterwardi  observe 
the  Altitude  of  the  other,  (not  on  the  Meridian,)  and  note  the  time  by  the  Watch  or  the  Chronometer,  and 
reduce  it  to  the  Meridian,  (as  in  the  Examples  on  the  preceding  page.)  The  limits  must  be  the  same  a» 
that  given  in  Part  5th,  Table  XV. 


February  12th,  1854.  Sea  Time.  In 
tlie  Meridian  Altitude  of  the  Star  Spica 
foot  Star  of  the  Cross  was  66°  10'  South 

GreenwTi  Time  by  Chr..l5h.34m.20a 
Long.  25°  16'  W.in  T..  ._\. 41 4 

Mean  Time  at  Ship 13h.63m.168. 

Equa  of  T.,  contrary,  Sub^ 14      32 

pp.  Time  at  Ship 13h.  38m.  448. 

Mer.  Obs.  Alt.  of  #  Spica..  60°  34'  N. 
Cor.,  Table  XX 4 

True  Alt. 60°  30' 

Zenith  Dist 29°  80'   S. 

Dec  Spica 10    24   S. 

Lat.  Oba.  by  #  Spica. . . .    39°  64'  S. 

do    by  #  S.  Cross. .  J0_ 6'  S. 

Sum ^)80°    0' 

Correct  Latitude  ....      40^^'  S. 


EXAMPLE  1. 

Liititude,  by  Detvd  Reckoning,  about  40°  9'  S.,  and  Longitude  26°  16'  W.,. 
wafl  observed  t<>  be  60°  34'  North,  and  at  the  same  time  the  Altitude  of  th» 
.     Greenwich  Time  by  Chronometer,  16h.  34m.  20s.     Required  the  Lat'tud* 

Feb.  11th.  Sun's  R.  Asceu.,  N.  A 21h.  39m.  2Ss.. 

Corr.  for  Greenwich  Time Add  2      20 


•  Diff.  for  lh....98. 
.Green.  Time  .I5^h. 


Sun's  Correct  R.  Aseen 21h.  41m.  48s. 

#  Cross  R.  A.  12h.l8m.3l8.X24h.=36      18      32 


135 
b_ 

)T40 


*'8  Meridian  Passage 14h.  36m.  448. 

Time  of  the  Observation 13     38      44   Cor.    2m.208 

Time  before  Mer.  Passage 58m.   08.= Log.  8.202 

Lat  40°  S.,  Dec.  62°  17'  S.,  computed   Log.  0.274 


Cor.  for  Alt Add     1  ° 

Obs.  Alt  #  S.  Cross 66 

Merid.  Alt "67' 

Cor,  Table  XX  Sub.    

True  Alt _67° 

Zenith  Dist 22' 

Dec,  S.  Cross 62 

Lat  by  S.  Cross 40^ 


48'     Log.  8.47ft 

10      Table  XV. 

"63' S. 
4 

"49' 

TPn. 
r?  s. 

"  6'  S. 


EXAMPLE  2. 


March  2d,  1864.  S?a  Time.  In  Latitude,  by  Dead  Reckoning,  about  40*  80'  South,  and  Longitude  76*  SC  East, 
(he  Meridian  Altitude  of  the  Star  Sirius  was  observed  to  be  66"  14'  North,  and  at  the  same  time  the  Altitude  of 
the  Star  Canopus  was  77°  36'  South.     Greenwich  Time  by  Chronometer,  3h.  Om.  248.     Required  the  Latitude. 

March  1st  Sun's  R.  A.  in  N.  A 22h.  48m.  SOs Diff.  for  Ih.. .  9a» 

Cor.  for  Greenwich  Time   Add  27       Green.  Time 8h 

Correct  R. 


ur.llme  by  Chro Sh. 

Lon.75°  30'  E.  in  time.  6 

Om.  24s. 

2 

Mean  Time  at  Ship   . 

..  8h 

2m.  248. 

Equa.  of  T.,  contrary, 

Sub. 

12      87 

App.  Time  at  Ship. . 

.  7h. 

49m.  47s. 

Mer.  Alt  of  #  Sirius. 

.  66° 

14' N. 

Cor.  Table  XX..  Su 

, 

4 

True  Alt 

.  66° 

10 

Zenith  Dist 

.    23° 
16 

50'  S 

Dec    Sirius 

31  S. 

Lat  Obs.  by  Siiius  . . 

40~ 

21' S. 

do.     by  Canopus 

.    40 

32  S. 

Sum 

i)80° 

63' 

Correct  Latitude 

40° 

26'  80"S. 

Aseen 22h. 

#Canopu8  R.A.6h.20m.448.Add  24h.80 

do.         Mer.  Passage 7h.  31m. 

Time  of  Oba 7     49 

Time  before  Mer.  Passage 


48m.  678 Cor. 

20      44 


.27* 


.Log,   7.82» 


478. 

47   (Table  .XV.) 

18m.    Os Log.~7.188 

See  Example  6th,  page  112,  of  Computing  the. Log,   0.641 

Correction  for  Altitude Add     0°  23'       

Obs.  Alt  #  Canopus 77    36    S. 

Mw.  Alt 77°  69' 

Cor.,  Table  XX Sub.  4 

True  Alt 'nVYb'  & 

Zenith  Dist ."Tsi^     6'  N. 

Dec.  Canopus 62    37'  S. 

Lat  Obs.  by  Canopus 40°  §2'  S. 


^r^h7v7T^f\ '"'  Example  ?iven  above  is  not  a  jr.ood  case,  as  the  time  from  the  Meridian  passage  exceeds  the  Umito 
wu      r.         '•  ""*^,''".  ^'■'■'"'  '"  the  time  will  considerably  affect  the  result.  ■>."oo«o  i-uo  umiw 

.5      of  Stars,  take  the  one  whose  Declination  is  of  a  oontrarv  name  to  the  Latitude  of  the  nl 
Altitnde,  beca.ise  it  can  be  observed  farthest  from  the  Meridian,  and   an  error  in  the  time  aff 


When  there  is  a  ch 
f and  which  has  a  low 
[it  the  least.     In  this  case  an  error  of  1  minute 


aoe, 

.,     ^.  , ,         ,  ' .  — ■ •  •'■  »""  '■•'■i<=  affect* 

n   the  time   would  produce  an  error  of  4    minutes  in  the   correction  for 


Altitude ;  and  on  reversing  the  case,    that  is,  observincr  the  Cross  on  the  Meridian,  and  findincr  the  correction-'for'tJ^ 
Altitude  of  Spica,  an  error  of  1  minute  in  time  would  produce  an  error  of  3  minuted  in  the  oorr'ection  t^'r  SttU/ 


1)4  NAUTICAL    ASTRONOMY. 


f:nd.ng  the  latitude  by  an  altitude  of  the  moon  out  of  the  meridian. 

The  Latitude  may  be  found  by  an  Altitude  of  the  Moon,  taken  either  before  or  after  she  passes  th« 
Meridian,  within  the  limits  of  Part  5th,  Table  XV,  upon  the  same  principle  as  that  by  the  Sua  and  Stars, 
as  follows  : 

RULK 

To  Find  the  Apparent  Time  of  the  Ohservatton. 

1.  Note  the  Greenwich  Time  by  Chronometer,  when  the  Altitude  was  observed.  Turn  the  Ship's  Longitude  into 
Time.  Subtract  in  West  or  add  in  East  Longitude,  will  give  the  Mean  Time  at  Ship.  Apply  the  Equation  of 
Time  the  cmitrary  way  to  what  is  directed  for  Apparent  Time  in  the  column  of  the  Nautical  Almanac,  and  we  have 
ih«  Apparent  Time  at  Ship  at  whicli  the  observation  was  made. 

To  Find  the  Time  of  the  Moon's  Meridian  Passage. 

2.  Take  out  the  Moon's  Meridian  Passage  from  the  Nautical  Almanac,  against  the  day  of  the  month,  and  correct 
H  by  Table  XXI I,  which  will  give  the  Mean  Time  of  her  passing  the  Meridian  of  the  Sflaip.  to  which  apply  the 
Equation  of  Time  the  contrary  way,  as  above  directed,  and  the  result  will  be  the  Apparent  Time  of  her  passmg  th« 
Meridian  of  the  Ship. 

To  Find  the  Moon^s  Distance  from  the  Meridian. 

3.  Now  take  the  difference  between  the  Apparent  Time  of  her  passing  the  Meridian  of  the  Ship  and  the  Apparent 
Time  of  the  Observation,  with  which  enter  Part  Ist,  Table  XV,  as  a  time  from  Noon,  and  take  out  its  Logarithm. 

To  Find  the  Correction  for  Altitude. 

4.  Correct  the  Moon's  Declination,  taken  from  the  Nautical  Almanac,  to  the  Greenwich  time  of  the  observation  bj 
the  Rules  given  at  page  102,  No.  6,  with  which,  and  the  Latitude  by  Dead  Reckoning,  proceed  as  before  to  find  the 
Correction,  (as  in  the  case  of  the  Sun  and  Stars,)  to  be  added  to  the  observed  Altitude.  The  Latitude  is  then  found 
IB  the  usual  way 

Sometimes  the  Meridian  Altitude  of  the  Moon  is  lost,  in  consequeuee  of  being  too  late  in  beginning  th« 
observation.  The  Latitude  may,  however,  still  be  obtained  as  correctly  as  by  the  Meridian  Altitude,  by  the  abov« 
miethod.  if  the  Longitude  of  the  Ship  can  be  ascertained  within  a  few  miles  of  the  truth. 

EXAMPLE. 

June  3d,  1854.  Sea  Time.  Li  Latitude,  by  Dead  Reckoning,  49°  25'  North,  and  Longitude  46°  "W.,  the  observed 
Altitude  of  the  Moon's  Lower  Limb  was  56°  29'  South,  before  her  Meridian  passage,  and  the  Greenwich  time  by 
"Chronometer,  7h.  56m.  Os.     Height  of  the  eye,  24  feet     Required  the  Latitude  of  the  Ship. 

>  's  Dec.  Noon,  18"  24'  N,  June  2d 

>'b  Mer.  Pas.,  June  2d,  N.A.,  5h.  21m.  Green.  Time  by  Chro.. .  7h.  56m.    Os.  Ali.lnight, 16    19 

'  June  3d, ._& 5      Lon.  45°  W.  in  time. . .    8 0_ 0    Change  in  12h.     2°    6') 

Tab.XXII  Lon45°W.,D.Varia.    44m.  Mn.  Time  at  Ship 4b.  56m.    Os.  G.  T.  from  Noon,  8h.       [•  -'  T  22' 

Gives  the  correction  . . .     -"T^^s.  ^qua.  of  Time. . .  .Add  2      22        in  Table  XXIII      .  ) 

Mer.  Pass.,  June  2d 5h.  21m.  0    App.  Time  of  Obs 4h.  58m.  22s.  Dec,  Noon.  June  2d 18    24 

M.TimeofM.Pas.atShip,-^h:26^.-0i:^PP-l'i'-««fM-P^^^-    ^     ^^      ^^      5 's  Cor  Dec 17°    2'N 

Equa. of  T.,  contra.  . Add  2    22    Moon's  Dist  from  Mer..   Oh.  30m.    Os. Log.  7.631  |  ,j,^y^  j-y 

App.TuneofMer  Pas...6h.  28m.228.  Lat.  D.R  49°  25' N.,  Dec. .    0°  17' N. Log._a367  f 

Cor.forAit Add     0    34=- Log.  7.998 

Obs.  Alt.   D  's  L.  Limb  . . .   56    29  S. 

Mer.  Alt 57"    8' 

])  's  semid.  16,  Dip  5,  Add  10 


29 


App.  AIL 67°  13' 

Cor.  for  Hor.  Par.  55',  A.lt.  ) 

57°,  Table  XXV,.  Add  j"    " 

J-s  True  Alt 57°  42' S. 

Zenith  Distance 32°  18'  N. 

Correct  Dec 17      2  N. 


Lat.  Observed 49°  20'  N.  at  6h.  28m.  P.  M. 

QUESTIONS  FOR  EXERCISE. 

ituestton. — August  9th,  1854.     Sea  Time.     In  Latitude,  by  Dead  Reckoning,  about  56*  0' North,  Longi 
tude  75*  30'  West,  the  observed  Altitude  of  the  Moon's  Upper  Limb  was  14°  41'   South,  (about  1  hour  paat 
the  Meridian.)     The  Greenwich  Time  by  Chronometer  being,  August  8th,  18h.  52m.  SOs.     (Height  of  the 
eye,  T^  feet.)       Required  the  Latitude. 

Answer. — Latitude  56°  10'  North.  The  Apparent  Time  of  observation  at  Ship  was  13h.  45m.  68.  The 
Apparent  Time  of  the  Moon's  Meridian  Passage,  121".  45m.  6s.,  the  Moon  was  1  hour  past  the  Meridiaa, 
mad  the  Correction  for  Altitude,  1°  6',  and  Meridian  Altitude  15*  47'  South. 


FINDING  THE  LATITUDE  BY  THE  PLANETS 


115 


FINDING  THE  LATITUDE  BY  AN  ALTITUDE  OF  A  PLANET  OUT  OF  THE  MERIDIAN. 

The  Latitude  may  be  found  by  an  Altitude  of  a  Planet  out  of  the  Meridian,  upon  the  same  principle, 
And  in  a  similar  manner,  a«  that  by  the  Moon. 


RULE 

To  Fwd  the  Apparent  Time  of  Observation. 

1.  Note  the  time  by  Chronometer,  ■when  the  Altitude  of  the  Planet  was  observed,  and  from  which,  dednoe  th« 
Apparent  Time  of  the  Observation,  aa  directed  on  the  preceding  page. 

To  Find  the  Time  of  the  Planet's  Passing  the  Meridian. 

•  2.  Take  out  the  Planet's  Meridian  Passage  from  the  Nautical  Almanac,  against  the  day  of  the  month,  as  nsual, 
and  apply  the  Equation  of  Time  the  contrary  way  to  what  is  directed  for  Apparent  Time,  in  the  column  of  ih» 
Nautical  Almanac,  which  will  give  the  Apparent  Time  of  its  passing  the  Meridian  of  the  Ship. 

To  Find  its  Distance  from  the  Meridian. 

3.  Now  take  the  DiflFerence  between  the  Apparent  Time  of  its  passing  the  Meridian  of  the  Ship,  and  the  Appa- 
rent Time  of  the  Observation  will  be  the  Planet's  Distao?"  from  the  Meridian  iu  time,  the  Logarithm  of  which  fin«^ 
in  Part  Ist,  Table  XV. 

■  To  Find  the  Correction  for  Altitude. 

4.  From  the  Nautical  Almanac  take  out  the  Planet's  Declination,  and  correct  it  to  the  Greenwich  Time  of  th« 
Observation,  in  a  similar  manner  as  at  page  104,  with  which,  and  the  Latitude  by  Dead  Reckoning,  take  out  th« 
Logaritlim  from  Parts  2d  or  3d,  Table  XV.  The  Sum  of  these  two  Logarithms,  in  Part  4th,  gives  the  Correction 
for  the  Altitude  required,  which  is  always  additive. 


EXAMPLE  1. 

Sept  25th,  1854,  Sea  Time,  in  Latitude  by  Dead  Reck. 
44°  25'  N.,  Longitude  by  Chronometer  65°  W.,  an  Alti- 
tude of  the  Planet  Jupiter  was  observed  to  be  21°  62'  S. 
(before  the  Mer.  Passage),  Greenwich  Time  by  Chronome- 
ter, lOh  34m  16s,  R  K  Height  of  the  eye  18  feet.  Re- 
•quired  the  Latitude. 

Sep.  24th,  G.  T.  ),.,   „.      ..     Mer.  Pass. )  ^v,    a      oc 
of  Observation  \  ^^"^  24m  16s       j^^^.^^^_  J  7h    4m  368 

Long.  65°  W.  in  )    ^    ^^       ^     Equa.ofT.Add  8       7 

Time. Sub.  )  A  pp.  T.  of  / 

Mean  T.  at  Ship.. .   6h  14m  I'eT     Pass.'      \  '^^  ^^™  ^^^ 

Equa.  of  Time.  Add 8 7 

App.  T.  at  Ship..  ...6h  22m  238"  Decl.  Jupiter. 22°  44'  S. 
A  pp.  T.  of  Passage .  7    1 2     43 

Time  before  Mer..  7.      50m  208  Log.  8.078  )  Table 

Lat  44°  i  N.,  Decl.  22°  44'  S Log.  0.156  f  XV. 

Corr.  for  Altitude Add  0°  69'  =  Log.  8.234 

Oba.  Alt.  of  Jupiter 21    52 

Meridian  Altitude "22^  51'  S. 

Corr.,  Table  XX Sub.  6 

True  Altitude .22°  4? 

Zenith  Distance. .67°  15'  N. 

Declination 22    44   S. 

Latitude  in. ii^ir  N.  at  6h  23m  P.  M. 


EXAMPLE    2. 

Jan.  29th,  1854,  Sea  Time,  in  Latitude  by  Dead  Reck- 
oning, 25°  10'  S.,  Long,  by  Chronometer  0°  0'  0",  an  Alt 
of  the  Planet  Saturn  was  observed  to  be  47°9'  N.,  (past 
the  Meridian),  Greenwich  Time  by  Chronometer  7h  31ra 
38s,  and  the  height  of  the  eye  18  feet  Required  th^ 
Latitude. 

Jan.  28th,  G.  T.of  )  ^,   „,      „„_^  Mer.  Pass.  )  ^,     ,      ,  . 
Observation. . .  \  ^^  ^^"^  ^^^      Saturn.  \  ^^    ^"^  1^" 

Long,  in  time ODD    Equa.  of  T...       13      16 

Mean  T.  at  Ship. .  .7h  81m  388~App.  T.  of )  TT".-        7" 
Equa.  of  Time .  Sub.      13      16        Passage  f  ^^  ^^"^    ^' 

^^t"Ship°.*^  .°!*!'  [  ''^  ^^"^  228      Decl.  Saturn  17°  2'  N 
App  Time  of  Pass. 6h  48m    28 

Time  past  Mer 30m  201  Log.  7.641  )  Tabl* 

Lat  25°  S.,  Decl.  17°  N Log.  0.413  \  XV 

Corr.  for  Altitude Add  0°  39'  Log.  8.054 

Obs.  Altitude  of  Saturn 47      9  N. 

Meridian  Altitude 47^48^ 

Corr'.,  Table  XX Sub. 5_ 

True  Altitude 47°  iF  N. 

Zenith  Distance .42°  17'  S. 

Declination 17      2    N. 

Latitude  in .26°  15'  S.  at  7h  18m  P.  M 


Note. — In  all  the  preceding  Examples,  where  the  Chronometer  is  used  in  deducing  the  Apparent  time  at  Ship,  the 
Difference  of  Longitude  the  Ship  has  made  in  the  interval  between  the  time  the  Long'itude  by  Chronometer  was  ascer- 
tained, and  the  time  the  Altitude  of  the  body  was  observed  for  Latitude,  must  be  applied,  by  the  rules  in  Middle  Lati- 
tude Sailincr,  in  order  to  get  as  near  as  possible  the  correct  Longitude  of  the  Ship  at  the  time  the  Altitude  of  the  body 
was  observed;  bearing  in  mind  that  for  every  1'  of  error  in  the  Longitude,  there  will  be  a  corresponding  error  of  4 
ieconds  in  time  in  deducing  the  Apparent  Time  at  Ship  from  it.  In  general,  when  sights  for  Chronometers  are  taken, 
both  morning  and  afternoon,  the  error  in  the  Ship's  Longitude,  brought  on  by  the  Dead  Reckoning,  will  rarely  exceed  6 
miles.  And  it  will  be  perceived  that  in  thus  findincr  the  Latitude  from  bodies  out  of  the  Meridian,  the  Chronometer 
renders  valuable  assistance  in  finding  the  Apparent  Time  at  Ship,  at  the  time  the  Altitude  was  observed,  when  it  would 
be  diflioult  to  get  it  otherwise. 

^  Many  of  the  foreg^oing  Examples  of  finding  the  Latitude  from  the  Meridian  Altitude  of  the  Stars,  are  given  for  Twi- 
ight,  because  the  horizon  is  then  distinctly  visible,  and  the  observation  can  be  depended  on.  But  it  sometimes  hap 
pens  that  there  are  no  Stars  on  the  Meridian  at  Twilight.  In  that  case,  if  an  Altitude  be  observed  at  Twilight,  either 
before  or  after  it  passes  the  Meridian,  and  the  time  noted  by  Chronometer,  the  Latitude  is  found  by  the  preceding  rule* 
•s  correctly  as  if  its  Meridian  Altitude  had  been  observed.  In  the  two  last  Examples,  the  Planet  Jupiter  p>assed  th» 
Meridian  after  darkness  had  set  in,  but  his  Altitude  was  obtained  in  good  Twilight,  50  minutes  before  that  time.  Saturn 
had  passed  tlie  Meridian  in  stroncj  Sun-light,  and  30  minutes  afterwards,  or  as  soon  as  he  became  visible,  hia  Altit;ul« 
was  observed  and  the  Latitude  found  as  above. 


Il« 


NAUTICAL  ASTROJNOMY. 


FINDING  THE  VARIATION  OF  THE  COMPASS  BY  AN  AMPLITUDE 

An  Amplitude  means  the  Distance  of  any  Heavenly  body  from  the  True  East  or  West  points  of  th* 
Horizon  at  Rising  or  Setting,  and  is  found  by  inspection  in  Table  XXXV,  by  entering  it  with  the  Latitude 
of  the  Ship  at  the  side,  and  the  Decimation  of  the  body  at  the  top,  and  at  the  angle  of  meeting  will  b«  th« 
required  Amplitude  in  degrees  and  minutes,  to  be  called  East  in  the  morning  and  West  in  the  evening,  and 
towards  the  North  or  South,  according  as  the  Declination  of  the  body  is  North  or  South,  as  the  foilowing 
figure  will  show  • 

DIAGRAM 

Of  an  Amplitude  in  45°  North  Latitude. 

A  Fig.  17. 


This  Figure  represents  the  North  Pole  of  the  Heavens  elevated  above  the  Horizon  equal  to  the  L«iitaac 
of  the  place,  and  the  Celestial  Eqaator  at  Right  Angles  to  it.  The  line  drawn  perpendicular  to  the  Hori- 
zon is  called  the  Prime  Vertical  Circle,  and  which  passes  through  the  East  and  West  points  in  the  centre. 
The  dotted  Circles  on  each  side  of  the  Equator  are  the  Sun's  Parallels  of  Declination  North  and  South. 
The  Circles  from  the  Zenith  passing  through  the  Sun's  place  in  the  Horizon,  are  called  Amplitude  Cirole«» 
and  measure  the  Sun's  Amplitude  or  Distance  from  the  East  or  West  points  of  the  Horizon. 

Hence,  it  will  appear  that  the  Sun  and  all  the  other  Heavenly  Bodies  Rise  and  Set  to  the  Northward  of 
the  East  and  West  points,  when  their  Declinations  are  North,  and  that  they  Rise  and  Set  to  the  Southward 
of  the  East  or  West  points  when  their  Declii»tions  are  South. 


EXAMPLE  1. 

June  21  fit,  1854.  Required  the  Sun's  True  Amplitude 
at  Rising  and  Setting,  in  Latitude  45°  N. 

Answer. — The  Sun's  Deelination  on  the  2lBt  of  June  is 
23*  28'  N.,  with  which  and  the  Latitude  46°,  the  true  Am- 
plitude is  found  in  Table  XXXV,  at  Rising,  to  be  E.  34° 
18'  N.,  and  at  setting  W  34°  18'  N, 

EXAMPLE   3. 

March  2l8t,  1 854.    Required  the  Sun's  True  Amplitude 
Hising  and  Setting,  in  Latitude  45°  N. 

Answer. — The  Sun  being  on  the  Equator,  his  Declina- 
tion is  0° ;  he  therefore  Rises  and  Sets  in  the  East  and 
West  poiuts  of  the  Horizon. 


EXAMPLE  2. 

December  21st,  1854.    Required  the  Son's  True  Afl» 

plitude  at  Rising  and  Setting,  in  Latitude  46*  N. 

Anstoer. — The  Sun's  Declination  on  the  2l8t  of  Dee 
is  23°  28'  S.,  with  which  and  Latitude  45*.  the  True  Am 
plitude  is  found  in  Table  XXXV,  at  Rising,  to  be  K  8* 
18'  S.,  and  at  Setting,  W.  34°  18'  S. 


EXAMPLE  4. 

Sept  2l8t,  1854.  Required  the  Sun's  True  Amplitoa* 
at  Rising  and  Setting,  in  Latitude  46°  N. 

Answer. — Tlie  Sun  being  on  the  Equator,  his  Dechna 
tion  is  0° ;  he  therefore  Rises  and  Sets  in  the  East  and 
"West  points  of  the  Horizon. 


Note. — All  heavenly  bodies  whose  Declinations  are  0°  0',  Rise  in  the  True  East  point  of  the  norizon,  and  Set  in  the 
True  West  point.  Hence,  when  the  Sun's  or  Moon's  Declination  is  0°  0',  that  is,  wlien  they  are  on  the  Celestial  Eqaa- 
tor,  and  their  Bearing  be  taken  by  an  Amplitude  Compasa,  when  Risinp;  or  Setting,  if  they  bear  by  Compa.«is  Easv  at 
West,  there  is  no  Magnetic  Variation.  But  suppose  the  Sun  was  observed  to  Set  by  Compass  W.  12°  N.,  that  would  h* 
the  amount  of  Magnetic  Variation  Westerly.  Or,  suppose  he  was  observed  to  Set  West  12°  S.,  that  would  be  tb« 
Knonnt  of  Magnetic  Variation  Easterly,  and  he  would  rise  in  the  first  case  E.  12°  S.,  and  in  the  second  case,  £.  18°  N 
which  would  furnish  the  Variation  in  the  same  manner. 


I 


1-hVDING  THE  VARIATION  OF  THK  COMPASS. 


IP 


FINDING  THE  VARIATION  OF  THE  COMPASS  BY  AN  AMI'LlTUDfi,. 

The  manner  of  observing  the  bearing  of  the  Sun,  or  other  heavenly  body,  at  rising  or  belting,  by  an 
Amplitude  Compass,  and  other  remarks  coimected  with  the  observation,  will  be  found  at  page  81. 

When  the  Magnetic  Amplitude,  or  bearing  of  the  body  by  the  Compass,  and  the  True  Amplitude, 
are  both  on  the  same  side  of  the  East  or  West  points,  that  is,  when  they  are  both  North  or  both  South, 
their  difference  is  the  Variation  of  the  Compass. 

But  when  one  is  North  and  the  other  South,  their  Surn  is  the  Variation,  and  the  following  Diagram  wii) 
«bow  wliether  tiie  Vn'      ion  is  Easterly  or  Westerly. 

DIAGRAM,.. 

Showing  Easterly  and  Westerly  Variation 

FiQ.  18. 


BXAMPLE  1. 

April  2d.  1864.  In  latitude  88*  30'  North,  LoDgi- 
♦ode  52'  West,  ibe  Sun  -was  observed  to  Set  by  Ccmpass 
W.  22°  N.     Required  the  Variation  of  the  Compass, 

April  2d,  Sun's  Declination  4°  55'  N.  and  Lat.  88°  30'  N. 
In  Table  XXXV,  g:ive3  the  True  Ampli..  .W.  6  2S  N. 
Sun's  bearing  by  Compass  at  Sotting W.  22      0    N. 

Magnetic  Variation 15*  87'  W. 

or  1^  points,  (nearly,)  Westerly. 


EXAMPLE  2. 

Oct  8th,  1854.  In  Latitude  40°  South,  Longitude  76 
West,  the  Sun  was  observed  to  Rise  by  Compass  E.  9 
N.     Required  the  Variation  of  the  Compass. 

Oct  8th,  Sun's  Declination  6°  52'  S.  and  Lat  40'     0'  S 
In  Table  XXXV.  gives  the  True  Ampli 


E.  7 
Bearing  by  Compass  at  Rising R  V 

Magnetic  Variation 

or  1|  points  Easterly, 


61  S 

0  N. 


le'fti'K 


Taking  the  Ist  Example,  and  referring  it  to  the  abov«  Figure,  it  will  be  perceivea  that  both  Amplitude* 
•re  to  the  North  of  the  West  Point,  their  difference  is  therefore  the  Variation ;  and  looking  towards  the 
Sun's  bearing  by  the  Compass,  the  true  Amplitude  is  on  the  left  of  the  Compass  bearing ;  the  variation  is, 
therefore,  Westerly. 

In  the  2d  Example,  (and  referring  it  to  the  same  figure.)  one  Amplitude  is  on  the  North  and  the  other 
OP  the  South  of  the  East  Point,  and  their  Sum  is  the  variation. 

And  looking  towards  the  bearing  of  the  Sun  by  Compass,  the  true  Amplitude  is  to  the  right  of  th« 
Compass  bearing;  the  ■Variation  is,  therefo.-e,  Easterly. 

And  in  the  1st  Example,  if  we  make  the  Compass  bearing  coincide  with  the  North  point  in  the  aboTe 
Figure,  the  true  Amplitude  will  then  be  on  the  West  side  of  the  North  ;  hence  it  is  called  Westerly  varia- 
tion. And  in  the  2d  Example,  in  like  ma-^ner,  the  true  Amplitude  will  be  on  the  East  side  of  the  North  , 
tence  it  is  called  Easterly  variation. 

In  the  above  Examples  the  Latitude  used  is  that  brought  on  from  Noon  by  Dead  Reckoning,and  the  Sun's 
Declination  taken  out  for  the  nearest  Noon,  but  if  greater  accuracy  is  requii-M,  the  Declination  must  be  cor 
fected  to  the  time  of  the  observation,  by  Table     XI}      but  this  is  seldom  necessary  at  Sea. 

QUESTIONS  FOR  EXERCISE 

Question  let. — July  3d,  1854.  In  Latitude  9'  36'  South,  the  Sun's  bearing  by  Compass  at  Rising  was 
E.  12°  42'  N.     Required  the  Variation. 

Answer. — The  True  Amplitude  is  E.  23*  22'  N.,  and  the  Variation  10*  40'  Westerly. 

Question  2d. — Sept.  2l8t,  1854.  In  Latitude  26"  32' North,  the  Sun's  bearing  by  Compass  at  Settinc 
was  West  6°  15'  South.     Required  the  Variation. 

Answer. — The  True  AmpHtude  is  W.  1*  7'  N.,  and  the  Variation  7*  22'  Easterly. 


MA 


NAUTICAL  ASTROPiuMY. 


FINDING  THE  VARIATION  OF  THE  COMPASS  FROM  AN  AZIMUTH. 

An  Azimuth  means  an  Angle  at  the  Zenith,  contained  between  the  Meridian  of  the  Observer  and  a  Oirah 
*i  Altitude  passing  through  the  body. 

DIAGRAM 
Of  an  Azimuth  in  381°  North  Latitude. 

Fig.  19. 


Ir  this  Figure  the  Sun's  True  Altitude  is  25",  his  Declination  17°  South,  and  the  Latitude  38'  SO^Nortl  ; 
•fil  'i  will  be  perceived  that  the  Co-Altitude,  or  the  Sun's  distance  from  the  Zenith,  the  Polar  Distance, 
and  the  Co-Latitude  are  given,  which  form  the  three  sides  of  an  Oblique  Spherical  Triangle,  to  find  the 
Angle  of  Azimuth  at  the  Zenith,  which  is  measured  on  the  Horizon  by  a  Circle  of  Altitude  passing  through 
the  body,  and  cutting  the  Horizon  at  right  angles.  The  Azimuth  Angle  in  the  above  Figure  is  meas- 
ured from  the  North  point  of  the  Horizon,  because  the  North  Pole  of  the  heavens  is  elevated,  and  it  contains 
141°  46'  :  but  for  convenience'  sake  its  Supplement  is  generally  used,  that  is,  what  it  wants  of  180°,  and 
is  reckoned  from  the  opposite  point  of  the  Horizon,  because  the  Sun  is  South  of  the  observer  in  North  Lati 
tude,  and  North  of  the  observer  in  South  Latitude. 

RULE. 

Correct  the  Sun's  observed  Altitude  by  Table  IX.  Correct  the  Sun's  Declination  by  Table  XI,  and  find  his  Polar 
Distance  by  adding  the  Declination  to  90°,  when  the  Latitude  and  Declination  are  of  contrary  names,  or  taking  tfae 
difference  between  it  and  90°  when  they  are  of  the  same  name. 

Then  add  together  the  Sun's  Polar  Distance,  his  True  Altitude,  and  the  Latitude.  Take  half  their  Sum,  and  take 
the  difference  between  the  half  Sum  and  the  Polar  Distance,  which  call  the  difference. 

Enter  Table  XXVII,  and  take  out  the  Log.  Secant  of  the  Altitude,  and  also  the  Log.  Secant  of  the  Latituae. 
Enter  Table  XXVIII,  and  take  out  the  Log.  Co-Sine  of  the  Half  Sum  and  the  Log.  Co-Sine  of  the  Difference.  Add 
together  these  four  Logs.,  and  their  Sum  found  iu  Table  XXIX,  will  give  an  angle  in  time.  Turn  this  into  Degreei 
and  Minutes  by  Table  XXVI,  which  will  be  the  Angle  of  Azimuth  required.  To  be  reckoned  from  the  South  in 
North  Latitude,  and  from  the  North  in  South  Latitude ;  towards  the  East  in  the  morning,  and  towards  the  West  im 
the  afternoon. 

The  Magnetic  Azimuth  having  been  observed  by  the  Azimuth  Compass,  as  directed  at  page  81,  at  the 
the  time  of  taking  the  Altitude.  Then  the  difference  between  the  True  Azimuth  and  the  Magnetic 
Azimuth,  (both  of  which  being  reckoned  from  the  same  Meridian,)  is  the  Variation  of  the  Compass  when  they 
are  on  the  same  side  of  the  Meridian,  that  is,  both  East  or  both  West ;  but  when  one  is  East  and  the  other 
West,  their  Sum  is  the  Variation 

Finding  the  Variation  at  Noon. 

In  High  Latitudes,  where  the  Sun's  Meridian  Altitude  is  low,  the  variation  may  be  found  at  Noon,  from 
the  Magnetic  Azimuth  observed.  But  to  do  this,  it  is  necessary  to  have  the  watch  previously  regulated 
to  Apparent  Time  at  the  Ship,  so  that  the  Sun's  Azimuth  bearing  may  be  observed  at  the  instant  the 
watch  shows  12  o'clock ;  because  the  Sun  is  then  True  South  in  North  Latitude,  and  True  North  in  South 
Latitude  And  supposing  the  bearing  by  the  Azimuth  Compass  to  have  been  South  also,  there  would  in 
that  caae'ne  no  variation.  On  the  other  hand,  if  the  bearing  by  the  Azimuth  Compass  was  S,  22*  30'  W., 
then  there  would  be  that  amount  of  Magnetic  Variation  Westerly  ;  but  if  the  bearing  by  Azimuth  Compasi 
lad  been  S.  22*  30'  E.,  then  there  would  be  that  amount  of  Magnetic  Variation  Eatterlv.  _ , 


FINDING  THE  VARIATION  OF  THE  COMPASS  BY  AN  AZIMbTH. 


n» 


EXAMPLE  1. 

February  2d,  1864,  Sea  Time,  in  Latitude  38"  30'  N.,  Longitude  60'  W„  the  Altitude  of  the  Sun's  Lower  Lfaak 
was  observed  to  be  24°  50',  and  his  Miiijnetic  Azimuth  S.  16°  0'  E.,  at  about  9h  30m  in  the  forenoon.  Hei{;ht  of  tk» 
eye  18  feet     Required  the  Variation  of  the  CompasB. 


Sun's  Declination,  February  1st,  Table  X.,  17* 
Corr.  for  Lon.  60°  W.,  Table  XI,  Subt.  3  )  g^j^ 


CJorr.  for  Time  before  Noon,  2h  30m  Add  2 

Sun's  Correct  Declination 17° 

90 


6'  S. 
1 


Observed  Altitude  Sun's  Lower  Limb. .  24*  60' 
Corr.,  Table  IX Add 10 

Sun's  True  Altitude 25*    (f 


Sun's  Polar  Distance   107° 

True  Altitude 25 

Latitude. 38 


5'  S. 
0 

6' 

0' Log.  Secant 

30 Log.  Secant 


Sum ..170°  36' 

Half  Sum 85°  18'. Log.  Co-Sine  ) 

Difference 21°  47' Log.  Co-Sine  ) 


Table  XXVII 


Table  XXVIII 


0.04272 
0.10646 


3.91849 
4.9678S 


Fig.  19,  Supplement  of  the  Angle  in  Time,  2h  32m  578,  Table  XXIX Log  9.03050 


Tamed  into  space  by  Table  XXVI,  gives  the  True  Azimuth S.  88°  14'  R 

Magnetic  Azimuth S.  16      0'  R 

Magnetic  Variation 22°  14'  Wester^. 


DIAGRAM, 

Showing  Easterly  and  Westerly  Variation. 

Fig.  20. 


In  the  above  fi^re,  (to  the  left),  both  Azimuths  are  on  the  same  side  of  the  Meridian,  and  their  Differ 
ence  is  the  Variation  Westerly,  because  the  True  Azimuth  is  to  the  Left  of  the  Magnetic  Azimuth. 

EXAMPLE  2. 

April  16th,  1864.  Sea  Time,  in  Latitude  40°  N.,  Longitude  120°  W..  the  Observed  Altitude  of  the  Sun  was  82°  ISf 
Magnetic  Azimuth  S  57°  22'  W.,  at  about  3  P.  M.     Required  the  Variation. 


April  15th,  Sun's  Declination 9°  46'  N, 


Add 


10 


Corr.,  Long.  120°  W.,  Table  XI,  7'  ) 
Corr.  for  3h  past  Noon 3   )  ' ' 

Sun's  Correct  Declination 9°  65'  N. 

90      0 
Sun's  Polar  Distance 80°    6' 


Sun's  Observed  Altitude  Lower  Limb 32*  Ifr' 

Corr.,  Table  IX Add 10 

Sun's  T^ue  Altitude 82*25 


Correct  Altitude 82    25     Log.  Secant  /  m  ,,    yxvtt  ^■O'^^'^T 

Latitude 40      0   Log.  Secant  P^^'® -^^^^^^.IIS?* 


Sum 152°  30 

Half  Sum ~76 

Difference 


15' 


3°  60' 


•J;;;|g°;|i°^[  Table  XXVIII*' 


,87600 
gpoQg 


Angle  in  Time  4h  68m  10s,  Table  XXIX Log.  9.6648ft 

Turned  into  space  by  Table  XXVI,  gives  the  True  Azimuth S.  74°  «3'  W. 

Magnetic  Azimuth S.  67°  22'  W. 

Magnetic  Variation 17°  11'  Easterly 

Because  on  referring  to  the  above  figure  on  the  right,  we  find  the  True  Azimuth  is  to  the  Right  of  the  Magneti* 
Azimuth. 


IfO 


NAbl'lLAl.  ASTRONOMY. 


EFFECT  OF  LOCAL  ATTRACTION  ON  THE  SHIP'S  COMPASS. 

This  is  a  very  important  matter  for  investigation,  and  should  be  attended  to  at  the  earliest  possilDle  oppor- 
^tunity,  because,  in  consequence  of  not  knowing  that  Local  Attraction  existed  on  board,  many  vesseli  have 
been  -wrecked  from  that  very  cause. 

There  being  large  quantities  of  Iron  now  used  in  the  construction  of  Ships,  besides  the  quantities  which 
ithey  carry  to  and  fro,  and  stowed  in  different  parts  of  the  vessel  as  cargo,  renders  every  Ship  liable  to 
nave  her  Compasses  deranged  by  Local  Attraction.  And  the  general  effect  which  Iron,  s^ituated  in  th»»  lor- 
ward  part  of  a  vessel,  has  on  the  Compass,  is  to  draw  the  North  end  of  the  Needle  forward  in  North  Lat» 
4tude,  and  the  South  end  of  the  Needle  forward  in  South  Latitude,  and  which  the  following  Diagram  will 
<^ow- 


DIAGRAM, 

%,owing  the  Effect  of  Local  Attraction. 

Fig.  21. 


fflten  the  Attracting  Force  is  Forward. 

In  the  above  figure,  the  dotted  line  will  show  the  course  intended  to  be  steered,  which  in  the  one  ca*e  u 
4!ast.  But  the  North  end  of  the  Needle  being  drawn  forward  from  the  effect  of  the  Local  Attraction, 
.{Caused  by  the  Iron  forward  acting  on  it),  the  Ship  is  actually  going  E.  by  S.  ;  and  in  the  other  case, 
•«teering  West,  the  North  end  of  the  Needle  being  drawn  forward  in  like  manner,  the  Ship  is  actually  going 
"W.  by  S. 

Now  suppose  the  Ship  to  steer  North,  the  North  end  of  the  Needle  will  point  in  the  direction  of  the  dis- 
turbing force,  and  which  being  then  on  the  same  line  as  the  Magnetic  Meridian,  no  Local  Attraction  will 
•be  perceptible. 

Hence,  when  tlie  Ship's  head  is  at  North  or  South,  little  or  no  deviation  will  be  found  in  the  Compass  :  but 
when  her  head  is  at  East  or  West,  or  nearly  so,  the  greatest  deviation  may  be  expected.  The  above  figure  it 
irawn  for  North  Latitude,  but  by  sub.«tituting  South  for  North,  it  will  answer  for  South  Latitude.  In  that 
case,  the  South  end  of  the  Needle  is  drawn  forward  from  the  effect  of  Local  Attraction,  and  in  steering 
East,  in  the  one  case,  the  Ship  would  actually  be  going  E.  by  N.  ;  and  in  the  other  case,  steering  West 
*he  Ship  would  actually  be  going  W.  by  N. 


When  the  Attracting  Force  ts  Abaft. 

We  havt  .iitherto  been  considering  the  case  where  the  Attracting  Force  is  situated  forward  in  the  \ew 
ii*i  it  someLimes  happens  that  it  is  situated  abaft  the  Steering  Compass,  as  in  the  case  of  some  Steamshipa, 
waere  the  Steering  Apparatus  is  placed  in  the  forward  part  of  the  vessel  ;  and  in  this  case,  on  referring  to 
4he  figur*  in  North  Latitude  steering  East,  the  North  end  of  the  Needle  is  drawn  aft.  when  the  Ship  would 
nctually  be  going  E.  by  N.  Acain,  in  steering  West,  the  North  end  of  the  Needle  being  drawn  aft,  the 
sShip  would  actually  be  going  W.  by  N. 

^n  South  Latitude,  and  supposing  the  disturbing  force  to  be  abaft  the  Compass, 
tJeedle  is  drawn  aft,  and  in  steering  East  the  Ship  would  be  going  E.  by  S.,  and 
<would  be  going  W.  by  S. 

Having  thus  shown  the  effect  of  Local  Attraction  on  board  Ship,  the  most  practical  remedy  derived  from 
experience  in  this  matter,  is  as  follows  : 


the  South  end  of  th« 
in  steering  West,  sh* 


TATAT.  ATTBACTtON.  i«l 


FINDING  THE  LOCAL  ATTRACTION  ON  BOARD  SHIPS  AT  SEA. 

Contrivances  to  Counteract  Local  Attraction  not  to  be  Depended  on. 

Many  contrivances  have  been  proposed  to  counteract  the  Local  Attraction  on  board  Ships  "where  it  k 
known  to  exist,  but  none  of  them  can  be  depended  upon  under  all  circumstances  •  especially  in  merchanl 
vessels,  where  it  is  liable  to  vary  at  different  times,  and  from  the  fact  that  the  Poles  of  the  Magnetic  Needle 
change  thai"  attracting  power  on  entering  the  Southern  Hemisphere. 

Mode  of  Detecting  Local  Attraction. 

The  simplest  mode  of  detecting  Local  Attraction  on  the  Ship's  Steering  Compass  at  Sea,  is  to  observe 
an  Amplitude,  that  is,  to  take  the  bearing  of  the  Sun  at  rising,  by  it,  as  directed  at  page  81,  and  find  the 
variation  of  the  compass  by  the  Rules  given  at  page  116,  at  the  time  the  Ship's  head  is  in  a  Northerly  or 
Southerly  direction  by  the  Compass.  Repeat  the  operation  at  Sunset,  at  the  time  the  Ship's  head  is  in  an 
Easterly  or  Westerly  direction.  Then,  if  the  variations  so  found  agree  within  one  degree  of  each  other 
allowing  for  a  probable  error  in  the  observations,)  it  may  be  concluded  that  there  is  no  Local  Attraction 
of  any  consequence  on  board. 

But  if  they  do  not  so  agree,  the  difference  will  be  the  amount  of  the  Local  Attraction  which  exisw  on 
board.  Always  providing  that  the  variation  found  when  the  Ship's  head  was  at  North  or  South,  agrees 
with  that  laid  down  on  the  newest  Charts. 

By  ascertaining  the  variation  from  bearings  taken  by  the  Steering  Compass  (or  one  situated  near  the 
Bmnacle)  with  the  Ship  s  head  in  any  given  direction,  we  have  the  whole  amount  of  the  deviation  of  the 
Compass  from  the  true  Meridian  due  to  the  course  on  which  the  vessel  is  then  steering.  This  includes 
both  Variation  and  Local  Attraction,  and  is  the  proper  quantity  to  be  allowed  in  correcting  the  course  steereo 
to  a  True  Course.  And  when  the  course  has  been  changed,  the  variation  should  again  be  found  in  like 
manner,  ajnd  applied  in  the  room  of  that  taken  from  the  Charts. 

Local  Attraction  may  also  be  detected  by  the  bearing  of  objects  on  the  Land,  when,  after  allowing  th» 
variation  proper  to  the  place,  they  do  not  agree  with  the  True  Bearings.  The  Steering  Compass  will  also 
show  Local  Attraction  when  the  Ship  appears  to  sail  within  5  points  of  the  wind  on  the  one  tack,  and  7 
points  from  the  wind  on  the  other. 

Tlie  Binnacle. 

One  Steering  Compass  only  should  be  used,  because  when  there  are  two  near  each  other,  the  one  attraci* 
the  other,  and  the  Binnacle  should  be  constructed  so  as  to  prevent  improper  substances  (such  as  iroh)  being 
placed  therein. 

On  Fixing  the  Standard  Compass  as  a  Remedy 

When  Local  Attraction  is  decidedly  known  to  exist  on  board,  the  only  proper  remedy  is  to  fix  up  a 
Standard  Compass  on  some  part  of  the  vessel's  deck,  which  shall  be  free  from  all  Local  Attraction.  This 
can  only  be  ascertained  from  actual  trial.,  and  in  some  Ships  the  Standard  Clompass  requires  to  be  raised  5 
or  6  feet,  more  or  less,  above  the  deck.  In  general,  the  most  convenient  place  for  fixing  it.  is  on  the  Centre 
Line  of  the  Quarter  Deck,  where  the  true  direction  of  the  Sliip's  head,  or  the  bearing  of  the  land,  ca.i  at 
any  time  be  easily  ascertained.  Observations  of  Amplitudes  or  Azimuths  should  also  be  made  with  this 
Compass,  if  it  be  provided  with  proper  sight-vanes,  otherwise  with  the  Azimuth  Compass  on  its  site. 

The  Course  mu.^t  be  shaped  by  the  Standard  Compass,  and  when  the  Ship's  head  is  exactly  in  the  proper 
direction  by  the  Standard  Compass,  note  the  direction  of  her  head  by  the  Steering  one,  and  which  will  be 
the  approximate  Course  required  to  steer  by  that  Compass,  in  order  to  allow  for  the  effect  of  the  Local 
Attraction,  and  the  difference  between  the  two  Compasses  is  the  amount  of  the  Local  Attraction  on  board, 
(so  long  as  the  Ship's  head  continues  in  the  same  direction,)  but  on  ch3.nging  the  Course  this  difference 
between  the  two  Compasses  will  be  found  to  vary  according  as  her  head  approaches  to  or  recedes  from  the 
Magnetic  Meridian.  When  the  Ship's  head  is  at  North  or  South  they  will  be  found  to  agree  nearly, 
because  the  disturbing  force  is  on  the  same  line  as  the  Magnetic  Meridian,  and  the  greatest  difference  will 
be  found  when  her  head  is  at  East  or  West,  as  previously  explained.  Consequently,  when  it  is  required 
to  change  the  Ship's  cour.se.  she  is  brought  to  her  proper  course  by  the  Standard  Compass,  and  the  direciion 
of  her  head  then  shown  by  the  Steering  one  is  the  approximate  course  required  to  steer.  The  correctnes-s 
of  the  Standard  Compass  may  be  further  verified  by  taking  Amplitudes,  &c.,  with  the  Ship's  head  on  all 
the  noints  of  t^re  Compass  ;  then,  if  the  variation  so  found  agree  with  that  assigned  to  the  place  of  obser- 
▼alio.-.,  and  with  each  other,  the  Compass  is  correct.  All  bearings  should  be  taken  with  this  Compass, 
»rd  the  courses  made  good  by  this  Compass,  when  the  Ship  is  close-hauled,  must  be  entered  on  the  Log 
*^ard,  in  the  room  of  those  by  the  Steering  one. 


122  NAUTICAL  ASihO:>OM\, 


FINDING  THE  TIME  AT  SEA 

It  will  be  necessary  here  again  to  premise  that  there  are  three  different  modes  of  reckcning  Time,  vitli 
respect  to  the  commencement  of  the  day,  viz.,  Civil,  Astronomical,  and  Nautical. 

The  Civil  Day, 

Which  is  that  used  by  the  generality  of  mankind,  begins  at  Midnight  and  ends  at  the  Midnight  following. 
It  is  divided  into  two  equal  parts  of  twelve  hours  each.  The  first  is  marked  A.  M  ,  signifying  before  Noon, 
and  the  latter  P.  M.,  or  afternoon. 

The  Astronomical  Day 

Begins  12  hours  after  the  Civil  Day,  that  is,  at  Noon,  or  when  the  Sun's  centre  is  on  the  Meridian,  and 
ends  at  the  following  Noon ;  and  it  is  reckoned  through  the  24  hours,  from  Noon  to  Noon ;  and  what  are 
called  the  morning  hours  of  the  common  day  are  by  Astronomers  reckoned  in  succession  from  12,  or  mid- 
night, to  24  hours.  So  that  8  o'clock  on  the  morning  of  June  5th,  CivU  Time,  is  by  Astronomers  called 
June  4th,  at  20  hours. 

The  Nautical,  or  Sea  Day, 

Commences  at  Noon,  or  12  hours  before  the  Civil  Day,  and  24  hours  before  the  Astronomical  day,  and 
ends  at  the  Noon  of  the  Civil  Day,  and  at  the  beginning  of  the  Astronomical  Day.  It  fe  divided  into  two 
parts  of  12  hours  each;  the  former  being  marked  P.  M.  and  the  latter  A.  M.,  so  that  occurrences  whicii 
hippened,  for  instance,  on  Sunday,  the  10th,  afternoon.  Civil  Time,  are  entered  in  the  Log  as  Monday,  the 

nth,  p.  M. 

Hence  it  appears  that  the  Noon  of  the  Civil  Day,  the  Beginning  of  the  Astronomical  Day,  and  the  End 
of  the  Nautical  Day  take  place  at  the  same  period  of  time. 
Time,  as  inferred  from  observations  of  the  Sun,  is  denominated  Apparent  and  Mean  Solar  Time. 

Apparent  Time, 

Is  that  which  is  immediately  derived  from  the  Sun,  either  from  the  middle  of  the  times  of  his  Equu* 
Altitudes,  that  is  at  Apparent  Noon,  or  by  observing  his  Altitude  at  a  proper  distance  from  the  Meridian 

Mean,  or  Uniform  Time, 

Is  thai  shown  by  Clocks,  or  Watches,  which  keep  a  constant,  uniform  time  throughout  the  year. 

The  reason  of  these  two  different  modes  of  dividing  Time  is  explained  in  Figure  4,  page  62,  and  i» 
jaused  by  the  unequal  motion  of  the  Earth  in  her  orbit,  combined  with  the  inclination  of  its  axis  to  the 
plane  of  the  Ecliptic. 

The  difference  between  Apparent  and  Mean  Time  is  called  the  Equation  of  Time,  and  amounts  to  over 
16  minutes  sometimes.  It  is  computed  for  the  Noon  at  Greenwich,  and  set  down  on  page  Ist  of  the 
Nautical  Almanac,  against  the  day  of  the  month,  throughout  the  year,  and  the  precept  at  the  head  of  the- 
joluran  shows  whether  it  must  be  added  to  or  subtracted  from  Apparent  Time,  to  obtain  Mean  Time. 

The  Greenwich  Date, 

Or  the  Mean  Time  at  Greenwich,  is  referred  to,  because  it  is  for  the  Time  at  this  Meridian  that  the 
•lements  of  Astronomical  calculations  (which  are  in  perpetual  change)  are  given  in  the  Nautical  Almanac. 

The  Greenwich  Date  is  therefore  always  expressed  in  Mean  Time,  (unless  the  contrary  i?  notified.)  and 
it  may  be  defined  as  being  the  time  at  Greenwich,  corresponding  to  any  given  time  elsewhere,  and  in  lakiiig 
observations  at  Sea,  the  Noon  at  Greenwich  is  referred  to,  in  order  to  find  on  which  side  of  Greenwu-h  Noon 
the  observation  has  been  made 

Note. — In  observing  Altitudes  for  time,  the  observation  should  be  made  when  the  body  is  on  or  near  the  Prime  Vc. 
tioal,  that  is,  when  it  bears  true  East  or  West ;  because  then,  errors  in  both  the  Latitude   of  the  observer  and  of  the- 
Altitude  observed,  produce  the  least  effect  on  the  Hour  Angle. 

In  geiieral,  the  change  of  Altitude  should  not  be  less  than  6  minutes  to  1  minute  of  time.  An  error  of  1  minute  m 
the  Altitude  would  then  produce  an  error  of  about  10  seconds  in  time.  In  High  Latitudes,  an  error  in  the  Latitude 
produces  a  great  effect  on  the  Hour  Angle. 

On  the  other  hand,  in  the  Tropics  the  time  can  be  more  correctly  determined  when  the  body  is  at  less  than  an  hoar 
from  the  Meridian  than  when  at  several  hours  from  it  in  His'h  Latitudes. 


FINDING  THE  TIME  BY  THE  SUN. 


VZ6 


FINDING  THE  APPARENT  TIME  FROM  AN  ALTITUDE  OF  THE  SUN. 
This  \B  one  of  the  most  important  problems  in  Nautical  Astronomy,  and   for  the  solution  of  which  we 
require  to  have  the  Altitude  and  Polar  Distance  of  the  body,  and  the  Latitude  of  the  place  of  observation, 
being  three  sides  of  an  Oblique- Angled  Spherical  Triangle  given,  to  find  the  Hour  Angle  at  the  Pole,  and 
which  is  measured  on  the  Celestial  Equator,  between  the  Meridian  and  the  Time  Circles. 

DiAORAM  of  Qn  Hour  Angle.     Latitude  and  Declination  of  the  Same  Name, 

Fir..   22. 


Diagram  of  an  Hour  Angle.     Latitude  and  Declination  of  Contrary  Names. 

Fui.  23. 


In  Figure  22,  the  Sun  is  on  the  Prime  Vertical,  the  Latitude  and  Declination  being  of  the  same  name  the 
Declination  subtracted  from  90°,  gives  the  Polar  Distance.  ' 

In  Figure  23,  the  Latitude  and  Declination  being  of  contrary  names,  the  Declination  added  to  90*.  gives 
the  Polar  Distance.  ' 

RULES  FOR  USING  THE  TABLES. 

Ist  Add  together  the  Sun's  True  Altitude,  the  Polar  Distance,  and  the  Latitude  of  the  place  of  Observation  find 
the  Half  Sum,  and  the  Difference  between  the  Half  Sum  and  the  Sun's  True  Altitude.  ' 

2d.  To  Uie  Loe;8.  of  the  Polar  Distance,  and  Latitude  found  in  Table  XXVIL  add  the  Logs,  of  tie  Half  Sum  and 
Difference  found  in  Table  XXVIIL  and  the  Su7n  of  these  four  Logs.,  found  in  Table  XXIX,  will  give  the  Sun'i 
Hour  Angle,  at  the  Top  of  the  Page,  and  which  is  also  the  Apparent  Time  from  Noon,  when  the  Altitude  is  observed 
in  the  Afternoon.  But  when  the  Altitude  is  observed  in  the  Forenoon,  the  Apparent  Time  from  the  preeedine  Nooa 
or  Midnight,  is  found  at  the  Bottom  of  the  page.  5         ". 


EXAMPLE  1. 
Figure  22.     Given  the  Sun's  True  Altitude,  37°,  Polar 
Distance,  66'  33',  and   Latitude  40°  43'  N.      Required 
the  Hour  Ane:le. 

Sun's  True  Altitude 37°    0' 

Polar  Distance 66    33 Log.  0.08744 

Latitude  in ^0   43 Log.  0.12036 

Sum 144M6' 

Half  Sum ~^2' 


Sun's  True  Altitude 37 

Difference 35 

Eoiir  Angle 


4.48686 


8'.... Log. 
0 


8' Log.  4.76003 


4h.  2m.  48.  .  . .  Log.  9.40469 


EXAMPLE  2. 
Figure  23.     Given  the  Sun's  True  Altitude,  13*  20 
the   Polar  Distance,  113°  27',  and  Latitude  40°  North 
Required  the  Hour  Angle. 

Sun's  True  Altitude 13°  26' 

Polar  Distance 113    27  . 

Latitude  in 40    00  . 

Sum 166°  63' 

Half  Sum 83°  27'. 

Sun's  True  Altitude 13    26 

Difference » 70°  ~T'., 

Hour  Angle  8h.  3m.558.' 


. .  .Log.  0.03744 
...Log.  0.1167 

..Log.  4.067 It 

..Log.  4.9780» 
.     —  9.18839 


124 


NAUTICAL  ASTRONOMY. 


FINDING  THE  TIME  AT  SEA  BY  THE  SUN. 


Methoa  of  Observing  Altitudes  for  Time. 

Hold  the  instrument  with  the  right  hand  and  the  watch  in  the  left ;  bring  the  Sun's  Lower  Limb  in^ 
eontact  with  the  Horizon,  and  clamp  the  Index,  and  at  the  instant  the  Second-hand  of  the  watch  has  com- 
pleted the  full  minute,  bring  the  Sun's  limb  in  contact  by  using  the  Tangent  screw  ;  note  the  Time  by  the 
watch  and  read  off  the  Altitude,  and  write  them  down.  When  the  Second-hand  of  the  watch  has  again 
completed  the  full  minute,  take  the  Altitude,  &c.,  as  before,  and  write  them  down.  This  may  be  repeated 
three  or  five  times.  In  general,  three  Altitudes,  and  their  corresponding  times,  is  sufficient.  If  tha 
difference  between  the  Altitudes,  or  the  Sun's  change  of  Altitude  in  one  minute  of  time,  correspond  with 
each  other,  it  is  a  guarantee  that  the  Altitudes  have  been  correctly  observed ;  but  if  they  do  not  so  agree, 
add  them  together,  and  divide  by  the  number  taken,  will  give  the  mean  of  the  Altitudes  corresponding  to 
the   middle  of  the  times  they  were  taken,  which  may  be  taken  as  the  correct  observed  Altitude 


EXAMPLE. 

A.  M.,  2l8t  June,  in  Latitude  40°  North. 

Alt  L.  Limb 37°  13'    0"  Time  by  Watch,  3h.  58m, 

25    30  3     59 

38      0  •  _4 0 

Obs.  Altitude. . .  37°  26'  30"    Time 3h.  59m. 

7%t»  Altitude  has  been  correctly  taken. 


EXAMPLE. 

P.  M.,  December  2l8t,  in  Latitude  40°  North. 

Altof  L.  Limb 13°  26'         Time  by  Watch,  3h.  3m 

19                                             4 
10  5 

Number  taken . . . 


3)55 


3)12 


Obs.  Altitude 13°  18' 20"  Time Rh.    4m 

TTie  above  Altitudes  have  not  been  correctly  taken 


To  Find  the  Apparent  Time,  and  thence  the  Mean  Time,  at  Skip. 

RULK 

To  Correct  the  Altitude. 

1    Add  the  Correction,  taken  from  Table  IX,  to  the  Sun's  Observed  Altitude,  will  give  nis  True  Central  Altitud 

To  Find  the  Greenwich  Date 

2.  Turn  the  Ship's  Longitude  into  Time,  by  Table  XXVI,  and  Add  it  to  the  Time  of  the  Observation  by  Watch  a 
Weet  Longitude,  or  Subtract  it  in  East  will  give  the  approximate  Greenwich  Time,  which,  if  before  Noon,  Subtract 
a  frum  12h.  will  give  the  Time  from  Greenwich  Noon,  A.  M.,  otherwise  it  is  the  Time  from  Noon,  P.  M. 

To  Correct  the  Declination. 

8  Take  out  the  Sun's  Declination  from  the  Nautical  Almanac,  against  the  Day  of  the  Month,  and  the  Differens;* 
or  Change  of  the  Declination  in  one  hour,  found  in  the  adjoining  column.  Multiply  this  Difference  for  1  hour  by  th« 
Time  from  Greenwich  Noon,  and  divide  by  60,  will  eive  the  Correction  in  Minutes  and  Seconds. 

To  Correct  the  Equation  of  Time. 

4  Take  out  the  Equation  of  Time  from  the  Nautical  Almanac  in  hke  manner,  and  the  Difference,  or  Change  o^ 
Equation  in  one  hour,  (which  is  given  in  Decimal  parts  of  a  Thousand,)  found  in  the  adjoining  column.  Multiply 
tins  Difference  for  1  hour  by  the  Time  from  Greenwich  Noon,  and  strike  off  the  Right  hand  figure,  prefix  a  DecimiJ 
poiiii  to  the  Left  of  the  next  two  figures,  which  are  now  hundredth  parts  of  a  second,  and  the  figure  to  the  Left-hand 
IS  Sfionds  of  Time,  and  is  the  required  correction. 

For  Applying  the  Corrections  for  Declination  and  Equation.  ^ 

ft    Inspect  the  oolumns  in  the  Nautical  Almanac,  and  ascertain  whether  they  are  Increasing  or  Decreasing. 

Greenwich  Time.     Before  Noon.     Declination  or  Equation ■>  r)p„,.ea8ino-  Add       ' 

Greenwich  Time.     After  Noon.       Dechnation  or  Equation j  De^.^n^g,  Subtract, 

to  or  from  the  Declination,  or  the  Equation  of  Time,  taken  from   the  page  in  the  Nautical  Almanac,  will  give  them 
0«.rr<»cted  to  the  Greenwich  Time  of  the  Observation. 

To  Find  the  Sun's  Po.ar  Disiance. 


A    Subtract  the  Declination  from  90°,  when  tlie  Latitude  and  Deoliuatioi'  are  of  the  same  name,  or  Add  the  Deeh 

ixioo  t«^  90"  when  they  are  of  contrary  names 


FINDING  THE  TIME  AT  SEA  BY  THE  SUN.  135 


FINDING  THE  APPARENT  TIME,  AND  THENCE  THE  MEAN  TIME,  AT  SHIP. 


To  Correct  the  Latitude  to  the  Time  of  the  Observation. 

1.  Th«  usual  mode  of  doing  this  at  Sea,  ia  to  find  the  DiffereDce  of  Latitude  the  Ship  has  made  in  the  iaterval  be 
Iweea  the  time  the  Sights  were  taken  and  Noon,  (the  correct  Latitude  having  been  obtained  from  the  Sun's  Meridiai 
Altitude),  and  applying  it  to  the  Latitude  Observed,  according  to  the  course  the  vessel  has  been  Bteering,  rii  ^ 

o-  Li   t  u     x.  e      vr        •    -nt  _ii.  t   t-t.  j    (  Sailing  North,  Subtract  Difference  of  Latitude. 
Sights  taken  before  Noon,  in  North  Latitude  j  ^^^^^  ^^^^^  ^^^  Difference  of  Latitude. 

Q-  1  i    *  u        fl.      xr        •     XT    ii.  T   f4_  J    I  Sailing  North,  Add  Difference  of  Latitude. 
Sights  taken  after  Noon,  in  North  Latitude  j  g^jj^^  ^^^^^^^  g^^^^^^^  Difference  of  Latitude. 

Which  will  give  the  correct  Latitude  of  the  Ship  at  the  time  of  the  Sights.    To  apply  this  Rule  in  South  Latitude, 
we  subetitute  South  for  North. 

Thus  having  the  Sun's  True  Altitude,  Polar  Distance,  and  the  Correct  Latitude  of  the  place  of  Observation,  find 
the  Apparent  Time  by  the  Rule  for  using  the  Tables  already  given  at  page  128. 

To  the  Apparent  Time  apply  the  Equation  of  Time  as  directed  in  the  precept  at  the  head  of  the  column  headed 
Equation  of  Time,  in  the  Nautical  Almanac,  by  Adding  or  Subtracting  it,  and  the  result  is  the  Mean  Time  at  the 
Ship. 


EXAMPLE  L 

4.pnl  JJOth,  1864,  (Noon  at  Sea),  in  Longitude  by  Dead  Reckoning  25°  0'  W.,  the  Observed  Altitude  of  the  Suns 
1  ^er  Limb  was  22°  7'.  Time  by  Watch,  7h  6m  in  the  Morning.  Ship  then  sailed  on  a  true  N.  E.  by  E.  Course, 
%'  x\ixtB,  until  Noon,  when  the  Latitude  observed  was  86°  82'  N.  Required  the  error  of  the  Watch  on  both  Appa- 
IV  4i  and  Mean  Time. 

Obs.  Alt. . .  22°    V  T.  by  Watch.    7h    6m  Decl.  80th  April. .  14*  46'  81"  N.  Diffi  for  Ih 46  " 

Oorr,  Tab.  )         j^  Lon.  25°  W.  )    ^    ^^      Corr Snb.         2  29         G.  T.  fi-om  Noon_8}h 

I^ ) in  Time..  )  Correct  DeoL 14°  43'    2"  IsF" 

True  Alt. .  22°  17'  Greenwich.)    _,    .  90     0     0  11 

Polar  Dist.  75    17    Log.  0.01449   Time,  A.  M.  ^    "''  ^'"^  Pdar  Distance. . .  .76°  16'  68" 
Latitude....  36    18    Log.  0.09824   Subtfrom..   12      0 


60)149 


Sum 188°  47'  G.  T.  from    ,    „.   ,^ 

8h  14m 


Corr.  2'  89, 


sm    ) 

Half  Sum..   66°  6"7"  Log.  4.59366  Noon. ...  J    **"  ^'*'"  Equa.  of  Time 2m  58s-68      Diff.  for  Ih -828 

Difference...  44°  37'  Log.  4.84656  Corr. Sub.  1  "06      G.  T  from  Noon..      Zjh 

App.  T..  .7h"8mT9rLog.^9^64795  Correct  Equation..  ..2m  62862                                   -984 

Equa.  of  I       o     53  Course  N.  E.  by  E.  35  miles  =  D.  Lat.  0°  19'                                                 82 

Time..  $■ Latitude  observed  at  Noon 86    82  N.           Corr. 1'06'6 

Mean  T.  )  „,   .     ~  Latitude  in  at  Time  of  Sights 86°  18'  N. 

at  Ship,  i-  ^^  ^"^  268 
T.  bv... 
Watch.  ^^ 


\ 


Watch On.  bis  fast  of  Mean  Time. 

And  Watch .  2m  1 9s  slow  of  Apparent  Time. 

Note.— When  the  Sights  are  taken  in  the  Morninor,  we  look  for  the  sum  of  the  4  Logarithms  in  Table  XXIX,  and 
take  the  time  from  the  bottom  of  the  pacje,  and  if  the  figures  are  found  exactly,  the  Hours  are  found  at  the  bottom,  th« 
Minutes  at  the  right  side  opposite  the  Logarithm,  and  the  Seconds  in  the  &ame  column  at  the  bottom  of  the  Table. 
But  if  the  Sum  of  tlie  4  Logarithms  cannot  be  found  exactly,  take  the  nearest  Usi  Logarithm,  and  find  the  differene* 
between  it  and  the  given  Logarithm,  with  which  enter  the  adjoining  proportional  columns,  and  take  out  the  correspond- 
ing Seconds  of  Time,  which  must  be  subtracted  from  the  Seconds  found  at  the  bottom  of  the  cohimu  fron.  wnenoe  tlie 
Dearest  leas  Logarithm  was  taken,  which  will  be  the  Apparent  Time  from  the  preceding  Noon  or  Midnight. 

When  the  Sights  are  taken  in  the  Afternoon,  the  time  is  taken  from  the  top  of  the  Table.  And  in  like  manner,  we 
mnst  look  for  the  nearest  ^.«s  Logarithm,  ami  find  the  difference  between  it  and  the  given  one,  and  the  proportional 
parts  for  Seconds,  found  in  the  adjoining  coluniu,  must  be  added  to  the  Seconds  found  at  the  top  of  the  column,  from 
whence  the  nearest  less  JjOgarithm  was  taken. 

All  Hour  Angleo  are  taken  from  the  top  of  the  page,  and  which  is  also  the  Apparent  Time  past  Noon  by  th« 
Son. 


126 


NAUTICAL  ASTRONOMY. 


FINDING  THE  TIME  AT  SEA  BY  THE  SUN. 


EXAMPLE  2. 


April  80th,  1864,  (Noon  at  Sea),  in  Latitude  by  Observation  36"  32'  N.,  Longitude  24*  26'  W.,the  Sun's  Obeeriid 
Ititude  was  13°  48'.     Time  by  Watch,  5h  SOm   in  the  afternoon,  and   the  Ship  had  sailed  since  Noon  on  a  trn* 
El  N.  K  course,  distance  29  miles.     Required  the  Error  of  the  Watch  on  both  Apparent  and  Mean  Time. 


Obs.  Altitude 13°  48' 

Corr,  Table  IX...  8 


True  Altitude 13°  56' 

Polar  Distance 75      9 

Latitude 36    43 


Time  by  Watch  P.  M.  . 
Lon.  24°  26'  W.  in  time 

Greenh.  Time  P.  M 

Log.  0.01475 
Log.  0.09604 


Sh  SOm    Os  Decl.  April  30th.   14°  45'  31"  N.  Diff.  for  Ih     46" 
1    37     448  Decl.  Increasing,  Add     5  22  7h 

7h    7m  448  Correct  Decl 14°  50'  53"  N.  60)322 


Polar  Distance. 


14' 
90 

75= 


50'  53" 
0     0 

9'    7" 


Corr., 


.5' 22" 


12_5M_8^ 

Half  Sum 62"^T'Log.  4.65863 

Difference 48°  58'  Log.  4.87756 

App.  Time. .  .6h  34m    Ss  Log.  9.64688 
Equa Sub.        2     66 


Equation  of  Time  April  30th  2m  539  68 
Equation  Increasing Add  2  29 

Correct  Equation 2m  568'27 

Course  E.  N.  E.  29  miles  =■  D.  Latitude 


Diff.  for  lb     -328 

7h 

Corr 2-2»6 

0°  11' 


Latitude  observed  at  Noon 36    32  N. 


Latitude  in  at  time  of  Sights. 86° 


Mean  Time. .  .5h  31m   78 

T.  by  Watch... 6    SO      0 

Watch Im    7a  slow  of  Mean  Time,  and  4m  38  slow  of  Apparent  Time 


43' N. 


EXAMPLE  3. 


March  26th,  1864,  (Noon  at  Sea),  in  Latitude  by  observation  12°  21'  S.,  Longitude  65°  30'  E.,  the  Sun's  Observed 
Altitude  was  26°  26'.  Time  by  Watch  7h  47m  in  the  forenoon.  Ship  had  sailed  on  a  N.  W.  Course,  true,  17  miles, 
since  the  Sights  were  taken,  until  Noon.     Required  the  Error  of  the  Watch  on  both  Apparent  and  Mean  Time. 


25° 


25' 
10 


Obs.  Altitude. . 

Corr.,  Table  IX 

True  Altitude....  26°  35' 
Polar  Distance.. .  92  3 
Latitude 12    33 


130°  11' 
65°  6' 
39°  81' 


Log. 
Log. 

Log. 
Log. 


4    22 


Decl.  26th  Mar.  2 
Corr. Sub_ 

Correct  Decl 


Time  by...    .  Kv., 

Watch  A.  M.  f  ^^  *^°^ 
Lon  65°  3.0'  E.  ( 

0.00028      ■"  *'™® )  

0.01050  G.  Time  A.M.   3h25m  Polar  Distance  92^ 
Sub.  from.   ...12       0 

T.  fm  G.  Noon 


11'  40' 
8   21 


N. 


Diff.  for  Ih. 
Timo  fm  N. 


59  " 


2° 
90 


3'  19" 
0      0 


3'  19" 


4.62432 
4.80366 


8h  35m 


Equation 5m  60s-02  Diff.  for  Ih 

Corr Add  6-52 


472  '• 
29 

60)501" 

Corr.  for  Decl.  8'  21" 

•768 
8ib 


App.  Time....  7h  47m    98  Log. 
Equa Add  6      67 

Mean  Time.. .  7h  68m    68 
T.by  Watch..  7    47       0 

Watch 


9.43876  Correct  Equa..5m  568-64 

Course  N.  W.  17  miles,  D.  Lat    0°  12' 
Latitude  by  Obs.  at  Noon 12    21    S. 

Lat  in  at  time  of  Sights 12°  33"'  S. 

6m    68  slow  of  Mean  Time,  and  Om  9s  slow  of  Apparent  Time, 


•6144 

•384 

Corr.  for  Equa.  6-52-8 


QUESTIONS  FOR  EXERCISR 

Quest.  1st. — May  12th,  1854,  (Noon  at  Sea),  in  Latitude  Observed  at  Noon  47°  60'  N.,  Longitude  by  Dead  Reckon- 
mg  60°  30'  W.  In  the  morning  the  Sun's  Observed  Altitude  was  34°  5'.  Time  by  Watch  8h  6m  A.  M.  The  Ship 
bad  made  4'  of  Diff.  Latitude  to  the  Southward  since  the  Sights  were  takea     Required  tb**  Error  of  the  Watch. 

Answer. — The  Apparent  Time  is  8h  5m  398,  and  Watch  fast  Om  2l8.  Mean  Time  8h  Im  478,  and  Watch  fast 
4m  18s. 

Quest.  2d. — On  the  same  day  as  above,  in  Latitude  47°  50'  N.,  Longitude  50°  80'  W.,  in  the  Afternoon  the  Sun's 
Observed  Altitude  was  10°  14'.  Time  by  Watch  6h  17m'  P.  M.  The  Ship  had  sailed  on  a  true  W.  by  S.  ^  & 
Course,  52  miles  since  Noon.     Required  the  Erroi   if  the  Watch  as  before. 

Answer. — The  Apparent  Time  is  6h  18m  168.  Watch  slow  Im  168.  Mean  Time,  6h  14m  288.  Watoh  fast 
tm  37  s. 

Quest.  Sd — June  1st,  1854,  (Noon  at  Sea),  in  Latitude  39°  25'  S.  by  Observation,  and  Longitude  90°E.,  at  Noon.  In 
tbe  Morning  the  Observed  Altitude  of  the  Sun  was  12°  15'.  Time  by  Watch  8h  35m  A.  M.  The  Ship  h;id  soiled 
•n  a  true  S.  E.  Course,  28  miles,  until  Noon.     Required  the  Error  of  the  Watch. 

4»i«M«r.— The  Apparent  Time  is  8h  84m  56s.  Watch  fast  Om  48.  Mean  Time  8h  82m  208.  Watch  faal 
2m  408. 

NoTB.— In  the  foregoing  E.xamples,  and  also  those  which  follow,  the  height  of  the  eye  is  supposed  to  be  18  feet  above 

the  Sea  level.  .        -   ,      .  ■    ,   r^ 

Noon  at  Sea  means  the  end  of  the  Sea  Day,  and  which  also  corresponds  to  Ine  beginnmg  of  the  Astronomical  U»T 
uid  to  the  Noon  of  the  Civil  Day. 


FINDING  THE  APPARENT  TIME  AT  SEA  BY  THE  SUN. 


12? 


FINDING  THE  APPARENT  TIME  AT  SEA  BY  THE  SUN,  W«EN  THE  SHIP  IS  ON  THF 

EQUATOR. 

When  the  Ship  is  on  the  Equator,  and  the  Sun  is  also  on  the  Equator,  that  is,  when  his  Declination  v 
9,  the  Poles  of  the  Heavens  are  in  the  Horizon  and  the  upper  end  of  the  Celestial  Equator  is  then  in  th« 
l^nith.  and  the  Sun  rises  and  sets  vertically. 

DIAGRAM 

Of  the  Hour  Angles  on  the  Equator. 

Fig.  24. 


In  this  case,  the  Son's  change  of  Altitude  is  15'  in  one  minute  of  Time,  or  15'  in  one  hour,  ttxronghoat 
the  entire  day.  The  time  can,  therefore,  be  as  correctly  found  near  the  Meridian,  that  is,  near  Noon,  as  it 
can  at  any  other  time  of  the  day,  and  an  error  in  the  Latitude,  in  working  out  the  time,  does  not  affect  the 
result. 

It  will  be  perceived  by  this  figure,  that  when  a  Ship  sails  to  the  Southward,  after  leaving  the  Equator, 
she  raises  the  South  Pole  of  the  Heavens,  and  that  in  sailing  North  from  the  Equator,  she  raises  the  North 
Pole,  and  that  the  Polar  Distance  and  Hour  Angles  are  always  measured  from  the  elevated  Pole.  But  in 
this  case,  both  Poles  being  in  the  Horizon,  and  the  Sun  on  the  Equator,  his  Polar  Distance  90',  and  the 
Hour  Angles,  (measured  on  the  Equator),  are  the  same  at  both  Poles. 

If  we  therefore  observe  the  Sun's  Altitude  at  any  period  of  the  day,  under  the  above  circumstances, 
and  after  correcting  it  in  the  usual  manner,  to  obtain  the  True  Central  Altitude,  and  then  subtract  it  from 
90°,  we  have  the  Sun's  Hour  Angle  at  once,  in  space,  which,  turned  into  degrees  and  minutes  by  Table 
XXVI,  will  give  the  Apparent  Time  at  the  Ship  in  the  afternoon,  and  subtracting  it  from  12h,  will  give  the 
Apparent  Time  in  the  forenoon. 


EXAMPLE  1. 

Jjstitude  and  Declination  0 ;  the  Sun's  Observed  Alti- 
tude in  the  forenoon  was  74'  48'.  Required  the  Appa- 
rent Time  at  the  Ship. 

Obs.  Altitude  L.  Limb 74°  48' 

Corr,  Table  IX, \2^ 

Sun's  True  Altitude 75'    O' 

90      0 

Hour  Angle  in  space 15°    0'  =  Ih,  or  llh  A.  M. 

This  may  be  verified  by  the  Time  Tables,  as  follows 

True  Altitude 75'  0' 

Polar  Distance 90  0      Log.  0.00000 

Latitude 0  0      Log.  0.00000 

Sum 166°  0' 

Half  Sum 82°  80'     Log.  4.11570 

Altitude 75      0 

Difference Y°~30'     Log.  4.11570 

Apparent  Time llh  Om  Os     Lot?.  8J3140 


EXAMPLE  2. 

Latitude  and  Declination  0  ;  the  Sun's  Observed  Alti- 
tude was  29°  50'  in  the  afternoon.  Required  the  Appa* 
'rent  Time  at  Ship. 

Obs.  Altitude  L.  Limb 29'  60' 

Corr.,  Table  IX, 10 

Sun's  True  Altitude 30°    0' 

90      0 
Hour  Angle  in  Space 60°    0    =  4h  Om  P  M 

True  Altitude 80*  C 

Polar  Distance 90    0      Log.  0.00000 

Latitude 0    0      Log.  0.00000 

120^' 

Half  Sum 60'  0'     Log.  4.69897 

Altitude 30    0 

Difference 30°  0'     Log.  4.69897 

Apparent  Time     4h  Om  Os     Log.  9.397^ 


128  NAUTICAL  ASTRONOMY. 

FINDING  THE  APPARENT  TIME  WHEN  THE  SUN  IS  RISING  OR  SETTING.      . 

This  method  is  upon  the  same  principle  as  that  of  measuring  the  Hour  Angle  from  the  Elevated  Pole, 
but  in  the  room  of  observing  his  Altitude  above  the  Horizon  with  a  Quadrant,  we  observe  with  a  Spy- 
Glass  the  contact  of  either  of  his  Limbs  with  the  Horizon  at  Rising  or  Setting,  and  note  the  time  bv  thf 
watoh 

RULE 

When  the  Lower  Limb  ts  Observed. 

Take  the  Difference  between  the  Sun's  Semi-diameter,  N.  A.,  and  the  Mean  Horizontal  Refraction,  84'  17",  to 
vhich  add  the  Dip  of  the  Horizon,  found  in  Table  V.     Call  this  the  Correetion. 

Correct  the  Declination,  and  fiuc'.  tbi  Polar  Distance,  as  usual  Also  correct  the  Latitude  to  the  place  of  Obser 
ration  by  the  rules  already  given. 

Add  together  the  Latitude  and  ^o^B.r-  Distance,  from  which  tubtract  the  above  Correction.  Take  half  this  Sum, 
Jd  which  add  the  same  co''r«>ct'OR  -*n<i  call  it  the  Differenca  The  Appaient  Time  is  then  found  by  the  usual  RuU 
ji  working  th«  time  by  'jx  Ti)- ■/.«*• 


DIAGRAM 

If  the  Sun's  Hour  Angle  at  Rising 
Fig    25. 


Setting. 


This  figure  represents  the  elements  for  computing  the  Hour  Angle  m  the  usual  maimer,  being  the  thret 
B-ies  of  an  Oblique  Angled  Spherical  Triangle,  viz :  the  Co-Latitude  51°  18',  the  Polar  Distaace  108*  51', 
and  the  Co- Altitude  90",  to  find  the  Hour  Angle  at  the  Pole,  and  which,  measured  on  the  Equator,  is  74* 


i1'  30  ',  or,  in  time,  4h  58m  31s. 


EXAMPLE  1. 

Jan.  25th,  1854,  (Noon  at  Sea),  the  Latitude  Observed  was  38°  O'  N.,  and  Longitude  104°  W.,  at  Noon.  Ship  then 
•ailed  N.  E.  60  miles,  when  the  Sun's  Lower  Limb  was  observed  to  set  at  6h  3m  258  by  the  Watch.  Required  it* 
error  on  Apparent  uiid  Mean  Time. 


Time  by  Watch. . . . 
Lou.  104°  W  in  time. 


5h    3m  25s  Sun's  Decl.  N.  A .  1 8' 
6    66        0     Corr Sub. 


57'  58" 
7  24 


Uor.  Ref  34'  17",  |  „,,     ., 
less  Par  9"...  P'*      " 
Suns  Semid.  N.  A...16    16     Greenwich  Time.  . . .  1  Ih  59m  2os  P  M.    Corr.  Decl.  fs^O^S?'' 

Difference 17' 52"  90      0     0 

Dip  of  the  Horizon...  4     8      Course  N.  E.  60  miles.     0°  42' 


0° 

38 0'  N. 

Latitude  at  Sunset .T^ ^38°  42' 

Polar  Distance 108    51 


S.  Diflf.  Ih 37" 

G.  T.  past  Noon.l2h 

60)444'' 

Corr. V  24'- 


Con-ection f  22'    0"    Lut.  Obs.  at  Noon. 


Polar  Distance.  108°  50'  84" 


147°  33' 
Correetion Sub.      f  22 

l47°"Tr 

Hall  Sum 73°  36' 

Correction Add        f  22 

Difference 7:^'  5S' 


Log.  0.10767 

Log.  0.02394  Equa.  of  T..12m  38.658  Diflf.  Ih. 
Corr...  Add  6.65 


.664 
If 

Corr.  Equa.  12m^5~208  Cor.. .  -  .76.^4 J 


Log.  4.45077 


Lot;.  4.98277 


Apparent  Time  at  Ship,  past  Noon 4h  58m  .298  =  Log.  9.565U 

Equation  of  Time Add      12      45 

Mean  Time  at  Ship 5h  11m  lit 

Time  by  Watch,  Sunset 5      3     25 

Watch  slow  of  Mean  Time 


7nJ  498.  and  fast  of  Apparent  Time  4nr  66a 


FINDING  THK  TIMK. 


129 


FINDING  THE  APPARENT  TIME  WHEN  THE  SUN  IS  RISING  OR  SETTING 


RULE. 
When  the  Upper  Limb  is  Observed. 

Correct  the  Decli„.li,,„  and  Latitude  as  before,  and  find  the  Sun'.  Polar  Di.tance 

The  Apparent  Time  is  then  found  by  the  usual  Rule  for  working  the  Tables. 

DIAGRAM 
Of  the  Sun^s  Hour  Angle  at  Rising  or  Setting. 

Fig.  26. 


Equator,  or  .„T,me  is  6h.  47m.  4&,  »hioh  subtracted  from  llhours  giv'i  AppTrermme^Sh  12m  l£^ 

EXAMPLE  2 
June  Ist,  1854.     (Noon  at  Sea.)     In  Latitude  26"  O'  North  and  Lono-!ti,r1*>  rc  v„.t  u    r.     j  r.    ,_    •      . 

Dip  of  the  Horizon 4     8     o^.^n  t-         a  \t  .^       »      «     Corr.,..Sub.         3   40  Ht 

Correction t  IlLf'  SubTacTrn.^-  "" l^^^"  T  o'  '"^-  ''^"-  '^'^'"  «"^)il 

LaHt  d    •      .  .      •                                 '''"^  '^'"'•^  «-^«--  •  •  i^^^S^^  Polar  Dist   el-TO'"""'*^^^-^ 
Latitude  iM  at  Sunnse 25'    0'. ..  .Log.  0.04272^ i^olar  Di8t..68      0   17 

Polar  Disbince 68      0  ...  .Lo|.  0.03283 

Sum ,  QQO    ni 

Correction Sub       +  B4  7,^^^'  °^  '^^''' ....  2m.  318-92     Dif.  Ih.      S-80 

—~~  Corr..,..Add..  4  -18  Hl^ 

Half  Sum %-t       r       .».,oo         ^^''^^^tEqua.. . .    jtn.  86s-10     Cor..— jj-lfrp-- 

o  .•       4b      S     ..   Loff.  4.84138  

CoTection Add       f  54 

J'^«'':°"« r4FT7'.... Log.  4.86377 

^pp.  Time  at  Ship  at  Sunrise.     5h.  1 21^7 2777.:!^^:^ 8070 
Equation  of  Time.  2       86  s      ■      ." 

Time  by  Watch 5     j^        q* 

Watch  Fast  of  Mean  Time. . . .  7^724,.  and  Fast  of  Apparent  Time  4m.  48.. 

)m  the  fact  that  when  the  Son's- 
below  it.    And  when  his  Upper 

Ihi.  Ub-erV-ai-hliTi'T  ''■'  ""  *«fa«>l»»  of  ■he"A,;„„7pT,cV,'. •"'""■"  "'''"'  "*  "'""■"••    fti.,  »  b.&r, 

«.f«.,  .nd  ™,  bT£;'isyr:;^;'bf^?„*rdt'r'/^f'sft™i;:'  "'"*•  ■• «» ''°"»-  » ■-  >■»''—•  -n- 


tso 


NAUTICAL  ASTRONOMY. 


FINDING  THE  APPARENT  TIME  FROM  EQUAL  ALTITUDES  OF  THE  SUN  NEAR  NO<")N. 

This  is  a  very  convenient  and  simple  mode  of  finding  the  Apparent  Time  at  Noon,  or  when  the  Sun  ia 
on  the  Meridian,  that  is,  at  12  o'clock  Apparent  Time  at  the  Ship;  and  as  it  is  independent  of  Latitude 
and  Declination,  and  all  the  other  corrections,  it  is  a  useful  check  on  the  more  regular  method  of  finding 
the  time. 

This  observation  can  be  depended  on  in  Low  Latitudes,  because  the  Sun's  change  of  Altitude  is  very 
rapid  near  the  Meridian.  But  in  High  Latitudes  the  Sun's  change  of  Altitude  near  the  Meridian  is  very 
slow,  especially  in  the  Winter  months ;  hence  an  error  in  the  time  of  observation,  in  the  latter  case,  may 
be  committed  which  may  render  it  worthless. 

Besides,  the  greater  the  distance  of  the  observer  from  the  Equator,  the  time  from  Noon,  at  which  the 
Altitude  is  observed,  must  be  greater,  (because  the  correctness  of  the  Time  so  found  depends  entirely  upon 
the  rapidity  with  which  the  Sun  rises  and  falls.)  This  involves  a  tedious  system  of  corrections,  for  the 
Ship's  change  of  place  and  the  Sun's  change  of  Declination  in  the  interval  between  the  observations,  and 
which  is  unnecessary  labor,  because  the  Time  can  be  found  as  correctly  by  one  of  the  Altitudes  in  the  usual 
manner. 

When  a  Ship  sails  due  East  or  West  in  the  interval  between  the  Altitudes,  in  that  case  it  becomes  a 
■question  of  time  only.  But  when  she  makes  much  Northing  or  Southing,  it  is  evident  that  the  same  Alti- 
tudes  will  no  longer  give  the  correct  Middle  Time  at  Apparent  Noon.  The  error  in  the  P.  M.  Altitude 
will  be  equal  to  the  difierence  of  Latitude  made  in  the  interval.  Therefore  the  Rule  is,  when  sailing 
towards  the  Sun,  we  must  increase  the  A.  M.  Altitude  which  is  on  the  Quadrant,  by  advancing  the  Index 
■of  the  instrument  equal  to  the  difference  of  Latitude  made  in  the  interval. 

But  in  sailing  from  the  Sun,  we  must  decrease  the  A.  M.  Altitude  by  screwing  back  the  Index  equal  te 
the  difference  of  Latitude  made  in  the  interval;  and  when  the  Sun  falls  to  that  Altitude  in  the  afternoon. 
we  note  the  time  by  the  same  watch  by  which  the  time  of  the  A.  M.  Altitude  was  noted. 

Limits  of  the  Time  from  Noon. 

The.  Altitudes  should  not  be  taken  nearer  to  Noon  than  in  the  proportion  of  One  Minute  of  Time  for  everj 
Oegroe  of  Latitude  the  Ship  is  North  or  South  of  the  Equator. 

The  Observation. 

Observe  an  Altitude  of  the  Sun's  Lower  Limb  according  to  the  above  limits  before  Noon.     Note  the  tira 
t>\  the  Watch,  and  clamp  the  Index  of  the  instrument.     When  the  Sun's  Lower  Limb  falls  again  to  th« 
•ame  Altitude  in  the  afternoon,  note  the  time  by  the  watch. 

RULE. 


Add  together  the  two  times,  and  take  their  ITalf  Sum  for  the  Middle  Time.  If  the  Middle  Time  is  exactly  It 
Iwurs,  the  Watch  is  correct  for  Apparent  Time  ;  because,  at  the  instant  of  this  Middle  Time  by  the  Watch,  the  Sun 
u  on  the  Meridian  and  it  is  Apparent  Noon,  or  12  o'clock,  Apparent  Time  at  the  Ship. 

But  should  this  Middle  Time  exceed  12  hours,  then  the  excess  is  what  the  Watch  is  Fast  of  Apparent  Time. 

If  the  Middle  Time  be  leas  than  12  hours,  then  what  it  wants  of  12  hours  is  what  the  Watch  is  Slow  of  Apparent 
Time.  And  by  applying  the  correct  Equation  of  Time,  in  the  usual  manner,  to  Apparent  Noon,  or  12b.,  we  have 
the  Mean  Noon  at  Ship,  the  difference  between  which  and  the  Middle  Time  is  the  error  of  the  Watch  on  Mean  Time. 


EXAMPLE  1. 

April  2d,  1864.  In  Latitude  5°  52'  North,  and  Lon- 
gitude 28°  West,  at  llh.  64m.  by  the  Watch,  the  Sun's 
Altitude  was  85°  40'  A.  M.,  and  at  12h.  20ni.  by  the 
same  Watch,  he  had  fallen  to  the  same  P.  M.  Required 
the  error  of  the  Watch  on  both  Apparent  and  Mean 
Time. 

Sun's  Alt. .  85°  40'  A.  M.       Time  by  Watch,  llh.  54m. 
Same    P.  M.  do.         do.        12     20 

Equa. of  T.. 3m.  418-71  Dif.  •'ZeO     Sum )24h.  14m. 

€orr.  ..Sub. 1-50  Long.    2h. Mid.  Time,  12L    7m. 

Equa. 


.Add  3m.  40a. 

Ap.  N'n,  12b.O       0 

Mn.  N'n,  1211.3 
Mid.T..  12    7 

Watch . , 


1'50K)     App.  Noon,  12 0 

Watch  Fast,  Oh.    7m. 


408. 
0 


3m.20s.  Fast  of  Mean  Time. 


EXAMPLE  2. 

April  16th,  1854.  In  Latitude  30°  North,  Longitude 
45°  East,  at  llh.  20m.  by  Watch,  the  Sun's  Altitude  was 
68°  20'  A.  M.,  and  at  12h.  34m.  by  the  same  Watch,  be 
had  fallen  to  the  same  Altitude  P.  M.  Required  the 
error  of  the  Watch  on  both  Apparent  and  Mean  Time. 

Sun's  Alt. .  68°  20'  A.M.      Time  by  Watch,  llh.  20m. 
Same     P.M.         do.  do.    12     34 

Equa. of  T.. .    Om.  1 1887  Di£  .603     Sum . . . .  23h.  54m 

Corr.. .  .Sub. 


1  -80 


Equa... Sub.     Om.  lOs. 

Ap.  N'n.  12h.    0        0 

Mn.  Nn.  llL69m.5'0B! 
Mid.  T...  11     57 

Watch. . . . 


3h.  Mid.Time,llh.67m. 
1.80-9     Ap.Noon,  12       0 
Watch  Slow,  Oh.    8m. 


2m.  6Cs.  Slow  of  Mean  Time 


Note. — It  is  not  necessary  to  read  off  the  Altitude  if  the  Index  of  the  instrument  remains  untouched,  because  we  have 
only  to  wait  until  the  Sun  mils  again  to  the  same  Altitude  in  the  afternoon,  unless  the  Ship  makes  much  Northing  or 
bouthiug  in  the  interval,  when  it  must  be  corrected  as  aba/e.  But  to  guard  against  accident,  or  if  the  instrument  ii 
required  for  use  in  the  interval,  we  have  only  to  read  it  ofl  and  write  it  down,  and  set  the  Index  to  the  same  Altitude 
«cain,  ready  for  the  P.  M.  Altitude,  and  in  case  of  cloudy  weather  several  Altitudes,  and  their  corresponding  timee, 
«aould  be  taken  before  Noon,  as  a  reserve. 


FINDING  THE  TIME. 


121 


FINDING  THE  TIME  ON  SHORE  FROM  ALTITUDES  BY  THE  ARTIFICIAL  HORIZON. 


As  a  full  description  of  the  method  of  taking  Observations  with  this  Instrument  is  given  at  page-s  77  and 
T8,  it  will  only  be  necessary  here  to  give  a  few  Examples  of  finding  tiie  Apparent  Time,  and  thence  the 
Mean  Time,  on  Sliore. 


EXAMPLE  M. 


March  6th,  185-1.  at  New  York,  in   Latitude  40°  42'  42"  N.,  and  Longitude  74°  0'  1"  W.,  the  following  Altitude* 
were  observed  by  an  Artificial  Horizon  iu  the  Moruiug,  to  ascertain  the  Ei-ror  of  the  Watch  on  Mean  Time. 


Obs.  Altitude  L.  Limb.   24' 


14'  30' 
35    89 
5fi    30 


8)106'  39" 


24° 


35' 
2 


83' 
0 


Mean  of  the  Altitudes. 

Index  Error Sub, 

Angle  of  Double  Reflex.  24^33^33' 
Suns  Obs.  Alt.  L.  L. . .  12M6'  46" 
Sun's  Seinid Add  16     9 


Apparent  Altitude 12^  32'  55 

Refraction.    Sub.  4    18 


Suns  True  Altitude. ...    12°  28'  37- ' 

Polar  Distance 96      2    46 

Latitude 40   42   42 

Sum 149°  14'    4" 


Half  Sum 74' 

True  Altitude.. _12^ 

Difference 62 

Apparent  Tim«. ., 


37'    2' 
28   37 


Time  by  the  Watch. 


Mean  of  the  Times. 
Lon.  74°  W.  iu  time- 
Mean  Time  at  G. . , 
Sub. 
T.  past  Noon  at  G.. 


Log.  0.0024S 
Log.  0.12083 

Log.  4.42370 


7h  32m  20s  Declination.   6' 
33      36    Corr..Sub.. 

__li_Jii    Cor.  Decl. .  ~6^ 
3)10Um  268  90 

7h  33m  28fl  Polar  Dist.  96° 
4    56        0 


14"  S. 

29 


2'  45" 
0      0 


Diff.  for  Ih  68" 
G.  Time  )       ,, 

pastN.   S 

Correction  29" 


2'  45' 


12h  29m  28s 
12       0        0 


Equa.  of  T.  11m  45s-78  Diff.  for  Ih     -684 


29m 


283   ^orr..  .Sub. 


•29 


Corr. 


•29-4 


Correct  Eq.  11m  45849 


8'  25"  Log.  4.94650 


7h  28m  468  =  Log.  9.49296 


Apparent  Time  of  Observation  7h  28m  468 
Equation  of  Time Add        11     45 

Mean  Time 7h  40m  3l8 

Time  by  Watch 7    33 28_ 

Watch  slow Oh    7m    Ss  of  Meaa  Tune. 


EXAMPLE  2. 


p  October  20th,  1854,  at  the  Cape  of  Good  Hope,  in  Latitude  34°  22'  S.,  and  Longitude  18°  30'  E.,  the  following 
Altitudes  were  observed  by  an  Artificial  Horizon  in  the  Afternoon,  to  ascertain  the  Error  of  the  Watch  on  Mean 
Time. 

Sun's  Altitude  L.  Lunb.   36°  30'  30"  Time  by  Watch    4h  58m  10s  Declination  10°  19'  47"  S.  Diff  Ih 54  " 

36      6     0      4    59      20    Corr.. Add  8   22  Sfb 

lLJi_J^     6      0     40    Corr.  Decl  10°  28'    9"  162^' 

3)108°  17'  40"  3)1 4h  58m  10s  90      0_0  27 

Meauof  the  Altitudes...  36°    5'  53"  Mean  of  Times.  ^iT9m~233  Polar  Dist.  7'9°"36'~5r'  1£_ 

jidex  Error Add  1^  lo  Lon.  18°  .30'.  )  60)202" 

Augle  of  Double  Reflex.  86°   "r~l"       E.  iu  time,  j" (j^rr 3^2~^ 

Suns  Obs.  Alt.  L.  Limb.    18°    3'  siT'  G-  Time  P.  M..     3h  45m  238 

U    Add  Semid 16      6 

Apparent  Altitude 18°  !!»'  38"  Equation  of  Time  15m  68^7     Difflh..     AOt 

Subtract  Refraction 2    58  Correction-.  .Add  1  '62  Sfh 

Sun's  True  Altitude 18°  16'  40"  Correct  Eqnatioa  15m  7829  -1218 

Polar  Distance. 79    36   51  Log.  0.00717  -208 

Latitude 34    22     0  Log.  0.08881  •101 

Sum r32^T5"'^"  Oorr TmT" 

HalfSum t;6°     7'  45"  Log.  4.60711 

True  Altitude 18    16   40 

Difl'erence 47°  61'    5"    Log.  4.87006 

App.  Time  at  the  Place  4ii  5ym  HOs     Log.^6766 
Equa.  of  Time. ..  .Sub.         15        7 

Mean  Time 4h  44m  233 

Time  by  Watch 4    59      23 

^  Watch 16m    Os  fast  of  Mean  Tune  at  the  plao*. 

I 


133  NAUTICAL  ASTRONOMY 


FINDING  THE  TIME  AT  SEA  FROM  AN  ALTITUDE  OF  THE  MOON. 

The  Apparent,  and  thence  the  Mean  Time,  at  Ship,  may  be  found  by  an  Altitude  of  the  Moon  at  a  di» 
taooe  from  the  Meridian. 

In  the  first  place  we  must  hare  the  txact  Greenwich  Date  at  the  time  of  the  observation  at  the  Ship,  Id 
order  to  reduce  her  Semi-diameter,  Horizontal  Parallax,  Right  Ascension,  and  Declination  taken  from  the 
Nautical  Almanac  to  that  time,  and  as  before  stated  at  Page  101,  (in  the  case  of  finding  the  Latitude  by 
th«  Moon's  Meridian  Altitude,)  if  the  Longitude  of  the  Ship  be  not  known,  neither  the  Latitude  nor  the 
Time  can  be  found  by  the  Moon.  But  m  cases  where  a  Ship  carries  a  good  Chronometer,  the  Longitudecan 
at  any  time  be  found  tolerably  correct  by  applying  the  Difference  of  Longitude  made  by  Dead  Reckoning  to 
the  Longitude  last  found  by  Chronometer. 

The  Moon's  Observed  Altitude  must  be  corrected  as  usual,  to  obtain  her  centre,  and  another  correctioD 
for  her  Parallax  in  Altitude,  and  which  is  always  additive  to  her  Apparent  Altitude,  because  she  alwav* 
appears  below  her  true  place  in  the  heavens.     (See  page  67.) 


RULES  FOR  COMPUTING  THE  VARIOUS  CORRECTIONS, 

To  Find  the  Greenwich  Date. 

let.  Turn  the  Ship's  Longitude  into  Time  by  Table  XXVI,  and  add  it  to  the  Mean  Time  at  the  Ship,  (al 
the  time  the  observation  was  made),  in  West,  or  subtract  it  in  East  Longitude,  will  give  the  Greenwich 
Date,  which  must  be  always  one  day  less  than  the  Sea  Date.  Or  it  may  be  more  correctly  found  by  noting 
the  times  of  the  Altitudes  by  Chronometer,  which,  after  allowing  for  its  error  on  Greenwich  Time,  will 
give  the  required  Greenwich  Date. 

To  Correct  the  Moon's  Altitude. 

2d.  Take  from  the  Nautical  Almanac  the  Moon's  Semi- diameter  and  Horizontal  Parallax,  for  the  near- 
•et  Noon  or  Midnight  correpponding  to  the  Greenwich  Date.  Then  if  the  Moon's  Lower  Limb  be  observed, 
add  the  difference  between  the  Dip  of  the  Horizon  and  her  Semi-diameter  to  the  Observed  Altitude.  But 
if  her  Upper  Limb  be  observed,  subtract  their  Sum,  will  give  the  Moon's  Apparent  Central  Altitude. 

3d.  Enter  Table  XXV  with  the  Apparent  Altitude  at  the  side,  and  the  Horizontal  Parallax  at  the  top, 
and  take  out  the  Correction,  which  is  expressed  in  Minutes  and  tenths  of  Minutes,  and  proportion  it,  if 
required,  for  the  odd  Minutes  of  Altitude,  and  the  odd  Seconds  of  Parallax.  This  correction  is  always 
additive,  and  will  give  the  Moon's  True  Altitude. 

To  Correct  the  Moon's  Right  Ascension.  ^ 

4th.  When  the  large  Nautical  Almanac  is  used,  and  the  Greenwich  Date,  for  the  full  hour,  the  Right 
Ascension  is  found  opposite  that  hour  ;  but  when  there  are  odd  Minutes,  take  the  Difference  between  that 
and  the  following  hour,  and  apply  the  proportion  of  this  difference,  corresponding  to  the  odd  Minutes,  to 
the  Right  Ascension  at  the  preceding  hour,  according  as  it  is  increasing  or  decreasing,  will  give  the  Moon's 
correct  Right  Ascension. 

5th.  When  the  small  Almanac  is  used,  and  the  Greenwich  Date  exactly  at  Noon  or  Midnight,  take  out 
the  Right  Ascension  found  opposite.  But  when  it  is  between  them,  take  it  out  for  the  nearest  Noon  or 
Midnight  preceding,  and  the  nearest  Noon  or  Midnight  following  this  Greenwich  Date,  and  take  their  Dif- 
ference, which  will  be  that  for  12  hours,  and  note  the  number  of  Hours  and  Minutes  which  the  Green- 
wich Date  is  past  Noon  or  Midnight.  Then  say,  as  12  hours  is  to  the  Difference  in  12  hours,  so  is  the 
Greenwich  Time  pa.st  Noon  or  Midnight  to  ihe  required  correction,  which,  applied  to  the  Right  AscensioB 
at  the  preceding  Noon  or  Midnight,  according  as  it  is  increasing  or  decreasmg,  will  give  the  Moon's  correct 
Right  Ascension.     (See  the  Note  on  the  next  page.) 

To  Correct  the  Moon's  Declination. 

6th.  When  the  large  N.  Almanac  is  used,  proceed  by  the  rule  already  given  at  page  102,  No.  6,  for  cor- 
recting the  Moon's  Declination  when  on  the  Meridian. 

When  the  small  Nautical  Almanac  is  used,  proceed  in  like  manner  by  Rule  No.  7,  on  the  same  page, 
and  the  result  will  be  the  Moon's  correct  Declination,  corresponding  tc  the  Greenwich  Date. 

7b  Find  the  Moon's  Polar  Distance. 

7lh.  When  the  Latitude  and  the  Moon's  Declination  are  of  the  same  name,  the  Difference  between  hei 
Declinaaon  and  90°  is  her  Polar  Distance.     But  when  of  contrary  names,  their  Sum  is  her  Polar  Disttnor 


FINDING  THE  TIME.  138 

To  Correct  the  Latitude  to  the  Time  of  Observatiim. 

8th.  Enter  the  Traverse  Tables  with  the  Course  and  Distance  made  good,  and  find  the  Difference  of  Lati- 
tude the  Ship  has  made  since  the  last  Observation  for  Latitude  was  obtained,  and  apply  it  by  the  Rule  given 
At  page  125,  which  will  give  the  correct  Latitude  in 

To  Find  the  Moon's  Hour  Angle. 

9th.  Thus  having  the  Moon's  True  Altitude,  Polar  Distance,  and  the  Latitude  of  the  place,  proceed  (a« 
with  the  Sun)  to  find  the  Moon's  Hour  Angle,  or  her  Distance  from  the  Meridian,  (which  with  the  Sun  ii 
the  time  from  Noon.)  this  being  added  to  the  Moon's  Right  Ascension,  if  the  Moon  be  to  the  Westward  of 
the  Meridian,  or  subtracted  from  it  if  the  Moon  be  to  the  Eastward,  the  Sum,  or  remainder,  will  be  the 
Right  Ascension  of  the  Meridian. 

To  Correct  the  Sm7i's  Right  Ascension. 

10th.  Take  out  the  Sun's  Right  Ascension  and  the  Difference  for  1  hour  from  the  Nautical  Almanac,  mul- 
tiply this  Difference  by  the  Time  from  Greenwich  Noon,  and  add  this  correction  to  the  Right  Ascension, 
taken  from  the  Nautical  Almanac,  (because  the  Sun's  Right  Ascension  is  constantly  increasing,)  will  giv« 
the  Sun's  correct  Right  Ascension. 

To  Find  the  Apparent  Time  at  Ship 

11th.  From  the  Right  Ascension  of  the  Meridian,  (increased  by  24  hours,  if  necessary,)  subtract  the  Suu'i 
eorrect  Right  Ascension,  and  the  remainder  will  be  the  Apparent  Time. 

7b  Correct  the  Equation  of  Time. 

18th.  Take  out  the  Equation  of  Time  from  the  Nautical  Almanac,  and  the  Difference  for  1  hoar,  and 
eorrect  it  by  the  Rules  given  at  page  124,  will  give  the  correct  Equation  of  Time. 

To  Find  the  Mean  Time  at  Ship. 

13th.  Apply  the  correct  Equation  as  directed  in  the  precept  at  the  head  of  the  column  in  the  Nautical 
A.lmanac,  to  the  Apparent  Time,  by  adding  or  subtracting  it,  and  the  result  is  the  Mean  Time  at  the  Ship 

EXAMPLE. 

Miirch  lOtb,  1854.  At  Noon  the  Latitude  observed  was  88°  15'  North,  Longitude  by  account  60°  45'  West.  Ship 
tad  sailed  N.  E.  (true)  40  miles  since  Noon,  when  the  observed  Altitude  of  the  Moon's  Lower  Limb  was  40°  82'  to 
the  Eastward  of  the  Meridian,  and  the  Greenwich  Time  by  Chronometer  9h.  44m.  87s.  P.  M.  Required  the  time  at 
Ship. 

Ob«.  Alt.  D's  L.  Limb.  40°  82'  Gr.  Time  by  Chro 9b.  44m.  37s.  J  'b  Dec,  Noon.  24°  14'  N. 

Semid.  15'.  Dip  4 11^                                          Midnight.  23 4 

Hor.  Par.65',  and....  40°  43'  Lat  at  Noon 88°  15'  N.  T.XXIILDit  12h.  1°  10'  )  .,   ..     _^.  .., 

Gives  Coi-.,  Tab.  XXV, 40   Course  N.  E.  40  miles,  D.L. 28  and  G.  T.  from  Noon. .  f  »'i-45d^-=-0   Ofl 

J  'b  True  Alt 41°  23'  Lat.  at  time  of  Sights 38°  48'  ^^^■'  ^00°-  •  •  •  ^4    14  N 

Polar  Dist 66    42    Log.  0.03695  >  's  Cor.  Dec.. .  23°  18'N 

Latitude 38    43    Log.  0.10777  90      0 

Sum 146°  48'  J)  's  Polar  Dist  66°  42' 

Half  Sum 78°  24' Log.  4.45589  ^,    t,    .    >t 

n-ff  oo°     T  T         A^oAAi  D'sR.  A.  Noon..  8h.  12m.  218. 

D'ff«^'«Dce ••     82      1    . . .  .Log.  4.72441  Midnight.  888      26 

I '8  Hour  Angle  3h.  38m.  53s Log.  9.32502  g       ^  ^gh.^       26         5i.-9h.  46m. 

J)  sR.  Aseen...    8     33      S3 

H.A.ofthe  Mer..  4h.  54m.  858.  Sun's  R.  A.  23h.  21m.  588.  Dif.  lb.   98.  *  10.0000 

Add  24       0        0    Cor... Add  1 30  _10_  Pro.  Log  12h..  1.1761  Table  XXXIV 

R.  A.  M.  Tncrea.  28h.  54m.  35s.  Corrected.  23h.  23m.  238.  908.  Arth.  Co 78!8239 

finn's  R.  Ascen.    23     23       23  Pro.L(>g.26m.5  0.8389 

App.  T.  at  Sliip     5L  31m.  128.  Equation. .  10m.  3 ls-55  Di£   lh.-665         ^o-  9b.  45m.  1.2663 

Eg.  of  T...  Add  10      25  6^5  10  0.9291 

Mean  Time 5h.  41m.  878.  Corrected.  10m.  24890  6 66-0  Pro.  Log. OL  21m.  12a.  CJor.  for 9h. 43a 

>  '8  KA.at  N'n  8 12      21 

j)  'b  Cor.  R.A..8h.S3m.  838. 

•  The  Proportional  Logs.,  Table  XXXIV,  are  very  nseful  for  the  purpose  of  performing  Rule  of  three  qnestiona* 
bstto  make  the  terms  all  additive  we  must  eubtract  the  Pro.  Log.  of  the  first  term  from  10.0000.  It  is  then  called  Um 
4rithmetical  Cnnipleinent. 

But  as  this  Table  only  extends  to  8  hours,  we  must  enter  it,  (when  they  exceed  that  quantity,)  with  the  hourn  as 
ininntos  and  the  minutes  as  seconds,  «fec.,  <fec.,  as  in  the  above  ilxamplc,  which  will  be  round  a  much  more  oorreot 
ooie  than  when  taken  from  Tables  which  are  generally  constructed  for  that  purpose. 


134  NAUTICAL    ASTRONOMV'. 

FINDING  THE  TIME  AT  SHIP  FROM  AN  ALTITUDE  OF  A  PLANET. 

The  Time  may  be  found  as  correctly  by  an  Altitude  of  a  Planet  at  a  distance  from  the  Meridian  at 
twilight,  as  by  the  Sun,  and  the  name  of  the  Planet  of  which  the  Altitude  is  observed  may  be  easily  ascer- 
tained, lif  we  refer  to  the  Diagrams  and  Rules  for  finding  the  Meridian  Altitudes  of  the  Stars,  at  pages  64 
and  66.  There  it  will  be  perceived  that  the  Elevation  of  the  upper  end  of  the  Celestial  Equator  is  equal 
to  the  Co-Latitude  of  the  place.  Now,  it  is  easy  to  imagine  a  semicircle  in  the  heavens,  (in  an  opposite 
direction  to  the  Elevated  Pole,)  to  be  elevated  equal  to  the  Co-Latitude  of  the  place,  and  that  this  semi- 
circle passes  through  the  true  East  and  West  points  of  the  Horizon,  which  will  represent  the  Celestial 
Equator,  and  that  if  the  Planet  is  seen  to  the  North  of  this  semicircle,  it  must  have  North  Declination, 
otherwihe  South,  and  to  note  by  its  bearing  whether  it  is  to  the  Eastward  or  Westward  of  the  Meridian. 
Now  inspect  the  Nautical  Almanac  on  that  day  of  the  month,  and  find  which  of  the  Planets  agree  with  the 
above  Declination,  and  find  the  time  of  its  Meridian  passage.  If  it  be  observed  to  the  Eastward,  it  will 
pass  the  Meridian  later  than  the  time  of  observation,  but  if  it  be  observed  to  the  Westward,  it  will  have 
passed  the  Meridian  earlier  than  the  time  of  observation.  And  bearing  in  mind  that  all  the  heavenly 
bodiei  rise  and  set  to  the  Northward  of  the  true  East  and  West  points,  when  their  Declinations  are  North, 
otherwise  to  the  Southward  of  these  points  when  their  Declinations  are  South ;  and  that  in  High  Latitudes, 
when  the  Declination  is  of  the  same  name  as  the  Latitude,  the  Planets  will  have  a  high  Altitude,  and 
they  pass  the  Prime  Vertical  above  the  Horizon.  But  when  the  Latitude  and  Declination  are  of  contrary 
nameu,  their  Altitudes  wil  be  low,  and  they  pass  the  Prime  Vertical  below  the  Horizon,  or  set  before  they 
reach  **•  « 

RULES 
For  Computing  the  Corrections. 

1st.  Find  the  Greenwich  Date  by  turning  the  Ship's  Longitude  into  Time,  by  Table  XXVI,  and  add  it  to 
the  Time  at  Ship  in  West  Longitude,  or  subtract  it  in  East ;  or  it  may  be  found  from  the  Chronometer,  and 
to  be  called  always  one  day  less  than  the  Sea  date. 

To  Correct  the  Planefs  Observed  Altitude. 

2d.  Enter  Table  XX  with  the  Height  of  the  eye  at  the  top,  and  the  observed  Altitude  at  the  side,  and 
take  out  the  correction  for  Dip  and  Refraction,  which  is  always  subtractive. 

To  Correct  the  Planefs  Declination. 

3d.  Take  out  its  Declination  from  the  Nautical  Almanac  for  the  nearest  Noon  preceding  the  Greenwid* 
Date,  (except  when  the  Change  of  Declination  is  small  it  may  be  taken  for  the  nearest  Noon  of  the  Green- 
wich Date,)  and  also  for  the  Noon  of  frhe  following  day,  and  take  their  Difference.  Then  say,  as  24  hourt 
is  to  the  Difference  in  24  hours,  so  is  the  time  past  Noon  at  Greenwich  to  a  proportional  part,  which  applied 
to  the  Declination  at  the  preceding  Noon,  according  as  it  is  increasing  or  decreasing,  will  give  the  Planet's 
Correct  Declination. 

To  Find  the  Planefs  Polar  Distance. 

4th.  When  the  Latitude  and  Declination  are  of  the  same  name,  the  difference  between  the  Declination 
and  90*  is  the  Polar  Distance ;  otherwise,  their  Sum  is  the  Polar  Distance. 

To  Correct  the  Latitude  to  the  Time  of  Observation. 

5th.  Find  the  Difference  of  Latitude  the  Ship  has  made,  and  apply  it  to  the  Latitude  last  observed. 

To  Find  the  Hour  Angle  of  the  Planet.  '^ 

6th.  Having  thus  the  True  Altitude,  Polar  Distance,  and  the  Latitude  of  the  place,  proceed  as  with  tne 
t<un  to  find  the  Planet's  Hour  Angle,  or  Distance  from  the  Meridian,  (which  with  the  Sun  is  the  time  from 
ffoon.) 

To  Correct  the  Planet's  Right  Ascension. 

7th.  Take  out  the  Right  Ascension  from  the  Nautical  Almanac  for  the  Noon  preceding  the  Greenwich 
Date,  and  also  for  the  nearest  Noon  following  it,  and  take  their  Difference  ;  then  say,  as  24  hours  is  to  the 
Differenee  in  24  hours,  so  is  the  time  past  Noon  at  Greenwich  to  a  proportional  part,  which  applied  to  the 
Right  Ascension  at  the  preceding  Noon,  according  as  it  is  increasing  or  decreasing,  will  give  the  Correct 
Right  Ascension. 

To  Find  the  Right  Ascension  of  the  Meridian. 

Sth.  If  the  Planet  be  to  the  Eastward  of  the  Meridian,  subtract  its  Hour  Angle  from  its  Right  Ascension, 
but  if  to  the  Westward  of  the  Meridian,  add  its  Hour  Angle  to  its  Right  Ascension,  will  give  the  Right 
Ascension  of  the  Meridian. 


nNUlNG  THE  TIME.  IbS- 

To  Correct  the  Sun's  Right  Ascension. 

0.  Take  out  the  Sun's  Right  Ascension  and  the  difTerence  for  1  hour  from  the  Nautical  Almanac,  mulb' 
ply  the  difference  for  1  hour  by  the  time  from  Greenwich  Noon,  and  add  this  correction  to  it. 

To  Find  th«  Apparent  Time  at  Ship. 

10.  From  the  Right  Ascension  of  the  Meridian,  (increased  by  24  hours  if  required,)  subtrcut  the  Sun'* 
eorrect  Right  Ascension,  and  the  remainder  will  be  the  Apparent  Time  at  Ship. 

To  Find  the  Mean  Time  at  Ship. 

11.  Take  out  the  Equation  of  Time  from  the  Nautical  Almanac,  and  correct  it  as  usual,  and  apply  it  to 
the  Apparent  Time,  according  to  the  precept  at  the  head  of  the  column,  and  the  result  is  the  Mean  Tim* 
at  the  Ship.     (See  the  Rules  at  page  124.) 


EXAMPLE  1. 

April  7th,  1864  Sea  Time.  In  Latitude  28°  26'  North,  and  Longitude  70'  0'  West,  at  twilight  in  the  morning 
the  observed  Altitude  of  the  Planet  Venus, was  24°  21'  to  the  Eastward  of  the  Meridian.  Greenwich  Time  by  Chro- 
nometer. 22h.  16m.  6s.    Required  the  Apparent  and  Mean  Time  at  Ship.     Elevation  16  feet. 

Obe.  Alt.  Venus,  24°  21'  Dec  Venus,  April  7th 6°  7'  S.  Gr.  Time  by  Chro. .22h.  16m.  6«. 

Cor,  Tab.  XX,  Sub^ 6^  A  dd_90 Qr  Date,  April  6th 22h.  1 6m.  6» 

Venus  T.  Alt. .  24°  16'  Polar  Distance  of  Venus. . .   96°  7' 

Polar  Dist    96     7  .  Log,  0.00248  Sun's  R.  A.  lb.  Dm.  ISs.  Dif.  IL. .  .9a. 

Latitude 28    26  .  Log.  0.05583  Ven  R.  A.  )  ^^^  27m.288.  ^"' -^^^^ H2     ^  '^'       ^^^ 

Sum 148^  48'  -^P-  6th  J        •    m-    a.  Corrected,  lb. 8m.  88a.  198 

Half  Sum 74°  24' .  Log.  4.42962  ^^jjp^.j'^  [  22   29     44  2_ 

Diflference  . . . .    50°    9'.  Log.  4.88521  ^  „,i,  t-—- r — —       .   _„.,.  60)200 

„  ,  ° Say  a8  24h.  isto  2m.  16s.80is22L16m.  — I 

VeDU8H.An.8h.  52m.  358.Log.  9.37314  8m.  208. 

RAscen.  22     29 34  10.0000  by  Pro.  Logs. 

R.AofMer.l8h.36m.598.  0.8751  P. Log.  of  24L,Table  XXXI V.  Eq.ofTime.  .2m.80s-60  Di£  lb.. -726 

Bun's  R  A.  J 3__38  "9l249  Arith.  Complement  Cor.. ..  .Sub. lejlS  22ih. 

App.  Time  17h.  33m.  218.  1.8999  P.  Log  of  2m.  169.  Correct  Eqa.  2m.  14  "37  1460 

Equa. .  Add 2 14  0.9076  P.  Log.  of  22h.  16m.  1460 

Md.  Time. .  nk  35m.  368.  from  Noon,    1.9324  Pro.  Log.  Cor.— 2m.  68.  ^^^ 

Subtract..  12       0         0         [A  p.  6th.  16-13-1 

lia  Time.  ."5h.  35m.  358.   from    mid-  ^enus  R.  A.,  April  6th. 22h. 27m.  28a. 

night,  or  on  the  morning  of  the  Correct  R  Ascea. . . .    22h.  29m.  348.  . 

7  th  April,  Civil  Time. 

( 

0 

EXAMPLE  2. 

Dec  6th,  1854.  Sea  Time.  The  Latitude  at  Noon  was  88*  10'  South,  and  tne  Longitude  by  Chronometer  92*  SO* 
East.  Ship  then  sailed  S.  W.  (true)  40  miles,  when  the  Altitude  of  the  Planet  Jupiter  observed  was  36°  10'  to  th« 
Westward  of  the  Meridian,  at  7h.  16m.  by  the  Watch,  at  twilight  b  the  evening.  Required  the  error  of  the  Watch 
on  Apparent  and  also  Mean  Time,  at  Ship.     Eleyation  16  feet. 

JupVsObs.  AIL  86°  10'  Time  by  Watch 7h.  16m.    Oa 

Oor,  Tab.  XX,  Sub.     6  Loa  92°  14'  K  in  time.  6       8      66    Eq.  of  Time.  9m  l2a-43  Dif  lLl-049 

True  Alt..  36°    5'  Greea  Date,  Dec.  5th  . .   lb.    6m.    4a.  Correction  . . 1  04  1 

Polar  Dist.  68   45  .Log.  0.03058  Correct  Equa,  9m.  118-89  l8-041> 

Latitude 38    38    Log.  0.10726  Jupiter's  Dec  N'n.  Dec  6th.  21°  15'  S. 

Sum 143°"28'  ^Q     0 

Half  Sum. . .  ."71°  44'.  Log.  4.49616  Jupiter's  Polar  Dist 68°  46' 

Difference  . .  ."j5^.  Log.  ^76^  gun's  R  A.  16h.  46m.  86..  Di£  Ih..  lU  ^5-  ^^-  i   l9h.  67m.  ISs. 
Jup.'saA.   4L    0m.293.Log.  9.89953  Correction.   0       0      11  Dec 6th  I 

RAscen.  19    67      15  Corrected  . leOeSri?^  D^fth  }  ^^     ^^        * 


R.A  of  Mer.23h.57m7?4 

Sun'8RA.l6    46      47  LatObs.at  N'n  38°  10' S.  Long 92"  fto' R  Say  as  24h.  is  to  6ls.8oi8lh.6ia 

Ap.T  at  S'p77hTo^~578.  Co.  S.W.  40=D.L.    28  S.  Dep.  28  — D.L.36W.  *91249  A.  C.  R  Log.  24h,T«.XXXlV 

Eq,  of  T,Sub. 9_  JU  Lat  time  sight8.38°  38'  S.  Long.. ...  92*  14'  E.    ^J  J69  go.  Log.. .  61^  ^^ 

Mn.  Time,     7h.  Im.  468.  -'"  '^  „    \         ' 

T.  by  watch  7    16        0  App. 'Hme  at  Ship 7h.  10m.  67s.  3.664/  Pro.  Log.  Corr.       Om.    iA. 

W.  fast  M,  T — 18m.  14s  '^™«  by  Watch 7     15        0  ^  Ascen,  Dec  6th.l9h.  67      18 

"^      *■  ^   Watch  fast  of  App.  T. .  (*.    4m.    3a.           CorrectR.  Aacea  . .  .19h,  67m.  16* 

•  See  the  Note  at  page  133.  for  worklnir  bv  the  Proportional  liogm. 


136  NAUTICAL  ASTRONOMY. 


FINDING  THE  TIME  AT  SHIP  FROM  AN  ALTITUDE  OF  A  STAR. 

The  Time  may  also  be  found  as  correctly  by  an  Altitude  of  a  Star  at  a  distance  from  the  Meridian, 
twilight,  as  by  the  Sun  ;  and  the  name  of  the  Star  of  which  the  Altitude  is  observed,  may  be  found  in  Iik« 
manner  as  the  Planets,  by  referring  to  the  Diagrams  and  Rules  for  finding  the  Meridian  Altitude  of  th« 
Stars,  at  pages  64  and  65.  The  names  of  any  of  the  Stars,  in  Table  XIX,  when  observed  out  of  the  Meridian, 
may  be  found  by  imagining  a  point  in  the  heavens,  in  an  opposite  direction  to  the  elevated  Pole,  which  is 
equal  in  Altitude  to  the  Co-Latitude  of  the  place.  This  point  will  represent  the  Upper  part  or  Elevation 
of  the  Celestial  Equator.  Then  suppose  a  semicircle  drawn  from  thence  through  the  true  East  and  West 
points  of  the  Horizon,  will  represent  the  Celestial  Equator. 

Then  all  the  Stais  seen  to  the  Northward  of  this  semicircle  will  have  North  Declination,  and  those  seen 
to  the  Southward  of  it  will  have  South  Declination,  and  it  can  at  once  be  determined  whether  the  Star 
observed  has  North  or  South  Declination.  Now  estimate  its  distance  in  Degrees  from  this  supposed  line  or 
Equator,  and  enter  Table  XIX,  and  find  which  of  the  Stars  corresponds  nearest  to  this  estimated  Deoli- 
oation. 

The  bearing  of  the  Star  will  show  whether  it  be  to  the  Eastward  or  Westward  of  the  Meridian.  Now 
•enter  Table  XVI II  with  the  day  of  the  month,  and  find  at  what  time  it  would  pass  the  Meridian  on  that 
day.  Then,  if  the  Star  be  to  the  Eastward  when  observed,  and  it  is  the  proper  Star,  the  Table  wil'  give 
its  Meridian  passage  later  in  the  day  ;  but  if  observed  to  the  Westward,  it  will  give  it  earlier  in  the  day. 
Thus  the  Declination  and  Meridian  passage  will  point  out  the  name  of  the  Star. 

And  as  before  stated,  all  the  Stars  having  North  Declination  rise  and  set  to  the  Northward  of  th^  true 
East  and  West  points  of  the  Horizon,  while  those  having  South  Declination  rise  and  set  to  the  Southward 
■of  the  East  and  West  points. 

And  in  Hish  Latitudes,  when  their  Declinations  are  of  the  same  name  as  the  Latitude,  their  Altitudes 
are  high,  and  they  pass  the  Prime  Vertical,  that  is,  they  pass  the  East  or  West  points  above  the  Horizon. 
But  when  the  Latitude  and  their  Declinations  are  of  contrary  names,  their  Altitudes  are  low,  and  they  do 
iiot  reach  the  East  or  West  points  (at  rising  or  setting)  when  above  the  Horizon. 

RULES 
For  Computing  the  Corrections. 

1.  Turn  the  Ship's  Longitude  into  Time,  and  add  it  to  the  Time  by  Watch,  in  West  Longitude,  or 
tubtra&t  it  in  East,  will  give  the  Greenwich  Date. 

To  Correct  the  Starts  Observed  Altitude. 

2.  Take  out  the  Correction  from  Table  XX.  and  subtract  it  from  the  observed  Altitude,  will  give  the 
Star's  true  Altitude. 

To  Correct  the  Star''s  Declinatiori. 

3.  Take  out  the  Star's  Declination  from  Table  XIX,  and  the  annual  Variation;  multiply  this  by  the 
number  of  years  elapsed  since  1854,  and  divide  by  60,  if  above  60",  will  give  the  correction  in  Minutes 
and  Seconds,  and  apply  it  according  to  the  sign  of  addition  (+)  or  subtraction  ( — )  found  in  the  Table. 

To  Find  the  Star''s  Polar  Distance. 

4.  When  the  Latitude  and  Declination  of  the  Star  are  of  the  same  name,  the  Difference  between  th« 
Declination  and  90°  is  the  Polar  Distance,  otherwise  their  Sum  is  the  Polar  Distance. 

To  Find  the  Latitude  at  the  Time  of  Observation. 

6.  Find  the  Difference  of  Latitude  the  Ship  has  made,  and  apply  it  to  the  Latitude  last  observed. 

To  Find  the  Starts  Hour  Angle. 

6  Having  thus  the  True  Altitude  and  Polar  Distance  of  the  Star,  and  the  Latitude  of  the  place,  pro- 
•eed  as  with  the  Sun  to  find  the  Star's  Hour  Angle,  or  Distance  from  the  Meridian,  (which  with  the  Sun 
is  the  time  from  Noon.) 

To  Correct  the  Starts  Right  Ascension. 

7.  Take  out  the  Star's  Right  Ascension  from  Table  XIX,  and  the  annual  Variation;  multiply  this  by 
the  number  of  years  elapsed  sine  1854,  and  divide  by  60,  (if  above  60s.,)  will  give  the  correction,  which 
«  always  culditive. 


» 


•J'O  FIND  THE  TIME.  IST 

FINDING  THE  TIME  AT  SHIP  FROM  AN  ALTITUDE  OF  A  STAR. 
To  Find  the  Right  Ascension  of  the  Meridian. 

8.  If  the  Star  be  to  the  Eastward  of  the  Meridian,  subtract  its  Hour  Angle  from  its  Right  Ascension,  Bat  if  ta 
the  Westward,  add  its  Hour  Angle  to  its  Right  Ascension,  will  give  the  Right  Ascension  of  the  Meridian 

To  Find  the  Sun's  Right  Ascension. 

9  Take  out  the  Sun's  Riglit  Ascension,  and  the  Difference  for  1  hour,  from  the  Nautical  Almanac,  for  the  Nooa 
of  the  Greenwich  Date.  Multiply  the  Difference  for  1  hour  by  the  time  from  Greenwich  Noon,  and  divide  by  60 
(fl  above  60),     This  Correction  is  always  additive. 

To  Fi7}(l  the  Apparent  Time  at  Ship. 

10.  Fi-om  the  Right  Ascension  of  the  Meridian,  (increased  by  24  hours,  if  necessary),  subtract  the  Sun's  Oorreot 
Right  Ascension,  and  the  remainder  is  the  Apparent  Time. 

To  Find  the  Mean  Time  at  Ship. 

11.  Take  out  the  Equation  of  Time,  and  the  Difference  for  1  hour  from  the  Nautical  Almanac,  and  correct  it  to 
the  Greenwich  Date  by  the  rules  at  page  124,  and  apply  it  to  the  Apparent  Time,  according  to  the  precept  at  the 
head  of  tlie  column  in  the  Nautical  Almanac,  by  adding  oi  subtracting  it,  and  the  result  is  the  Mean  Time  at  Ship 

EXAMPLE  1. 

February  10th,  1854,  Sea  Time,  in  Latitude  40°  10'  N.,  Longitude  68"  20'  W„  in  the  Evening  Twilight,  the  Obd 
Altitude  of  the  Star  Sirius  was  12°  29'  to  the  Eastward  of  the  Meridian.  The  Time  by  Watch  was  5h  28m.  Re 
quired  the  error  of  the  Watcli  on  both  Apparent  and  Mean  Time.    Elevation  16  feet. 


Obeei-ve.l  Altitude  of  Sirius  12°  29' 
Corn,  Table  XX Sub.  8 


True  Altitude 12"  21' 

Polar  Distance 106    31 

Latitude 40    10    Log.  0,11681 

6um 


Time  by  Watch 5h  2Sra    Oe     Sirius's  Declination,  1864..  16°  31'  a 

Long.  68°  20'  W.  in  time  4    33      20  90      0 

Green.  Date,  Feb.  9th . .    lOh    Im  20s     Polar  Distance 106°  81' 


Log.  0.01830 


Sirius's  Right  Ascension,  1854,  6h  38m  48« 


159°     2' 

Half  Sum 79°  31' 

Oifference 67°  10' 

Sirius's  Hour  Angle. . .    3h  48m  409 
eiiius's  Right  Ascen.. ..  6    38      43 

A.  A«ceo.  of  the  Mer. .   2li  50m    33 
Add. 21       0        0 

increased  ti.  A.  M 2tih  50m    Ss 

Suo'b  il.  Adcen 21     33      14 


Log.  4.25995 
Log.  4.96466 
Log.  9.35962 


Sun's  R.  A,  Feb.  9th  21h  31m  34s     DiflF.  Ih lOi 

Add  1      40  10 

60)100i 

lm408 


Correct  Right  Asceu.  21  h  33m  148 


App.  Time  at  Ship.  ...    5h  16m  49b 
Equation Add         14      32 

Mean  Time  at  Ship. .     5h  81m  21b 


Time  by  Watch 5h  28m    Oa 

Apparent  Time 5     16      49 

Watch  fast Oh  11m  lis  of  Apparent  Time. 

Time  by  Watch 5h  28m    Os 

Mean  Time 5    31      21 

Watch  slow Oh    3m  2l8  of  Mean  Time. 


EXAMPLE  2. 

"May  13th.  1854,  Sea  Time.  Ship's  position  at  the  preceding  Noon  was  Latitude  37°  44'  S,  Longitude  68*  9'  K 
She  then  sailed  E.  S.  S.,  120  ti.-'les,  until  4h  40m  A.  M.,  when  the  Altitudes  of  Antares  was  observed  42°  86',  to  the 
Westward.     Required  the  error  yj  the  Watch  on  both  Apparent  and  Mean  Time.    Elevation  18  feet. 

Obs.  Alt.  of  Antares 42°  86'  Time  by  Watch 4h  40m     Antares's  Declination  1864  26*    6'  S 

Corr..  Table  XX... Sub.  5  Add.  12      0  90      0 

:True  Altitude 42°  81'  From  preced.  Noon  "l6h  40m      Antares's  Polar  Distance...  63°  64' 

Polar  Distance 63    54   Log.  0.04671  Lon.  70°  30' E.in  T..   4    42 

^^^'^^»<i« ^!2.  ^"S- 0-10646  Q  Date,  May  1 2th. . iThSSiii  Antares's  R.  A.,  1854,  16h  20m  24t 

Bum .144°  55' 

Half  Sum 72°^  Log.  4.47894  Noon  previous  Lat 37°  44'  S.,  and  Long 68*    9'  E 

Difference 29°  57'  Log. 4.69831   Course  E.  S.  E.  120m]3.D.L.  0    46   S.,  Dep.  Ill  =  Diff.  )    2    21   K      " 

Antares's  H.  AngU  3h  40m"278  Log"9;33042  ^at.  in  at  Time  of  Sights. ,  .38°  30'  S.,      ^'^^S-  141  =  .  ) 

Antares'  Right  a.. 16    20     24  Longitude  in 70°  80'  K 

R.  Asc,  of  the  Mer.2(.h    Om  6 Is  Sun's  Right  Ascension,  May  12th,  3h  15m  508  Diff  Ih         lOi 

Sun's  R.  Asoeu SJ7      50  Add  2         0  12 

App.  Time  from  )  ,„,     „        ,  Sun's  Correct  R.  A 3h  17m  60s  30)120a 

previous  Noon.  {  ^^^  ^^"^    *»  "g^ 

Sub.  22 0 0  Equi.<don  of  Time.3m  52s34     Diff.  Ih     -53 

App.  T.  at  Ship....  4h  43m    Is  ^'""^    ■^^'^     '^  12h 

Equa.  of  Time 3      58  3m  52897     Corr.      ■63-6 

Mean  T.  at  Sliip. ..  4h  39m~8s  Apparent  Time  at  Ship 4h  43m  Is 

T.  by  the  Watch..  4    40       0  Time  by  Watch 4    40     0 

Watch  Fast   oh    Om  52s  ^i  Mvan  "^use.       "Kntch  Slow   Oh    3m  Is  of  Apparent  Time 


138  NAUTICAL  ASTRONOMY. 


FJNDING  THE  LONGITUDE  BY  CHLi)NOMETER. 


7%c  Cause  of  a  Ship  Losing  or  Gaining  Time. 

Having  thus  given  all  the  most  practical  methods  of  finding  the  Time  at  Sea,  it  will  be  necessary,  betor« 
preceding  to  find  the  Longitude,  to  premise,  that  when  a  Ship  sails  Westward  she  loses  Time ;  that  is,  the 
Time  shown  by  the  Watch,  which  was  regulated  to  Apparent  Time  on  the  preceding  day,  will  be  in  advance 
of  that  found  by  observation  on  the  following  day.  And  that  when  a  Ship  sails  Eastward  she  gains  Time 
that  is,  the  Time  shown  by  the  Watch,  which  was  regulated  to  Apparent  Time  on  the  preceding  day,  will 
be  behind  that  found  by  observation  on  the  following  day. 

The  Rotation  of  the  Earth  is  the  Cause  oj  the  Difference  of  Time  between  Places. 

'xhe  velocity  of  the  Earth's  rotation  on  its  axis  from  West  to  East,  is  360°  in  24  hours  of  time,  or  at  tha 
rate  of  15°  to  the  hour,  and  1'  to  every  4  minutes.  It  is  evident  that  any  place  that  lies  Eastward  of 
another  place,  will  come  sooner  under  the  Sun,  or  will  have  the  Sun  earlier  on  the  Meridian,  consequently 
the  hour  of  the  day  will  be  in  advance  of  the  other.  On  the  other  hand,  any  place  that  lies  to  the  Wesy- 
ward  of  another  place,  will  be  later  in  coming  under  the  Sun.  or  will  have  the  Sun  later  on  the  Meridian, 
consequently  the  hour  of  the  day  will  be  behind  that  of  the  other.  Thus,  at  a  place,  say  Greenwich 
Observatory,  situated  74°,  or  4h  56m  in  time,  to  the  Eastward  of  New  York,  when  it  is  Noon  at  Greenwich, 
it  wants  4h  56m  of  being  Noon  at  New  York  ;  and  when  it  is  Noon  at  New  York  it  is  4h  56m  past  Noon 
at  Greenwich.  And  at  a  place,  say  San  Francisco,  situated  48°,  or  3h  12m  in  time,  to  the  Westward  of 
New  York,  when  it  is  Noon  at  San  Francisco  it  is  3h  12m  past  Noon  at  New  York,  and  when  it  is  Noon  at 
New  York,  it  wants  3h  12m  of  being  Noon  at  San  Francisco.  Hence  the  difference  of  Time  between  any 
two  places,  indicates  their  difference  or  Longitude. 

Longitude  Reckoned  from  the  Meridian  of  Greenwich. 

Longitude  is  reckoned  from  a  first  Meridian,  and  in  this  work  we  use  the  Meridian  of  Greenwich  as 
first   Meridian,  and  from  which  the  Longitude   is  reckoned   Eastward    180°  and  Westward  180°,  which 
together  are  equal  to  the  circumference  of  the  globe. 

On  Circumnavigating  the  Globe.,  steering  West.,  Ship  loses  one  Day. 

Suppose  a  Ship  to  sail  from  Greenwich,  with  her  Chronometer  accurately  set  to  Greenwich  Mean  Time, 
and  steering  to  the  Westward,  when  she  has  made  15°  of  Longitude  the  Mean  Time  at  the  Ship  will  be 
found  to  be  1  hour  behind  that  by  the  Chronometer.  She  has  therefore  lost  1  hour  of  time.  And  sup- 
posing the  Ship  to  continue  her  course  to  the  Westward  until  she  reaches  the  Longitude  of  180'  W.,  the 
Mean  Time  at  the  Ship  will  be  12  hours  behind  that  of  the  Chronometer,  and  she  will  have  lost  12  hours 
in  time.  The  Ship  being  now  in  East  Longitude,  and  continuing  her  course  to  the  Westward,  her  Longi- 
tude decreases,  and  finally,  when  she  arrives  again  on  the  Meridian  of  Greenwich,  (after  circumnavigating 
the  Globe)  it  will  be  found  that  the  Mean  Time  at  the  Ship  is  24  hours  behind  the  Mean  Time  at  Green 
wich,  consequently  she  has  lost  one  entire  day  on  the  voyage. 

On  Circumnavigating  the  Globe,  steering  East,  Ship  gains  one  Day. 

On  the  other  hand,  a  Ship  sailing  East  from  Greenwich,  under  the  same  circumstances,  when  she  ha« 
made  15°  of  Longitude,  the  Mean  Time  at  the  Ship  will  be  found  to  be  1  hour  in  advance  of  the  Green- 
wich Time  by  Chronometer,  and  she  has  therefore  gained  1  hour  of  time.  And  continuing  her  course  to 
the  Eastward  until  she  reaches  the  Longitude  of  180°  E.,  the  Mean  Time  at  the  Ship  will  be  12  hours  in 
advance  of  the  Greenwich  Time  by  Chronometer,  and  she  will  have  gained  12  hours  of  time.  Being  now 
in  West  Longitude,  and  continuing  her  course  to  the  Eastward,  her  Longitude  decreases,  and  finally,  when 
«he  arrives  again  on  the  Meridian  of  Greenwich,  (after  circumnavigating  the  Globe),  it  will  be  found  that 
the  Mean  Time  at  the  Ship  is  24  hours  in  advance  of  the  Mean  Time  at  Greenwich,  consequently  ehe  haj 
gained  one  entire  day  on  the  voyage. 

In  Circumnavigating  round  by  the  West,  one  Day  is  subtracted  from  the  Greenwich  Date. 

In  the  case  of  Circumnavigating,  the  general  practice  is,  that  when  on  reaching  the  opposite  Meridian 
to  Greenwich,  (or  the  Longitude  of  180°  W.),  in  sailing  round  by  the  West,  into  East  Longitude,  and  with 
the  view  of  making  the  general  rule  applicable,  which  is,  that  the  Greenwich  Time  should  be  the  least  >B 
East  Longitude,  we  subtract  one  day  fro'u  the  Greenwich  Date,  so  that  when  the  Ship  arrives  again  on  tW 
Meridian  of  Greenwich,  the  time  at  Ship,  and  the  Greenwich  Time  by  Chronometer  will  coincide. 


FINDING  THE  LONGITUDE  BY  CHRONOMETER  !»» 

In  Circumnavigating  round  by  the  East,  one  Day  is  Added  to  the  Greenwich  Date. 

In  Circumnavigating  round  by  the  East,  the  general  practice  is,  that  on  reaching  the  opposite  Mendiai 
to  Greenwich,  or  the  Longitude  of  180°  E.,  thence  passing  into  West  Longitude,  and  with  the  view  of 
making  the  general  rule  applicable,  which  is.  that  the  Greenwich  Time  should  be  the  greatest  in  We«l 
Longitude,  we  add  one  day  to  the  Greenwich  Date,  and  on  the  Ship's  arrival  again  on  the  Meridiau  of 
Rreenwioh,  the  time  at  Ship  will  coincide  with  the  Greenwich  Time  by  Chronometer. 

On  Ascertaining  the  Greenwich  Ti-ne  from  the  Chronometer. 

As  only  12  hours  are  given  on  the  face  of  the  Chronometfcr,  it  shows  only  the  time  after  Noon  or  Mid- 
night, therefore  when  it  is  A.  M.  at  Greenwich,  by  adding  12  hours  to  it,  we  have  the  time  since  the  ))r«- 
ceding  Noon. 

If  it  .<;hows  P.  M.  at  Greenwich,  the  Noon  of  the  present  day  will  be  the  preceding  Noon  at  Greenwich, 
or  tlie  beginning  of  the  Astronomical  day.  which,  with  the  day  of  the  month  prefixed,  is  called  the  Grren 
wich  Date. 

To  know  whether  the  Time  by  Chronometer  is  P.  M.  or  A.  M.  at  Greenwich. 

To  the  Astronomical  Mean  Time  at  the  Ship  (which  is  found  by  taking  one  day  from  the  Sea  Date,  and 
eounted  through  the  24  hours),  add  the  Ship's  Longitude  in  time  in  West  Longitude,  or  subtract  it  in  East  . 
the  Sum  or  DitTerence  will  be  the  Mean  Time  at  Greenwich.  If  it  be  less  than  12  hours,  the  face  of  ilie 
Chronometer  will  show  P.  M.  at  Greenwich  ;  but  if  the  Greenwich  Time  be  more  than  12  hours,  the  face 
of  ihe  Chronometer  will  show  A.  M.  at  Greenwich,  to  which  we  must  add  12  hours  to  get  the  Time  from 
the  iireceding  Noon. 

Longitude  is  the  Difference  of  Time  between  two  Meridians^  and  how  Found. 

it  will  be  perceived,  from  the  above  remarks  that  Longitude  is  merely  a  question  of  the  difference  of 
Time  between  two  Meridians.  If  we,  therefore,  have  the  correct  Mean  Time  at  the  first  Meridian  ♦ 
Greenwich,  shown  by  a  Chronometer,  we  can  at  any  time  find  the  Longitude  of  the  Ship  by  simply  taking 
the  difference  between  the  Mean  Time  at  Greenwich  and  the  Mean  Time  at  the  Ship,  fouiid  by  any  of  tbe 
.T.etiiods  already  given  in  this  work,  which,  turned  into  Degrees  and  Minutes,  by  Table  XXVI,  is  the  Shij  » 
Longitude 

Then,  it  the  Greenwich  Time  be  greater  than  the  time  at  the  Ship,  the  Longitude  is  West;  but  if  the 
Greenwich  Time  is  the  least ^  the  Longitude  is  East.  ^'j;.-^^'" 

When  one  of  the  Times  is  P.  M.  and  the  other  A.  M.  on  the  same  day,  we  must  add  24  hours  to  that  at 
P    M.,  and  take  their  difference  for  the  Longitude  in  time. 

And  when  the  P.  M.  and  A.  M.  Times  fall  on  different  dates,  their  difference,  counted  from  their  preced- 
iu2  Noons,  is  the  Longitude  in  Time. 


) 


Rate  of  a  Chronometer, 

The  Chronometer  would  therefore  be  a  most  useful  instrument,  were  it  to  keep  a  steady  uniform  rate 
throughout  the  voyage,  and  nothing  more  would  be  required  ;  but  as  this  is  seldom  the  case,  (see  remarki 
at  Pages  79  and  80),  it  is  necessary  that  it  should  be  verified  from  time  to  time  during  the  voyage,  in  order 
to  ascertain  its  error  on  Greenwich  Mean  Time,  at  the  place  of  observation,  and  its  present  rate.  Th« 
manner  of  doing  this  will  be  found  at  page  155. 

Method  of  Keeping  an  Account  of  the  Rate. 

Calculate  the  daily  error  of  the  Chronometer  on  Greenwich  Mean  Time  by  applying  the  Rate  for  each  da^i 
for  several  days  in  advance,  and  write  it  on  the  margin  of  the  Nautical  Almanac,  each  day's  error  opposit* 
the  day  of  the  month.  So  that  the  error  of  the  Chronometer  can  be  taken  out  and  applied  at  once  from 
the  same  page  that  the  Sun's  Declination  and  Equation  of  Time  are  taken  from.  This  will  be  found  a 
▼ery  convenient  mode,  and  save  some  time  and  trouble. 

To  Find  the  Accumulated  Error  of  a  Chronometer ,  after  a  lapse  of  Time. 

Multiply   the    Daily  Rate,  which   is   generally  given  in   Seconds  and   Tenths  of  Seconds,  by  the   days 
apsed  since  the  last  Rate  was  ascertained,  and  divide  by  60,  (if  it  is  above  60),  will  give  the  accumula- 
ted Rate,  lu  x.Iinutes  and  Seconds.     This  applied  to  the  original  error, 

f  Fa.st,  and  the  Daily  Hate  Gaining,  Add, 
^j^      tb    Pt  t      '    }  ^''''^)  ^"*^  ^^^  Daily  Rate  Gaining,  Subtract, 

I  Fast,  and  the  Daily  Rate  Losing,  Subtract, 
[  Slow,  and  the  Daily  Rate  Losing,  Add, 

will  give  the  whole  error  of  the  Chronometer  on  Greenwich  Mean  Time  on  that  day;   and  it  is  applied  la 
[■    the  8am<)  manner  as  for  a  common  watch,  and  requires  no  explanation. 


140  J^AtJTIOAL  ASTEONOMY. 

Mode  of  Observing  Altitudes. 

In  taking  Altitudes  of  any  of  the  Heavenly  Bodies,  for  the  purpose  of  finding  the  time  at  the  Ship,  th« 
times  by  Chronometer  at  which  they  were  observed,  must  be  noted,  and  the  Altitudes  are  then  added 
•together  and  divided  by  the  number  taken.  The  times  by  Chronometer  are  in  like  manner  added  together, 
and  divided  by  the  number  taken.  This  gives  the  Mean  of  the  Altitudes,  and  the  Mean  of  the  Times 
'by  Chronometer.  By  this  mode  we  are  supposed  to  obtain  a  more  correct  result  by  taking  the  Arith- 
imetical  Mean  of  the  Altitudes  than  can  be  obtained  from  one  Altitude  alone.  At  all  events,  it  prevent" 
imistakes  in  the  readings  off.     (See  also  the  method  given  at  page  1-24.) 

TTie  Times  at  which  the  Altitudes  were  observed  to  be  taken  by  a  Watch. 

A«  the  Chronometer  must,  on  no  account,  be  removed  from  tlie  place  where  it  has  been  fixed  for  the 
TOyage,  it  may  not  be  convenient  to  note  the  time  direct  from  the  Chronometer  at  the  time  of  taking  the 
Altitudes,  and  in  that  case  we  use  a  Hack  or  common  Watch,  furnished  with  a  Second  Hand,  with  which 
the  Times  of  the  Altitudes  are  taken.  It  is  then  immediately  afterwards  compared  with  the  Chronometer, 
and  their  difference  noted.  This  difference  being  then  applied  to  the  Mean  of  the  Times  by  "Watch,  at 
ivhich  the  Altitudes  were  observed,  will  give  the  Time  of  the  Altitudes  by  Chronometer.  Its  error  being 
then  appHed,  we  have  the  Greenwich  Time. 

The  Mean  Time  at  Ship  by  an  Altitude  of  the  Sun  is  then  found  in  exactly  the  same  manner  as  that  given  at 

Eage  124,  using  the  Greenwich  Time  by  Chronometer,  in  making  the  Corrections,  in  the  room  of  the  approx- 
oate  Greenwich  Time.     The  following  is  an  example  of  the  whole  process,  as  is  usually  done  at  Sea,  and  both 
Latitude  and  Longitude  found  at  Noon. 

EXAMPLE  1. 

March  6th,  1854  (at  the  end  of  the  Sea  Day),  a  Ship  which  sailed  from  her  last  port  5  days  previously  had  the 
following  observations  in  the  morning:  The  Error  of  her  Chronometer  on  Greenwich  Time,  March  1st,  was  Oh  2m 
148  fast,  and  the  Daily  Rate  2s  and  6-10  gaining.  Ship  sailed  N.  W.  60  miles  until  Noon,  when  the  Sun's  Merid- 
ian Altitude  observed  was  46°  32'  S.,  and  the  Longitude  by  Dead  Reckoning  being  about  54°  W.  Required  her 
Latitude  and  Longitude  in  at  Noon. 

Bun's  Obs.  Altitude  L.  Limb..  10°  12' Times  by  the  Watch 1h  Urn  24a 

0    22 0     12     30 

0    35 0     13     60 

S)69'  3)37m  443 


1 


Mean  of  the  Altitudes 10°  23' Mean  of  the  Times  by  Watch 7h  12m  353 

Oorr.,  Table  IX Add  7  Comparison  Chro.  fast  of  Watch 3   49     64 

Sun'i  True  Altitude 10°  30'  Time  by  Chronometer  A  M llh  2m  298 

Sun's  Polar  Distance 96  41   Log.  0.00214         Accumulated  Error  Fast Sub.  2     27 

Latitude ^8 5_Log.  0.10396         Greenwich  Time  from  Midnight llh  Om    28 

Sum 144°  16'  Add.    12      0       0 

HalfSum ^2°    8'  Log.  4.48686         Greenwich  Date,  March  5th •  23h   Om  23 

Difference "6 1V38^  Log.  4.94445  Mer.  Alt.  Obs 46°  32' S.  Difif.  Decl,        lh=.68 

Apparent  Time 19h  12m  24s  Log.  9.53^41"        Corr.,  Table  LX ..  Add 11       Cor.  for  Ln.   54°W.  Sjh 

Equation  of  Time Add         11     32  True  Altitude 45°  43'  174  " 

Mean  Time 19h  23m  56s  Zenith  Distance 44°17'N.  ^^ 

Greenwich  Time 23      0       2  Declination 6    37  S.  60)203  " 

Longitude  in  Time 3h  36m    6s  =  54°  1'  30"  W.  Lat.  at  Noon 38°  40'  N.  Corr 3'  23   " 

Departure  made  to  Noon,  35' — Diflf.  Long.        45     0    W.  Course  N.  W.  50m  D.  L. 35        Decl 5°  40'    0  S. 

Long,  of  the  Ship  at  Noon 64°  46'  30"  W.  Lat.  at  Sights 38°    6'  N.  Decl 5°  36'  37"S. 

To  find  the  Comparison.  Sun's  Dec.  Noon,  March  6th.    5°  40'    2"  S.  Diflf  Ih.  .58" 

Time  by  Chronometer llh    5m  548  Corr.  Ih  before  Noon.  .Add 68 

Time  by  Watch 7    16        0  Corrected  Dec 6°  41'    0" 

(Jomparison  Chro.  fast  of  Watch 3h  49m  54s  _90j_0_0 

Polar  Distance 95°  41'  0" 

To  find  the  Error  of  the  Chronometer. 

Chronometer  fast  March  1st Oh    2m  14s  Equation  of  Time 11m  31s -74  Diflf.  Ih   60-J 

Days  elapsed  5,  daily  rate  2s  6-10  — 13    Corr.  Ih  before  Noon.  ...Add     '60 

Accumulated  Error Oh    2m  27s  Correct  Equa 11m  328  -34 

RULE  FOR  TURNING  TIME   INTO  LONGITUDE  BY  COMPUTATION. 

Tom  the  Hours  into  Minutes,  and  divide  by  4     This  gives  Degrees,  Minutes,  and  Seconds. 
JBrompfc.— 3h  36m  68  is  216m  68,  which,  divided  by  4,  gives  54*  1'  30". 

,  RULE  FOR  TURNING  LONGITUDE  INTO  TIME  BY  COMPUTATION. 

Multiply  the  Longitude  by  4.     This  turns  the  Degrees  into  Minutes  of  Time  (which,  divided  by  60,  gives  Houri 
and  Minutes),  the  Minutes  of  Longitude  into  Seconds  of  Time,  and  the  Seconds  of  Longitude  into  Thirds  of  Time. 

Example.— LougMwdQ  64°  1'  30",  multiplied  by  4,  gives  216m  6s  =  3h  36m  6s. 


FINDING  THE  LONGITUDi;:.  Ul 

FINDING  THE  LONGITUDE  BY  CHRONOMETER  FROM  THE  SUN'S  ALTITUDE. 

Referring  to  the  1st  Example,  it  will  be  perceived  that  the  Time  shown  by  the  face  of  the  Chronometei 
it  llh  2m.  29s.,  and  the  accumulated  Error  subtracted,  would  give  the  Greenwich  Time  from  midnight, 
111..  Om.  2s.  The  Mean  Time  at  Ship,  from  the  preceding  midnight,  being  7h.  23m.  66s.,  their  Difference, 
8h.  36m.  6s.,  is  the  Longitude  in  time.  This  mode  of  reckoning  the  two  times  from  the  same  midnight  '« 
frequently  done  at  Sea,  because  it  is  more  convenient  than  to  reckon  them  from  the  preceding  Noon.  Th« 
result  in  either  case  is  the  same.  The  Time  from  Noon,  A.  M.,  in  the  one  case  is  found  by  subtracting  it 
from  24  hours,  and  in  the  other  from  12  hours. 

In  the  Example  referred  to,  the  time  from  Noon  is  1  hour,  and  the  difference  of  the  Sun's  Declination 
and  Equation  ef  Time  for  1  laour,  in  the  column  of  the  Nautical  Almanac,  is  the  correction  required,  tc 
ke  applied  as  directed  at  page  124,  No.  7. 

RULE 

For  Correcting  the  Sun's  Declination  at  Noon  of  the  Ship  by  the  Nautical  Almanac. 

Multiply  the  difference  for  1  hour  by  the  Longitude  in  Time,  and  divide  by  60,  if  requiised,  will  give  th« 
correction  in  Minutes  and  Seconds,  to  be  applied  to  that  taken  from  the  Nautical  Almanac,  as  follows : 

In  West  Longitudt,  and  Declination     .     .     .     ." (  Increasing,  Add 

(  Decreasnig,  Subtract, 

In  East  Longitude  and  Declination  \  }°«'-«^^ingi  ^ub^t'"*''^ 

'^  (  Decreasing,  Add, 

RULE 
To  Reduce  the  Longitude  by  Chionometer  at  Time  of  Sights  to  Noon 

Take  the  I  ^'-tude  in  as  a  Course,  and  the  Departure  made  in  the  interval,  in  the  Latitude  column,  the 
Hifferenee  of  Longitude  is  found  in  the  Distance  column.     Apply  this  as  follows : 

Observation  taken  in  the  morning,  in  West  Longitude     ....    {  gSlini  S' Subtract, 

Observation  taken  in  the  afternoon,  in  West  Longitude     ....    ]  OnHin^  EasV  Add        ' 
To  or  from  the  Longitude  by  Chronometer,  will  give  the  Longitude  in  at  Noon. 
By  substituting  East  for  West,  the  same  Rule  may  be  applied  in  East  Longitud*. 

EXAMPLE  2 

April  2d,  1854.  (End  of  the  Sea  day.)  The  Latitude  observed  was  30'  S7'  North.  Ship  then  sailed  S.  R(true) 
60  miles,  when  the  following  observation  was  made  in  the  afternoon,  the  Error  of  her  Chronometer  on  Greenwich 
Mean  Time,  on  the  23d  of  March,  was  ascertained  to  be  Oh.  9m.  3l8.  fast,  and  the  daily  rate  38  4-lOth  losing.  Re- 
quired her  Longitude  in  at  time  of  Sights  and  Noon. 

Sun'i  Obs.  Alt 10°  13' Times  by  Watch ...  5h.  24m.    Os.  To  find  the  Comparison^ 

10     0 25        0    Timeby  Chro..  8h.  42m.  48s 

9  47 26        0    Time  by  Watch,  6     28      0 

8)80°  0'  3)7  5m.    Oa.  Comparison . .    8h.l4m.48& 

Mean  of  the  Alt 10°  0' Mn,  of  the  Times  by  W,. .    5hr26m.    Os. 

Corr.,  T»)-,le  IX  ...Add  7 Comparison 3     14      48 

True  Alt ...10°    7' Time  by  Chro 8h.39m.48B. 

Polar  L)i9t 84°  67'. .  .Log.  0.00169  Accuma  error.  .Sub.       8      57 

LatitMe 80      2.  ...  Log.  0.06262  Gr.  Vnt^,  April  2d .  8h.  80m.  f  > 

Sum   .'T25°     6'  Chr  fast,  MarcL  aivi.         Jb.    9m.  81b. 

Half  Sum 62°  33',. . .  Log.  4.66368  Days  elap.  10.  Rate  3s.  4-1 0th    =-34 

Difference 52°  26'. . . Log.  4.89908  Accumulated  error Oh.    8m.  57b.  fast 

App.Time 5h.  24m.  548.. .  .Log.  9.62707*  „     .    ^    ,.         .      .,     ,        .«  =..  rr/' xt  T^•*  iu  ^t,n 

E^iktion ...  Add  8      35  Sun's  Declina,  April  2d . . .  4°  54'  55'  N.  D.f.  Ih    ........  ^1" 

,,       rp.  71—^ — ^  Correction Add  8     4  Time  from  Noon .    ijk 

Mean  Time 5h.  28m.  298.  ^  ^    ,.      .  ,.    ^,  ,.,  rz^ — 

Green  Time ....   8     30      51  Correct  Dechnation 5269  466 

Long,  in  Time  . .   3h.    2m.  22s.=45°  35'  SO"  W.  ^"      ^,     \  -„TT^7— 

Dep.  made  since  Noon  35' =Diff  Lon.  40  30  Polar  Distance 84    67      1  60)484 


Long,  in  at  Noon 46°  16'    O"  W. 


F*^ 


Course  S.E.  50  miles,  D.Lat      85' Dep.  85'      Equation  of  Time,  April  2q . .        8m.  418-71     Dif.  Ih  .      .  -760 

Lat  Obs.  at  Noon 80°  37'  N.  Correction Sub. 6^    Time  fr.  N  n, 8_ib 

Lat  Time  of  Sights 30°    2'  N.  3m.  368-34  6  000 

6-87-6 

Note. — Tie  Longitude  obtained  from  Morning  Altitudes  and  brought  on  to  Noon,  very  seldom  agrees  with  the  Lon* 
fitude  obtaii  ed  from  Afternoon  Altitudes  and  reduced  back  to  Noon.  This  is  supposed  to  be  caused  by  uneqaal 
Mfraction  in  the  Atmosphere,  together  with  errors  in  the  observed  Altitudes,  errors  in  the  Instrnments,  and  that  oiaa 
kioorrect  Latitude  used  in  the  computation. 


142  NAUTICAL  ASTRONOMY 

FINDING  THE  LONGITUDE  BY  CHRONOMETER  FROM  THE  SUN'S  ALTITUDK 

EXAMPLE  3. 
May  20th,  1854.  (Eud  of  the  Sea  day.)  A  Ship  being  in  South  Latitude,  and  in  about  77°  East  Longitude,  ih 
the  morning  the  Mean  of  several  Altitudes  of  the  Sun  was  observed  to  be  12°  10',  and  the  Time  by  the  Watch  8h 
10m.  20s.,  which,  on  being  compared,  was  found  to  be  fast  of  the  Chronometer  5h  15m  38s,  and  on  the  30th  April 
this  Chronometer  was  found  to  have  been  slow  on  Greenwich  Mean  Time  Oh  om  10s,  and  the  rate  losing  daily 
4  sec.  and  7-lOth.  Ship  then  sailed  on  a  S.  E.  Course  (true)  20  miles,  until  Noon,  when  the  Sun's  Meridian  Altitud« 
(Sbserved  was  33°  14'  N.     Required  her  Latitude  and  Longitude  in  at  Noon. 

Time  by  Watch 8h  10m  20s  ,7,   ^    , .,     ^ 

Comparison 5    15      38    „         To  ,fmd  the  Comparison^ 

^  Time  by  Chronometer, .   2h  57m  42i 

FaceofChro.  A.M 2h  54m  42s -jj^g  ^    ^^^^^j^ g    ^3     20 

Log.  0.02674    Accum.  Error Add  6     44  

Log.  0.09435    G, 


Sun's  Obs.  Alt  12°  10 

Cor.,  Tab.  LK  . 8 

True  Alt.....    12°  18' 
Polar  Dist...    109    54 


26 

158°  37' 


Latitude 36 

Sum 

Half  Sum 

"•ifference 

App.  T...20h  13m 
Eq.  of  T.. 3_ 

Mn.  Tirae20h        ' 
Gr.  Time  15 

Lon.  in  T.liT 


T.fi-omMid 3h 

Add  12h 

79M8y    Log.  4.26840   Gr.  Date,  May  19th 15h 

Subtract  from 24 

Time  Before  Noon 


67°    Oj' 

5s 

47 


Log.  4.96405 
Log.  9.35354 


Comparison 6h  15n^  388 

Chro.  Slow,  April  30th Oh  5m  10a 

Im  268  Days  elapsed  20X4s.7-10th  =   1  34 

0 0    Accumulated  Error Oh  6m  44« 


Im  268 
0       0 


8h  68m  34s 


9m  188 
1      26 


Dep.  made  | 
to  Noon  \ 

Lon 


7m  52     76"  68'    0" 
14  . .— D.  L.  17'  30 


E. 


Sun's  Dec.  20th  May 19 

Correction Sub. 

Correct  Declination  . 


58'  19"  N. 
4   39 


19° 
90 


53'  40" 
0     0 


Diff.  Ih -81" 

Before  Noon  . .     9h 

60)279 
Correction...    4*39 


'"•^fS'^'Pt 77°  16' 30"  K 

at  Noon     J 


Eq.  of  Time..  3m  468-15  Diflh.-140 
Correction...  Add  1  '26  Bef.  N       9h 

Correct  Eqa..3m  47s-41  Corr..l-26-O 


Polar  Distance 109°  53'  40" 

Meridian  Altitude 33°  14'  N.  Dif.  Dec.  lh= 

11         Long...  77°= 


=31" 

=.  5h 


_332 

Zenith  Distance 56° 

Declinatinn 19 

Lat.  of  Ship  at  Noon . . 
Course  S.  E.  20  miles. 


Dif  Lat. 


36°  39' 
14 


25' 

35'  S. 
56    N. 

""    S. 


Dec.  19' 


60)165 

2'  35" 
58'  19 


19°  55'  44"  ^f 


Latitude  at  Time  of  Sighta 36°  26'  S. 


EXAMPLE  4. 

October  10th,  1854.  (End  of  the  Sea  day.)  Latitude  observed  at  Noon  20°  41'  South,  Longitude  in  by  Dead 
Reckoning  179°  30'  East  at  Noon.  Ship  had  sailed  N.  E.  54  miles  since  Noon,  when  the  Mean  of  several  Altitudes 
of  the  Sun  was  observed  to  be  18°  45'.  Time  by  Watch  4h40ra  85s,  which,  on  being  compared  with  tlie  Chronome- 
ter, was  found  to  be  fast  of  the  Chronometer  Oh  14m  223,  and  on  the  10th  of  September  this  Chronometer  was  slow 
of  Greenwich  Mean  Time  Oh  10m  268.,  and  gaining  58.  2-lOth  per  day.  Required  the  Longitude  of  the  Ship  at  th« 
time  of  the  Sights  and  at  Noon. 


Sun's  Obs.  Alt 

Correction,  Table  IX. 


18' 


Add 


45' 
9 


True  Altitude 18°  54' 

Polar  Distance 83   29 

Latitude _20 3 

Sum 122°  26' 


Log.  0.00282 
Log.  0,02715 

Log.  4.68260 

Log.  4.82816 

App.  Time 4h "48m  538  Log.  9.54073 

Equation  of  Time. . . .  Sub.  12     60 

Mn.  Time  at  Ship,  Oct  10th~4h  36m    38 
Add  24      0       0 


Half  Sum 61 

Difference ; "iP" 


3s 
3 


Mn.  Time  at  Ship,  Oct  9th  28h  36m 
Mn.  Time  at  Green',  Oct  9th  16    34 

Long,  in  Time 12h    2m    0=180' 

Subtract  from 360 

Long,  of  Ship  at  time  of  Sights 179 

Dep.  made  since  Noon    38m  —  D.  Long. 


30' 
0 


30' 

40 


0"E. 
_0 

"OsW 
30 
W 


Reckoned  from  Greenwich 180°  10'    0' 

Subtract  from 360      0      0 

Long,  of  Ship  at  Noon 179°  49'  30"  K 


Lat  Obs.  Noon ;20'  41'  S. 

Course  N.  K  64  miles=Dif.  Lat  Sub.   0    38 
Lat  at  time  of  Sights    20*    S'S. 


Time  by  Watch 4h  40m  358 

Comparison . . . , 0    14     22 

Face  of  Chron.,  A.  M 4h  26m  138 

Add    12      0       0 

Time  by  Chronometer "Tch  26m  138 

Accum.  Error,  slow. . . .  Add  7     50 

Gr.  Date,  Oct  9th 16h  34m    38 

Subtract  from 24      0  0_ 

Time  Before  Noon 7h  25m  67b 

Chron.  slow,  Sept  10th Oh  10m  268 

Days  elaps.  30.  Rate  5s  2-lOth.        2      86 

Accumulated  Error Oh    7  m  50'' 

To  find  the  Comparison. 
Time  by  Chronometer. . .    4h  29m  iSs 

Time  by  Watch 4    43      35 

Comparison Oh  14m  22 

S 


Sun'.s  Dec,  Oct  9th.  S.  .6°  37'  30" 
Correction Sub.       6    58 

Correct  DecUnation. . .  .6°  30' 
90      0 


32" 
0 


Polar  Distance 83°  29'  28' 

Equa.  of  Time 12m  65818 

Correction  .^.  - .  Sub.  4  74 

Correct  Equation. . .  .12m  508'44 


Di£  lh=-57" 
7tt 

399 
19 

60)418 


Corr 


6'  58" 
•647 
7>b 

4-529 
216 


Corr   4-74-6 


NoTB. — In  the  4th  E.xample  the  Ship  has  crossed  the  Meridian  of  180°  Enst,  in  the  interval'  between  Noon  and  tlni 
4me  the  Sights  were  taken  in  the  afternoon,  havin?  passed  from  East  into  West  Long-itude,  and  if  bound  to  the  Ea»*- 
«rard,  we  would  add  one  day  to  the  Greenwich  Date.     (See  page  139.) 


FINDING  THE  LONGITUDE  BY  CHRONOxMETER. 


143 


EXAMPLE  5. 


August  6th,  1854,  (end  of  the  Sea  day,)  a  Ship  beiug  iu  North  Latitude  and  about  179°  West  Longitude.  In 
the  Morning  the  Sun's  observed  Altitude  was  36°  6',  and  the  Time  from  the  Face  of  the  Chronometer  was  8h  89m 
22s.  (beiug  P.  M.  at  Greenwich,)  which  was  fast  of  Green.  M.  T.  Oh  3Uiu  353.  Ship  then  sailed  due  West  48  mile* 
until  noon,  when  the  Suu3  Meridian  Altitude  observed  was  76°  11'  S.  Required  the  Ship's  Latitude  and  Longitud« 
•n  at  Noon. 


Sun's  Observed  Altitude 36" 

Corr.,  Table  IX Add. 

True  Altitude 35' 

Polar  Distance 78 

Latitude ^ 

Sum ._13£ 

Half  Sum 69' 


6' 

_n_ 

ir 

4  Log.  0.01925 
30  Log.  0.06468 

'  26'  Log.  4.54567 


Time  by  Chronometer 8h  39m  228 

Chronometer  fast  of  Greenwich 30      35 


Difference 34°    9'  Log.  4.74924 


44'  Log.  9.37884 
43 


Apparent  Time 20  5' 

Equation  of  Time Add       6 

Mean  T.  Ship  Aug.  4 20h  11m  278 

Green.  Date,  Aug.  4 .32      8     47 

Longitude  m  Time llh  57m  20s=179' 

Departure  made  to  Noon,  48=— Diff.  Long. 


Greenwich  Time  Aug.  5th 8h    8m  478  F   M 

Add.     24h    Om    Oa 

Greenwich  Date  Aug.  4th 32h    8m  478 

Meridian  Altitude 76°  11'  S.      Dif.  Dec.  41'- 

Corr. Add.  12  12h 

True  Altitude 76°  23'  60)492 

Zenith  Distance 13°  37'  N.  8'  12" 

Declination 16    53   S.        17*     1'    0    S. 


Latitude  at  Noon. 30°  30'  N,  D.  16°  51'  48"  & 


20'    0"W. 
55  45  W. 


Reckoned  West  from  Greenwich. 180°  15'  45"  W. 

Sub.  from 360      0     0 

Long,  of  the  Ship  at  Noon 179°  44'  15"  E. 

Note. — Here  the  Ship  has  crossed  the  Meridian  of  180° 
West,  between  the  time  the  Sights  were  taken  and  Noon, 
and  she  is  now  in  East  Longitude.  We  therefore  Sub- 
tract one  day  from  the  Greenwich  Date,  if  the  Ship  ia 
bound  West.    See  page  139. 


Sun's  Declination 17° 

Correction -. .  .Sub. 


1'    2"  N,  Dif.  Ih  41" 
5    28  8h 


Correct  Declination 16°  65'  34  "  N. 

90      0     0 


)328 
6'  28" 


Polar  Distance 73°    4'  26' 


Equation  of  Time 'im  448  64  Dif,  Ih  0*268 

Corr Sub.  2   "06  8h 


Correct  Equation 6m  428  "68 


2-06-4 


EXAMPLE  6 


November  28th,  1864,  (end  of  the  Sea  day,)  the  Sun's  Altitude  in  the  Forenoon  was  observed  to  be  50°  25',  whec 
the  Face  of  the  Chronometer  showed  9h  33m  10s  A.  M.  at  Greenwich,  and  which  was  correct  for  Greenwich  Mean 
Time.  Ship  then  sailed  E.  by  N.  31  miles,  when  the  Sun's  Meridian  Altitude  observed  was  68°  23'  S.  Required 
the  Ship's  Latitude  and  Longitude  at  Noon. 


Sun's  Observed  Altitude 60°  25' 

Corr.,  Table  IX 11_ 

True  Altitude 50°  36' 

Polar  Distance 68    42  Log.  0.03073 

Latitude _^_2.  ^°S-  0.00000 

Sum 119°  18' 

Half  Sum 59°  39' Log.  4.70358 

Difference 9°    3' Log.  4.19672 

Apparent  Time 9h  44m    9s  Log.  8.93098 

Equation 11      54 

Mean  Time  at  Ship 9h  32m  15  from  Midnight 

Greenwich  Mean  Time 9    33     10  from  Midnight 

Long,  in  Time Oh    Om  55s=  0°  13'  45"  W. 

Departure  made  to  Noon  3U=Diff.  Lon.  30     0    E. 

Long,  in  at  Noon 0°  16'  18"  E. 


Sub.  from 12h    Om    Ss 

Greenwich  Time  by  Chro 9    33      10 


Time  before  Noon 2h  26m  608 

Sun's  Meridian  Altitude 68°  23'  S. 

Correction 12 

True  Altitude 68°  35' 

Zenith  Distance 2r°  25'  N. 

Decliuatiou 21    19    S. 


Latitude  in  at  Noon 

Course  E.  by  N.  31  miles  D.  L. 

Lat  time  of  Sights 


0° 


6'N. 

6 — &  Dep.  »tl 


0°    0' 


Sun's  Declination 21' 

Correction 


19'  21"S.  Dif.  26" 


1-5 


Declination 21°  18'  16"  S. 

Polar  Distance 68^°  4I'  44'" 


Note. — Here   the   Ship   has   crossed   the    Meridian  of     " 
Greenwich,  between  the  time  the  Sights  were   taken  and  rjorrectioa 
Noon,  from  West  into  East  Longitude.  


11m  628  -4  Dif 


2  -17 


6il 
13 

•871 
24 


Equation Hm  543  -21 


1742 
436 

217-7 


QUESTIONS  FOR  EXERCISE. 

Quest.  1.  July  20th,  1854.  In  the  Morning  the  Sun's  observed  Altitude  was  33'  19',  when  the  Face  of  the  Ohroa 
•hewed  9h  28m  408  A.  M.  at  Green.,  and  which  was  fast  Oh  6m  47s  S.  Ship  sailed  on  a  S.  S.  W.  ^  W.  Course  32  mile« 
•ntil  Noon,  when  the  Lat.  Obs.  was  26°  27'  N.     Required  the  Long,  of  the  Shipat  the  time  of  the  Sights  and  at  Nooa 

Answer. — Longitude  at  time  of  Sights  21°  12'  W.,  and  at  Noon  21°  29'  W. 

Quext.  2.  September  25th,  1854.  In  the  Afternoon  the  Sun's  observed  Altitude  was  18*  20'.  Time  by  the  Chroa 
Dh  7m  388,  beiug  P.  M.  at  Greenwich,  and  which  was  fast  Oh  7ni  2s.  The  Latitude  observed  at  Noon  was  87°  67'  S 
«nd  the  Course  was  E.  N.  E.  29  miles  since  Noon.     Requiied  the  Long,  in  at  the  time  of  the  Sights  and  at  Noon. 

Antwrr. — Longitude  at  time  of  the  Sights  64°  49'  E,'aud  at  Noon  64*  15'  E. 


114  NAUTICAL  ASTRONOMY. 


TO  CORRECT  THE  LONGITUDE  BY  CHRONOMETER  AT  NOON  WHEN  THE   LATITUDE 

IS  IN  ERROR. 

'n  the  foregoing  Six  Examples  the  Latitude  used  in  computing  the  time  at  Ship  has  been  deduced  from 
the  Latitude  by  Observation  at  Noon,  and  when  the  Altitudes  are  observed  in  the  morning  we  have  io 
^hat  case  to  wait  until  Noon,  before  the  Ship's  position  can  be  accurately  ascertained. 

And  as  it  is  sometimes  of  importance  to  know  the  Longitude  by  Clironometer  as  soon  as  possible  after 
the  Sights  are  taken  in  the  morning,  with.in  a  few  minutes  of  the  truth,  we  have  in  that  case  to  use  the 
Latitude  by  Dead  Reckoiiinir  from  the  preceding  Noon  in  working  the  Time,  and  which  may  be  considerably 
In  error,  and  as  before  explained  at  page  122,  greatly  affects  the  Hour  Angle,  (except  when  the  Sun  is  on 
ihe  Prime  Vertical.)  so  that  after  finding  the  correct  Latitude  we  have  to  work  it  over  again. 

To  save  all  this  trouble  Tables  A  and  B,  No.  XXX.,  are  given  for  the  purpose  of  correcting  the  Longitude 
iy  Chronometer,  brought  on  to  Noon  for  the  effect  of  an  error  in  the  Latitude  used  in  computing  the  time 
ftt  the  Ship,  and  all  we  have  to  do  is  to  take  out  the  Correction  for  the  Longitude  from  the  Tables,  (which 
ts  expressed  in  minutes  and  seconds)  for  each  mile  of  Latitude.  This,  multiplied  by  the  mimber  of  miles 
»f  error  in  the  Latitude  worked  with,  gives  the  whole  correction  to  be  applied  to  the  Longitude  brought  on 
m  Noon,  and  the  result  is  the  correct  Longitude  of  the  Ship  at  Noon. 

RULE 
For  Using  Table  XXX.  , 

Enter  Table  A  with  the  Latitude  worked  with  at  the  side,  and  the  Hour  Angle  at  the  Top,  and  at  the 
Angle  of  meeting  take  out  the  Correotion. 

Enter  Table  B  with  the  Declination  at  the  Side  and  the  Hour  Angle  at  the  Top,  and  at  the  Angle  of 
meeting  take  out  the  Correction. 

When  the  Latitude  and  Declination  are  of  the  same  name,  the  difference  between  the  Corrections  found 
In  Tables  A  and  B  is  the  Correction  of  Longitude  for  each  mile  of  Latitude  in  error.  And  Note  whether 
the  Correction  found  in  Table  A  be  greater  or  less  than  that  found  in  Table  B. 

When  the  Latitude  nnd  Declination  are  of  contrary  names  the  Sum  of  th«  Corrections  in  Tables  A  and 
B  IS  the  Correction  of  Longitude  for  each  mile  of  Latitude  in  error. 

Multiply  the  Correction  for  Longitude  by  the  number  of  miles  of  error  in  the  Latitude,  which  will  g  iv* 
the  whole  Correction  for  Longitude. 

To  Apply  this  Correction. 

When  the  Corrections  in  Tables  A  and  B  are  subtractive  and  the  -one  found   in  Table  A  is  leas  than  thej 
one  in  Table  B,  apply  the  Correction  as  follows  : 

Latitude  worked  with  being  too  Small,  Add  in  West  Longitude,  Subtract  in  East. 
Latitude  worked  with  being  too  Great,  Subtract  in  West  Longitude,  Add  in  East. 

When  the  Corrections  in  Tables  A  and  B  are  additive,  and  also  when  the  Correction  in  Table  A  is  greattf^ 
than  that  in  Table  B,  Subtractive,  as  follows  : 

Latitude  worked  with  being  too  Small,  Subtract  in  West  Longitude,  Add  in  East. 
Latitude  worked  with  being  too  Great,  Add  in  West  Longitude,  Subtract  in  East. 

To  or  from  the  Longitude  by  Chronometer,  brought  on  to  Noon   by  the  Dead  Reckoning,  will   give  thej 
Ship's  Correct  Longitude  by  Chronometer  at  Noon. 

EXAMPLES 
In   Using  the  Tables 
Lat  worked  with  30°  30'  N,  H.  A.  3h  15m  Tab.  A— 31"  Lat.  worked  with  60"  10'  N.,  H.  A.  2h  45m  Tab.  A  1'  21 


Dec  22°  30  N. (same  name)  H.  A.  3h  15m  Tab.  B     33"  Dec.  23°  S.  (contrary  names)  H.  A.  2h  45m Tab.  B       39" 

The  Diflf.  is  tlie  Ccrr.  for  each  mile  of  Lat 2"  The  Sum  is  the  Corr.  for  each  mile  of  Lat 2'    0"' 

Lat.  worked  with  fouud  to  be  too  amall. lOm        ,  Lat.  worked  with  found  to  be  too  great 10 

Whole  CoiT.  for  Lonsr.  to  be  Added 20"  Whole  Corr.  for  Long,  to  be  Subtracted 20' 

Long  by  Cliro.  brought  on  to  Noon 60°  13'  30"  W.      Long,  by  Chro.  brought  on  to  Noon 30°  14'     'W, 

Clorr.  Long  by  Chr...  at  Noon '^O*  13'  60"W.      Coireet  Long,  by  Chro.  at  Noon 29°  54'    Wj 

The  Latitude  and  Declination  being  of  the  same  name  The  Latitude  and  Declination  being  of  contrary  namei 

the  Difference  of  the  Corrections  in  the  Tables  io  the  Cor-  the  Sum  of  the  Correction  in  A  and  B  is  tbe  CorrectiottJ 

rectioD  Additive,  because  the  Latitude  was  too  small  and  Subtractive,  because  the  Latitude  was  too  great  and  th»| 

llie  longitude  West.                          .  Longitude  West 


TO  CORRECT  THE  LONGITUDE 


146 


ro  CORRECT  THE  LONGITUDE  BY  CHRONOiMETER  AT  NOON  WHEN  THE  LATITUDE 

IS  IN  ERROR 


EXAMPLE  9. 


March  6th,  1854.     (End  of  the  Sea  day.)     At  about  7h  30m  in  the  morning,  the  Sun  s  observed  Altitude  waa  10* 


Time  at  the  Ship  was  found,  and  the  correct  Longitude  by  Chronometer  at  Noon. 


Sun's  Obs.  Alt 10°  23 

Cor.,  Tab.  LX...  Add  7 


30' 
40 
53 


Ti-ue  Alt 10 

Polar  Dist 95 

Latitude 37 

Sum 144°    3 

Half  Sum 72°_2' 

32' 


Log.  0.00213 
Log.  0.10278 

Log.  4.48920 
Log.  4.94404 


Difference 61' 

H.  A.4h47m  I      j^  7B-.Log.  9.53815 

63s  Ap.  Time  )  ° 

Equa.  of  T. .  Add       11     32 
Mn.  T.  at  Ship.  19h  23m  398 
Gr.  Time 23      0       2 

Long,  m  Time."~3h  36m  238  Lo.54*    r45"W. 
Dep.  maiie  to  Noon       36'«=«=D.  L.        45     0 
Approx.  Lon.by  Chro.at  Noon.  .54°  50'45"W. 
Cor.  from  Taoie  XXX Sub.  4  12  W. 


Gr.  T.  by  Chro.  A.  M..  llh.  Om  28     Same  as  Examp.  Ist,  page  141. 
Add.  12     0      0      Sun's  Corr.  Dec 5°  40'  S. 

Gr,  Date,  March  5th,  23h.  Om  28  90      0 

Polar  Dist, 96°  40' 

Equa.  of  Time. .     11m  32e 

True  Course  to  Noon  N.  W.  50,  D.  Lat  36'  N.  and  Dep,  35  W 

Lat  by  D.  Reckon,  at  time  of  Sights. . .  37°  53'  N. 
Lat.  by  D.  Reckon,  at  Noon 38' 


Lat  by  Observation 38 


28 
40 


Error  in  the  Latitude  worked  with  12'  too  small. 

Lat.  worked  with  38°  and  H.  A.  4h  48m  in  Table  A,     Corr.  16" 
Dec.  5°  40'  of  (contrary  names)  H.A.  4h  48m  in  Tab.B.  Corn « 

Their  Sum  as  the  Correction  per  mile 21 

Number  of  miles  error  in  the  Latitude 12 


60)252"^ 
Whole  Correction  for  Longitude     4'  12" 


Cor,  Lon.  by  v'hro,  at  Noon 64°  46'  83"  W.  Agreeing  within  3"  of  the  Long,  in  Example  Ist,  page  140. 


EXAMPLE  10. 

May  20th,  1864.  (End  of  the  Sea  day.)  At  about  8  o'clock  in  the  morning,  the  Sun's  observed  Altitude  wtut 
12°  10',  and  the  Greenwich  Time  by  Chronometer  3h  Im  268,  A.  M.,  or  l6h  Im  268,  from  the  preceding  Noon.  The 
Latitude  in  by  the  Dead  Reckoning  from  the  preceding  Noon  was  36°  40'  S.  Ship  then  sailed  S.  E.  (true)  20  milet 
until  Noon,  when  the  Latitude  observed  was  36°  39'  S.  Required  the  Error  in  the  Latitude  used  in  finding  the 
Time  at  the  Ship,  and  the  correct  Longitude  by  Chronometer  at  Noon. 


Sun's  Obs.  Alt 12°  10' 

Corr,  Table  LX Add 8 

True  Alt 12°  18' 

Polar  Dist 1C9    54 

Latitude 36    40 

Sum 158°  52 

Half  Sum 79°  26' 


Difference 67 


Log.  0.02674 
Log.  0.09676 

Log.  4.26335 
Log.  4.96445 


H.A.3h46m.   Ap.  T..20h  14m  Os 
Equa.  of  Time . .  Sub. .  3    47 

Mn.Tirae  at  Ship. ,  ,20hTom  133 

Green.  Time 15       1      26 

Loner,  in  Time . , . 


Log.  9.35030 


. .    6h    8m  47& 
Dep.  made  to  Noon  14'— D.  Long. 

Approx.  Long,  by  Chro.at  Noon. . 
Corr.  from  Table  XXX 

Correct  long,  by  Chro  at  Nooo . , 
Til  is  agrees  exactly  with  the 


;=.Long.  77°11'45"  E. 
made.  17'  46"  E. 


77' 


■  Sub. 


29'  30"  K 
14     0 

K 


77°  15'  30" 

Long,  in  Example  3, 


G.T.by  Chro.,  A.M.  3h  Im  26s  Same  as  Ex.3d,  page  142. 
Add  12    0        0   Sun's  Dec  cor.  19°  54'  It 

90     0 


Gr.  Date,  May  19th,  16h  Im  268 

Polar  Dist..  109°  54' 
Equation  of  Time 3m  478 

True  Course  to  Wn  S.  E.  20  miles.  D.  L.    0°  14'  Dep.  14 
Lat.  by  D.  Reck,  at  the  time  of  Sights. _36   40 

Lat.  bv  D.  Reckoa  at  Noon 36°  54'  S. 

Lat  by  Obs.  at  Noon 36    39   S. 

Error  in  the  Latitude  worked  with  16'  too  great, 

Latworked  with  37°  S.  H.  A.  3h  46m  in  Tab,  A.  Corr.  80" 
Dec.  20°  N.  (eon.  name)  H.  A,  3h  45m  Table  B.  Corr.  26 

Their  Sum  is  the  Correction  per  mile 56' 

Number  of  miles  of  error  in  the  Latitude 15 

280 
56 


60)840" 


Whole  Correction  for  Longitude Sub,. .     14'  0" 


Note. — When  it  is  of  irjportance  to  know  the  Ship's  trni,' position  at  Noon  directly  the  Latitude  is  observed,  TabJ* 
XXX  will  be  found  of  great  service. 

For  instance,  after  Seven  Bells  we  can  estimate  the  Course  and  Distance  the  Ship  will  have  made  to  Noon  new 
enough,  so  as  to  work  up  the  day's  work  and  find  the  Latitude  by  Dead  Beckoning,  and  also  to  bring  up  the  approxi- 
mate Longitude  by  Chronometer  to  Noon. 

Then  the  instant  the  Latitude  by  Observation  is  determined,  the  Error  of  the  Latitude  by  Dead  Beckoning  can  h9 
found,  and  the  approximate  Longitude  by  Chronometer  corrected,  as  in  tlie  above  Examples. 

This  Table  will  also  show  at  once  the  effect  of  an  error  of  one  mile  of  Latitude  in  produciug  an  error  m  the  Loo^i 
hide  by  Chronometer  in  any  given  Latitude;  and  it  will  be  perceived  that  an  error  of  this  kind  has  the  greatest  effeot 
'~  Tiigh  Latitudes. 


140  NAUTICAL  ASTRONOMY. 


TO  FIND  THE  LONGITUDE  BY  CHRONOMETER  AT  SUNRISE  OR  SUNSET. 

The  method  of  finding  the  Time  at  the  Ship  from  the  Sun's  Rising  or  Setting  is  given  at  pages  128  and 
129,  and  the  same  Examples  will  answer  the  purpose  of  finding  the  Longitude  by  Chronometer ;  because 
we  have  only  to  compare  the  Watch  with  the  Chronometer,  and  thence  find  the  Greenwich  Time  at  which 
the  Sun  rose  or  set,  or  the  Time  may  be  taken  at  once  from  the  Chronometer  without  the  Watch.  Then 
the  difference  between  the  Mean  Time  so  found  at  the  Ship,  and  the  Greenwich  Time  by  Chronometer 
is  tri*-.  Longitude  in  Time. 

EXAMPLE  I.— (See  page  128.) 

Jan.  25th,  1864.  Latitude  in  38°  42'  North,  the  Sun's  Lower  Limb  was  observed  to  Set,  by  Watch,  at  5h  3m  258, 
which,  on  being  compared  with  the  Chronometer,  was  found  to  be  7h  7ra  lis  slow  of  the  Chronometer.  The  Mean 
Time  at  the  SLip  was  found  to  be  5h  11m  16s,  and  the  error  of  the  Chronometer  on  Greenwich  Mean  Time  3m  208 
too  fast     Required  the  Longitude  of  the  Ship. 

Tim*  by  Watch  at  Sunset 6h    3m  258 

Watch  Slow  of  Chronometer 7      *?     11 

Time  by  Chron.  at  Sunset T 12h  10m  36s       Green.  Mean  Time   at  Sunset,  Jan.  26tb. .  12h    7m  16a] 

Chroa  fast  of  Greenwich  Mean  Time 3     20s      Mean  Time  at  Ship         do         Jan.  25th..     5    11      16» 

Oraen.  Mean  Time  at  Sunset 12h    7m  168      Long,  of  the  Ship   at  Sunset,  104°  0'  W.  =^^6h~66m~~OiJ 

EXAMPLE  2.— {Same  as  at  page  129.) 

June  Ist,  1854.     In  Latitude  26°  North,  the  Sun's  Upper  Limb  was  observed  to  Rise  at  the  instant  the  Tim«] 
moted  on  the  Face  of  the  Chronometer  was  lb  6m  12s  A.  M.  at  Greenwich,  and  which  was  Slow  of  Greenwich  Mean 
Time  2m  24s.     The  Mean  Time  at  the  Ship  was  found  to  be  5h  9m  36s,  the  Ship  being  in  East  Longitude.  Required 
ibe  Longitude  of  the  Ship. 

Time  by  Chronometer  at  Sunrise Ih  6m  12s,  being  A.  M.  at  Greenwich. 

Chronometer  Slow  of  Greenwich  Mean  Time 2      24 

Greenwich  Mean  Time  from  Midnight,  June  Ist Ih  8m  36  or  May  31st. .  13h  8m  86s 

Mean  Time  at  the  Ship  from  Midnight,  June  Ist 6    9     36  or  May  31st. .  17    9      86 

Longitude  of  the  Ship  at  Sunrise,  60°  16'  0"E.=  4h  Im    Os 

As  no  reflecting  instrument  is  required  in  this  Observation,  (we  use  in  its  room  the  common  Spy-Glass.^ 
its  accuracy,  therefore,  rests  entirely  upon  the  instant  of  time  noted  by  the  Chronometer  at  which  the  Sun  ■ 
Upper  Limb  at  rising,  or  his  Lower  Limb  at  setting,  touches  the  horizon.     This  is  liable  to  a  small  error,! 
eometimes,  in  consequence  of  unequal  refraction  and  mirage  at  the  horizon.     (See  Note  at  page  129.) 

The  Latitude  of  the  Ship  may  also  be  determined   by  an  Altitude  of  a  Star  or  Planet  at  twilight,  anjl 
the  Ship's  position  found  as  correctly  as  at  Noon,  as  follows  : 

Enter  Table  XVIII  with  the  day  of  the  month,  and  find  what  Star  will  pass  the  Meridian  a  few  minutes 
before  Sunrise,  or  after  Sunset;  or  inspect  the  Nautical  Almanac,  and  find  what  Planet  will  pass  th« 
Meridian  about  that  time,  as  directed  at  page  104,  No.  2. 

Compute  the  Altitude,  and  find  the  Star  as  directed  at  page  106,  No.  3,  or  find  the  Planet  as  directed 
page  104,  No.  3,  and  observe  the  Meridian  Altitude. 

EXAMPLE 

Of  Finding  the  Latitude  at  Sunset  by  a  Star. — (See  Example  1st.) 

January  25th,  1854.  (End  of  the  Sea  day.)  The  Latitude  at  Sunset  being  required,  we  look  into  Table  XVIH 
•nd  find  the  nearest  Star  on  the  Meridian  to  be  the  N.  Pole  Star,  which  passes  at  4h  37m,  and  ie  not  vis'ble  on  accouni 
•f  the  Sun-light,  but  at  5h  15m,  or  15m  after  Sunset,  its  Altitude  was  observed  to  be  40°  18'.  We  Cod  iia  Latitude 
U)  be  88°  42'  North.     (See  this  method  at  page  109.) 

EXAMPLE 

Of  Finding  the  Latitude  at  Sunrise  by  a  Star. — {See  Example  2d.) 

June  Ist,  186't.  (End  of  the  Sea  day.)  The  Latitude  at  Sunrise  being  required,  we  first  add  12  hours  to  tjh 
Apparent  Time  at  Ship,  6b  12m,  which  gives  the  App.  Astrou.  Time,  May  81st,  17h  12m,  and  on  ref<>rrir.g  to  Table'' 
XVIII,  we  find  that  the  Star  Gruis  passes  the  Meriiliuu  at  17h  24m,  or  12m  after  Sunrise,  and  "Cy  computing  the 
Meridian  Altitude,  and  setting  the  Index  of  the  Quadraut  at  17°  20',  the  Star  will  be  found  at  that  Altitude  in  tha 
Soutii  point  of  the  horizon  at  a  few  minutes  before  Sunrise,  and  supposing  the  observed  Altitude  to  have  been 
17°  27  ,  the  Latitude  in  would  be  25°  0'  NortL 

NoTB. — As  the  change  o  Akitiide  of  these  two  Stars,  when  near  the  Meridian,  is  very  slow,  an  error  of  a  few  minate* 
ta  the  time  at  the  Ship  wil  je  of  no  eonseonenoe.  Hence  both  the  Latitude  aud  Longitud*  of  the  Ship  may  be  found 
4T  ObserTation,  at  Suurisa    :  Sunset. 


FINDING  THE  LONGITUDE.  147 


FINDING  THJ^.  LuNoITUDE  BY  CHRONOMETER  AT  NOON  FROM  EQUAL   ALTITUDRS 

OF  THE  STI>J 

The  method  of  finding  ihe  Apparent  Noon  at  the  ship  from  Equal  Altitudes  of  the  Sun  near  the  Mcridiaa 
and  thence  the  Mean  Noc  o,  is  given  at  page  130,  and  in  finding  the  Longitude  by  Chronometer  at  Noor.  we 
have  on^y  to  compare  theiWatch  with  the  Chronometer,  and  apply  the  comparison  to  the  middle  Time  by 
the  Wc'ch,  which  will  give  the  time  by  Chronometer  at  apparent  Noon.  Or  if  we  Note  the  time  by  Chrc 
nomet.  -  when  the  Sun's  Altitude  is  the  same  both  before  and  after  Noon,  the  middle  of  the  times  is  the 
time  by  Chronometer,  at  apparent  Noon,  (See  Note  at  the  bottiom  of  the  page,)  to  which  its  error  on  Green- 
wich, applied  as  usual,  gii'es  the  Greenwich  time  by  Chronometer,  when  it  is  Noon  at  the  Ship. 

The  only  Correction  necessary  in  this  case  is  for  the  Equation  of  Time,  which  must  be  Corrected  a« 
usual  to  the  Greenwich  Time  by  Chronometer,  and  applied  as  directed  in  the  Nautical  Almanac  to  Apparent 
Noon,  will  give  the  Mean  Noon  at  the  Ship.  Then  the  difference  between  the  Mean  Noon  at  Ship  and  the 
Greenwicli  Mean  Time  by  Chronometer  is  the  Longitude  in  time,  which  turned  into  Degrees  and  Minutes 
by  Table  XXVI.,  in  the  Longitude  of  the  Ship  at  Noon. 

EXAMPLE  l.—{See  Page  180.) 

April  2d,  1854.  (Ebd  of  the  Sea  day.)  The  Altitude  of  the  Sun's  L.  Limb  was  observed  to  be  85°  40'  at  a  few 
minutes  before  Noon.  Tinoe  by  Chronometer  Ih  46m  lOs  P.  M.  at  Greenwich,  and  when  the  Sun  fell  again  to  the 
•ame  Altitude  in  the  Afte.uoon,  the  Time  by  Chronometer  was  2h  12m  168,  and  its  Error  3m  SSs  Fast.  Required 
the  Longitude  by  Chronom  ■Xier  at  Noon. 

Sun's  Observed  Altitude A.  M.  85°  40'  Time  by  Chronometer. . .    Ih  46m  lOs  P.  M.  at  Oreea 

do do P.  M.  85   40        do do 2    12      16     do.  do. 

A)3h  58m  26s 

Lqua.  of  Time  April  2d 3m  4l8  71   Diff.  Ih -760     rj.-       ,     o,  ,,   ,„ — — - 

CJrr. SuU  1     60  2h  3^:°"«  ^7  ^^^^^ •  • ' '   ^^  ^^'"  ^^s  at  App.  Nooa 

„  „         .  .  ,, Chro.  Past  of  Green.,  Sub.  3      33 

Correct  Equation Add  3m  40s -21  ISOO  ^  .,        t,.  -rr 

App.  Noon  at  Ship Oh  0      0  Green.  Mean  Time Ih  65m  408 

»/       »T  r,,  •  — ; Mean  Noon  at  Ship 0      3      40 

Mean  Noon  at  Ship Oh  3m  408  t         r  *i     01  ■    •  ^-  ,.  ^, „„„    ,  „, 

^  Lon.of  the  Ship  in  time..    Ih52m    08  =  28   O'W.  at  Noon 

EXAMPLE  2.— (5«<!  Page  130.) 

April  16th,  1854.  (End  of  the  Sea  day.)  The  Altitude  of  the  SuuiS  L.  Limb  was  observed  to  be  68°  20',  Time 
by  the  Watch  llh  20m  in  the  Forenoon,  and  when  the  Sun  had  fallen  to  the  same  Altitude  again  in  the  Afternoon,  the 
time  by  the  Watch  was  12h  34m  68,  which  on  being  compared  was  found  to  be  3h  Om  23s  Fast  of  the  Chronometer, 
and  the  Error  of  the  Chronometer  on  Greenwich  Mean  Time  was  3m  10s  too  Slow.  Required  the  Longitude  by 
Chronometer  at  noon. 

Sun's  Observed  Altitude A.  M.  68°  20'  Time  by  Watch llh  20m    0 

do do P.  M.  68    20        do do 12    34       6 

.  rr..              .,        ,  i)a3h  64m    6s 

Equa.  of  Time  April  16th Om  lis -87  Diff.  Ih  "603     ^-j  t-       i,    w  ^  u         ,,,    -„ ^7 

Corr Sub.            1-81  3h  ^"^-  ^™«  ^^  ^^^«^  •  •  '    ^  ^^  ''^'^    ^' 

-  ,  „  „   ,     Comparison Sub.     3      0       23 

Correct  Equa. Sub.  Om  10s    .6  1-80-9  rp-       u    n\                       —^ — r 

App.NoouatShip 12      0       0  lu'^^^  ^Jn ;  V>     S^^  56m  40s  at  App.  Nooa 

^/'^   ,^             ^,^ Chr.  Slow  of  Green.,  Add.           3      10 

M.-an  Noon  at  bhip llh  6'Jm  50s  .^          ,.        t,-                  — ; — r 

^  Green.  Mean  Time 8h  59m  oOs 

Comparison.  Mean  Noon  at  Ship 11    59      50 

oi:™S°e7stw;d;;:-.::;-.::;-.;::-.::: '? IT  ,T  ^-■■»'*'^'"p'°^'°-  ^^  »■»  »•=«•  ''•■^■■"•'««» 


WaiAifa  Fast  of  Chronometer 3h    Om  2bs 

Degree  of  Dependence. 

This  method,  as  before  observed  at  page  130,  is  most  suitable  for  Low  Latitudes  ranging  to  30°  on  each 
Bide  of  the  Equator.  Because  when  the  Ship  makes  much  way,  and  the  interval  between  the  Altitudes  i» 
great,  the  First  Altitude  will  not  be  equal  to  the  Second,  on  account  of  the  Ship's  change  of  place  of  Ob- 
lervation  and  the  Sun's  change  of  Declination.  Except  when  she  Sails  due  East  or  West,  in  that  ca&e  it 
becomes  a  question  of  Time  only,  and  does  not  affect  the  result 

Note.— Bat  when  she  makes  much  Northing  or  Southing  in  the  interval,  it  is  evident  that  the  sume  Altitudes  will  no 
cnger  give  the  correct  middle  time  at  Apparent  Noon.  The  Error  in  the  Altitude  will  be  equal  to  the  Difference  of 
Latitcde  the  Ship  has  made  in  the  interval.  For  instance,  a  Ship  Sailing  South  in  North  Latitude,  the  P.  M.  Altitude 
would  be  too  small,  and  Sailing  North  the  P.  M.  Altitude  would  be  too  great  by  the  Amount  of  the  Difference  of  Lati- 
tude made  in  the  interval,  therefore  the  Kule  is,  when  Sailing  towards  the  Sun,  ve  must  increase  the  A.  M.  Altitude 
which  is  on  the  Quadrant  by  advancing  the  Index  of  the  Instrument  equal  to  the  Difference  of  Latitude  made  in  the 
interval.  But  in  Sailing/rw»  the  Sun  we  decrease  the  A.  M.  Altitude  by  screwing  back  the  Index  equal  to  the  Diflfer- 
euce  of  Latitude  made  in  the  interval,  and  when  the  Sun  falls  to  that  Altitude  in  the  Afternoon,  and  the  time  noted  by 
Watch  or  Chronometer,  the  correct  middle  time  is  found  at  Apparent  Noon  as  before.  But  as  this  method  is  much 
used  at  Sea  in  its  present  form,  because  of  its  extreme  simplicity  and  independence  of  both  Latitude  and  Declination 
»nd  which,  w.th  ordinary  caution,  it  is  well  adapted  for  the  use  of  Seamen  in  detecting  any  very  gross  error  in  the  mora 
rej^iar  mod>  ?.'  working  out  the  Time  at  Sea. 


148  NAUTICAL  ASTRONOMY. 


FINDING  THE  LATITUDE  BY  THE  SUN,  AND  THE  LONGITaOE  BY  CHRONOMETER,  BY 

THE  MOON'S  ALTITUDE  AT  NOON. 

When  tne  Sun  is  on  the  Meridian,  his  Altitude  determines  the  Latitude,  and  when  the  Moon  is  at  • 
proper  distance  from  the  Meridian  her  Altitude  will  give  the  Time  at  the  Ship,  and  thence  the  Longitud* 
y  Chronometer  at  Noon.  • 

Or  the  Moon  may  be  on  the  Meridian,  when  her  Altitude  will  give  the  Latitude,  and  an  Altitude  of  th« 
Sun  at  the  same  time  will  give  the  Longitude  by  Chronometer. 

Or  Altitudes  of  the  Moon,  Planets 'or  Stars  taken  in  like  manner  will  give  both  Latitude  and  the  Longi* 
tude  by  Chronometer  at  the  same  lime. 

The  advantage  of  this  method  is  that  the  Latitude  being  correctly  known  at  the  time  of  taking  the  Sights 
for  Chronometer  the  Altitudes  of  the  object  for  Time  mu.y  be  taken  nearer  to  the  Meridian  than  other- 
wise without  producing  an  Error  in  the  H.  Angle,  alway.s  providing  that  their  change  of  Altitude  be  not 
less  than  6'  in  one  minute  of  time. 

EXAMPLE  BY  THE  SUN  AND  MOON  AT  NOON. 

March  24th,  1854.  (End  of  the  Sea  day.)  The  Latitude  observed  from  the  Meridian  Altitude  of  the  Sun  ■wa* 
40°  10'  S.  and  at  the  same  time  the  Altitude  of  the  Moon's  Upper  Limb  was  observed  to  be  +1°  40'  to  the  West- 
ward of  the  Meridian,  and  the  Greenwich  time  by  Chronometer  was  17h  48m  278.  Raquired  the  Longitude  in  by 
Chronometer  at  Noon. 

Obs.  Altitude  ])  's  Up  Limb 41'  40'  Green.  Time  by  Chron.,  March  23 17h  48m  21i 

Semid.  16',  Dip.  4' Sub. 20_  12      0       <> 

Hor.  ParL  59' and  Altitude 41°  20'  Green.  Time  past  Midnight 5h  48m  27l 

Gives  the  Corr.,  Table  XXV ^3 

rr,        Auv  ^  X9'    1'  Sun  R.  A.  23d Oh    9m  228  Diff.  Ih     9i 

True  Altitude *z      6  aji          o      ^o                   lok 

PolarDist 66    53    Log.  0.03636  Add 2_J2_  18h 

Latitude  Observed 40    10    Log.  0.11681    Sun's  Cor.  R  A Oh  12m    48  60)162 

gum 149°    6'  Corr 2m  42i 

Half  Sum                74°  33'  Log.  4.42553 

'^^"^""^ r-^^,     r         .nonoo     5 '8  Declination  March  23d,  Mid 23°  51    & 

difference 32_^     Log.  4.73022  ^^  March  24th,  Noon 22    20    a 

J '8  Hour  Angle,  W«8t 3h  34m  878    Log.  9.30891    Difference  of  Declination  in 12h=  1°  34' 

D  's  R  Ascen ^0    38 ^20  ^^^.^   rpj^j^j^  xXIII 0°  44' 

R.  Ascen.  of  the  Meridian 24h  12m  578  Declination  at  Mid 23    61 

Sun's  K.  Ascen Sub.  0    12       4  Correct  Declination 2'3°     V'S. 

App.  Time  at  Ship 24h    Om  538  ^yO 0 

Equation  of  Time Add. &      31  ^  .^  p^j^^j.  Djgtance 66°  53" 

Mean  T.  at  Ship,  March  23. .  .24h    7m  248 

G.  M.  T.by  Chr.  March  23.  ...17    48      27  p  's  R.  A.  Mar.  23d  .  ..20h  23m  588  at  Mid. 

Longitude  in  Time 6b  18m  578  Mar.  24 tb.  ..20    63      47  at  Noon. 

T^nmUiAe  of  the  Shin                       94°  44'  15"  E.  at  Noon.               Say  as  12b  is  to  29m  548  so  is  5h  48m  T.  from  Mid 

^                            ^ Pro.  Log.  of  12h,  Table  XXXIV.  1.1761 

Arith.  Comp 8.8239 

Eaustion  of  Time 6m  458  27       -766     Pro.  Log.  of  29m  54s 0.7796 

^    Oorr Add         138-79 18b  Pro.  Log.  of    5h   48m 1-4918 

Correct  Equation 6m  318-48  13-78-8  1.0953  Corr.  14m  27l 

^  R.  Ascen.  at  Mid 20b  23m  53 

> '8  Correct  R.  Ascen 201i  38m^0t 

Finding  the  Latitude  by  a  Planet,  and  the  Longitude  by  Chronometer  by  the  Moon's  Altitude  at  the  same  time. 

QUESTION, 

October  Sd,  1354.     In  North  Latitude  and  West  Longitude  at  Twilight  in  the  evening  the  Meridian  Altitude  of 
the  Planet  Jupiter  was  observed  to  be  39°  8'  S.     About   the  time  the  Altitude  of  the  Moon's  L.  Limb  was  la"  19 
East  of  the  Meridian,  and  the   Greenwich   Time   by  Chronometer,  October  3d,  llh  23m  62s    P.  M.      Required   the 
Latitude  by  Observation  and  the  Longitude  by  Chronometer. 

A7iswer.—ln  this  case  the  Correct  Altitude  of  the  Moon  is  14°  24',  her  Polar  Distance  102°  28',  her  Hour 
An^le  4h  28m  40s,  R.  A.  22h  52m  438,  R.  A.  of  the  Meridian  18h  29m  38,  the  Sun's  R.  A.  12h  88rn  198,  Apparent 
Time  at  Ship  5h  s'om  448  P.  M.,  and  the  Mean  Time  6h  39m  40s.  The  Latitude  observed  28°  16'  N.,  and  Longitude 
by  Chronometer  86°  3'  West 

Note 1     -av  perhaps  be  necessary  here  to  repeat  the  remarks  already  made  at  pages  101  and  104,  wnich  iSj  that  the 

Meridian  psnrMiges  of  the  Moon  and  Planets  are  given  in  the  Nautical  Almanac  for  Mean  Time,  and  which  must  oe  turned 
Into  Apparent  Time  by  Applying  the  Equation  of  Time  the  contrary  way  to  what  we  would  do  in  turning  Apparent 

In  the  ease  of  the  Planet  Jupiter  in  the  above  Question  he  passes  the  Meridian  by  the  Almanac  at  6h  81m.  The  Eqna- 
teon  of  Time,  11m,  added,  gives  the  Apparent  Time  6h  41m,  at  whioli  lie  passes  the  Meridian,  or  that  shown  by  ■ 
W»toh  regulated  to  Apparent  Time  at  the  Ship.    The  Moon's  Meridian  passage  is  found  in  like  manner. 


FINDING  THE  LATiri)DE  AND  LONGITUbE 


149 


riNDING  THE  LATITUDE  BY  A  STAR,  AND  THE  LONGITUDE  BY  CHRONOMETER,  BV 

A  PLANET. 


EXAMPLE. 

Api-U  2d,  1854.  (End  of  the  Sea  day.)  In  North  Latitude  and  West  Longitude,  the  Meridian  Altitude  of  thf;  Star 
Castor  was  observed  to  be  77°  52'  North,  and  at  the  same  time  tLe  Altitude  of  the  Planet  Saturn  was  37°  53'  tc 
the  Westward  of  the  Meridian  iu  the  evening  twilight,  aua  the  Greenwich  Tinje  by  Chronometer  was  lOh  68m  lOa 
P.  M.     Required  the  Latitude  in  and  the  Longitude  by  Chronometer. 


Mer.  Alt  #  Castor  77°  52'  N. 
Corr.,'rab.  XX.Sub.  4 


True  Alt 77°  48' 

Zenith  Dist 12°  12'  S. 

#'8  Dec.  1864     ..    32°  12  N 

Latitude  in 20°    O'N. 

at  the  time  Castor  passed 

the  Merid.,  or  at  6h  40m 

P.M. 


Obs.  Alt.  Sat    37°  63' 
Corr.Tab.  XX,  Sub.  5 

True  Alt 37°  48  , 

Polai   Dist        71    50  Log.  0.02221 
Lat  Obs 20 


G.  T.  by  Chro.  | 
Ap.  2d,         f 


lOh  6&m  108  DecSat  18'  10 

^0 0 

Polar  Dist.,    7>°  50 


12^°  38 


0  Log.  0.02701 


Half  Sum 
Difference 


64°  49'Log.  4.62892 


27      I'Log.  4.65729 


Sat  H.  Angle    3h  41m  50s.  Log.  9.33543 
R.  Ascen.. . .  ■  3    47      27 
R.A.  of  Mer..  7h  29m  178 
Sun's  R.  A.  . .  0    47      22 

App.  Time. . .  6h  41m  658 
Equa Add         3      33 

Mean  Time  at  Ship.   6h  46m  28s 
Gr.  M.  T  by  Chro.  .  10    68      10 


Saturn's  R.  A.  \pn^  2X  8h  47m  153 
April  ^d,  3    47     41 

Say  as  24h  is  tr> 
to  the  Ourroctior 

Right  Ascen.,  Apnl  2q 

Correct  Right  Ascen 3h  ilis^  27a 


263,  so  is  llh 
Oh    Om  128 
3    47      15 


Sun's  R.  A.  April  2d. .   Oh  45m  43s.  Di:  Ih,  9» 
Correction Add  1      39  Un 


Correct  K  Ascen.. 


Oh  47m  229 


90* 


ft 


Long,  of  Ship  63*  10'  30"  W.—  4h  12m  428  at  6h  41ra  56s 

[P.M. 


Equa.  of  Time 3m  4l8  '71  Dift.  ih.  .-761 

Sub.  8-25  11 


Correct  Equa 3m  338  47 

Finding  the  Latitude  in  and  the  Longitude  by  Chronometer  at  the  same  time  by  Two  Stars. 


•8-25-C 


EXAMPLE. 

August  22d,  1854.  (End  of  the  Sea  day.)  In  South  Latitude  and  East  Longituds,  the  Meridian  Altitude  of  thf 
Star  Aldebaran  was  63°  26'  North,  and  at  the  same  time  the  Altitude  of  the  Star  Siriua  was  63°  47'  East  of  th« 
Meridian,  at  twilight  in  the  morning,  and  the  Greenwich  Time  by  Chronometer  ^  as,  October  ilet,  14h  57m  41i 
Required  the  Latitude  iu  and  the  Longitude  by  Chronometer. 


26' 
4 


N. 


Mer.  Alt  #  Aldebaran 63 

Correction,  Table  XX Sub. 

True  Altitude 68°  22' 

Zenith  Distance 26°  38^  S. 

#'s  Deehuation 16    13  N. 

Latitude  iu  by  Observation 10°  25'  S. 

At  the  time  Aldebaran  passed  the 
Meridian,  Aug.  21st,  ISh  18m,  or  on 
the  morning  of  Aug.  22d,  at  6h  18m. 


<ireen.  Time  by  Chron.,  Aug.  2l8t 14h  57m  4l8 


Gd9.  Alt  of  Sirius. ... 
Correction,  Table  XX . 

Correct  Altitude  .... 

Pol«-    distance 

xiatitude  Observed   . . 


63' 


Sub. 


63'^ 
73 

10 


47- 
5 

"42' 
29 
26 


Log.  O.OlSSt' 
Log.  0.0O72'i 


137°  36' 


Half  Sum 

Difference 

#'8H.  A..... 

^'s  R.  Ascension 

R  A.  of  the  Meridian . . 
Add 


Declination  Sirius  1854. 


16' 
90 


31' S. 

0 


2h  27m  258 
6    38      43 

4h  lira  188 
24      0        0 

28h  11m  188 
10      3        9 


68°  48  Log.  4.66828 
15°  6'  Log.  4.41682 
Log.  8.999  W 


Sirius'  Polar  Distance 


78°  29' 


^ 


Right  Ascension  Sirius,  1854 6h  33m  438 


Sun's  R.  Ascension  . . 

Apparent  Time 18h    8m    98 

Equation Add  2      50 

Mean  Time  at  Ship  . . .      18h  10m  59s 
Green.  Time  by  Chron..      14    57      41 

Lon.ofShip48°  19'30"E.=  3h  13m  ISs,  at  6h  8m  A.M 


Sun's  R.  Ascension,  Aug.  21st 
Correction    Add 

Correct  R.  Ascen 


lOh  Om  548  Dif  Ih. 
2      16 


I5h 


Equation,  Aug.  2l8t 2m  68s  97 

Correction Sub.  9     16 

_10h_8m_98  60)135       Correct  Equation 2m  49s  82 


Diflh. 


.    610 
15h 

9-16-0 


215 


Finding  the  Latitude  in  by  the  Moon,  and  the  Longitude  by  Chronometer,  by  a  Star. 

QUESTION. 

h'etiruarv  7th,  1854.     (End  of  the  Sea  day.)     In  North  Latitude  and  West  Longitude,  (he  Meridian  Altitude  of  th« 
Moon's  Lower  Limb  was  observed  to  be  63°  9'  South,  and  »t  the  same  time  the  Altitude  of  the  Star  Regulus 
21°  47'  to  the  Eastward  of  the  Meridian  at  about  8  o'clock  in  the  evening,  and   the  Greenwich  Time  by  Chron 
ter,  Feb.  7th.  8h  66m  40s.     Required  the  Latit\ide  in  ami  tiie  Longitude  by  Chronometer. 

Answer. — The  Moon's  Correct  Altitude  is  63°  45'  South,  her  Decimation  24°  14'  North,  and  the  Latitude  in  60* 
?9'  North.  The  Star  Regulus'  Polar  Distance  77°  19',  his  H.  Angle  4h  44m  Sis,  his  Right  Ascension  lOh  Om  S6a. 
'iie  Right  Ascension  of  the  Meridian  6h  15m  44s,  (to  be  increased  by  24h,)  the  Sun's  Right  Ascension  21h  25m  to, 
the  Apparent  Time  at  Ship  7h  60m  388  P.  M.,  the  Mean  Time  at  Ship  Bh  5m  Ss,  and  the  Longitude  m  by  Cbrooom- 
•ter  12°  63'  46"  West 


waa 
ronome- 


IttO 


NAUTICAL  ASTRONOMY. 


FINDING  THE  LONGITUDE  BY  CHRONOMETER,  AND  THE  SUNS  TRUE  i  iiMUTH,  BY 

THE  SAME  ALTITUDE. 

This  is  a  very  convenient  mode  of  finding  the  Variation  of  the  Compass,  the  Sun's  True  Azimuth  being, 
obtained  from  the  same  Altitude  used  in  working  the  time  for  Chronometer,  and  which  may  be  practiced 
every  day  at  Sea,  with  only  the  additional  trouble  of  taking  the  Sun's  bearing  by  the  Azimuth  Compass  at 
the  time  the  Sights  are  taken,  as  directed  at  page  81,  and  also  the  Rule  for  working  an  Azimuth  at  page 
118.  By  this  method  we  have  only  to  take  out  the  Log.  Secant  of  the  Altitude  as  a  Latitude,  at  the  top 
of  the  page,  and  the  Log.  Co-Sine  of  the  Difference  between  the  Polar  Distance  and  the  Half  Sum,  as  a 
Half  Sum.  The  Logs.  Secant  of  the  Latitude  and  Co-Sine  of  the  Half  Sum  serving  for  both  Hour  Anglo 
and  Azimuth,  and  the  Angle  in  Time  in  the  latter  case  turned  into  space  by  Table  XXVI,  will  ^ve  the 
Sun's  True  Azimuth. 


i 


EXAMPLE  1. 

July  12th,  1354.  *  (End  of  the  Sea  day.)     In  Latitude  39°  25'  North,  Longitude  by  Dead  Reckoning  12'  0'  West* 
the  Sun's  observed  Altitude  in  the  morning  was  36°  38',  bearing  by  the  Azimuth  Compass  South  81°  30'  East,  and 
the  Greenwich  Time  by  Chronometer  Oh  48m  438  P.  M.  at  Greenwich.     Required  the  Variation  of  the  Compass  and 
the  Longitude  in  bj'  Chronometer. 
Sun's  Obs.  Alt.. . .     35°  38'  G.  Tune  by  Chro.  12h  48m  438    Reckoned  from  Midnight 

Corr.,  Table  IX.  Ad_d J^ 

True  Altitude  ...     35°  48' Alt. .  35°  48'     Log.  Secant 0.09094  Sun's  Correct  Dec.  .22*  0'  N. 

Polar  Distance    . .      68      0    Log.  0.03283  RDist  68°    0'  90    0 

Latitude 39   25    Log.  0.11207 Same  Log 0.11207  Polar  Dist 68*0' 

Sum 143°  13' 

Half  Sum 71°  37'  Log.  4.49882  H.Sum7r37'     Same  Log 4.49882  Correct  Equa 5ra  15b 

Difference _35°  49'  Log.  4.76730  DiE. .     3°  37'     '^*^S-  Co-Sine 4.99913 

App.  Time. . . .  7h"65n  Isa  Log.  &Inb2  9.70096— Angle  6h  Im  Sb 

Equation.  .Add  5     16  ,      , 

xt        rp-  ^,      ,     -r„  Angle  6h  Im  38  m  Table  XXVI=-True  Az.  S.  90°  16'  R 

G.TLyTbra.-lf48"ir  Magnetic  Azimuth S.81_J^'K 

Long,  in  Time  -^h-47^.  i5s-7 1  °  62'  30"  W.  Long.  ^'^'^^"^  ^'^"^^''^^ [We^ttlj. 

EXAMPLE  2.  **• 


Sept  6th,  1854.  (Ena  of  the  Sea  day.)  In  Latitude  36°  6'  South,  Longitude  by  Dead  Reckoning  10°  30'  East 
the  Sun's  observed  Altitude  in  the  afternoon  was  12°  38',  bearing  by  Compass  N.  44°  W.,  and  the  Greenwich  Time 
by  Chronometer  3h  52m  148  P.  M.  at  Greenwich.  Required  the  Variation  of  the  Compass  and  the  Longitude  io 
by  Chronometer. 

G.  Time  by  Chro.  Sh  62m  14s  Past  Noon  at  Greenwich 


38' 
8 


Sun's  Obs.  Alt...   12 
Corr.,  Table  IX,  Add 

True  Alt 12°  46' 

Polar  Distance. . .   96    25 
Latitude 36      6 


Alt         12°  46'     Log.  Secant 0.010S7  Correct  Dec. 

Log.  0.00273  P.  Dist  96    26 

Log.  0.09259   Same  Log 0.09259  Polar  Dist. . 


6' 
90 


25'  N 
0 


146°  17' 


53 


Half  Sum 72° 

Difference 69° 

App.  Time. .  .4h  3^  138  Log.  9.6U686 
Equa Sub.      1      45 


39'  Log.  4.47462  H.  Sum  72°  39' 
~    Log.  4.93702  Diff...  23*  46' 


96"  25' 


.Im  45« 


Mean  Time. .  .4h  34m  283 
G.  T.  by  Chro.  3    52      14 

Long,  in  Time  Oh  42m  14»— 10*  33'  SO"  Eaat  Long 


Same  Log 4.47452  Correct  Equa.. 

Log.  Co-Sine 4.96151 

9.63949=Angle  4h  48m  248 

Angle  4h  48m  25s,  Table  XXVI,  True  Az.  N.  72* 
Magnetic  Azimuth N.  44 


6'  W 
3    W 


Magnetic  Variation 28°  0' 

[Westerl, 


FINDING  THE  SHIP'S  POSITION.  15^ 


I 


FINDING  THE  SHIP'S  POSITION  AT  SEA  BY  SUMNER'S  METHOD 


This  Method  consists  in  a  new  use  or  application  of  a  Single  Altitude  observed  for  the  Longitude  bf 
Chronometer,  and  is  very  useful  when  a  Ship  is  near  the  Land,  especially  in  high  Latitudes,  where  th* 
weather  is  generally  unsettled  and  the  observations  for  Latitude  uncertain.  The  method  is  also  best  adapted 
for  High  Latitudes,  because  the  Sun's  change  of  Azimuth  is  more  rapid  there  than  in  Low  Latitudes,  and 
the  greater  the  change  of  Azimuth  in  a  given  time  the  more  accurately  the  Ship's  position  can  be  defined. 

In  the  Tropics  when  tne  Sun  rises,  passes  the  Meridian,  and  sets  Vertically,  the  Ship's  position  cannot  be 
found  by  this  method. 

Having  been  in  the  habit  of  using  this  method  at  Sea  for  many  years,  I  can  testify  to  its  great  utility  in 
defining  a  Ship's  place  on  the  Chart,  when  she  is  near  the  Land  or  a  danger,  and  Captain  Sumner  deserve* 
great  credit  in  making  its  value  known  to  Seamen. 

I  propose  here  to  give  a  sketch  of  his  method  as  done  in  the  practice  at  Sea,  which  may  be  found  useful 
to  those  who  have  not  seen  his  book,  where  they  will  find  the  whole  matter  fully  explained,  and  which  ought 
to  be  in  the  possession  of  every  practical  Navigator, 


Explanation  of  Sumner^s  Method. 

In  some  cases  where  the  Latitude  is  not  correctly  known  the  Longitude  by  Chronometer  cannot  be  cor- 
rectly found,  as  explained  in  the  Note  at  page  122  of  this  work,  and  it  is  on  this-'-^ry  circumstance,  and  the 
having  the  correct  Greenwich  Time  by  Chronometer,  that  the  method  is  founded. 

Suppose  an  Altitude  of  the  Sun  to  be  observed  in  the  Forenoon,  and  the  Longitude  by  Chronometer  found 
in  the  usual  manner,  the  Longitude  so  found  will  correspond  to  the  Latitude  worked  with.  The  sam« 
Altitude  worked  with  another  greater  or  less  than  the  first  Latitude,  the  Longitude  so  found  will  corres- 
pond  to  the  Latitude  worked  with  in  like  manner,  so  that  for  each  point  of  Latitude,  with  a  given  Altitude, 
there  will  correspond  a  certain  point  of  Longitude  and  no  other. 

These  several  points  or  positions  laid  off  on  the  Chart  in  their  respective  Latitudes  and  Longitudes,  and 
a  line  drawn  through  them,  the  ship  will  be  somewhere  on  this  line,  providing  the  Chronometer  is  right 
and  the  Latitude  assumed  is  not  very  greatly  in  error. 

If  this  line  produced  passes  thoughany  point,  of  Land,  the  true  bearing  of  this  Land  from  the  Ship  ia 
showir,  and  thus,  though  neither  the  Latitude  nor  the  Longitude  of  the  Ship  is  correctly  known,  yet  the 
true  bearing  of  any  place  on  the  Land  which  lies  in  the  direction  of  either  end  of  the  line  joining  the  two 
positions  is  certainly  known.  A  line  drawn  perpendicular  to  the  above  mentioned  line,  towards  the  side  on 
which  the  Sun  is,  shows  the  True  Azimuth  of  the  Sun. 

This  is  easily  understood,  because  the  several  Latitudes  and  Longitudes  laid  ofi"  by  means  of  the  same 
Altitude,  constitute  a  curve  of  equal  Altitude,  and  the  observer  in  moving  so  as  to  keep  the  Sun  at  the 
same  Altitude,  would  keep  him  always  on  the  bearing  at  right  Angles  to  the   direction  of  his  own  motion. 

The  effect  of  an  error  in  Altitude  -s  easily  shown  by  considering  that  the  place  of  any  part  of  the  circle 
of  equal  Altitude  on  the  Chart  move-  i^e  mile  for  each  l'  of  error  of  Altitude,  and  thus  the  corrected  posi- 
tion of  the  line  will  be  parallel  to  that  already  down,  and  distant  from  it  the  amount  of  the  error  of 
Altitude. 

When  the  coast  trends  parallel  to  the  line  of  equal  Altitudes,  the  distance  of  the  Ship  from  the  shore  ia 
ascertained,  though  her  absolute  place  is  uncertain,  provided  always  that  the  Ship  is  really  not  far  from 
her  supposed  Latitude,  and  that  the  Chronometer  is  right. 

When  a  single  Altitude  is  observ^ed  near  Noon  the  parallel  of  equal  Altitude  is  evidently  near  the 
parallel  of  Latitude  on  which  the  Meridian  Altitude  would  place  the  Ship,  and  the  bearing  of  Land  nearly 
East  or  West  is  very  nearly  ascertained.  On  the  other  hand,  when  the  Sun  is  near  the  East  or  West  points, 
the  line  of  equal  Altitude  lies  nearly  North  or  South,  and  its  position  in  Longitude  depends  entirely  on  the 
Chronome4er.  Also  errors  of  Altitude  affect  the  Longitude  by  Chronometer  most  when  near  Noon,  in  which 
case  it  can  have  no  inlluence  on  the  bearing  of  Land  near  East  or  West. 

As  a  Single  Altitude  gives  thus  the  line  on  which  the  Ship  is,  a  Second  Altitude  gives  a  second  line,, 
except  when  the  Sun  is  Vertical  and  has  no  change  of  Azimuth.  In  this  case  only  one  line  can  be  pro- 
jected  on  the  Chart,  which  will  always  lie  North  and  South. 

The  intersection  of  the  second  line  wiih  the  first  is  the  Ship's  true  place,  and  the  place  of  the  jntersecticn 
u  more  decisively  marked  as  the  two  lines  he  more  at  Right  Angles  to  each  other,  and  as  the  Sun  is  per- 
pendicular to  each  of  the  said  lines   at  the  time   the  Altitude  was  observed,  from  which   they   were  com 
puted,  they  will  cross  each  other  more  nearly  at  Right  Angles,  when  the  Sun  has  the   greatest  change  o. 
Azimuth. 


152 


NAUTICAL  ASTRONOMY. 


Rule  for   Working  by  Sumner's  Method. 

Having  obtaiied  an  Altitude  of  the  Sun  and  the  Greenwich  Time  by  Chronometer,  compute  t>e  Latitude 
m  by  Dead  Reckoning,  Take  a  Latitude,  say  30',  to  the  Southward  of  the  Dead  Reckoning,  with  which 
•nd  the  True  Altitude,  and  tlie  Sun's  Polar  Distance,  find  the  Longitude  by  Chronometer  as  usual. 

Again,  take  a  Latitude,  say  30',  to  the  Northward  of  the  Latitude  by  Dead  Reckoning,  and  with  the  same 
Altitude  and  Polar  Distance  find  another  Longitude  in  by  Chronometer. 

I>ay  ofi"  these  two  positions  on  the  Chart  and  Draw  a  pencil  line  between  them,  which,  extended  t«  any 
Land  in  the  vicinity,  will  give  the  true  bearing  of  that  place  from  the  Ship,  or  if  the  Land  trends  parallel 
with  the  line  it  will  give  the  Ship's  distance  from  the  Shore.  At  an  hour  or  two  or  more  after  the  first 
Altitude  was  taken,  or  when  the  change  of  Azimuth  exceeds  2  points,  take  another  Altitude,  and  with  the 
«ame  Ijatitudea  and  Polar  Distance  find  two  other  positions.  A  line  drawn  between  them  will  cross  the  first 
line,  which  will  be  the  Ship's  true  place  in  Latitude  and  Longitude  by  Chronometer. 

But  if  the  Ship  has  changed  her  place  between  the  Observations,  lay  off  the  True  Course  and  Distance 
Sailed  in  the  interval,  from  any  part  of  the  first  hue,  and  through  the  point  so  obtained,  draw  a  line  parallel 
to  the  first  hue  projected,  and  at  the  intersection  of  tkis  line  with  the  second,  is  the  Ship's  true  place  in 
Latitude  and  Longitude. 


EXAMPLE. 


December  10th,  1854.  A  ship  in  Latitude,  by  Dead  Reckoning,  37°  N.,  and  Running  for  Cape  Henry,  at  about 
8  o'clock  in  the  Morning  observed  the  Sun's  Altitude  to  be  9°  35',  and  the  Greenwich  Time  by  Chronometer  Ih 
fim  55a  P.  M.  at  Greenwich,  and  after  Sailing  W.  by  S.  True  20  miles,  a  second  Altitude  was  observed  to  be  27°  10', 
Greenwich  Time  by  Chronometer  3h  39m  16s.  Required  the  Bearing  of  or  Distance  from  Ae  Landin  the  vicinity, 
•t  the  time  of  each  Altitude,  and  also  the  Ship's  Correct  Latitude  and  Lon^tude  in  at  the  tim<9  of  the  last  Altitude. 

Latitude  and  Longitude   in  at  the  Time  of  the  Last  Altitude.  ^ 


Sun's  Ist.  Obs.  Alt. .  9°  35'  G.  Time  by  Chro.  Ih 

Corr.,  Table  IS 7  Add  12_ 

Sun's  True  Alt 9°  42'  Time  from  Mid.    13h 

Polar  Distance 112  56    Log.  0.03576 

Latitude 36  30    Log.  0.09482 

159°  8' 

Half  Sum 79°  34'  Log.  4.25790 

Difference 69°  52'  Log.  4.97262 

8hl0m558  Log.  9.36110 
Equation Sub.       7       0 

iL  Ship  Time. . .  8h  3m  55s  1st  position. 
Green. Time....  13     5     55    with  Lat.  36°  30  N. 

5h  2m    08=Long.      76°  30  W. 


Sun's  2d  Obs.  Alt.  ..27°  10' 
Corn,  Table  IK. .  .^ 1£ 

True  Altitude 27°  20' 

Polar  Distance 112   56 

Latitude 36   30 

176°  46' 

Half  Sum 88°  23' 

Difference 61°    3' 

1  Oh  3  5m  498 
Equation. .  .Sub.        6     58 

M.  Ship  Time. .  10h28m51s 
Green.  Time 15   39    16 

51ilOm258 


G.  Tune  by  Chro.  3h 
Add  12 

Time  from  Mid.    15h 
Log.  0.03576 
Log.  0.09482 

Log.  3.45044 
Log.  4.94203 


Log.  8.52305 

1st  Position, 
with  Lat.  36°  30' 

=  Long.     77°  36'  W. 


5m  558  -  Lat.  in  D.  R.  37°   0'  N.  Dec.  22'  66'  S. 

0       0  90      0 

6m  55s  True  Altitude 9°  42'        Polar  Dist.  112°  66' 

Polar  Distance 112    56  Log.  0. 03-6  7  6 

Latitude 37   30  Log.  0.10053 

160°  8'  Equ.Sur.7m08 

Half  Sum 7~80^'  Log.  4.23679 

Difference 70°  22'  Log.  4.97399 

8h  14m  55s  Log  9.34707 

Equation Sub  7      0 

M.  Ship  Time. . . .  8h   7m  65s  2d  position. 

Green. Time 13      5     55  withLt.37°30'N.)  timeof 

4li58m0s=Long.74°30'W.|  Ist  Alt 

Lat.  in  by  D.  R.  37°  0'  N.  Dec.  22°  66'  S. 
39m  16s  90 

_2 9    True  Altitude 27.^20'       Polar  Dist.  112°  56' 

39m  168  Polar  Distance 112    66  Log.  0.03576 

Latitude 37    30  Log.  0.10053 

177°  46'  Equ.Sub.6m588 

f  Sum 88°  53'  Log.  3.28927 

'erence 61°  33'  Log.  4.94410 

10h49m  34s  Log.  8.36966 
Equation . . . Sub.  6      58 

M.  Ship  Time . . .  1  Oh  42m  36s  2d  position. 

Green.  Time 15    39    16s  with  Lat.  37°  30' N. 

4h  56m  403  =-  Long  74*10'  W.  at  th» 
t?me  of  the  2d  Alt 


See  the  Projection  on  the  Chart,  next  page. 


The  positions  by  the  first  Altitude  laid  off'  and  the  first  line  drawn  between  them  strikes  the  Shore 
tbout  10  miles  to  the  Southward  of  Currituck  Inlet,  hence  the  true  bearing  of  that  part  of  the  Shore  is  3.  W.  ^S., 
•sd  the  Coast  of  Maryland  is  38  miles  distant  in  a  N.  W.  direction. 

The  Positions  by  the  Second  Altitude  laid  off  and  the  second  line  drawn  between  them  passes  through  Cap* 
Henry.     Hence  its  true  bearing  is  W.  by  |  S.  from  the  Ship. 

The  Ship's  True  Course  and  Distance  W.  by  S.  20  miles,  being  now  laid  off  from  the  first  line  and  a  line  drawn 
parallel  to  it,  then  where  it  cuts  the  second  line,  is  the  Ship's  True  place  (at  the  time  of  the  last  Altitude),  in  Latitude 
37°  13'  N.  and  Longitude  75°  8'  W.,  and  distant  from  Cape  Henry  50  miles. 

A  line  drawn  parallel  to  the  Course  made  in  the  interval,  through  the  True  place  of  the  Ship,  back  t9  the  first  line 
will  show  the  Ship's  place  on  that  line,  when  the  first  Altitude  was  observed,  in  Latitude  37'  18m  N.  and  Longitude 
14°  43'  W.  Hence  the  Ship's  Latitude  by  Dead  Reckoning  was  found  to  have  been  18  miles  in  Error,  or  that  much 
too  far  to  the  Northward  of  her  proper  position,  in  running  for  Cape  Henry. 


FINDING-  THE  SHIP'S  POSITION  BY  SUMNER'S  METHOD. 


153 


Fm.  27. 


#' 


1 


■^k"- POSITION 


\T/il/£  P/AC£  AT-  THE    TIME 
\    OrTHE    SH'    ALT? 


\^W3 


2"*  POSITION 


n"   POSITION 


l^wV  2 "i  POSITION 


20  30  'tO  50  3-7  = 


20  30 


PROJECTION  OF  SUMNER'S  METHOD  ON  THE  OHAiiT. 


NAUliJAL  ASTRONOMY. 


FINDING  THE  SHIP'S  POSITION  AT  SEA  BY  SUMNER'S  METHOD 


1  he  Ship's  place  may  be  found  in  the  same  manner  in  the  Afternoon,  should  the  Latitude  not  have  boe» 
•btsiined  from  an  observation. 

The  Altitude  observed  in  the  Afternoon  is  worked  with  the  same  two  Latitudes  unless  she  has  made 
much  Northing  or  Southing  in  the  interval,  but  the  Decl.  and  Equa.  of  Time  is  generally  corrected  to  thf 
time  of  observation,  and  two  positions  are  again  found,  which  laid  off  on  the  Chart,  and  a  line  drawn  be- 
tween them,  will  give  the  bearing  of  the  Land  or  the  distance  off,  as  the  case  may  be.  The  Course  and 
Distance  made  good  in  the  interval,  laid  off  as  before,  and  another  line  drawn  parallel  to  the  former,  will 
cut  the  last  line  projected,  at  the  Ship's  true  place. 

But  when  the  Ship  has  been  sailing  in  the  same  direction  as  the  former  line  it  is  not  necessary  to  lay  off 
either  Course  or  Distance,  because  the  place  of  intersection  of  the  two  lines  as  above,  will  give  both. 

Thus  the  Ship's  place  on  the  Chart  may  be  found  every  hour  of  the  Day  from  Sunrise  to  Sunset^  (Seo 
the  method  at  page  128,)  if  his  change  of  Azimuth  be  sufficiently  rapid  to  cause  the  lines  projected  on  the 
Chart  to  cross  each  other  at  an  angle 

By  this  method  also  the  Ship's  position  may  be  found  every  hour  of  the  Night  by  using  the  Staris.or 
Planets,  that  is,  finding  the  Longitude  by  Chronometer,  by  them,  using  two  assumed  Latitudes  as  with  the 
Sun.  But  unfortunately  the  Horizon  is  generally  so  obscured  at  night  that  not  much  dependence  can  be 
placed  on  the  Altitudes  observed. 

In  laying  off  the  Course  and  Distance  run  in  the  interval  between  two  Altitudes,  when  the  Ship  is  in  a 
Tide-way  or  Current,  the  Set  and  Drift  of  which  is  known,  it  can  easily  be  allowed  for,  by  forming  a 
small  traverse  Table,  composed  of  the  true  Course  and  Distance  sailed,  and  the  True  Set  and  Drift  of  the 
Current.  Then  the  Difference  of  Latitude  and  Departure  made  good  -vvill  give  the  Course  and '  D-stance 
made  good,  which  is  then  laid  off  as  usual. 


CONTINUATION  OF  THE  FORMER  EXAMPLK 


Decemoer  10th,  1854.     No  observation  for  Latitude  having  been  obtained,  the  Ship  had  been  hauled  up  W.  S.  W 
ou  the  bearing  of  Cape  Henry,  (from  the  Altitude  which  had  been  obtained  about  an  hour  before  Noon),  and  at  11 
80m  in  the  Afternoon  another  Altitude  was  observed  to  be  26°  15'.     Greenwich  Time  by  Chronometer  6h  24m  388, 
havinK  run  in  the  interval  W.  S.  W.  True  25  miles,  and  been  Set  by  the  tide  in  the  same  direct  on  6  miles.     Re- 
quired her  true  place  on  the  Chart  and  hei-  Bearing  and  Distance  from  the  Land  in  the  vicinity. 


Sun's  3d  Obs,  Alt. 26°  15'  G.  T.  by  Chr.  6b  24m    38b 

Corr,  Table  IX-. . J^ 

True  Alt 26    25 

Polar  Dis 112   57    Log.  0.03681 

Latitude 36    30    Log.  0.09482 

175°  5i' 

Half  Sum 87    56    Log.  3.55705 

Difference 61    31    Log.  4.94397 

lb  35m  32s  Log.  8.63165 
Equa Sub.       6     54 

M.  Ship  Time.Th~28m  38a 

G.  T.  by  Chro.  6    24     38   with  Lat.  36°  30'  N. 

4h  56m    0=  Long.       74°    0'  W. 


Sun's  Corn  Dec.  22° 

^                              90 

67' S. 

0 

Same  Alt  26°  25' 

Polar  Dis.  112    57  Log.  0.03581 

Lat 37    30   Log.  0.10053 

112° 

57 

176°  52                 Equa.  7m  Is  -53  Diff  lb  1-148 

Half  Sum.  88    26  Log.  3.43680          7  -46 

H 

Diff 62°     1'  Log.  4.94600    6m  548  '7 

6-888 

Ih  23m  47s  Log.  8.51914 

574 

Equa... Sub.  6     54 

7.46t 

M.S.  T.  Ih  16m  53s 

G.  T. ..  6    24     38  with  Lat.  37°  30'  N. 

5b  7m  45s=.Long.     76°  56'  W 

The  above  positions  being  laid  off  on  the  Chart  as  before  directed,  and  a  ..ne  dvawu  through  them,  w.U 

e  found  to  pas,s  over  the  Lisht-House  on  Smith's  Island,  near  to  Cape  Charles,  and  as  th"*  Ship  has  been 

sailing  on  the  line  of  bearing  of  Cape  Henry,  obtained  from  the  last  Altitude,  do  parallel   line  is  required 

to  be  drawn  nor  Distance  laid  off  in  this  case,  because  at  the  intersection  of,  tb^  two  last   lines  is  the  tru» 

place  of  the  Ship,  at  the  time  of  the  last  Altitude. 

It  now  appears  from  the  above  that  the  Li?ht-House  on  Smith's   Ulf^n^  bes«s  from  the  ship  W,  N.  W, 
nearly  12  mile;?,  and  Cape  Henry  W.  S.  W.    /•»~e  29  miles. 


Hence  if  the  Chronometer  is  right,  and  th'   j"*a,ol^.r  t,^*-a 
lb«  deck. 


H>«vs»»  «»i)i^cts  will  soon  beco;  ae  viniblo  froui 


HATING  THE  CHRONOMKTKR. 


loS 


RATING  THE  CHRONOMETER  AT  SEA. 


Ab  Chronometers  are  frequently  found  to  alter  their  rates  after  having  been  a  few  days  tin  bcful^aa 
explained  at  page  80,  they  should  be  verified  from  time  to  time  during  the  voyage,  or  in  othe-r  ff^iO.^,  the 
Sea  rate  should  be  found  at  every  convenient  opportunity,  which  is  easily  done  in  the  followiiii,'  r/.<iMner  : 
When  a  Ship  is  leaving  port,  if  the  weather  permit,  a  set  of  Altitudes  should  be  carefully  t«i;tia  v. ith  a 
Sextant,  and  the  Times  noted  by  Chronometer,  or  by  the  Watch,  if  found  more  convenient,  in  ti.e  usual 
manner  of  taking  Sights,  as  explained  at  page  124,  or  at  page  140,  and  the  Sextant  should  bo  p/eT'ously 
idjusted,  and  its  Index  error,  if  any,  applied  to  the  Mean  of  the  Altitudes,  (see  page  73,)  and  the  same 
Sextant  should  be  always  used  for  taking  the  Altitudes  for  the  purpose  of  rating  the  Chronometer,  so  as  to 
insure  a  uniform  result  throughout  the  voyage. 

The  Ship's  position  at  the  time  of  the  Sights  must  be  carefully  ascertained  from  Cross  Bearings  of  objects 
on  the  land,  by  an  Azimuth  Compass,  as  directed  at  page  31,  or  by  the  Chart,  at  page  53.  But  if  Cross 
Bearings  cannot  be  obtained,  run  the  Ship  into  the  Meridian  of  any  Cape,  Light- House,  or  other  object  on 
the  land,  the  position  of  which  is  well  laid  down ;  that  is,  get  it  to  bear  True  North  or  South,  (ttie  varia- 
tion of  the  Compass  being  allowed  for  in  advance,  which  can  easily  be  done  when  the  Ship  is  passing  it,) 
and  take  a  set  of  Altitudes  at  that  instant  indicated  by  the  Compass. 

The  Ship  will  then  be  in  the  Longitude  of  that  place,  and  her  Distance  from  it  is  the  correction  to  be 
applied  to  the  Latitude  of  the  place  to  find  the  Latitude  of  the  Ship,  according  as  she  is  to  the  North  or 
South  of  it.  In  working  out  the  time  in  this  case,  we  must  use  the  seconds  in  the  computation,  and  take 
out  tlie  proportional  parts  of  their  Logs.,  and  which  is  easily  done  by  considering  what  proportion  the  num- 
ber of  odd  seconds  bears  to  a  minute,  such  as  30"  is  i,  20"  is  i,  or  15  is  i  of  60".  Then  take  the  difier- 
ence  between  the  Log.  of  the  nearest  preceding  minute,  and  that  of  the  following  minute,  and  apply  the 
corresponding  i,  i.  or  i  of  this  difference  to  the  preceding  Log.  according  as  it  is  increasing  or  decreasing, 
or  multiply  the  difierence  by  the  odd  seconds  and  divide  by  60,  will  give  the  proportion  required. 

The  Mean  Time  at  the  Sliip  is  found  in  exactly  the  same  manner,  only  it  is  more  carefully  done.  The 
Ship's  Longitude  being  then  turned  into  Time  by  Table  XXVI,  and  added  to  the  Mean  Time  at  the  Ship, 
in  West  Longitude,  or  substracted  from  it  in  East,  will  give  the  Greenwich  Mean  Time  of  the  Observation. 
Then  the  Diiference  between  the  Greenwich  Mean  Time  so  found  and  the  time  shown  by  Chronometer  at 
the  time  of  the  Observation,  is  the  error  of  the  Chronometer  on  Greenwich  Mean  Time,  and  is  fast  or  slow 
accordingly. 

The  error  so  found  may  differ  considerably  from  that  given  by  the  Shore  rate.  However,  note  the  Sea 
error  so  found,  and  the  date  of  the  Observation,  and  at  the  next  favorable  opportunity  when  land  is  in  sight, 
repeat  the  observation,  and  find  the  error  anew.  Then,  if  the  two  errors  have  continued  the  same  after  the 
lapse  of  several  days,  the  Chronometer  is  running  on  Greenwich  Mean  Time,  but  if  the  errors  differ,  then 
the  difierence  is  the  amount  of  what  the  Chronometer  has  gained  or  lost  in  the  interval  between  the  timet 
of  Observations,  which  divided  by  the  number  of  days  elapsed  into  seconds  and  tenths  of  seconds,  will  give 
the  daily  rate  gaining  or  losing  accordingly. 

EXAMPLE 


P.  Dist..98' 

Lat 36' 

H.  Sum. 77° 
Dift ...5ft° 


20'  20" 
10'  28" 
81'  40" 

58'  45" 


Of  Proportioning  the  Logs,  to  the  Odd  Seconds. 


Log.  of  98°  20'  is  0.00461 
Log.  of  .S6°  10'  is  0.09296 
Log.  of  77°  31'  is  4.33477 

Lo! 


98°  21'  Log.  0.00463  DifiF.    2  pro.  for  20"  is    1  Additive —C.0046S 
36°  11'  Log.  0.09306  Ditf.  10  pro.  for  28"  is    6   Additive  =0.09301 
°  32'  Log.  4.33420  Ditf.  57  pro.  for  40"  is  38  Subtract.— 4.33439 
Diff.    8  pro.  for  45"  is    6  Additiva  —4.92349 


77 
56 


59 


Log.  4.92351 


This  Example  is  merely  given  for  the  purpose  of  showing  the   nature  of  the   proportions  jf  the  Logs. 

required  for  the  odd  seconds,  and  which  have  a  considerable  effect  on  the  time  when  working  for  the  nearest 

•econd.     In  practice  we  just  take  the  difference  between  the   Logs,  as  they  stand  in  the  Table,  and  apply 

«he  propor;ioiis  mentally  as  we  write  them  down.      This  saves   considerable  time,  and  the  learner.  \>j  u 

ittko  OACioiise  of  his  mental  powers   will  soon  acouir«»  the  habit  of  doin"^  the  same  with  ease 


15« 


NAUTICAL  ASTRONOMT. 


HATING  THE  CHRONOMETER  AT  SEA. 


EXAMPLE  1. 

March  10th,  1854.  A  Ship  bound  out  from  New  York  Harbor,  observed  the  following  set  of  Altitudes  and  Times 
by  Chronometer;  her  True  Position  at  the  same  time  being  found  from  the  bearing  of  the  land,  as  follows.  Required 
the  Error  of  the  Chronometer  on  Greenwich  Mean  Time.    Elevation  18^  feet. 


Runs  Obs.  Alt 10°  15'  20" 

A.K...10    26    30 

10    37    50 


8)79'  40" 


Mn.  of  the  Alt 10°  26' 

Ir,driX  Error. Sub.         2 

Seniid 16'    7 

Dip  4' 12")        ,11 
Ref.4'59"J^  ^^ 

True  Alt, 


33' 


T.by  Ch.Oh  16m  248 
0    17      26 

0    18      28 

3)52m  18s 
Mn.of  Ts . Oh  17m  26s 
by  Chroa 


10°  24'  33" 
Add  6   66 


10' 

Polar  Dist 94 

40 


31'  29" 
6    15 
23    40 


145°     1'  24' 


Log.  0.00111 
Log.  0.11827 


72°  30'  42  •  Log.  4.47787 
61°  69'  13"  iiOg.  4.94589 

Ap.  I.  at  Ship 7h  10m  128   Log.  9.64314 

Equii. Add        10     31 

Mn.  T.  at  Ship .7h  20m  438 

Long,  in  Time 4    55     40 

I2h  16m  23a 
Less 12      0       0 

sr.  Mn.  Time Oh  I6m  238 


Neversink  Light-H.  bore  W.  f  N.  4  mil»3,  or  True  West. 
Sandy-Hook  Light-House  N.W.  7  "  or  "N.W.fW 
The  Float  Light  Vessel  K  f  E.      3     "     or    "         North. 

These  Bearings  laid  off  on  the  Chart  gives  the  Ship's 
True  position  at  the  time  of  the  Sights, 

Latitude  in  40°  23'  40"  N.     Longitude  73°  65'  W 
And  the  Longitude  in  Time  4h  6om  408. 


Sun's  Dec.  at  Noon 4°  6'  30"  S. 

Correction   Sub.  15 

Correct  Dec 4°  6'  15" 

90   0     0 


Diff.  lh..i)69 


Polar  Distance 94°  6'  16" 

Equation  of  Time 10m  3l8 'oS 

Correction Sub.  16 

Correct  Equation 10m  3l8  "39 


Green.  Time  of  the  Observation.  .Oh  I6m  2.<ii 
Time  of  the  Obs.  by  Chron 0    17      26 

Chroa  Fast  of  Gr.  Mean  Time. 


Ifi 


Diff.  lh..i)666 


•16« 


Im    Ss^arcblOtk 


EXAMPLE  2. 

Miircn  25th,  1854.  Wreck  Hill,  in  the  Island  of  Bermuda,  in  Sight,  bearing  S.  4°  W.  by  Compass,  distant  10 
miles,  and  at  the  same  time  the  Mean  of  several  Altitudes  of  the  Sun  was  15°  19'  26",  Index  Error  2.  suotractjve, 
Mrtiui  of  the  Times  by  Chronometer  llh  36m  15s,  and  the  Sun's  Magnetic  Azimuth  beary^g  S.  78°  E.  Required  the 
Erri.r  of  the  Chronometer  on  Greenwich  Mean  Time,  its  Rate  since  leaving  New  York  on  the  10th  Maroh,  and  tho 
Variation  of  the  Compass.     Elevation  18^  feet. 

Sun's  Obs.  Alt 15°  19'  25"  A.  M.     Time  by  Chron..  llh  36m  15s     Bear,  of  Wreck  Hill  by  Com. .««  *•'  W. 

Index  Error Sub.  2     0  Reckoned  from  Midnight.  Var.  of  Com.  per  Azimuth 4    W. 

Semid....^..,.16'    4"  j  15°  17'  26"  True  Bear.  S.  lO' 

Re?.  3'  22"  I  "■'^'  ^'^"  \  ^'^'^  ^    ^^  Lat  W'k  Hill  32°  16'  N.  Loa  64°  55'  W 

True  Alt "15°  25'  55"  Log.  0.01695  Lat  of  Ship  .  .32°  £8'  N.  in  T.  4n  19m  408 

Polar  Dist   88    12    22  Log.  0.00021   88*12' 

Latitude 32    26 0  Log.  0.07365                  Log.  O.073bo  Sun's  Dec,  Noon  1°  48'    7"  N.  Dif.  lh.69 

136°    4'  17"  Correction Sub.      _29^  "~2S 

Half  Sum 68°    2'    8"  Log.  4.57291  68 2     Log.  4.67291  Correct  Dec. . .   1°  47'  38  " 

Diffeience 62°  36'  13"  Log.  4.90007  20°  10'    Log.  4.97252  Polar  Dist 88°  12'  22" 

App.  Time 7h    8m  46s  Logr9!64684                            9.63603=6h  28m  328=-True  Azimuth  S.  82°  8'  E 

Equ«'ion Add           6        9  Mag.Azimuth  S.  78   0   K 

Mean  Time Vh  Hm  64s  Mag  Variat'n. .     4°  8' 

Long,  in  Time 4h  19     40  [Westerly 

Grci-a  Mean  Time llh  34m  348  Days  elapa.  15  )388(  28  5-lOth  i  Daily  Rate.  Equa.  of  T.  frm  8s  46    Dif  Ih. 761 

Time  by  Chron 11     36      15  80                        Gaining         Corr...Add             38              -SSi 

Chro  Fast,  March  25th,          lm"4rs  15)80(6                                        Corr.Equa.  6m  Ss^ 

Jo.    March  10th.           18  75 

Accumulated  Error. . .  388  A(4- 

Hence  the  ChroDometer  is  this  day.  March  25th.  Fast  of  Greenwich  Oh  Im  418,  and  gaining  28  and  5-lOth  and  l-ti 
if  a  tenth  per  day. 

NoTK.— -Observations  for  Rating  Chronometers  at  Sea  should  be  all  taken  in  the  morning,  or  else  all  in  the  afterno^o, 
beeaaee  of  the  irregularity  in  the  time  deduced  from  the  morning  Altitudes  when  compared  with  those  taken  in  tkt 
•/teraoon.    (See  the  Note  at  page  141.) 


RATING  THE  CHRONOMETER  AT  SEA. 
EXAMPLE  8 


151 


A.pnl  Isl  1854.     A  Ship  oflF  Cape  Cod,  bearing  S.  9"  W.  by  Compass  3  miles  distant,  in  the  eTeniDgob««rTed  th« 
"e  t.)  be  6"  89   23".      Ou  the  Prime  Vertical,  Index  Error  1' 20"  A 


Sunla  Mean  Altitude 

8.  99*  20'  W.,  and  Time  by  Chronometer  lOh  22m  30s. 

Time  and  the  Ma^etie  Variation.    Elevation  16  feet. 


Additive,  Maguetio  Aziinutk 
Required  the  Error  of  the  Chronometer  on  Greenwich  Mcaa 


Sun's  Ob«.  Alt 6°  89'  28"  Tin,e  by  Chro.  10b  22m  308.  Beariog  of  Cape  Cod  by  Compaas  K    9*  W. 

Index  Error Add 1_20^  Magnetic  Var'n 9    West'ly. 

Semid 16'    1")       6*40' 48"  True  Bearing  South ..  Dist     3'    0"           0 

Dip.3'53"  )  _jj,29'f  Add    4  32  LatCapeCod 42°    2'  24  Log  70°   8'  18"W 

Ref..-' 36"  )                   )         ^ '                LaL  Ship..  42"   6' 24"  In  toe  4h  40m  1 8* 

True  Altitude 6°  45'  20"  Log.  0.00302 

Polar  Disiauce 85    18    12    Log.  0.00146  85*  18 

Latitude 42      5    24    Log.  0.12955  Log.  0.12965  Sun's  DecL    4*  81'  49"  N.    diff  Ih  68" 

134"    8'  56"  Cor.,.. .Add           9   69                           10^ 

HalfSum 67'    4   28"  Log.  4.69055  67'    4'  Log.  4.69055  Cor.  Dec. ..  4°  41'  48"                  'VJ'*"" 

Ditfereuce .60"  19'    8"  Log  4.93892  18°  14'  Log.  4.97763  Polar  Dis.  .85°  18'  12" 

App.  Time  at  Ship 5h  40iii  328= Log. "9166048  9.70076=6h    Om  56s=True  Az.  S.  90'  14'  W. 

Equation Add         3     52  Magnetic  Azimuth S.  99    20' W. 

Mean  T.  at  Ship 5h  44m  243  Eq.  of  T.  3m  598  "84  Dif  Ih  -755        Magnetic  Variation 9°    6'  Wly 

Long  in  Time 4    40     13    Corr.,  Sub.    7  "80  lOj 

Time  at  Greeewich. .  ..lOh  24m  378  Cor.  Equ.  3m  628  '4  7"80-2 

Time  by  Chron_ 10     22     30 

Hence  the  Chron.  is  Oh  2m  7s  Slow  of  Green.  Mean  Time.  April  1st,  and  the  Magnetic  Variation  9°  Westerly 
and  as  the  Magnetic  Variation  found  by  the  Azimuth  agrees  nearly  with  that  known  to  exist  off  Cape  Cod,  it  may 
be  concluded  that  there  is  no  Local  attraction  in  that  part  of  the  vessel  where  the  Compass  stood  when  the  Bearingf 
were  taken. 

EXAMPLE  4. 

April  21st,  1864.  The  Isle  of  Corvo,  one  of  the  Azores  Islands,  in  8ight  bearing  S.  24'  W  by  Compass  Distant 
16  miiea,  in  the  evening  the  Sun'*  Mean  Observed  Altitude  was  18'  38'  9",  Index  Error  1'  30"  Additive,  Tim* 
by  Chronomecor  7h  Um  59s,  and  the  Magnetic  bearing  of  the  Sun  at  Settmg  was  W.  39*  46'  N.  Required 
^he  Error  and  the  Daily  rate  of  the  Chron..  aince  leaving  Cape  God  on  the  iBt  of  April,  and  the  Magoetio  Vi 
.0.     Elevation  18  feet 

Suns  Observed  Altitude,.. .   18*88'    9"  Time  by  Chron. 7h  Om  69s 

Index  Eri-nr. Add  1    20 

Semid 15'  67" 

Dip.. 
Ref. 


■4"8''i'_    , 
2'4o"\  =  ^ 


63' 


18° S»'  29" 
Add  9      4 


True  Altitiuie 18°  48'  88" 

Polar   Distance 78      8    27    Log.  0.00951 

Latitude.    * 39    56      0    Log.  0.11532 

136° 48'    0" 


24'    0"  Log.  4.56599 
35' 27"  Log.  4.88168 


HalfSum 6^ 

Diffeience -. .   4y° 

Apparent  Time  at  Ship..    6h     1  in  27s=Log.  9.67245 
Equation Sub.  1     24 

Mean  Time  at  Ship 5h    Om    33 

Long,  in  Time 2      4      12 

Mean  Time  at  Green 7h    4m  158 

Time  by  Chron 7      0      69 

Chr.  Slow  of  G.  April  21st 
Chr.  Slow  of  G.  April  1st. 
Accumulated  Error 


Beanng  of  Corvo  by  Compass 8.  34°  W 

Variation  of  the  Compass 24  Westly. 

True  Bearing  South... DisL  16'  "o" 

Lat.of  Corvo 89°  41  N.  Long.  31    3' W. 

Lat  of  the  Ship 39°  66'  N.  In  time  2h  4m  12i 

Sun's  Declination,  Noon.. .    11°  50'  36"  N,  Dif.  Ih— 51" 
Corr Add  5   57  7h 


Correct  Dec. 11°  66'  83" 

Polar  Distance 78°  ~?~27' 


6' 67' 


Equa.  of  Time Im  20s    '6  Dif  lb— -514 

Corr .Add       3   -59  7k 


Correct  Equa Im  238  •65 


3-69  6 


3m  16s 
2       7 

"98 


Days  Elapsed. 


Im 
60 


Lat  40°  and  Dec  12°  N.  gives  True  Amp.  "W.  15°  46'  N. 
Magnetic  Ampli.  at  Sunset W.  39  46  N 

Magnetic  Variation 24'    Wesly 


.20)6V)m  (38  and  4-lOth  and  i  DaUy  Rate  Losing,  and  Slow  this  day  8m  1<U 

60 

20)90m  (4 
80 


10(  1 

515  Is 


^<"^---Jt-  Bi'certainiiig  the  Ship's  position  by  this  method,  it  is  necessary  to  find  the  exact  amount  of  Magnetic  Van 
t-.v  due  v~  fh«>  place,  and  the  Local  attraction  (if  any)  due  to   the  Ship  (See   page    121)  previous  to  the  Sights  beinf 
W«  "u  'oi  Chj-T.oaieter,  so  that  the  proper  Variation  mav  be  allowed  on  the  Compass  bearing,  for  the  purpose  of  iudi- 
•at  T)g  tt..«  lin;e  at  which  the  Object  bears*  True  North  or"  South. 

i  E  erroi  of  this  kind  will  cause  an  error  in  the  Longitude  so  deduced,  that  is.  the  Ship  will  not  be  on  the  same  M«'*- 
diai   or  in  ^hr  Longitude  of  that  place,  and  the  ereater  the  Distance   from  the  Object  the  greater  will  be  the  error  •• 
^arcd,  and  the  nearer  to  the  Object  the  less  will  be  the  error  from  that  cause. 


168 


NAUTICAL  ASTRONn\* 
RATING  THE  CHRONOMETER. 


EXAMPLE  B 


'September  7th,  ld64.  Ship  oflf  the  Gape  of  Good  Hope.  The  Magnetic  Variation  Observed  from  ao  Amplitude 
at  Sunrise  was  found  to  be  80°  Westerly,  and  when  the  Lion's  Head  Iwre  N.  30*  K  by  Compass,  Distant  30  mi)e«^ 
the  Sun's  Mean  Altitude  was  ooserved  to  be  11°  31'  49"  in  the  Morning.  Time  by  Chronometer  6h  8m  lOs  from 
Midnight     Required  the  error  of  the  Chronometer  on  Green.  Mean  Time.    Elevation  18  feet. 


Sun's  Observed  Altitude . . 

Semid 15  55"  | 

D.4'  8"  R.4'30"  =  8  38    j 

True   Altitude 

Polar  Distance 

Latitude 


T.  by  Chr.  6h  8m  lOs 
Reckoned    from  Mid't 


Sub, 


Half  Sum 

Difference 

App.  Time  at  Ship. 

Equa 

Mean  Time  at  Ship 

Long  in  Time Sub, 

Green.  Mean  Time 

Time  by  Chron , 

Error  of  the  Chron 


11°  31'  49" 
Add    7   17 

.   11° 89'    6" 
,  96    12     2 

142° 17'    8" 
.71°    8'  34"  Log.  4.5095 


Log.  0.00255 
Log.  0  08366 


Bearing  of  the  Lion's  Head N.  30°      E. 

Magnetic  Variation 30    West'ly. 

True   Bearing  North    30  miles. 

Lat.  Lion's  Head .  .33°  66'  S.  Long.     18°  24'  E. 

Lat  of  the  Ship.  ..34°  26'  S.  in  Time  Ih  13m  36s 


Sun's 
Corr. , 


Dec.  Noon 6°    6' 

Add.  5 


59°  29'  28"  Log.  4.93528 
7h  14m  603  Log.  9.5310© 
1_57_ 

7h  12m  588 
1  13     36 


Correct  Deel 6°  12'    2" 

Polar  Distance 96°  12'    2" 


26"  N.  Dif  Ih  56" 
86  T.  fr  Noon     6h 

2"  60)336 


6'  36' 


Equa.  of  Time 2m 

Corr Sub. 


28-14  Dif     lh-849 
6    OST.  fr.Noon    6b 


Correct  Equ. Im  57s   '5 


5h  59m  178 
,6      8     10 

8m  538  Faat  of  Green  Mean  Time  this  day,  September  7th 


6-09-4 


EXAMPLE  6 


September  30th,  1864.  Ship  in  Sight  of  St.  Paul's  Island,  in  the  Indian  Ocean,  the  Variation  of  the  Oompasa 
M  per  Amplitude,  being  21°  Westerly,  and  when  the  centre  of  the  Island  bore  S.  21°  W.  by  Compass,  Distant  26 
miles,  the  Sun's  Observed  Altitude  was  8°  26'  15"  in  the  Morning,  the  Time  by  Chronometer  being  Ih  21m  28,  reck- 
oned from  Midnight,  or  13h  21m  28  from  the  preceding  Noon.  Required  the  error  of  the  Chronometer  on  Green- 
wich Mean  Time,  and  its  rate  since  leaving  the  Cape  of  Good  Hope  on  the  7  th  of  September.     Elevation  19  feet. 


Sun's  Observed  Altitude 

Semid 16' 

Dip.  4' 15"  R.  6'    8"=  10' 23 

Ti-ue  Altitude 8 

Polar  Distance 87 

Latitude 38 


^\ 


8°  25'  15"  T.  by  Chr.  Ih  21m  2s 

A  jj  c   oo    Reckoned  from  Midt 
Add  5  38 


'  30   63 

23'  56"  Log.  0.00046 
22'    0''  Log.  0.10564 


Bearing  of  St.  Paul's  Island S.  21°  W. 

Magnetic  Variation S.  21°  Wes'ly 

True  Bearing  South 25  miles. 

Lat.  of  St.  Paul's 38°  47'  S.  Long.    77°  62'  E. 

Lat  of  the  Ship. 


38°  22'  S.in  Time  5h  11m  2«s 


Half  Sum. 


134°  16'  49" 


.67° 


8'  24"  Log,  4.58987 

Difference e'S"  37'  31"  Log.  4.93134 

App.  Time  at  Ship 6h  36m  18s=Lg.  9.62681 

Equation Sub.        9     49 

Mean  Time  at  Ship 6h  25^  24s 

Long,  in  Time Sub-  5    11     28 

Green  Mean  Time Ih  13m  56s 

Time  by  Chron 1    ^^       ^ 

Chron.  Fast,  Sep.  30th 7m    68 

Chron.  Fast,  Sep.  7th 8     68 

Aflcumnlated  Error lm47B 

60 


Sun's  Declination . 
Corr 


.Sub. 


Correct  Declination 2°  36'    4" 

20     0     0 


46'  27"  S.  Dif.  Ih  58" 
10   23  T.  fr.  Noon  lOJ 

580~ 


Povar  Distance 87°  28'  66" 


29 

14 


60)623 
10  23" 


Equa.  of  Time 9m  67s  -32  Dif     Ih  -808 

Corr Sub.  8    68  T  fr.  Noon  lOj 

8030 


Correct  Equa 9m  488  -69 


401 

20C 


•ag-l 


Davi  Elapsed   . . .     23)1078(4s  6-10  and  i  Daily  Rate  Losing,  and  this  day,  Sept.  SOtn,  Fast  of  l 
'  '^  92  Green.  M.  Time  Oh  7m  6a.  ( 


n 

28)160(6 
188 


RATING  THE  CHRONOMETER.  IM 


RATING  THE  CHRONOMETER  ON  SHORE. 


When  a  Ship  is  in  Port,  and  the  Sea  Horizon  visible  from  the  deck,  and  the  Sun  is  at  a  proper  distanoQ 
from  the  Meridian,  the  Rate  of  the  Chronometer  may  be  found  in  a  similar  manner  to  the  foregoing 
Examples  ;  or  thf  differenceof  its  Error  on  tlie  Mean  Time  at  the  place,  ascertained  after  the  lapse  of  several 
days,  will  give  us  Rate  per  day.  When  the  Sea  Horizon  is  not  visible  from  the  Ship's  deck,  it  may  happen 
that  70od  Sights  can  be  obtained  from  the  Sea-beach.  In  that  case,  compare  the  Watch  (with  which  the 
Time  li  intended  to  be  taken)  with  the  Chronometer,  before  leaving  the  vessel,  and  also  on  the  return  on 
board.  If  the  comparisons  are  the  same,  then  the  Watch  has  no  rate,  but  if  they  differ,  the  difference  is 
the  erri/r  of  the  Watch  in  the  interval.  Hence  its  rate  may  be  found,  (unless  the  Chronometer  has  itself 
y  very  large  rate.)  a  proportion  of  which  must  be  applied  to  the  Time  by  the  Watch  when  the  Altitudes 
"ve-e  observed. 

The  elevation  of  the  Observer's  eye  above  the  Sea-level  must  also,  in  this  case,  be  carefully  ascertained 
va  order  to  apply  the  proper  correction  for  the  Dip  of  the  Horizon,  found  in  Table  V.  An  Example  of 
doiiig  this  is  not  necessary,  as  it  is  worked  in  the  same  manner  as  in  the  preceding  Examples. 

By  the  Artificial  Horizon. 

The  use  of  this  instrument  is  fully  explained  at  pages  77  and  78,  and  the  manner  of  finding  the  Time 
(s  given  at  page  131.  It  is,  therefore,  considered  unnecessary  to  give  any  more  Examples  of  the  same,  and 
we  proce^  to  give  a  case  of  Rating  the  Chronometer  from  the  Mean  Time  at  the  Place,  supposed  to  have 
been  obtained  from  either  of  the  above  methods. 


EXAMPLE  1. 

October  3d,  1854.  A  Ship  lying  in  the  Port  of  Rio  Janeiro,  her  correct  position  by  bearing  \ra8  Latitude  22°  64 
South,  Longitude  43°  9'  West  At  8h  30m  25s  A.  M,  Mean  Time  at  the  place,  a  Chronometer  showed  lib  83m  12a 
Required  its  Error  on  Greenwich  Meau  Time. 

Mean  Civil  Time  at  Rio  Janeiro,  October  3d 8h  30m  25s 

Add...»  12      0        0 

Mean  Astronomical  Time,  October  2d 20h  30m  25s 

Longitude  of  the  Ship  43°  9'  W.  in  Time Add 2    62      36 

Mean  Abtronomical  Time  at  Greenwich,  October  2d 23h  23m     Is 

Astronomical  Time  bv  Chronometer,  October  2d 23    33      12 

Chronometer  Fast  of  Greenwich  Mean  Time Oh  10m  1  Is,  Oct.  3d. 

EXAMPLE  2. 

i>ov.  2d,  1854.  At  Rio  Janeiro,  Ship  in  the  same  position  as  before,  the  Mean  Time  at  the  place  was  Bh  10m  6t 
A.  M„  the  same  Chrononifter  showed  llh  14m  7s.  Required  its  Error  on  Greenwich  Mean  Time,  and  its  Rate  bIdm 
Ootober  8d,  at  which  time  it  was  10m  lis  too  fest 

Mean  Civil  Time  at  Rio  Janeiro,  Nov.  2d 8h  10m    58 

Add 12      0       0 

Mean  Astronomical  Time,  Nov.  1st 20h  10m    os 

Longitude  of  the  Ship  43°  9'  W.  in  Time Add 2    52      36 

Mean  Astronomical  Time  at  Greenwich,  Nov.  Ist 23h    2m  4l8 

Astronomical  Time  by  Chronometer,  Nov.  Ist 23    14        7 

Chronometer  Fast  of  Greenwich  Mean  Time,  Nov  2d 11m  26s 

do.  do.  Oct.  8d. 10      11 

Accumulated  Error TmTss 

60 
Number  of  days  elapsed 30)75(    29  6-1 0th  Daily  RaU  cai»iiiiB 

go  ^ 

The  Chronometer  is  this  day  Fast  of  Greenwich  11m  26«...  )160(6 

And  gaining  2  sea  6-lOtb  per  day 150 

0 

e^^^—l"  East  Longitude,  the  Longitude   in  Time  must  be  subtracted  from  the  Mean  Astronomical  Tim*  at  th* 
MM,  to  obtain  the  Greenwich  Mean  Time  ;  beoaase  the  Time  at  Greenwich  most  always  be  the  least  in  East  Lonjri- 


l*?) 


NAUTICAL  ASTRONOMY. 


FINDING  THE  LONGITUDE  BY  CHRONOMETER. 


Having  thus  given  all  the  various  methods  of  finding  the  Longitude  hy  Chronometer  which  are  of  prae 
lical  utility,  and  also  the  manner  of  Rating  the  same,  both  at  Sea  and  on  Shore,  this  part  of  the  s  ihjeet 
will  be  closed  by  the  following  Examples  for  Exercise. 


QUESTIONS  FOR  EXERCISE. 


Queshon  1st. — April  30th,  1854.  (Noon  at  Sea.)  Tn  North  Latitude,  and  24*  30'  West  Loiigitude.  in  the 
morning,  the  observed  Altitude  of  the  Sun  was  22°  7'.  Greenwich  Time  by  Chronometer  8h  46m  IDs, 
reckoned  from  midnight.  Ship  then  sailed  N.  E.  by  E.  (True  Course)  35  miles  until  Noon,  when  the  Sun's 
Meridian  Altitude  observed  was  68°  3'  South.  Required  the  Ship's  Latitude  and  Longitude  in  at  the 
time  of  the  Sights,  and  al.so  at  Noon. 

Answer. — Latitude  36° 
tude  24°  3r>'  W.  at  Noon 


13'  N.,  Longitude  25°  11'  W.  at  time  of  Sights,  and  Latitude  36°  32'  N.,  Longi- 


Ques.  2f/. — April  30th,  1854.  (Noon  at  Sea.)  Latitude  observed  at  Noon  36°  32'  North.  In  the  after- 
noon the  Sun's  observed  Altitude  was  13°  48'.  Greenwich  Time  by  Chronometer  7h  7m  15s.  Ship  had 
sailed  £.  N.  E.  (True  Course)  30  miles  since  Noon.  Required  the  Latitude  and  Longitude  in  at  time  of 
the  Sights,  and  also  the  Longitude  of  the  Ship  reduced  back  to  Noon. 

Ans. — Latitude  at  time  of  Sights  36°  43'  N.,  Longitude  24°  2'  W.,  and  Longitude  at  Noon  24°  37'  W. 

Ques.  3d. — March  26th,  1854.  (Noon  at  Sea.)  In  South  Latitude,  and  66°  30'  East  Longitude,  by  ac- 
count. In  the  morning  the  Sun's  observed  Altitude  was  25°  25'.  Time  by  the  face  of  the  Chronometei 
3h  29m  Is,  or  which,  reckoned  from  the  preceding  Noon  is.  March  25th,  15h  29m  Is  Astronomical  Time, 
the  Chronometer  being  2:n  24s  fast  of  Greenwich  Mean  Time.  Ship  then  sailed  N.  W.  (True)  17  miles 
nntil  Noon,  when  the  Sun's  Meridian  Altitude  observed  was  75°  20'  North.  Required  the  Latitude  and 
Longitude  in  at  the  time  of  the  Sights  and  at  Noon. 

^7W.— Latitude  12*  32'  S.,  Longitude  66°  37'  E  at  time  of  Sights,  and  Latitude  12*  20'  S.,  Longitude  66' 
84'  30"  E.  at  Noon. 

Qiies.  4th. — March  10th,  1854.  (Noon  at  Sea.)  In  North  Latitude,  and  60°  45'  West  Longitude,  the 
Sun's  Meridian  Altitude  observed  at  Noon  was  47°  32'  South.  Ship  then  sailed  N»rth  East  (True;  40  miles, 
and  in  the  afternoon  the  Moon's  observed  Altitude,  Lower  Limb,  was  40°  32'  to  the  Eastward  of  the 
Meridian,  and  the  Greenwich  Time  by  Chronometer  was  9h  41m  21s.  Required  the  Latitude  and  Longi- 
tude in  at  Noon,  and  also  the  Latitude  and  Longitude  in  at  the  time  of  the  Moon's  Altitude. 

Ans. — Latitude  observed  38°  14'  N.,  Longitude  60°  33'  W.  at  Noon,  and  Latitude  38°  42'  N.,  Longitude 
59°  57'  W.  at  the  time  of  Sights. 

Ques.  5th. — April  7th,  1854.  (Noon  at  Sea.)  In  North  Latitude,  and  West  Longitude,  at  twilight  in  the 
morning,  the  Meridian  Altitude  of  the  Star  Vega  was  observed  to  be  79°  51'  North,  and  at  the  same  time 
the  Altitude  of  the  Planet  Venus  was  24°  21'  to  the  Eastward  of  the  Meridian,  the  Greenwich  Time  bjr 
Chronometer  being  lOh  15m  55s  from  midnight,  or  April  6th,  22h  15m  55s  from  the  preceding  Nooiv. 
Required  the  Latitude  and  Longitude  in  at  the  time  of  the  Sights. 

Ans. — Latitude  observed  2o    26'  N.,  Longitude  by  Chronometer  70°  5'  W. 

Ques.  6th. — February  10th,  1854.  (Noon  at  Sea.)  In  North  Latitude  and  West  Longitude,  at  twiligl.t 
in  the  evening,  the  observed  Altitude  of  the  Star  Sirius  was  12°  27'  to  the  Eastward  of  the  Meridian,  ard 
the  Greenwich  Time  by  Chronometer  was  lOh  4m  41s,  and  at  li  hours  afterwards  the  Meridian  Altitude 
of  the  Star  Aldebaran  was  observed  to  be  66°  16'  South.  Ship  had  sailed  on  a  true  S.  W.  Course  12  mile* 
Ui  the  interval.  Required  the  Latitude  in  by  Observation,  and  the  Latitude  and  Longitude  in  at  time  of 
lights. 

^rw.— Latitude  observed  by  #  Aldebaran  40°  l'  N.  Latitude  in  at  time  of  Sights  40°  10'  N.,  and  Lon- 
eitude  68*  23'  W.  at  the  time  of  the  Sights 

Ques.  7th. — A  Chronometer  which  was  10m  14s  Fast  of  Greenwich  Mean  Time  at  New  York,  on  the 
10th  of  March,  1854,  showed  3h  Om  53s,  when  the  Mean  Time  at  Calcutta  was  8h  40m  10s  A.  M.,  on  the 
12th  of  June,  1854,  in  Longitude  88°  17'  E.,  or  in  Time  5h  53m  8s.  Required  its  Error  on  Greenwich 
Mean  Time,  and  its  Rate  since  leaving  New  York.    " 

Ans. — Its  Error  on  Greenwich  Mean  Time  is  13m  51s.  Accumulated  Error  3m  37s.  The  number  «i 
4ava  elapsed  94,  and  its  daily  Rate  2  see.  3- 10th  gaining  since  leaving  New  York. 

NoTi. — In  the  above  Examples  the  height  of  the  eye  above  the  Sea-level  is  supposed  to  be  17  or  18  feet. 


LUNAR  CjhSEllVATinit  loi 


'iHE  LUNAR  OBSERVATION 

Means  the  measurement  of  the  Angular  Distance  of  the  Moon  from  certain  Celestial  bodies,  and  tui 
the  Moon  is  constantly  advancing  to  the  Eastward  in  the  heavens,  at  the  rate  of  about  l'  in  2  minutes  of 
time,  she  overtakes  and  passes  all  the  other  Celestial  bodies  in  her  progress,  they  appearing  to  remain 
Btationary  in  the  heavens. 

The  Moon's  distance  from  the  Sun,  and  a  fevr  bright  Stars  and  Planetp,  are  calculated  for  the  end  of 
•very  3  hours,  (except  during  about  6  days  at  the  time  of  each  New  Moon,)  and  given  in  the  Nautical 
Almanac  for  the  Mean  Time  at  Greenwich.  The  observation  of  this  distance  from  any  part  of  the  Earth'» 
surface,  affords  the  means  of  determining  the  Greenwich  Mean  Time,  the  difference  between  which  and 
the  Mean  Time  at  the  Ship,  is  the  Longitude  in  Time.     This  constitutes  a  Lunar  Observation. 

If  the  distance  between  the  Moon  and  the  other  body  were  the  same  to  the  spectator,  whether  viewed  at 
the  surface  or  from  the  centre  of  the  Earth,  there  would  be  nothing  m«re  to  do  than  to  measure  the  dis- 
tance, (with  an  instrument,)  and  to  find  from  the  Nautical  Almanac  the  Greenwich  Time  corresponding  to 
it,  and  to  compare  this  with  the  Time  at  the  place.  But  the  Refraction  of  the  Atmosphere  has  the  ten- 
dency to  raise  the  Sun,  a  Star,  or  a  Planet,  above  its  true  place  in  the  heavens,  and  the  effect  of  Parallax 
is  to  make  them  appear  lower  ;  the  latter  has,  however,  very  little  effect,  in  consequence  of  their  great 
distance.  (See  explanation  given  at  page  67.)  On  the  other  hand,  the  Moon  being  near  the  Earth,  her 
Parallax  in  Altitude  is  greater  than  her  Refraction,  and  which  causes  her  to  appear  below  her  true  place 
in  the  heavens. 

Hence  the  Apparent  Distance  between  the  Moon  and  the  other  body  differ  from  the  True  Distance,  a» 
will  be  seen  in  the  following  Diagram. 

DIAGRAM, 

•      Showing  the  Effect  of  Parallax  on  tne  Lunar  Distance 

Fig.  28. 


A»  the  Moon  must  always  be  raised,  and  the  Sun  or  Star  lowered,  to  obtain  their  true  places,  the  Star  to 
the  right  in  the  above  Figure  being  higher  than  the  Moon,  it  is  evident  that  by  raising  her  the  True  Tft4- 
tance  will  be  less  than  the  Apparent  Distance. 

Again,  the  Star  to  the  left  being  lower  than  the  Moon,  by  raising  her  the  True  Distance  will  be  greater 
than  the  Apparent  Distance 

And  it  is  evident  from  the  above,  that  the  difference  between  the  True  and  the  Apparent  Distancet 
depend  almost  entirely  on  the  correction  of  Altitudes. 

It  is  therefore  useful  to  bear  in  mind,  as  a  check  against  gross  mistakes,  that  the  True  and  Apparent 
Distances  cannot  differ  by  more  than  the  Sum  of  the  Corrections  of  Altitude.  Again,  when  the  Moon's 
Altitude  is  equal  or  less  than  that  of  the  other  body,  the  True  Distance  is  less  than  the  Apparent  Distance. 
Bat  the  contrary  does  not  always  hold  good  when  the  Moon's  Altitude  is  greater  than  the  other  body 


Ift2  NAUTICAL  ASTRONOMY. 


THE  LUNAR  OBSERVATION 

IS  the  only  independt •  it  method  of  finding  the  Longitude  which  is  practical  at  Sea,  and  it  requires  gr«ai 
jjractice  to  measure  the  distance  successfully.  (See  the  Use  of  the  Sextant,  and  the  Remarks  on  Measur- 
ing the  Lunar  Distance^  at  pages  72  to  76.)  And  the  application  of  so  many  small  corrections  as  are  neces- 
«ary,  when  accuracy  is  required,  even  with  extraordinary  care  and  some  skill,  it  is  scarcely  possible  to 
arrive  at  extreme  precision,  although  the  observation  may  have  been  made  on  shore,  with  the  best  instru- 
ments ;  and  it  is  recorded  by  practical  surveyors,  and  other  scientific  men,  entitled  to  great  credit,  that  the 
Mean  Longitude  deduced  from  several  thousands  of  Lunar  Distances,  taken  equally  on  both  sides  of  the 
Moon  at  one  season  of  the  year,  have  differed  from  10'  to  12'  from  the  Mean  Longitude  deduced  from  an 
equal  number  of  Lunar  Distances  taken  in  like  manner  at  a  different  season  of  the  year. 

And  from  my  own  experience  in  observing  Lunar  Observations  at  Sea,  during  the  course  of  many  yearb, 
I  am  entirely  of  the  same  opinion. 

The  Lunar  Observation  is  certainly  an  excellent  mode  of  detecting  any  very  gross  error  in  the  Chro- 
nometer, and  is  valuable  on  that  account  alone,  and  also  for  correcting  the  Dead  Reckoning  within  certain 
limits ;  but  I  am  satisfied  that  a  Chronometer  cannot  be  rated  by  Lunars  at  Sea,  though  some  authors  of 
Nautical  works  persist  in  the  contrary  opinion. 

The  most  rapid  change  of  distance  between  the  Moon  and  a  body  is  1°  48'  in  three  hours,  and  the  effect 
of  an  error  of  1'  of  distance  is  25'  of  Longitude,  or  that  of  15"  error  of  Distance  is  6'  of  Longitude  in  the 
most  favorable  case. 

An  error  in  the  observed  Altitudes,  however  minute,  also  affects  the  True  Distance.     Then  there  are  the 
errors  in  the  Shades  or  Screens,  and  the  parallelism  of  the  Telescope,  all  which  are  explained  at  page  72 
and  rules  given  to  correct  them  :   and   lastly  the  errors  in  the  Tables,  however  small,  from  which  the  cor 
rections  are  taken.  , 

It  is  usual  to  take  Lunar  Distances  both  East  and  West  of  the  Moon,  and  to  take  the  Middle  of  the 
Longitudes  so  found  for  the  True  Longitude.  This  may  compensate  to  a  certain  extent  for  some  of  tlie 
errors,  but  it  may  nevertheless  be  several  minutes  of  Longitude  from  the  truth.  It  is,  however,  more 
likely  to  be  correct  than  either  of  the  others. 

From  the  above  facts  it  would  appear  that  in  general  the  Longitude  by  nf  set  of  Lunar  Distances  is 
liable  to  be  in  error,  even  with  the  greatest  care  and  by  the  most  practical  observer.  This  error  may  not 
exceed  10',  and  is  in  general  much  less  ;  but  even  this  amount  of  precision  is  a  very  valuable  acquisition 
to  a  Ship  on  a  long  voyage,  and  which  may  not  have  had  an  opportunity  of  verifying  her  Chronometer  by 
the  sight  of  land.  For,  if  after  several  sets  of  Distances  have  been  taken,  both  East  and  West  of  the 
Moon,  and  the  Longitude  deduced  from  each  set  differ  considerably  from  the  Longitude  by  Chronometer, 
and  they  all  point  in  the  same  direction,  that  is,  either  all  to  the  Eastward  or  all  to  the  Westward  of  the 
Chronometer,  it  may  be  concluded  that  the  Chronometer  is  in  error  to  the  amount  of  nearly  the  difference 
between  them.  And  in  the  case  of  a  Chronometer  thus  changing  its  error  and  rate,  it  wouid  be  unsafe  to 
trust  to  it  during  the  remainder  of  the  voyage.  And  as  the  following  method  of  observing  and  working  a 
Lunar  Observation  may  be  done  with  nearly  as  little  time  and  trouble  as  that  of  finding  the  Longitude  by 
Chronometer,  and  in  the  case  of  the  Chronometer  breaking  down  at  Sea,  the  Longitude  may  be  found 
sufficiently  near  for  all  practical  purposes  by  the  Lnnar  method,  bearing  in  mind  that  in  Low  Latitudes 
she  Degrees  of  Longitude  are  large,  and  where  an  error  of  a  few  minutes  of  Longitude  would  be  most  con 
•picuously  seen,  the  weather  is  generally  clear  and  fine,  and  the  land  may  be  seen  at  a  considerable  dis- 
tance off. 

On  the  other  hand,  in  High  Latitudes  the  Degrees  of  Longitude  are  small,  and  where  an  error  of  a  fe"» 
muxutes  of  Longi?.:de  occupy  only  a  small  portion  of  space,  or  miles  of  Departure,  consequently  *V.y  vrocid 
fcivi  ress  effect  o  j  the  Ship's  Distance  from  the  shore  than  it  would  in  Low  Latitudes. 


LUNAR  OBSERVATION  ]o3 


THE  LUNAR  OBSERVATION. 


In  taking  a  Lunar  Observation,  two  assistants  may  be'employed  to  observe  the  Altitudes  of  tiie  objects, 
■while  the  principal  observer  is  taking  their  Distance,  and  a  fourth  notes  the  Times  of  each  by  a  Watch 
or  Chronometer. 

The  Observation  is  then  written  down  in  the  following  order.     (See  page  76.) 

June  3d,  1864      In  the  Afternoon.  Height  of  the  Eye,  1 8  feeu 

Times  by  Watch.  .2h  t  .^m  668  Sun's  Altitude. .  49°  45'     Moon's  Alt,  L.  L.,.  .41*  10'  Dist.©  and  ]>  .  ,87°  41'  20'' 

2  68        0  do.  49    17  do.  0    32    To  the  Westward  0    42    20 

3  0        4  do.  48    49  do.  0    64  0    43    20 


3)8h  64m    0  3)147°  61'  3)96  3)127'^0^ 

Mn  of  the  Times.  .2h  58m    0  Sun's  Obs.  Alt.. . .  49°  17'     Moon's  Obs.  Alt.  .~4i'^32'  Mean  Obs.  Dist. 87°  42'  20'' 

When  no  assistants  are  at  hand,  one  person  may  take  the  whole  observation  himself;  indeed  it  is  more 
.satisfactory  to  de  so  than  to  have  to  trust  to  others,  because  it  is  very  rarely  possible  that  the  Altitudes  of 
the  bodies  can  be  seized  at  the  instant  of  taking  the  Distance.  By  adopting  the  following  method  the 
observer  will  be  independent  of  all  assistants,  and  learn  by  experience  to  trust  entirely  on  himself  in  using 
the  instruments  with  precision. 

Being  prepared  with  two  Quadrants  to  measure  the  Altitudes  of  the  bodies,  and  a  Sextant  to  measure 
their  Distance,  all  previously  adjusted,  (or  their  errors  known,)  and  a  Watch  to  note  the  Time.  Set  the 
Index  of  the  Sextant  roughly  to  the  Approximate  Distance.  (See  page  74  or  75.)  Set  the  Indices  of  the 
■Quadrants  roughly  to  the  Approximate  Altitudes  of  the  two  bodies.  Then,  holding  the  Watch  in  the  hand 
ar  place  it  where  the  movement  of  the  second  hand  can  be  distinctly  seen,  take  an  Altitude  of  one  of  the 
bodies,  (generally  the  one  farthest  from  the  Meridian,)  at  the  instant  the  second  hand  of  the  Watch  has 
completed  the  full  minute,  and  note  down  the  Time  and  the  Altitude  of  that  body  opposite.  Take  up  the 
other  Quadrant  and  observe  the  Altitude  of  the  other  body  at  the  time  the  second  hand  of  the  Watch  has 
■completed  the  next  two  minutes,  and  note  down  the  Time  and  Altitude  as  before.  Now  take  the  Sextant 
and  bring  the  Limbs  of  the  objects  in  contact,  at  the  instant  the  second  hand  of  the  Watch  has  completed 
the  next  two  minutes,  and  note  down  the  Time  and  the  observed  Distance.  Shift  backward  or  forward 
the  Index  of  the  Sextant  1',  (as  directed  at  page  76,)  and  await  the  contact;  note  the  Time  and  Distance 
down  as  before.  Shift  the  Index  again  1'  in  the  same  direction,  and  note  the  time  of  contact  as  before, 
rtiree  Distances  being  sufficient.  Take  up  the  Quadrant  and  observe  the  Altitude  of  that  body  which  wag 
last  observed,  at  the  completion  of  the  next  two  minutes,  which  note  down  as  before,  and  finish  with 
observing  again  the  Altitude  of  the  first  body  observed,  at  the  expiration  of  the  next  following  two  minutes. 
Thus  there  will  be  a  uniformity  of  Time  between  the  Observations,  which  will  render  it  easy  to  reduce 
them  all  to  the  Mean  of  the  Times  at  which  the  Distance  of  the  bodies  were  observed,  as  follows  • 

Form  of  Writing  down  the  Observation. 

JuneSd,  1864.  T.by  Watch  2h  52m  Os  Alt  of  the  Sun 60°  41'    0"       Height  of  the  Eye,  18  feet 

2  54      0  Moons  L.  Linio..  40    48      0 

(  2    56    56  Dist  Sun  and  Moon..     87  41  20     )    Sun  West  of  the  Moon. 

Mn.  of  Times  2h  58m    0s.-|  2    58      0  do.                      0  42  20     \    Mean  Distance 87°  41   W 

(304  do.                       0  43  20     ) 

3  2     0  Alt  of  Moon's  L.  Limb  42  16  0 
3      4      0    Alt  of  the  Sun 47  53  0 


To  Reduce  the  Altitudes  to  the  Mean  of  the  Times  that  the  Distance  was  Observed. 

To  Find  the  Sun's  Altitude.  To  Find  the  Moon's  Aliunde. 

Time  of  Ist  Alt.  2h  62m   Alt  50°  41'    T.  let  Alt  2b  52m  Time  of  Ist  All  2h  54m  Alt  40°  48'    T.  Ist  Alt  2h  54ni 

2d  .Alt  3 4      Alt  47    53     Mn.  of  T b  2    68  "       2d  Alt  3       2      Alt  42    lo     Mn.  ofT'8  2    68 

Say  as  r2in  is  to  2°  48'     So  is  6m  Say  as     8in  is  to  1°  28        so  is  Ara 

€m  being  half  of  12m,  and  the  Difference  of  AIti-  Am  being  half  of  8m,  and  the  Diffeieuc«»  of   Alti- 
tude bting  2°  48',  the  half  of  which  sublmct  1°  24'  tude  being  1°  28',  the  half  of  which  addded  0*  44 

1 8t  Alt  Obs.  ( and  decreasing)  was 50    41  1  st  A  It  ( increasing)  was 40    48 

Sun's  Alt  at  the  Mean  of  the  Times 49°  17'  Moon's  Alt  at  the  Mean  of  the  Times     41*  82 

Hence  we  have  tbe  following  Observation  • 

M<Mi  of  the  Times  by  Watch.  .2h  58m  Os  Sun's  Alt.  .49°  17'    Moon's  A        41*  82'  Dist  ©  and  ]>  .  .87*  4«'  30* 


iei4 


NAUTICAL  ASTRONOMY. 


TO  FIND  THE  APPARENT  ALTITUDES  OF  THE  BODIES  AND   THEIR  APPARENT 

DISTANCE. 

•  Add  12'  to  the  Observed  Altitude  of  the  Sun  and  Moon,  and  add  their  Semidiameter  to  the  Observed  Distanott 

Bon's  Oba.  Alt  .49°  17'     Moon's  Obs.  Alt,  L.  L..41'  32'     Obs.  Distance  of  Sun  and  Moon 87*  42'  20" 

12^  12      Sun's  Semid.15'48"  D's  Aug.  Semi  16'  21". Sum  81     9 

Bun's  App.  Alt.  .49'  29'     Moon's  App.  Alt  . . .  AV'ii      Apparent  Central  Distance 88'  13'  29" 

June  8d,  1854.     At  2h  68m  P.  M,  Latitude  in  30'  North,  Longitude,  Dead  Reckoning,  70*  W,  the  Sun's  Deolin»> 
lion  22*  21'  North,  the  Moon's  Decimation  12°  28'  N.,  given  to  Project  the  Figure. 

DIAGRAM  OF  A  LUNAR, 

Drawn  on  the  Plane  of  the  Meridian. 

Fir,.   29. 


In  this  Figure  th*  Sun  in  on  the  Prime  Vertical,  to  the  Westward  of  the  Meridian,  and  his  Hour  Angle 
measured  on  the  Equator  gives  the  Apparent  Time  of  the  Ob.servation,  2h  58m  P.  M.  The  Moon  having 
nearly  the  same  Hour  Angle  to  the  Eastward  of  the  Meridian,  appears  to  a  spectator  situated  at  a  great 
Jistauoe  to  the  Eastward  of  the  Earth,  (which  is  in  the  centre,)  to  be  nearly  in  the  same  line  of  bearing^ 
jut  the  following  Figure,  drawn  with  the  objects  facing  the  spectator,  will  place  them  in  a  better  point  of 
Tiew  for  showing  the  nature  of  the  case. 

DIAGRAM  OF  A  LUNAR, 
Drawn  on  the  Plane  of  the  Prime  Vertical.  0 

Fig.  30. 


7tNITH 


tp  "L 


OlST  ;     8  7^3^     12 


ISAeci-lA      THOKISSCHY. 


In  this  last  Figure  both  bodies  are  seen  on  the  Prime  Vertical,  East  and  West  of  the  Meridian,  their 
Altitudes  are  laid  off  from  the  line  of  Chords,  and  their  Apparent  Central  Distance  measures  on  the  scale 
88*  13'  29".  Now,  it  is  evident  that  by  raising  the  Moon  (which  the  correction  for  Parallax  does)  wo 
bring  the  Moon  nearer  the  Sun,  while  the  correction  for  Refraction  increa.ses  the  Distance  by  lowering  the 
bodies ;  but  as  the  former  has  more  effect  than  the  latter,  the  Moon's  True  Distance,  according  to  the 
Figure,  is  less  than  the  Apparent  Central  Distance.  This  quantity  is  found  by  the  Rules  given  on  th© 
oext  page,  and  which  is  termed  Clearing  the  Lunar  Distance. 

*  This  Correction  is  simply  the  Difference  between  the  Semidlameters  taken  at  16',  and  the  Pip  of  the  Horizon,  take» 
»t  4',  to  be  added  when  the  Lower  Limbs  are  taken. 


LUNAR  OBSERVATION.  lAf 


TO  FIND  THE  APPARENT  ALTITUDES  AND  DISTANCE. 

Turn  the  LongHude  by  Dead  Reckoning  into  time  by  Table  XXVI,  and  aaa  if  to  the  Time  at  the  Ship  a 
West  Longitude  or  subtract  it  in  East,  will  give  the  Approximate  Time  at  Green  ivich.  Prefix  the  day  of  the 
month  one  day  less  than  the  Sea  date,  and  call  it  the  Greenwich  Date. 

*  Take  out  the  Moon's  Semidiameter  and  Horizontal  Parallax  from  the  Nautical  Almanac  and  correct 
them  to  the  Greenwich  Date  by  Table  XXIV,  and  to  the  Moon's  Semid.  add  her  Augmentation,  taken  from 
Table  VII. 

To  the  observed  Altitude  of  the  Sun  and  Moon's  Lower  Limbs  add  12'.  But  if  the  Moon's  Upper  Limk 
06  observed,  subtract  20',  and  if  a  Star  be  observed,  subtract*^' . 

Take  out  the  Sun's  Semid.  from  the  Nautical  Almanac  and  add  both  it  and  the  Moon's  Augmentation 
Semidiameter  to  the  observed  Distance,  will  give  the  Apparent  central  Distance. 

If  a  Star  be  observed,  add  the  Moon's  Augmentation  Semidiameter  to  the  observed  Distance  if  the  nearest 
Limbs  be  observed,  but  subtract  it  if  the  farthest  Limbs  be  taken,  will  give  the  apparent  Distance. 

If  one  of  the  bodies  be  at  a  sufficient  distance  from  the  Meridian,  correct  its  Apjmrent  Altitude  for  refrac- 
tion by  Table  IV,  but  if  the  body  be  the  Moon,  by  Table  XXV,  will  give  its  true  Altitude,  with  which  find 
the  Mean  Time  at  the  Ship  as  usual ;  but  if  both  bodies  are  too  near  the  Meridian  an  Altitude  taken  after- 
wards will  give  the  Error  of  the  Watch  on  Mean  Time  at  the  Ship,  which  must  be  farther  corrected  for 
the  Difference  of  Longitude  in  Time  the  Ship  has  made  in  the  interval ;  but  it  is  much  more  convenient 
and  correct  to  time  tho  observation,  so  that  one  of  the  Altitudes  of  the  bodies,  (the  Sun  or  a  Star  is  pre- 
ferred) observed  with  the  distance,  may  also  be  used  to  find  the  Time  at  the  Ship. 

To  Clear  the  Lunar  Distance. 

RULE 

1.  To  the  Pro.  Log.  of  the  Moon's  Horizontal  Parallax,  Table  XXXIV,  add  the  Log.  Co-Secant  of  tb* 
Apparent  Altitude  of  the  Sun  or  Star,  taken  from  the  bottom  of  Table  XXVII,  and  the  Log.  Sine  of 
the  Apparent  Distance  found  in  Table  XXXI,  their   Sum,  will  be  the  Log.  of  i\iQ  first  correction. 

2.  To  the  Pro.  Log.  of  the  Moon's  Horizontal  Parallax  already  found,  add  the  Log.  Co-Secant  of  tk« 
Moon's  Apparent  Altitude,  taken  from  the  bottom  of  Table  XXVII.,  and  the  Log.  Tangent  of  the  Apparent 
Distance  found  in  Table  XXXI,  their  Sum  will  be   the  Log.  of  the  second  correction. 

3.  Take  the  first  and  second  corrections  from  Table  XXXII,  and    place  them  under  the  Apparent  Distance 

4.  Take  the  third  correction  from  Table  XXXIII,  and  alter  applying  to  it  the  correction  taken  from  TabU 
P,  on  the  same  page,  (which  is  only  used  when  the  Sun  is  observed)  and  place  it  under  the  Second  correction, 
add  all  these  corrections  to  the  Apparent  Distance,  and  their  Sum,  rejecting  lO  degrees,  will  be  the  true 
Distance. 

EXAMPLE  1. 

June  3d,  1854.  In  Latitude  30'  u  N.,  Longitude  by  Dead  Reckoning  69°  64'  W.,  the  Time  by  Watch  was  2b  68ia, 
Sun's  observed  Altitude  49°  17',  Moon's  observed  Altitude  L.  L,  41°  82',  and  the  observed  Distance  87°  42'  20". 
(See  page  164.)     Required  the  true  Distance,  tlie  Green.  Mean  'Time,  the  Mean  Time  at  Ship,  and  the  Longitude  ia 

Tnn#atShip 2h  58m   ©'sObs.Alt    49°  17'    D 's  Obs.  Alt 41°  32'  Obs.  Dis 87°  42' 20" 

Long.  69°  64' W.  in  time  4    40  Add         12  Add  12     Q'a  Semid....         16   48 

G-'»en.  Date,  June  8 7h  38m   ©'sApp.  Alt.   49°  29'    ]) 's  App.  Alt 41°  44'    P's  Aug. Semid.      16  21 

App.  Dist 88°  IS' 29" 

Moon's  Her.  Par.  0°  65'  37"  Pro.  Log... .  05101 Pro.  Log. . .  0.5101    J)  's  Sem.  Noon...  16'  8" 

Sun's  App.  Alt. 49    29     0    Log.  Co-Sec. 0.1191   ])  's  App.  Alt  41°  44'  Log.  Co-Sec.  0.1767    Corr.  7^  hours. . 8_ 

App.  Dist 88°  13'  29^  Log  Sine..  0.9998 Log  Tang. .  2.5087  15'  H" 

First  Correc. -I-    4    17' 43"  Log. 1.6290  ^"S • \^ 

Second  Corr.  4-    5      1      9  Log 8.1955    Aug.Semid 16' 21" 

Tbird  Corr..  -j-  1    61 

Less 10°=87°  34'  12"  True  Distance.  H*'^'-  Pf  Noon.  .66'  24'' 

Cor.  7i  hours. .         18 

Correct  H.  Par.. 66'  ST** 


NoTX. — The  manner  of  a.^lnp  the  Tables  for  clearing  the  Lunar  Distaaoe  are  the  same  a«  usually  done  with  others,  anc 
nqnires  nc  explanation,  and  in  Table  XXXII  directions  are  given  on  the  face  of  the  Table  for  taking  out  and  applying 
the  corrections,  and  in  'Table  P  alao  the  precept  Add  or  Subtract  to  or  from  the  correction  in  Table  XXXIII,  ar<)  givca 
•o  the  face  of  the  Table. 

*  Tha  Moon's  Semidiameter  and  the  Horizontal  Parallax  are  taken  oat  for  tie  nearest  Noon  or  Midnight,  and  tbcb 
Difierence  in  12  honrs  found,  with  which  we  enter  Table  XXIV  at  the  Top,  and  the  Greenwich  Time  from  Noon  or  Mi^ 
■ight  at  the  aide,  aud  at  the  angle  of  meeting  is  the  cor-«ntio't  to  be  Added  or  Subtracted,  according  aa  they  are  ia« 
(■f  or  deoraaaing 


166 


NAUTICAL  ASTRONOMY. 


HAVING  THE  TRUE  LUNAR  DISTANCE,  TO  FIND  THE  CORRESPONDING  GREENWICH 

TIME. 

Find  in  the  Nautical  Almanac  the  two  distances  between  wnich  the  True  Distance  falls.  Take  out  th« 
first  of  these  and  set  it  down  under  the  True  Distance,  and  note  down  the  hour  taken  from  the  head  of  th« 
•ame  column,  and  also  its  Prop.  Log.,  found  opposite  in  the  Nautical  Almanac. 

Take  the  Difference  between  the  two  Distances  thus  set  down,  with  which  enter  Table  XXXIV,  and  take 
out  the  Pro.  Log.  of  the  Difference  ;  from  this,  Subtract  the  Pro.  Log.  taken  from  the  Nautical  Almanac,  the 
remainder  is  the  Pro.  Log.  of  a  portion  of  Time  to  be  Added  to  the  Hour  taken  from  the  head  of  th« 
column,  and  the  result  is  the  Greenwich  Mean  Time. 

True  Distance  previousl/  found 87°  34'  12"  which  falls  between  VI  and  IX  honra 

Distance  at  VI  Hours 86    48    23     Pro.  Log.  .3208 

Difference 0°  45'  49"  Pro.  Log.  .6942      ^ 

Portion  of  Time  to  be  Added Ih  35m  55    Pro.  Log.  .2734 

To  the  Hour  of  the  preceding  Dist  N.  A .^. .  6      0       0 

Oreenwich  Mean  Time,  June  8d 7h  85m  55b  at  the  time  of  the  Observation 

To  Find  the  Mean  Time  at  the  Ship,  and  thence  the  Longitude. 

The  Sun  being  at  a  proper  Distance  from  the  Meridian,  in  this  case,  at  the  time  the  Distance  was  observed 
the  Mean  Time  at  the  Ship  is  found  from  his  Apparent  Altitude,  after  correcting  it  for  Refraction  by  Tabl« 
IV,  as  follows  : 

Sun's  App.  Altitude 49°  29'  Gr  Date.  June  8d,  7h  36m  Oa. 

Ref.  Table  IV Sub.  

True  Altitude 49° 

''olar  Distance - 67 

atitude 30 


28 

89 

0 


147°    7' 


Half  Sum.... 73°  34' 

Difference 24°    6' 


Log.  0.08892 
Log.  0.06247 

Log.  4.46163 
Log.  4.61101 


App.  Time  at  Ship 2h  68m  888=Log.  9.16903 

Equa.  of  Time Sub.  2     10 

Mean  Time  at  Ship. 2h  56m  288 

Green.  Time  by  Lunar...  7    85m  55 

Longitude  in  Time 4h  39m  828=Longitude  in  69"  53'    0"  West  at  about  8  P.  M. 


Sun's  Declination  Noon. , 

.  22°  19'  N.  Dif.  Ih  18' 

,                             Cor 

'        Correct  Declination. . . . . 

...Add 

2                      7 
.  22°  21'  N.        60)126 

[        Polar  Dist 

Equation  Noon 

90     0                     'A' 
.  67°  89' 

.2m  ISs  "SS  Dif.  Ih  410 

>                              Cor 

Correct  Equa 

.  ySub. 

3  -07                  7^ 

2m  108  -26             2870 
206 

807-5 


The  Difference  between  the  Mean  Time  at  the  Ship  and  the  Greenwich  Time  by  observation  is  the  Lon- 
gitude in  Time,  which  turned  into  Space  by  Table  XXVI,  oe  it  may  be  computed  by  the  rule  given  at  the 
bottom  of  cage  140,  and  the  result  is  the  Longitude  of  the  Ship  at  the  time  of  the  observation. 


REMARKS. 


If  the  times  of  the  observation  are  taken  by  a  Chronometer,  or  which  is  the  same  thing,  the  time  of  the 
Distance  by  Chronometer  obtained  from  a  comparison  with,  the  same  Watch  used  in  taking  the  times  of 
the  observation,  and  the  Error  of  the  Chronometer  on  Greenwich  Mean  Time  applied  to  it,  we  have  the 
Greenwich  Time  by  Chron.  at  the  time  of  the  observation  ;  then  if  it  agrees  nearly  with  the  Greenwich 
rime  found  by  the  Lunar  Distance,  the  correctness  of  the  Chronometer  is  confirmed  within  certain  limits  ; 
but  should  they  differ  considerably  after  several  observations,  it  may  be  concluded  that  the  Chronometer 
Has  altered  its  rate. 

The  learner  should  practice  measuring  the  Lunar  Distance  when  in  Sight  of  Land,  or  when  his  Longitude 
8  well  known,  and  by  that  means  establish  a  confidence  in  himself.  But  he  must  not  feel  discouraged 
hould  it  happen  that  his  first  attempts  fall  very  wide  of  the  truth,  (as  is  generally  the  case.)  but  by  a 
steady  perseverance,  and  profiting  by  his  former  errors,  he  will,  after  carefully  perusing  the  instructions 
given  at  pages  from  72  to  76,  soon  acquire  the  habit  of  measuring  the  Distance  tolerably  correct.  And  i1 
is  easy  to  know  whether  the  Distance  measured  has  been  too  great  or  too  small  by  simply  inspecting  the 
columns  of  the  Nautical  Almanac  and  finding  whether  the  Distance  between  the  bodies  is  increasing  ot 
decreasing:  if  increasing  and  the  Greenwich  Time  by  Lunar  too  great,  when  compared  with  the  Green- 
wich  Date,  found  as  above,  then  the  Distance  observed  has  been  too  great  by  the  amount  of  the  Difference 
of  Time,  say  as  3  hours  is  to  the  Difference  in  3  hours,  so  is  this  Difference  of  Time  to  a  proportion  ol 
Space,  will  give  the  amount  of  the  Error.  When  the  Distance  is  decreasing  and  the  Greenwich  Time  bj 
Lunar  too  great,  then  the*  Distance  observed  has  been  too  small,  and  the  amount  is  found  in  like  manner 
»nd  vice  versa.     (See  the  Rules  on  pages  16S  and  169.) 


7h  51m 

30s 

7  53 

40 

7  55 

45 

7  57 

40 

7  59 

60 

8   1 

58 

8   3 

59 

LUNAR  OBSERVATIf.N.  167 

FINDING  THE  LONGITUDE  BY  LUNAR  OBSERVATION. 

Distance  betweoi  the  Moon  and  a  Star. 
In  the  preceding  Example  the  Sun's  Distance  was  observed  W.  of  the  Moon,  and  in  the  following  Observa- 
tion the  Star's  Distance  is  observed  East  of  the  Moon,  for  the  purpose  of  showing  the  manner  of  connectinf 
the  two  Longitudes  so  deduced,  in  order  to  obtain  the  Mean  of  the  two  at  the  time  of  the  last  Observation. 

EXAMPLE  2. 

June  8d,  1854.  On  the  evening  of  the  same  day  as  in  the  preceding  Example,  the  following  Distances  wer« 
Bbeeived  of  Antares,  East  of  the  Moon,  and  East  of  the  Meridian.  Ship  had  sailed  from  Latitude  30°  North,  and 
Longitude  69°  52'  45"  West,  by  last  Lunar.  Course  S.  E.  (true)  40  miles.  Required  the  Longitude  in,  and  also  th* 
Mean  of  the  two  Longitudes,  at  the  time  of  the  last  Observation. 

June  3d.  Times  by  Watch 7h  51m  30s     Alt  of  Antares 12°  57'    0" 

L.  Limb  of  the  Moon...  60    2T      0 

Dist.  remote  Limb 85    35   40    ) 

Mean  of  the  Times  7h  57  ra  45s..  •{  7    57      40  do.  0    34   40    V  Mean  Dist. ...  86°  84' 87"^ 

do.  0   33    30    ) 

Alt.  of  the  Moon 59    31      0 

Altitude  of  Antares. ...  15    27      0 
The  Altitudes  are  now  reduced  to  the  Time  of  the  Mean  Distance  by  Pro.  Logs,  as  follows : 

To  Mild  the  Star's  Altitude.  To  Find  the  Moon's  Altitude. 

r.  of  Ist  Alt.  7  51  30  Ist  Alt  12°  57'  T  Ist  Alt  7'61  80  T.  of  Ist  Alt  7  53  40  1st  Alt.  60°  27'  T.  Ist  Alt7  58  40 

"     2d  Alt  8    3  59  2d  Alt  15    27     Mn.  of  T's  7  57  45  "    2d  Alt  8    1  58  2d  Alt  59    31  M.  of  T's  7  57  46 

Then  say  as~12  29       is  to      2°  80'         so  is          6  15  Then  say  a^     8^       is  to           66'  so   is         4    i 

12m  298  Pro.  Log.  1.1589  8m  18s  Pro.  Log.  1.3362 

Arith.  Compli 8.8411  Arith.  Compli 8.6638 

2°  30'  Pro.  Log.. .   0.0792  0°  56'  Pro.  Log.. .  0.5071 

6m  16s  Pro.  Log.  1.4694  1st  Alt.  Obs.  increas.  12°  67'  4m  5s  Pro.  Log.  1.6443  1st  Alt  Obs.  decreas.  60'  27' 

0.3797  Pro.  Log.  of  the  Corr.  1    15'  0.815'Z  Pro.  Log  of  the  Corr.    028' 

Ah.  of  Antares  at  the  Time  of  the  Mean  Dist 14°  12'  Alt  of  the  Moon  at  the  Time  ol  the  Mean  Dist. .  .69°  59 

To  Find  the  Greenwich  Date  and  the  Necessary  Preparations  for  Clearing  the  Distance. 

Time  at  the  Ship. .   7  67'  45  Co.S.E.  40=D.L.  0°  28'  Dep.  28'=D.  L.  0°  32'  45"  E.  D's  Sem.  Mid.  16'  13"  aPar.66'46' 
L-in  69°  20'W.in  T.  4  37  20  Lat  Left 30     0   Lon.  by  Lunar  69    52  45  W.         Aug.  13     Corr.  1' 

Gr.  Date,  June  3d,  12  36    6  Lat  In 29°  32N.  "  brought  on  69°  20'    0"  W.  Aug.Semid.  15' 26"  aPar.55'46' 

Alt  of  Antares 14°  12'     Alt.  of  Moon's  L.  L 59°  59'     Obs.  Dist  Moon's  remote  Limb. . .  85°  34'  87" 

Dip  for  21  feet Sub.    5  Add..    12      Aug.Semid Sub.         16    26 

#'s  App.  Alt 14°    7'     Moon's  App.  Alt .  60°  11'     App.  Central  Distance 85°  19'  11" 

To  Clear  the  Lunar  Distance  and  Find  the  Greenwich  Time. 

> 's  Hor.  Parallax 0°  55' 46"  Pro.  Log.  0.5089   Pro.  Log 0.6089 

#'sApp.  Alt 14     7     0     Co-Sec...  0.6128    B'sApp.  Alt 60°  11'     Co-Secant 0.0617 

App.  Distance 86°  19'  11"  Sine 0.9985    Tangent 2.0866 

First  Correction 4   46    21 . .  Log.  ....  2.1202  

Second  Corr 6      3    58     2.6679 

Third  Corr. 3    30 

True  Dist Less  10°=85°  13'    0" 

Dist  at  Midnight,  or  XII,    85    29    55     Pro.  Log.  0.2843 
Difference 16'  55"  Pro.  Log.  1.0270 

0.7427=  Oh  32m  38s  portion  of  Time  to  be  added 
to  the  Hour  of  the  precediog  Distance,  N.  A.  .12      0        0 

Gueenwich  Mean  Time     12h  82m  33s  at  the  Time  of  the  Distance. 

To  Find  the  Mean  Time  at  the  Ship,  and  thence  the  Lcmgitude. 

App.  Alt  of  Antares 14*    7'  Gr.  Date,  June  3d,  12h  35m  Sun's  R.  Ascen.  .4h  44m  13s  Di£  lh.l08X12h  8^ 

Corr.  for  Ret Subu  4  Correction 2       5 

#'b  True  Alt 14°    3'  Sun's  Corr.  R.  A.4h  46m  18s 

Polar  Distance 116     6    Log.  0.04671  Equa.. ..   2m  138 

Latitude 29   32    Log.  0.06045     Corr 5  #'s  Right  Ascen.,  1854 16h  ^Om  24* 

159°  41'  Corr.  Eq.  2m~~88 

Half  Sum ~79°  60'  Log.  4.24677  Wb  Declination,  1864 2(;°    •'  8 

Diflference 66    47    Log.  4.96000  90      0 

H.  An.',  of  #    East),,   ^,      ,_     j       „„,„„„  #'s  Polar  Dist 116°    6' 

p,,     ,,      J-       >■  3b  85m  588    Log.  9.31393 
of  the  Meridian  )  " 

#'8  R  Ascen 16    20     24  Mean  Time  at  Greenwich  by  Lunar 12h  32m  88i 

R.  A.  of  the  Merid. .  12h  44m  268  Mean  Time  at  Ship 7    56       0 

Sun's  R.  Ascen 4    46      18  Long,  by  Lunar 69°    8'  15'  —  4h  36m  88» 

App.  Time 7h  58m    Ss  Long,  by  last  Lunar  brought  on  by  D.  R.. . .     69    20      0 

Equation  of  Time  .Sub.      2       8.  ,  i)138°  28'  16" 

Mean  Time  at  Ship.     7h  66m    Os  Mean  Long,  by  Lunar    69*  14'    7  '  W.  at  time  ol 

[laDt  Ob* 


468  NAUTICAL  ASTRONOMY 

FINDING  THE  LONGITUDE  BY  LUNAR  OBSERVATIONS. 

Distance  Observed  between  the  Moon  and  a  Planet. 

EXAMPLE  8. 

Jnly  8d,  1864.  la  Latitude  89°  26'  South,  Longitude  by  Dead  Reckoning  about  80°  East,  at  8h  80m  P.  M 
Apparent  Time  at  Ship,  the  observed  Altitude  of  the  Planet  Jupiter  was  31°  35'  East  of  the  Meridian,  the  obseryea 
Altitude  of  the  Moon's  Lower  Limb  38°  61',  and  the  observed  Distance  between  the  centre  of  Jupiter,  East  of  tho 
Moon,  and  the  Moon's  remote  Limb  was  102°  31'  43".  Index  Error  1'  30",  subtractive,  and  the  Greenwich  Mean 
Time  by  Chronometer,  being  correct,  was  3h  14m  28s.  Required  the  Longitude  in  by  the  Lunar  Distance,  and  the 
F''ror  (if  any)  of  the  measured  Distance. 

Preparation  for  Clearing  the  Distance. 
•Green.  Time  or  Date,  by  Chrc,  July  3d, ,    . .  3h  14m  28s     Moon's  Semid.  Noon  15'  31"  and  H.  Par 56'  49' 

^t     T-,-  ..  «..            i    y„u                             ino"  oT  Ao"        *    '  *             n    >  Add  11     Gorr.  Gr.  Date..  Add         6 
Obs.  DisL  p  8  remote  Limb 102    31   43  Augm.    9    J  

Index  Error Sub. 1    30        Aug.  Semid 15'  42"  Hor.  Par 56^55^ 

Obs.  Distance 102°  30'  13" 

Moon's  Aug.  Semid Sub.  16   42       Obs.  Alt.  Jup.. . .   31°  35'  Obs.  Alt.  >  's  L.  L.. . .  38*  61' 

Apparent  Distance 102°  14' 31"     ^^P Sub. 4    Corr. Add         12 

App.  Alt  Jup.. .  31°  31'  App.  Alt.  of  the  >  ...   39°    3' 

To  Clear  the  Distance. 

|> 's  Hor.  Parallax 66'  55"  Pro.  Log.  0.6000     Pro.  Log.  0.5000 

Jupiter's  App.  Alt. 31    81      0     Co-Secant  0.2817    '  D  's  App.  Alt. ...  89'  8'     Co-Sec„ .  0.2007 

App.  Central  Distance 102°  14'  31"  Sine 0.9900     Tangent.  1.6687 

First  Correction 4   29   38     _' 1.7717  

Second  Correction 4   52    13     2.3644 

Third  Correction 2    23 

True  Distance,  less  10°     101°  38'  40" 

Distance,  N.  A.,  at  Illh 101    46    12     Pro.  Log.  0.2618 

Difference 0°    7   32"  Pro.  Log.  1.3783 

Pro.  Lo|.  1.1165— Oh  18m  468  portion  of  Time  V  be  added 

to  the  time  of  the  preceding  Distance,  Jr.  A.  ...  3      0 0 

Greenwich  Mean  Time  by  Lunar 3h  18m  468 

To  Find  the  Time  at  Ship,  and  thence  the  lo%fritude. 

App.  Alt  of  Jupiter. . .  31°  81'  Green.  Date . 3h  14m  28s  Sun's  R.  A.  Noon. .  .  6)x  48m  34s  Dif  lh.l0sX3ih— 32i 

Refraction ...  Sub^ 2  Corr A drt_     32 

True  Alt  of  Jupiter...  31°  29'  East  of  the  Meridian.  Corr.  R.  Ascen. ..    .   6h  49m    6s 

Polar  Distance 68    21    Log.  0.03177 

Latitude 89   25    Log.  0.11207  Jup.  Dec. .  .21°  39'  S.     Jup.  R  As^ien.. . .    19h  44m  26a 

139°  15'  90     0  Cor. Gr.  Date.  .Sub.  S 

flalf  Sum 69°  88'  Log.  4.64161  Polar  Dist.  68°  21'         Conevt  R.  A.. .    .   lOh  44nr~28i 

0'ff«'-^°«« "38^'  Log-±7907_9  Equa.  of  Time . . . .  3m49s-26   .^if.  .hw455K3i-l,  t- 

H.  Angle  of  Jup.  E.   4h  26m  23s  Log.  9.47624  Corr  Add  1    '47 

R.  A.  of  Jupiter. ..  19    44      23  „       ' '.''  -^rrTT;— I^TTi 

^ Correct  Equa. .. .   8m  oOs  "72 

R.  A.  of  the  Merid_.15h  19m    0 

fiun's  R.  Ascen 6    49        6 

App.  Time  at  Ship.  8h  29m  548  Greenwich  Mean  Tune  by  Lunar 3h  ISm  ^6» 

Equa.  of  Time.  Add  3     51  Mean  Time  at  Ship 8    83      46 

Mn.  Time  at  Ship. .  8h  33m  458  Longitude  in ...     79°  59' 46"  E.— 5h  19m  69<» 

To  Find  the  Amount  of  Error  in  the  Measurement  of  the  Lunar  Distance. 

Here  the  Correct  Greenwich  Time  by  Chronometer  given  being. ......       8h  14m  28s 

And  the  Greenwich  Time  by  Lunar  being 3     18     46 

Henoe  their  Difference  in  Time  is 42  sec. 

The  Greenwich  Time  by  Lunar  being  too  small,  and  the  Distance  between  the  bodies  decreasing,  the  N'^mv 
•baerved  has  been  too  great  the  amount  of  which  is  found  as  follows : 

Take  from  the  N.  A.  the  Pro.  Log.  of  the  Difference  of  Distance  in  3  hours,  (already  found,). . .   0.2618 

Place  under  it  the  Pro.  Log.  of  the  Difference  in  'Time,  which  is  42s=-2.4102 

Their  Sum 2.6710 

•ts  the  Pro.  Log.  of  a  portion  of  Space,  0°  0'  28",  and  which  is  the  error  of  the  measured  Distance  having  been  too  groat 

The  error  of  the  measured  Distance  may  also  be  found,  as  before  observed,  when  in  sight  of  land,  the 
|>08ition  of  which  is  well  laid  down,  by  first  finding  the  Ship's  true  position  by  bearings  of  the  land,  and 
turning  her  Longitude  into  Time  and  adding  it  to  the  Mean  Time  at  the  Ship  in  West  Longitude,  or  sub- 
tracting it  in  East,  will  give  the  true  Greenwich  Time.  Then  the  comparison  between  this  and  the  Green- 
wich Time  by  the  Lunar  Observation,  as  in  this  case,  affords  the  learner  the  means  of  judging  of  tho 
eorrectnete  of  his  observed  Lunar  Distance. 

In  observing  with  the  Planets,  the  usual  practice  at  Sea  is  to  bisect  the  middle  of  the  Planet  on  (h* 
found  limb  of  the  Moon.     Thia  saves  the  trouble  of  allowing  for  the  semidiameter  of  the  Planet. 


LUNAR  OBSERVATIONS.  100 

FINDING  THE  LONGITUDE  BY  LUNAR  OBSERVATIONS. 

EXAMPLE  4. 

July  4tb.  1864.  Id  Latitude  40*  20'  S.,  Longitude  at  about  81°  30'  E.,  at  2h  62in  Os  P.  M.  Apparent  Time  at  tb« 
Ship,  tlie  biiu's  oliserved  Altitude  was  15°  0',  the  Moon's  observed  Altitude  Lower  Limb  29°  11  ,  and  the  Sun's  Dis- 
tance Wesi  of  the  Moon  100°  12'  24",  Index  Error  2'  30"  Additive,  the  Greenwich  Time  by  Chronometer,  July  Sd, 
21h  30m  38,  and  which  was  known  to  be  correct.  Required  the  Longitude  in  by  the  Lunar  Distance,  and  also  tb* 
Error  ^if  any)  o{  the  measured  Distance. 

Preparation  for  Clearing  the  Distance. 

Green.  Time  or  Date,  July  3d 21h  SOni  3s  Moon's  Semid.  Mid 15'  38"  and  Hor.  Par.  57'  14" 

(By  Chronometer.)  Corr.  G.  Date  6"  A  ug.  8",  Add  14"  Corr.  G.  Date,  Add 21 

Obs.  Dist  nearest  Limbs 100°  12'  24"  Corr.  Au^.  Semid 15'  52"  Correct  H.  Par. .  57'  86^ 

Index    Error Add  2    30  ^ 

Observed  Dist.  Corrected 100°  14'  54"  Sun's  Obs.  Alt.  16°    0'  Moon's  Obs.  Alt  L.  L      29°  11' 

Sun's   Semid 15    46     ^orr Add    1^  Cor Add 12 

Moon's  Aug.  Semid 16    52     Sun's  App.  Alt 15°  12'  Moon's   App.  Alt 29°  28' 

Apparent  Dist 100°T6'  32" 

Clearing  the  Distance. 

Moon's  Hor.  Parallax 57' 85"  Pro.  Log.  0.4950 Pro.  Log. .  .0.495U 

Sun's  App.  Altitude 16°  12 Co-Sec.    0.5814    ( 's  App.  Alt 29°  23'  Co-Sec,  . .  .0.3092 

Apparent   Distance 100°  46'  32"  Sine....   0.9923 Tang 1.7205 

First  Correction 4   44    38  2.0687  

Second  Correction 4   54    37 2.5247 

Third    Correction 2    35 

True  Distance Less  10°=- 100°  28'  22 

Dist  Nautical  Almanac  at  XXI  hours.    100    13    12    Pro.  Log.  0.2876 

Difference 16'  10"  Pro.  Log.  1.0744 

Pro.  Log.  0.7868=-  Oh  29m  25s  PortioD  of  Time  to  be  Added 

To  the  Hour  of  the  preceding  Dist  Naut  Almanac 21h    0       0 

Green  Mean  Tim  i  by  Lunar 21h  29m  253 

To  Find  the  Time  at  the  Ship  and  thence  the  Longitude. 

Green.  Date,  July  3d. . .   21h  30m    3s  Dec.  Noon,  July  4th 22°  54'  N 

Sun's  App.  Alt 15°  12'  24      0       0     Corr.  for  2ih Add  1 

Refraction Sub.  Z_  Yn^ie:  from  Noon.  July  4,  2h  29m  578  22^65^ N 

Sun's  True  Alt 15°    9"  90      0 

Polar  Dist 112   55    Log.  0.03571  Polar   Dist 112°  55' 

Latitude 40    20    Log.  011788 

]^°  24'                    •                                                  Equa.of  T...4m    Os  .If  Qif:  lb  .441 

Half  Sum "84^T2~  Log.  4.00456  Corr.  2ih,  Sub.        1    •1(> 2^ 

Difference 69°    3'   Log.  4.97080                                               Corr.  Equa..  .3m  698    /  882 

App.  Time  at  Ship 2b  52m    4s  Log"9T2845  _??L 

Equa.  of  Time Add         8     69                  '  MO-2 

M.  T.  at  Ship,  July  4th .   2h  56m    3s 

Add  24      0       0       Green.  Mean  Time  by  Lunar,  July  8d 21h  29m  258 

or  July  3d 2(ih  56m    8s     Mean  Time  at  Ship,  July  3d 26    >6        8 

Longitude  in   by  Lunar 81°  39'  30'  E.=  5h  26na  888 

To  Find  the  Amount  of  Error  in  the  Measurement  of  the  Lunar  Distance. 

Here  the  Correct  Greenwich  Time  by  Chronometer  given  is  21h  30m    Ss 

and  the  Greenwich  Time  by  Lunar  being 21     29      25 

Their  Difference  in  Time  is 38s 

The  Greenwich  Time  by  Lunar  being  too  Small  and  the  Distance  between  the  bodies  increas*^*^  •'^«  lJi» 
lance  observed  has  been  too  Small,  and  the  amount  is  found  as  follows : 

Set  down  the  Pro.  Log.  of  the  Difference  of  the  Distance  in  8  hours  (already  found)  0.2876 
And  place  imder  it  the  Pro.  Log.  of  the  Difference  38s  in  'Time 2.4536 

Their  Sum ,..   2.7412 

*  the  Pro.  Log.  of  a  portion  of  Space  0°  0'  20",  and  which  is  the  Error  of  the  Measured  Distance,  bavu»<j  W      to* 
omall. 

Hence  the  following  Rule. 

r_„„,    n;  *„         T  •        f  Greenwich  Time  by  Lunar  too  Great=  Distance  Observed  is  too  Gnso*. 

uunar    Uistance  Increasing.  <  ^  ■  u  t«         u    t  *     c      h     t%-  ^  /->l  j  •    ^      o      t 

°   (  Greenwich  lime  by  Lunar  too  bmall^  Distance  Observed  is  too  Sini^u 

r»-  .  r*  •        f  Greenwich  Time  by  Lunar  too  Great=  Distance  Observed  is  too  Small 

nar  Distance   Decreasing.  <  ^  •  1   t^         \.    -i  *     o      h     t^    ,  nx.  3       ..      r^      ^ 

°  \  Greenwich  lime  by  Lunar  too Small=  Distance  Observed  is  too  Great 

ky  the  amrunt  of  the  Error  found  as  above. 


170  NAUTICAL   ASTRONOMY. 

FINDING  THE  LONGITUDE  BY  LUNAR  .BSERVATION. 

EXAMPLE  6. 

JV  Bodies  being  too  near  the  Meridian  the  Mean  time  at  Ship  is  found  Afterwards  by  an  Altitude  of  tht 

Sun,  and  showing  the  Manner  of  Applying  it. 

August  15th,  1854,  or  August  14th,  17h  28m  Os  Apparent  Astronomical  Time  by  Watch,  in  Latitude  10°  23'  N. 
Longitude  20°  15'  W,  the  observed  Altitude  of  the  Star  Aldebaran  was  69°  24',  the  Moon's  Altitude  L.  Limli 
DQ  the  Meridian  88°  24',  and  the  observed  Distance  Moon's  nearest  Limb  19°  16'  6",  Index  Error  1'  45'  Additive. 
rhe  Course  and  Distance  made  good  was  W.  by  S.  9  miles,  until  IBh  14m  288  Astroa.  Time  by  the  same  Watch, 
when  the  Sun's  observed  Altitude  was  6°  23'.  Required  the  Latitude  in  by  the  Moon's  Altitude,  the  Mean  Time  bj 
the  Sun's  Altitude,  and  the  Longitude  in  at  the  Time  of  the  Lunar  Distance. 

Preparation  for  Clearing  the  Distance.  ' 

App.  Astron.  T.  ktShip,  Aug.  14th.   ITh  28m  Moon's  Semid  Mid 15'  15"  and  Hor.  Par.  Mid  . ..  56'  62'- 

Long.  20°  15'  W.  in  Time Add.     1    21      Corr.  for  7  hours Sub. 3     Corr.  for  7h Sub.         18 

Greenwich  Date,  August  14th 18h  49m                                                    ~15'  12"  Correct  Hor  Par, ...  65'  89'' 

#  East  of  the  Moon. 

Observed  Distance  nearest  Limb.  19°  15'    6' 

Index  Error Add  1    46 

Observed  Distance  Corrected 

Moon's  Aug.  Semid 16   27 


15 


Apparent  Distance 19°  82'  18" 


Moon's  Aug. Add 

Aug.  Semid 7\b'  27" 

#'8  Obs.  Altitude 69°  24' 

19°  16'  51"  Dip Sub. 4_ 

#'8  App.  Altitude 69'  20' 


])  '8  Obs.  Alt.  L.  L.  83'  24'  N 
Corr Add       12 

J  'b  App.  Alt 88°  86' 


To  Clear  the  Distance 


Moon's  Hor.  Pari 56'  89"  Pro,  Log.  0.5098 Pro,  Log.  0.5098 

#'b  App.  Altitude 69°  20     0    Co-Sec.  0.0289   J 's  Apparent  Altitude. ..  .88' 86' Oo-Sec.  0.0027 

App.  Distance 19°  32'  IS"'  Sine 0.5244. Tang.. . .  0.5602 

First  Correction 2   24  20    Log. 1.0681  

Log.....  L0627 


Second  Correction 7    85   48 

Third  Correction 0     0   21 

True  Dis.  lesB  1 0° 19°  82'  47  " 

Difl.  N.  A.  at  XVIIIh    19   57    86    Pro.  Log.  0.8115 

24' 49''  Pro.  Log.  0.8605 

.6490=  Oh  50m  5  Is  Portion  of  Time  to  be  Added 

To  the  Hour  of  the  preceding  Dis.  N.  A 18     0      0 

Greenwich  Mean  Time  by  Lunar 18h  60m  5l8  0 

To  Find  the  Latitude  by  Observation  and  the  Mean  Time  at  the  Ship  when  the  Distance  was  Observed. 


Log.  0.01338 
Log.  0.00717 


Bun's  Obs.  Alt 6*23' 

Oorr., Add         3 

Sun's  True  Altitude 5°  26' 

Polar  Distance 75    51 

Latitude 10    23 

91°  40' 

Half  Sum „45°  60'  Log.  4.84308 

Difference 40°  24'  Log.  4.81166 

App.   Time 18h  12m  lOs  Log.  9.67529 

Equa Add  4     19 

Mean  Time 18h  16m  29s  at  Ship. 


Time  by  Watch 18h  14m  288    Sun's  Dec.  Noon,  August  15th ...   14*  6"  N 

Long.  20°  15  W.in  T,    1    21       0     Corr.  for  4ih .Add      .    R 

Greea  Date 19h  85m  288    Correct  Dec 14°    9 


Sun's  Polar  Dist 76*  61 


])  'sApp.Mer.  Alt.  .88°  36'  N. 
Corr.  for  Alt.  .-Add 6^ 

True  Alt .83°  42' 

Zen.  Distance 6°  18'  S. 

Declination 16   41    N. 


Equa.  Noon 4m  17i 

Cor4ih _Add 2_ 

Correct  Equa. . .  .4m  19f 


Latitude  in 10°  23'  N. 


To  Find  the  Mean  Time  at  Ship  at  the  Time  the  Distance  was  Observed. 

Fake  the  Difference  between  the  Times  shown  by  the  Watch  or  Chronometer  at  the  Time  the  Distance 
was  observed  and  the  Time  the  Altitude  of  the  Sun  was  observed,  which  call  the  Interval  Turn  the  Dif- 
ference of  Longitude  (made  in  the  Interval)  into  Time,  and  Subtract  it  from  the  Interval  if  Sailing  West 
or  add  it  to  Interval  when  Sailing  East,  will  give  the  Correct  Interval.  Subtract  the  Correct  Interval  fron 
the  Mean  Time  obtained  from  the  Sun's  Altitude,  and  the  result  is  the  Mean  Time  at  Ship  at  the  Time  th 
Liunar  Distance  was  observed  :  then  the  Difference  between  the  Greenwich  Mean  Time  found  by  Lunar  an 
this  Mean  Time  at  Ship  reduced  back,  is  the  Longitude  of  the  Ship  in  Time. 

EXAMPLE  IN  THE  ABOVE  CASE. 

Mean  Time  at  Ship 18h  16m  298  Time  of  Distance  by  Watch I7h  28m    0 

Corrected  Interval Sub.       45      52     Time  of  Sun's  Altitude  by  Watch 18     14      28 

2^ 
86 

4!Sm  62t 


Mean  Time  at  Ship  when  Dist  was  Obs. . .    17h  30m  378  Measured  Interval  by  Watch 46 

Green.  Mean  Time  by  Lunar,  August  14th.    18    50     51    Course  W.  by.  S.  9="D.  Lon.  9' W.  in  TimcSub. 

Longitude  in 20 


3'  30"  W.=   Ih  20m  14s  Corrected  Interval. 


If  the  Interval  is  great  it  will  be  more  correct  to  measure  the  Interval  by  Chronometer  but  if  the  Watch  keep 
imiform  Time,  the  Chronometer  is  not  necessary. 


LUNAR  OBSERVATIONS.  171 

FINDING  THE  LONGITUDE   BY  LUNAR  OBSERVATIONS, 

The  Sun  being  too  near  the  Meridian,  the  Time  is  found  by  the  Moon's  Altitude. 

EXAMPLE  6. 

August  16th,  1854,  or  August  14th,  at  22h  30m  Apparent  Astronomioal  Time  at  Ship,  the  Moon's  obeerrwd 
Altitude,  Upper  Limb,  West  of  the  Meridian,  was  18°  88',  Sun's  Altitude  87°  28',  and  liis  observed  Distance  Eaat 
of  the  Mjou  91°  7'  44".  Index  error  1'  46  ",  additive.  The  face  of  a  Chrouometer  at  the  same  time  showed  Ok 
lOm  23b.  The  Ship  sailed  S.  W.  (true)  15  miles  until  Noon,  when  the  Latitude  observed  was  9°  56'  N.,  the  Longi- 
tude by  account  at  the  same  time  being  21°  30'  West  Required  the  Longitude  by  Luaar  Observation,  and 
supposing  it  to  be  correct,  the  error  of  the  Chronometer  on  Greenwich  Mean  Time,  and  also  the  Longitude  by 
Lunar  brought  up  to  Noon  by  the  Dead  Reckoning.  * 

Preparation  for  Clearing  the  Distance. 

App.  Time  at  Ship,  August  14th, 22h  30m  Moon's  Semid.  Noon  ...  .16'    9"  and  Hor.  Par.  Noon 66'  80" 

Long.  21°  30"  W.  in  Time Add  1    26         Augment Add        5 

Greenwich  Date,  Aug.  14th 23h  66m  15'  14" 

Obs.  Dist  nearest  Limb 91°    7'  44" 

ludex  Error Add  1    46 

Obs.  Dist.  corrected 91°    9'  29'' 

Suu's  Semid Add         15   50     Moon's  Obs.  Alt.  Up.  Limb 18*  88'  Sun's  Obs.  AIL 67*  28' 

Moon's  Aug.  Semid.. .     Add 16    14  Sub.  20  Add         12 


App.  Central  Dist 91°  40'  33"   J>  's  App.  Central  Alt 18°  18'  Sun's  App.  AIL 67*  40' 

To  Clear  the  Distance 

Moon's  Hor.  Parallax 0°  56'  80"  Pro,  Log.  0.51 10  Pro.  Log.  0.6110 

Sun's  App.  Altitude 67   40     0     Co-Sec.     0.0339      J)*8  App.  Alt 18' 18'      Oo-Secant  0.6031 

Apparent  Distance ..   91°  40' 38"   Sine          0.9998  Tangent     2.6840 

First  Correction 4     8    89 1.5447  " 

Second  Correction 4   59    30.                              .  ....               8.6481 

Third  Correction 8     8 

True  Distance,  less  10* 90°  51'  60" 

DiBLN.  A.  at  Noon 90   61    60 

0°    0'    0"  Greea  Time,  Aug.  14th. . .  84h  Cm  Oa,  or  Noon  of  Aug.  IMh. 

To  Find  the  Mean  Time  at  the  Ship,  and  thence  the  Longitude. 

App.  Alt  of  the  Moon. ...  18'  18'  Time  by  Face  of  the  Chro.  Oh  10m  288.  J)  'b  R  A.  Noon,  Aug.  16th,  8h  16m  29i 
Cor.  for  AIL,  Table  XXV,  Add   49 

> '»  True  Alt 19'    7'  >  's  Dec.  Noon,  Aug.  16th,  17*  38'  N. 

J'sPolarDisL 72    22    Log.  0.02090  Polar  Dist 72   22 

Latitude  10     7    Log.  0.0068J 

101°  86'  Suns  R.  A.  Noon,  Aug.  16th,. . .  9h  88m  3ii 

Half  Sum 50°  48'  Log.  4.80074 

DiflFerence 81°  41'  Log.  4.72084  Equa.  of  Time,  Noon 4m  16i. 

]>  's  H.  A. West  of  Mer.  4h  52m    Os—Log.  9.54879 

>  s  R.  Ascen Add  3    16      29  Course  to  Noon  S.  W.  16  miles  D.  Lat  11'  Dep.  11'— D.Lon.— 0*11' 

R.  A.  of  the  Merid..     Sh    8m  29s  Latitude  Obi.  at  Noon 9*  56' N.  • 

Add  24      0       0  LaL  in  at  Time  of  Dist 30^'  N. 

82h    8m  29s 
Sun's  R.  Ascen.  .Sub.  9    38      33 

App.  Time  at  Ship. .  22h  29m  568  Greenwich  Mean  Time  by  Lunar,  Aug.  14th 24h    Om    0* 

Equa.  of  Time.  Add  4      16  Mean  Time  at  Ship,  Aug.  I4th 22    34     12 

Mean  Time  at  Ship  r~22h  84m  128  Long,  in  by  Lunar 21  °  27'    0"  W.^  Ih  26m  48b. 

Diff.  of  Long,  made  to  Noon 11     0     W. 

Long,  in  by  Lunar,  Noon 21'  38'     0"  W 

To  Find  the  Error  of  the  Chronometer. 

I^me  by  Chronometer  when  the  Distance  was  Observed. ...  Oh  10m  288  Past  Noon,  Aug.  16th. 

Greenwich  Mean  Time  by  Lunar 0      0       0   or  Noon  of  Aug.  16th. 

Hence  the  Chronometer  is  Fast  of  Green.  Mean  Time Oh  10m  238 

In  this  ca.se,  if  the  Time  at  Ship  had  been  found  from  the  Sun's  Altitude,  the  error  in  the  Time  woul« 
be  8  seconds  too  great,  the  Sun  being  too  near  the  Meridian. 

The  Moon  being  the  lower  body  in  this  case,  by  raising  her  the  True  Distance  is  48'  43"  less  than  the 
Apparent  Distance.  (See  Figure  30.)  And  as  before  observed,  the  Difference  betvs-een  the  Apparent  ana 
the  True  Distance  can  never  exceed  the  Sum  of  the  correction  for  Altitude.  (That  is,  the  Moon's  parallax  in 
Altitude,  found  in  Table  XXV,  and  Sun  or  Star's  correction  for  Refraction,  found  in  Table  IV.)  When 
the  difference  between  the  observed  and  the  true  Distance  exceeds  that  quantity,  it  may  be  concluded  t>  «k 
lomo  gross  error  has  been  committed  in  the  Clearing  of  the  Lunar  Distance. 


1^^  NAUTICAL  ASTRUNOMI. 


rO  COMPUTE  THE  ALTITUDES  OF  THE   OBJECTS  AT  THE   TIME  THE  DISTANCE  WAi 

OBSERVED, 

Having  the  Correct  Apparent  Time,  the  Latitude  of  the  Place,  and  thf  Approximate  Lor.gitude. 

li  nometimes  happens  at  Sea,  in  taking  a  Lunar  Observation,  that  the  Altitude  of  one  or  both  of  tn» 
obje&bS  are  lost  in  consequence  of  cloudy  weather  coming  on.  In  that  casr,,  if  the  Apparent  Time  at  th-. 
SWi.,  and  the  correct  Latitude  of  the  place  are  known,  the  Apparent  Altitudes  of  the  objects  may  be 
eom*  vJted  as  follows  * 

RULES 

To  Compute  an  Altitude. 

lit.  If  the  Time  at  Ship  is  not  known,  and  a  Chronometer  at  hand,  (and  its  error  on  Greenwich  known,) 
take  tne  Greenwich  Time  by  Chronometer  at  the  time  of  the  Distance,  from  which  subtract  the  Longitude 
in  Tiiiie  in  West,  or  add  it  in  East  Longitude,  will  give  the  Mean  Time  at  the  Ship.  From  the  Nautical 
Alman&c  take  out  the  Equation  of  Time,  and  apply  it  to  this  Mean  Time  the  contrary  waj^  to  what  is 
director  in  the  column  for  Apparent  Time,  and  the  result  is  the  Apparent  Time  at  the  Ship  at  the  time  the 
Di8tan».«  was  observed. 

If  an  Altitude  of  one  of  the  objects  has  been  observed  at  a  proper  Distance  from  the  Meridian,  tbt 
Apparent  Time  can  at  once  be  found  from  its  Altitude. 

Or,  the  Watch  may  be  corrected  to  Apparent  Time  by  an  Altitude  taken  either  before  or  after  the  Lunai 
Distance  has  been  observed,  allowing  for  the  difference  of  Longitude  in  Time,  made  in  the  interval. 

If  the  Apparent  Time  at  Ship  is  A.  M.,  add  12  hours  to  it ;  but  if  P.  M.,  both  will  then  be  the  Apparent 
Astronomical  Time  from  the  preceding  Noon,  which  must  be  dated  one  day  less  than  the  Sea  account ;  if 
the  Civil  day  is  used,  and  the  Apparent  Time  is  A.  M.,  date  it  also  one  day  less,  but  when  P.  M.  dfte  it 
the  same  as  Civil  Time. 

2d.  Find  the  Hour  Angle  of  the  object,  which,  if  it  be  the  Sun,  is  the  Apparent  Time  from  the  nearest 
Noon.  If  the  object  be  the  Moon  or  a  Planet,  find  the  Greenwich  Date  as  usualf  and  from  the  Nautical 
Almanac  take  out  their  Right  Ascensions  and  Declinations,  and  correct  them  to  the  Greenwich  Date  ;  but 
if  the  object  be  a  Star,  take  out  its  Right  Ascension  and  Declination  from  Table  XVIII,  and  correct  th« 
Sun's  Right  Ascension  taken  from  the  Nautical  Almanac  to  the  Greenwich  Date, 

Add  the  Sun's  Right  Ascension  to  the  Apparent  Time,  their  Sum  (less  24  hours,  if  it  exceed  thatquantityj 
will  be  the  Right  Ascension  of  the  Meridian,  the  difference  between  which  and  the  Right  Ascension  of  the 
object  in  Time  will  be  its  Hour  Angle ;  write  under  it  the  Latitude  and  the  Declination  of  the  object. 

3d.  Then,  if  the  Latitude  of  the  place  and  the  Declination  are  both  of  the  same  name,  that  is,  both  North 
or  both  South,  their  difference  will  be  the  Meridian  Zenith  Distance ;  but  if  one  be  North  and  *he  othe* 
South,  their  Sum  will  be  the  Meridian  Zenith  Distance. 

4th.  Add  together  the  Logs,  of  the  Hour  Angle,  found  in  Table  XXIX,  the  Log.  Co-Sines  of  the  Latitude 
and  Declination,  from  the  top  of  Table  XXVIII,  and  the  Log.  Secant  of  the  Meridian  Zenith  D:■^tance, 
from  the  top  of  Table  XXVII.  The  Sura  of  these  4  Logs.,  (rejecting  10  from  the  Index,)  found  in  Table 
XXIX,  will  give  an  Arch  in  Time. 

5th.  Turn  this  Arch  in  Time  into  Degrees,  &c.,  by  Table  XXIX,  and  from  the  top  of  Table  XXVII  take 
out  its  Log.  Secant,  which  add  to  the  Log.  Secant  of  the  Meridian  Zenith  Distance,  (already  found,)  the 
Sum  will  be  the  Log.  Co-Secant  of  the  True  Altitude  of  the  object,  found  at  the  bottom  of  Table  XXVlI. 

6th.  As  the  Apparent  Altitudes  are  used  m  correcting  a  Lunar  Distance,  it  is  necessary  to  reduce  lh« 
True  Altitudes  thus  found  as  above  to  the  Apparent  Altitudes.  When  the  object  is  the  Sun,  Planet,  or  a 
Star,  this  is  simply  the  correction  for  Refraction,  taken  from  Table  IV,  which  must  be  added  to  the  True 
Altitude.     Their  Sum  will  be  the  Apparent  Altitude. 

But  when  the  object  is  the  Moon,  enter  Table  XXV  with  the  Moon's  Ti  ae  Altitude  at  the  side,  aiid  her 
Horizontal  Parallax  at  the  top,  and  take  out  her  correction  for  Altitude.  This  subtracted  from  the  Tru» 
Altitude  will  give  her  Apparent  Altitude. 

In  the  night  time,  at  Sea,  a  Lunar  Distance  may  often  be  correctly  observed,  while  the  Altitudes  of  th< 
objects  may  be  in  great  uncertainty  from  the  obscurity  of  the  horizon;  and  in  the  case  of  the  M?on.  ib 
cloudy  weather,  long,  dark  shadows  are  sometimes  projected  on  the  Sea  under  her,  wliich  renders  it  impos- 
■ible  to  obtain  her  Altitude  correctly.  In  that  case,  the  Altitudes  may  be  computed  by  the  above  Rules. 
But  it  rarely  happens  that  a  time  cannot  be  chosen  to  observe  the  Altitudes  correct  enough  foi  Clearing 
the  Lunar  Distance,  as  precision  in  the  Altitudes  is  not  necessary,  and  thus  saviu"'  the  heavy  additional 
ealeulations  of  Altitudes  in  working  a  Lunar  Observation. 


LUNAR  OBSERVATIONS.  178 

TO  COMPUTE  THE  ALTITUDES  OF  THE  OBJECTS  AT  THE  TIME  THE  DISTANCE  WAS 

OBSERVED. 

To  Find  the   Sun's  Altitude. 

Suppo.se  it  was  required  to  find  the  Sun's  Apparent  Altitude  at  the  Time  of  the  Distance  Observed  1q 
Example  1st,  page  166,  the  Mean  Time  at  Greenwich  by  Chronometer  being,  June  3d,  7h  36m  Os,  Latitude 
113  30°  0'  N.  and  Longitude  69°  54'  15"  W.,  we  proceed  as  follows  : 

Green.  Time  bv  Chronometer,  June  3d 7h  36m    Os  Sun's   Dee.  Noon.    22°  19' N.   Equa.  of  TimeNoou  2m  I8f 

Long.  69°  54'  15"  W. in  Time Sub.  4    39      37    Corr.  for  7|h.  Add  2  Con:  for  7^. .  .Sub.  S 

Mean  Time  at  Ship 2h  Stim  23s  Correct  Dec 22°  glM^.  Correct   Equ 2m  lOt 

Equa.  of  lime Add         2      10        '* 

Appa/ent  Time  at  Ship 2h  58m  33s  Log.   Table  XXIX 9.15902 

Sun's  Declination 22°  21'  N.     Co-Sine  Table  XXVIII  4.96608 

Latitude 30      0    X.     Co-Sine  Table  XXVIII  4.93753 

Meridian  Zenith  Distance 7°  39'  Sec.  Table  XXVII   0.00388. .  .0.00388 

Arch,  in  Time 2h  39m  423  Log Table  XXIX     9.06651 

Turned  into  Degrees  by  Table  XXVI 39°  56' Sec Table  XXVII   at  Top. .  ,0.11532 

Sun's  True  Altitude 49    28 Co-Sec.  .Table  XXVII   at  Bottom  0.11920 

Refraction,  Table  IV Add  1 

Suu'a  Apparent  Altitude 49°  29' 

To  Find  the  Moo7i's  Altitude. 

Required  to  compute  the  Moon's  Altitutle  at  the  time  of  the  Distance  observed,  in  Example  2d,  page  167,  th« 
Apparent  Time  at  Ship  being,  June  3d,  7h  57m  453,  the  Latitude  in  29°  32'  N.,  and  Longitude  by  Acct  69°  20'  W. 
to  find  the  Moon's  Apparent  Altitude. 

App.  Time  at  Ship,  June  3d. .  .7h  57m  458  App.  Time  at  Ship 7h  58m  Sun's  R.  A.  at  Noon.   4h  44m  I3i 

Sun's  R.  Ascen , 4    46     18    Lon.  69°  20'  W.  in  Time  Add  4    37      Corr.  for  l?h  35m  Add       2        6 

R.  A.  of  the  Meridian 12h  44m  033  Greenwich  Date,  June  3d. .  12h  36m  Sun's  Correct  R.  A. .  4h  46m  18i 

Moon's  R.  Ascen 11       6      13  ^i    t^    .    ^.., 

J)  8  R.  A.  Mid. . .    .    Ilh4ml8 

Moon's  Hour  Angle   Ih  38m  50s  Log Table  XXIX      8.66664  Con-  for   Sftm      AAA  1        o 

Moon's  Declination 11°27'    N.   Co-Sine  Table  XXVIII  4.99127  ^,'  "    ••^"<^  1 i 

Latitude 29^32^J^  Co-Sine  Table  XXVIII  4.93955  ^  '  Correct  R.  A.      llh  5m  .13i 

Meridian  Zenith  Distance 18°    5'  Sec Table  XXVIl    0.02200  0.02200 

Arch,  in  Time Ih  34m  lis  Log.. .,  Table  XXIX      8.61946 

furned  into  degrees  by  Tab. XXVI  23°  33'  Sec. . .  Table  XXVII     at  Top  0.03777       J)  's  Dec.  Mid..    11°  86'  W 

Moon's   Tiue  Altitude 60°  38' Co-Sec.  Table  XXVII   at  bottom  0.05977      Corr  35m     Sub  8 

Corr.  for  AIL  Table  XXV,  Sub.  27  ^  '„  n        'i^    -  -rr5-;:;r^ 

J)  8  Corr.  Dec.    11°  27  N 

Moon's  Apparent  Alt 60°  11'  at  Time  of  the  Dist.  See  Ex.  2d,  page  167. 

To  Find  a  Star's  Altitude. 

Required  to  compute  the  Altitude  of  the  Star  Aldebaran  at  the  Time  of  the  Distance,  in  Example  5th,  page  IV  o, 
the  Apparent  Time  at  Ship  being,  August  I4th,  17h  28m  Os,  the  Latitude  in  10°  23'  N.,  and  Longitude  by  AcoL 
20°  15'^  W,  to  find  the  Star's  Apparent  Altitude 

App.  T.  at  Ship,  Aug .14th 17h  28m    Os  App.  Time  at  Ship I7h  28m  Sun'sR.A.Noon,  Aug.  14,9h84m488 

Suns  R.  Ascen 9     37      58     Long.  20°  16'   W.  in  T.  _J_  21_  Cor.for  G.Date  18h49m  Add  3     10 

27h  5m  588  Green.  Date,  Aug.  14...    18h  49m  Sun's  Correct  R.  A..    .  .9h  37m  58« 
Sub.  24    0        0 

K   A.  of  the  Meridiai' 3h    5m  588  #'8  R.  A.  Tab.  XIX. ..  4h  27m  8'ii 

#'b  R.   Ascen 4    27       32 

#'8  Hour   Angle Ih  21m  34s  Log.       Table  XXIX     8.49601  *'^  ^^'^  '^^^-  ^^^-  • '  ^^'  ^^'  ^ 

#'8   Declination -  16°  13' N.       Co-Sine  Table  XXVIII  4.98237 

Latitude .10    23'  N.       Co-Sine  Table  XXVIII  4.99288 

Meridian    Zenith    Dist 6°  60'  S^°-  •  •  '^'^'^l^  XXVI  I_0.00226=0.00225 

Arch    in  Time Ih  19m  27s  Log. . .  Table  XXIX     8.47346 

Tur.  into  degrees  by  T.  XXVI  19"  52' Sec.  Table  XXVIl  at  Top.. .  .0.02665 

*'•  '^>'«  ^'^'^"^« ;  V,  69    20    ....    Co-Sec  Table  XXVII   at  bottom  002890 

Oorr.  for   Ref Add  0 

*'8  App.  Altitude 69°  20'    at  the  Time  of  the  Dist.  See  Ex.  5,  page  170. 

It  may  be  remarked  here  that  considerable  care  is  required  in  correcting  the  R.  A.  and  DecMnatione  to  th« 
Green.  Date,  and  also  in  having  the  Apparent  Time  correct,  especially  when  the  object  is  neai'  the  Prime 
Vertical,  but  an  Error  in  the  Latitude  at  that  time  will  not  much  affect  the  result,  and  when  the  object  ii 
near  the  Meridian  any  probable  Error  in  the  Time  will  not  much  affect  the  computation,  but  an  Error  ia 
the  Latitude  will  cause  nearly  an  equal  Error  in  the  computed  Altitude. 

Note  -An  Error  of  2'  or  3'  in  the  Altitude  of  a  Star  has  more  effect  in  producing  an    Error  in  the  True  Lnnw 

2oS  a' LTar  ObreVvatrou"  ''""''  "'  ''   '""  ""  ^'"'^  ^'"^""^  """"^  ""'''■     '^^'^ '«  ™P-'-°'  ^°  be^rVn  a.ind  " 


|f4 


NAUTICAL    ASTRONOMY. 


FINDING  I'HE  LONGITUDE  BY  LUNAR  OBSKaVATIONS  ON  SHORE. 

A  Lunar  Observation  may  be  taken  on  Shore  by  the  aid  of  an  Artificial  Horizon  for  observing  ihe  Sun  i 
Altitude  (see  pages  77  and  78)  only  ;  the  Altitude  of  the  Moon  can  be  computed  by  the  preceding  ruies, 
and  the  observations  should  be  taken  when  the  Sun  is  at  a  proper  Distance  from  the  Meridian  with  the 
Tiew  of  obtaining  the  Time  at  the  place,  from  the  same  Altitude  observed  with  the  Distance. 

The  Observation 

Compute  the  Approximate  Distance  as  directed  at  page  74,  ready  for  use,  and  proceed  first  to  observe  ai. 
Altitude  of  the  Sun  in  the  Artificial  Horizon,  note  down  the  Time  and  the  Altitude,  set  the  Index  of  the 
Sextant  to  the  Approximate  Distance,  and  when  brought  into  the  field  of  view  bring  the  Limbs  in  contaci, 
note  down  the  time  and  the  observed  Distance,  proceed  to  take  any  odd  number  of  Distances  and  their  cor- 
responding Times,  as  recommended  at  page  76,  and  finish  with  an  Altitude  of  the  Sun,  noting  down  th« 
Time  as  before. 

Find  the  Mean  of  the  Times  of  the  Distance  and  the  Mean  of  the  Distances,  and  the  Difference  be- 
tween the  Times  of  the  Altitudes  and  the  Difference  of  the  Altitudes :  then  say,  as  the  Difference  of  the 
Times  is  to  the  Difference  of  the  Altitudes,  so  is  the  portion  of  Time  between  the  Time  of  the  first  Altitude 
and  the  Mean  of  the  Times  of  the  Distance  to  a  portion  of  Altitude,  which  Added  or  Subtracted  to  or  from 
the  first  Altitude,  according  as  it  is  Increasing  or  Decreasing,  will  give  the  Sun's  Altitude  at  the  Time  of  tha 
Mean  Distance. 

Having  the  Sun's  observed  Altitude,  the  Latitude  of  the  place  (which  may  be  obtained  in  like  manner  by 
the  Sun's  Meridian  Altitude,  see  page  92,)  and  the  Approximate  Longitude,  proceed  to  find  the  Apparent  Time 
as  in  the  Examples  at  page  ^31. 

Having  the  Apparent  Time  at  which  the  Distance  was  observed,  compute  the  Moon's  Apparent  Altitude 
(by  the  Rule  at  page  172),  and  proceed  to  work  the  Lunar  as  before  : 


EXAMPLE  OF  WRITING  DOWN  THE  OBSERVATION 

September  26th,  1854.     At  3h  57m  158  P.  M.  Mean  Time  at  New  York,  in  Latitude  40°  42'  42"   N.,  and  Lonjfi- 
tnde  74°  0'  15"  W.,  the  following  observation  was  made  to  find  the  Longitude. 


"nme  per  Watch Sh  63m 

(    3    56 
Mean  of  the  Times  3h  57  m  15s. 


3  57 

25 

8  69 

10 

4   1 

28 

Os  Alt.  Sun's  L.  L.  ArL  Hor. 
1 0    Dis.  of  Sun  and  Moon . . . 
do.           do. 
do.           do. 
Alt.  Sun's.L.  L. 


41' 

•32' 

0" 

66 

13 

10 

0 

14 

10 

0 

16 

10 

38 

38 

0 

Mean  Dis 66*14'  10" 

Index  Error.. Add  60 

Obs.  Dis 56*  16'    O" 


To  Find  the  Sun's  Altitude  at  the  Time  of  the  Mean  Distance  and  thence  the  Time  at  the  Place. 


Time  of  the  Ist  Alt. . 
do.      2d  Alt... 

Say  as 


8h  63m    Os 
4      1      28 


8m  28b  is  to 


Ist  Alt  41°  32'  Time  of  Ist  Alt  3h  63m    Os 
2d  Alt  38   33    Mean  of  the  T.. .  3    67 16 

So  is 


2°  59' 


4m  168 


Sun's  Obe.  Alt  Artit  Hor.  40'    2'    8" 
Index  Error Add  60 


8m  288  Pro.  Log 1.8276 

Arith.  Co 

2°    59'  Pro.   Log. . . 
4m  168 

Time  by  Watch 8h  67m  158  1°29'    6 2"= Pro.  Log.. 

Long.  74"  W.  m  Time  4    66      0  Ist  Alt  31    32       0       Decreasing 


8.6724 
0.0024 
1.6269 

0.3017 


Observed  Angle i)40°    2'  58  '  Greenwich   Date. 

Alt  of  Sun's  L.  Limb. .      20°    1'  29" 


2' 


18   81 


Sun's  Sem.  16'  Ref  2'  29"     

Sun'e  True  Altitude 20*  16'    0"~ 

Polar  Distance 91    21    84 

Latitude 40   42   42 

162°  ig'TF 
Half  Sum 


76°    9'  38' 


Log.  0.00012 
Log.  0.12038 

Log.  4.37876 
Log.  4.91812 


Difference 66*  64'  88' 

App.  "nme  "xt  Place 4h    6m    0«  =Log  0.41788 

Equation  of  Time... Sub  8     46 

Mean  TioM  tt  Plaee .... .  Sb  67m  Ifie 


.  8h  63m  08Ob8.Alt40 

Sun's  Declination  Noon . . . . 
Corr Add. 

Correct   Declinatioa 


8"  at  Time  of  Diet 

1°  12'  52"  S.  Dif.  Ih     68 
8   42    G.  Date         9b 


1* 
90 


21'  34"  S. 
0      0 


60)622 


Polar  Distance 91°  21'  34' 


Equation   of  Time,  Noon 
Correction Add 

Correct  Equation 


8m  87fi  -87  Di£  Ih      -840 
7    '66  G.  Date         9k 


8m  46b  -48 


7M-0 


FINDING  THE  LONGITl  DE  ON  SHORE. 


175 


TO  FIND  THE  LONGITUDE  BY  LUNAR  OBSERVATIONS  ON  SHORE 
Having  the  Apparent  Time,  to  Compute  the  Moon's  Altitude  at  the  Time  of  the  Distance. 


Corr. 


.Add     1      21 


App.  Time  at  place  . .  4h    6m    Os 

Sun's  Right  Ascen 12    12      33 

R.  A.  of  the  Merid.  . .  I6b  18m  33s 
>'b  R.  Ascen 15    47      12 

p  's  Hour  Angle Oh  81m  2l8  Log.  7.66891    R.  A.. .  12h  12ra  838 

D's  Declination 20°  80'  S.  Co-Sine  4.97159 

Latitude _40   43  N.  Co-Sine  4.87964 

>  's  Mer  Zen.  Diat. . .  61°  13'  . .  .Secant_031740=-0.3174O 
oh  88m  4s 


Green.  Date,  Sept.  26tb,  8b  53m  Ob.  >  's  R.  A.  at  Noon  16h  26ra  42i 

At  Midnight 15    54      24 

Sun's  R.A.  12h'llm  123  Dif.  Ih-  da  Diff.  in  12  hours. 


_9_  Diff.  12h.  Pro.  Log.. 


Oh  27m  42< 
1.1761 


•8.8239 
0.8128 


Arch  iu  Time. . 

In  degrees. 9°  81'  = 

Moon's  True  Alt 28°  21' 

Corr.,  Tab.  XXV,.  .Sub.  0   49 


'  Log.       7.83754 

Secant .    0.00602 

.  Co-Sec .~0.32342 


Moon's  App.  Alt 27°  32'  at  the  Time  of  the  Distance. 

Hence  we  have  the  following  Observation  to  Clear  the  Distacce  and  find  the  Longitude 


60)818  Arith.  Comp 

Im  2l8  27m  428  Pro.  Log.. 

G.  D.  8h  53m    Pro.  Log.  1.3067 

Corr. 20m  308="a9434 

R.  A I5h  26m  42s 

>  's  R.  A.T5h  47m  128 

)'8  Declination,  Noon 18°  68'  8. 

Corr.  Q.  Date  9h Add    1    87 

])  's  Correct  Dec 20°  30'  S 


Sun's  Oba.  Alt  20°  1' 


Mn.  Time  at  the  place  3h  57m  15s 

3h  57m  15s  Sun's  Obs.  Alt       20° 
4    56        0    Semid.  Add 


Mean  Time 

Loa  74°  W.  in  Time    

Or.  Date,  Sept  26th      8b  53m  158  Sun's  App.  Alt    20°  17' 


1' 
16 


D'a  App.  Alt  27°  82' 

])  's  Semid.,  Noon 
Corr.  2"  and  Augm.  8" 

])  's  Aug.  Semid.    . .  .T       16^ 
Sun's  Semid. 16 


Obs.  Dist  55 

15'  53 
10 


15'  0' 


Hor.  Par.     58'  12' 
Corr.  G.  D.  8 


3" 

0 

0 


D  's  H.Par.  58'  20" 


Obs.  Distance 65°  15 

App.  Distance 66°  47'    3" 


Moon's  Hon  Parallax 68'  20"   Pro.  Log.    0.4894 

Sun's  App,  Alt 20   17     0     Co-Secant  0.4601 


1>'b  App.  Alt.. 27*  82' 


App.  Distance 65°  47'  8" 

First  Correction 4   35  83 

Second  Correction   6    18  20 

Third  Correction 0      1  21 


Sine 0.9175. 

.     .    1.8670 


Pro.  Log.  0.4894 
Co-Secant  0.3851 
Tangent      1J674 


1.99S0 


True  Distance 65*  42'  16" 

Dist,  N.  A.,  at  Vlh. ..64  10  41 

Difference 1°  31'  35" 


Pro.  Log.  0.2769 
Pro.  Log.  0.2936 


Pro.  Log.  0.0166= 
to  the  Time  of  the  preceding  Distance,  N.  A., 


•2h  63m  168  portion  of  Time  to  be  added 
6      0       0 


Greenwich  Mean  Time 8h  53m  168 

Mean  Time  at  the  Place 3    67      15 

Longitude  of  New  York  in  Time 8h  56m    18^74°  0'  15"  W 

Another  Example  of  this  method  is  not  necessary,  as  all  the  various  cases  are  already  given  of  finding 
<he  Longitude  by  Lunar  Observations,  and  it  will  be  perceived  that  this  is  exactly  the  same,  except  in  the 
«ue  of  the  Artificial  Horizon,  where  no  correction  for  the  Dip  of  the  Horizon  is  required  in  findin<»  the 
Apparent  Altitudes. 

A  person  thus  having  a  good  Sextant,  an  Artificial  Horizon,  a  Nautical  Almanac,  and  an  Epitome  of 
Navigation,  which  together  will  form  an  excellent  portable  Observatory,  he  may,  by  the  aid  of  a  Compaes 
travel  far  inland,  remote  from  numan  habitations,  and  be  able  at  anytime,  when  the  Sun,  Moon,  and  Stari 
are  visible,  to  find  his  position  ;  and  although  the  Longitude  is  required  to  be  known  with  some  decree  of 
precision,  in  order  to  find  the  Greenwich  Date,  for  the  purpose  of  correcting  the  quantities  taken  from  the 
Nautical  Almanac,  it  may  be  remedied  by  working  the  Lunar  over  again,  using  the  Longitude  so  foun^ 
in  the  room  of  the  Approximate  Longitude  first  used,  to  find  the  Greenwich  Date,  and  to  correct  the  quan- 
titles  taken  from  the  Almanac  anew.  * 

Then,  suppo.'ie  he  wishes  to  know  n  what  direcnon  any  given  place  on  the  Sea-coast  lies,  the  True 
Bearing  and  Distance  can  be  found  by  Mercator's  Sailing. 

The  Variation  of  the  Compass  can  be  found  at  Noon,  when  the  Sun  is  on  the  Meridian,  by  simply  fixing 
a  wooden  pin  in  a  perpendicular  position  on  the  side  of  the  compass-box,  so  that  the  shadow  will  be  thrown 
over  the  centre  of  the  card,  this  will  be  the  True  M-ridian  line,  the  diflerence  between  which  and  the 
North  or  South  points  of  the  Compass  is  the  Variation.  (See  the  Note  at  page  118,  and  the  Diagram  at 
page  1 19.)  Or,  if  Ihe  Sun  is  too  near  the  Zenith,  it  may  be  found  in  tne  morning  or  eveniLg  by  an  ampli- 
tude, that  is,  if  the  surface  of  the  ground  is  level  and  not  very  high  d,bove  the  Sea.  (See  page  116.)  The 
variation  so  found  and  applied  to  the  True  Bearing,  will  give  the  Compass  Bearing  of  any  given  plao* 
'©quired. 


17«  NAUTICAL  ASTRONOMY. 

FINDmLr  THE  LONGITUDE  BY  OBSERVING  THE  MOON'S  DECLINATION. 

When  the  Moon  and  a  Star  are  on  or  near  the  same  Meridian  together,  the  Longitude  may  be  founa  oy 
measuring  their  Distance  ;  because  the  Star's  correct  Declination  being  given  in  the  large  Nautical  Almanac 
the  Moon's  Declination  can  be  deduced  therefrom. 

The  Greenwich  Time  correspondmg  to  this  Declination,  taken  from  the  large  Nautical  Almanac,  and 
compared  with  the  Mean  Time  at  Ship  at  which  the  Observation  is  made,  gives  the  Longitude  of  the  Ship. 

And  as  the  Moon  changes  her  Declination  at  the  rate  of  about  14'  in  1  hour  of  Time,  when  near  tht 
Equator,  an  error  of  l"  in  the  Observed  Declination  will  produce  an  error  of  1'  of  Longitude,  and  an  error 
of  r  in  the  Observed  Declination  will  produce  an  error  of  1°  in  the  Longitude,  even  in  the  most  favorabl* 
ease. 

This  method  is,  therefore,  not  capable  of  much  precision.  Besides,  it  can  only  be  used  to  advantage  when 
the  Moon's  Declination  changes  rapidly,  that  is,  when  she  is  near  the  Equator ;  but  when  the  Moon  has 
great  North  or  South  Declination  this  method  is  not  practicable.  It  may,  however,  be  found  useful  in 
some  cases,  as  the  Observation  (the  objects  being  on  the  same  vertical  line)  is  much  easier  to  take  than  a 
regular  Lunar  Distance. 

THE   OBSERVATION. 
Finding  the  Approximate   Distance. 

1st.  Inspect  the  large  Nautical  Almanac  and  find  whether  the  Moon's  Declination  changes  sufficiently 
rapid  for  the  purpose,  if  so,  then  find  at  what  time  she  passes  the  Meridian  at  Greenwich,  and  reduce  it  to 
the  time  of  her  passing  the  Meridian  of  the  Ship,*  which  will  be  the  Mean  Time  at  the  Ship.  Turn  the 
Longitude  by  account  into  Time,  add  it  to  the  above  Time,  in  West  Longitude,  or  subtract  it  in  East,  will 
give  the  Greenwich  Date.  Apply  the  Equation  of  Time  to  the  Mean  Time  at  Ship,  will  give  the  Apparent 
Time  at  Ship.  Now  inspect  Table  XVIII.  and  find  a  Star  which  passes  the  Meridian  at  or  as  near  this 
Apparent  Time  as  possible.  Take  out  the  Moon  and  Star's  Declinations  from  the  Nautical  Almanac. 
Then,  if  they  are  of  the  same  name,  take  their  difference  for  the  Approximate  Distance ;  but  when  of 
contrary  names,  take  their  Sum, 

Finding  the  Proper  Star. 

2d.  Set  the  Index  of  the  Sextant  to  this  distance,  find  the  Star,  and  bring  it  in  contact  with  the  round 
limb  of  the  Moon.  Now,  having  the  Watch  previously  regulated  to  Apparent  Time  at  the  Ship,  at  th» 
instant  of  Apparent  Time  by  Watch  at  which  the  Moon  is  on  the  Meridian,  observe  her  Distance  from  the 
Star,  and  note  down  the  Time  and  the  Distance  observed. 

Correcting  the  Observed  Altitudes. 
3d.  Observe  also  the  Altitudes  of  the  Moon  and  Star  roughly.      If  the  Lower  Limb  of  the   Moon  be 
ibserved   add  12'  to  it ;  if  the  Upper  Limb  be  observed,  subtract  20',  andsubtracf  A'  from  the  Star's  Altitude. 

Correcting  the  Semidiameter  and  Horizontal  Parallax. 

4th.  Take  out  the  Moon's  Semidiameter  and  Horizontal  Parallax,  correct  them  to  the-  Greenwich  Date, 
and  to  the  Semidiameter  add  the  Augmentation.  If  the  near  Limb  of  the  Moon  has  been  observed,  add  th© 
augmented  Semidiameter  to  the  observed  Distance,  but  if  the  far  Limb  has  been  observed,  subtract  it. 

Finding  the  Moon's  Parallax  in  Altitude. 

5th.  To  the  Secant  of  the  Apparent  Altitude  of  the  Moon  add  the  Pro.  Log.  of  the  Horizontal  Parallax^ 
their  Sum  will  be  the  Moon's  corTction  for  Altitude,  and  from  Table  IV  take  out  the  Refraction  for  her 
Apparent  Altitude. 

Applying  the  Correction  for  Parallax  in  Altitude. 

6th.  If  the  Moon's  Altitude  is  less  than  the  Star's,  subtract  her  correction  for  Altitude  from  the  Apparent 
Distance,  and  add  the  Refraction  to  it ;  but  if  the  Moon's  Altitude  is  greater  than  the  Star's,  add  her  cor- 
rection to  the  Distance  and  subtract  the  Refraction  from  it. 

Applying  the  Correction  for  Refraction. 

7th.  If  the  Star's  Altitude  is  less  than  the  Moon's,  add  its  Correction  for  Refraction  to  the  Distance ;  but 
if  the  Star's  Altitude  is  the  greatest,  .subtract  it,  and  the  result  will  be  the  True  Distance,  if  the  Star  is  9n 
the  Meridian  at  the  same  time  nearly  as  the  Moon. 

Finding  the  Correction  of  the  Star's  Altitude  when  not  on  the  Meridian. 

8th.  But  if  the  Star  is  not  ou  the  Meridian  at  the  Time  of  the  Distance,  find  the  number  of  minutes,  &c.^ 
it  is  distant  from  the  Meridian,  by  computing  its  Meridian  passage,  and  find  the  portion  of  Altitude  want- 
ing of  its  Meridian  Altitude,  by  the  Rules  given  at  page  111. 

To  Apply  the  Correction  for  fhe  Star's  Altitude. 

9th.  Then  if  the  Star's  Altitude  be  less  than  the  Moon's,  subtract  this  portion  of  Altitude  from  th6 
Apparent  Distance :  but  if  the  Star's  Altitude  is  greater,  add  this  portion  of  Altitude  to  it,  and  the  result 
u  the  True  Distance  between  the  Moon  and  the  Star. 

•  To  find  this  correction,  say  as  360"  is  to  the  daily  variation  of  the  Moon's  passina;  the  Meridian,  po  is  the  given 
lionptude  in,  to  a  portion  of  Time  to  be  added  to  the  Time  of  her  Meridian  Passage,  in  the  N.  A.,  in  West  Longritude^ 
•r  subtracted  from  it  in  East,  will  give  the  Mean  Time  of  her  Meridian  Passage  at  the  Ship. 


FINDING  THE  LONGITUDE  BY  OBSERVING  THE  MOONS  DECLINATION 


171 


Having  the  True  Distance  between  the  Moon  and  Star  to  find  the  Moon's   Declination. 

10.  Take  from  the  Large  Nautical  Almanac  the  Star's  Correct  Dec.  and  mark  it  North  :r  South;  thei 
if  the  True  Dis   be  less  than  the  Star's  Dec.  the  Diff.  is   the   Moon's  Dec.  of  the  same  name  as   the  Star's 

But  if  the  True  Dis.  be  greater  than  the  Star's  Decl.  the  DifF.  will  be  the  Moon's  Decl.  of  a  contrarj 
same  to  the  Star's.     When  the  True  Distance  and  the  Star's  Decl.  are  equal  the  Moon  is  on  the  Equator. 
Having  the  Moon's  Observed  Declination  to  find  the  Greenwich  Time  and  the  Longitude. 

11.  Find  in  the  large  Nautical  Almanac  the  two  Declinations  between  which  the  observed  DeclinatioB 
alls,  and  take  their  Difference  ;  take  the  Difference  also  between  the  preceding  Declination  and  the  observed 

Declination.  Then  say  as  the  Difference  of  the  Declination  in  one  hour  is  to  one  hour  of  Time,  so  is  the 
Difference  between  the  preceding  and  the  observed  Declinations  to  a  portion  of  Time,  which  Added  to  the 
Hour  marked  opposite  the  preceding  Declination  in  the  Nautical  Almanac,  will  give  the  Mean  Time  st 
Greenwich  at  the  time  the  Distance  was  observed.  * 

Having  the  Greenwich  Time  to  Find  the  Longitude. 

12.  The  Mean  Time  at  the  Ship  being  found  in  the  usual  manner,  and  it  is  required  to  have  the 
Watch  previously  regulated  to  Apparent  Time,  before  commencing  the  observation,  then  by  applying  th# 
Equation  of  Time  we  have  the  Mean  Time  of  the  Distance,  the  Difference  between  which  and  the  Green- 
wich Mean  Time  is  the  Longitude  in  Time,  to  be  turned  into  Degrees  and  Minutes  as  usual. 

The  following  Diagram  will  explain  the  nature  of  the  observation. 

PROJECTION  OF  THE  MERIDIAN  ALTITUDES  OF  THE  MOON  AND  STAR  SPICA. 
Given  the  Latitude  26°  N.,  Star's  Decl.  10°  23'  S.,  and  Dist.  9°  44'  21",  to  Find  the  Mom^s  Decl 

Fio.  31 


EXAMPLE  1. 

April  Uth,  1851.  In  Latitude  26°  2'  N.,  Longitude  by  Chronometer  carried  on  38°  0'  W.,  at  llh  23m  29s  M.  T 
»t  the  Ship,  the  observed  Distance  of  the  Star  Spica  from  the  near  Limb  of  the  Moon  was  9°  25'  82"  Vertically, 
Moon's  observed  Altitude,  L.L., 62°  41',  and  the  Star's  Altitude  53°  13'.     Required  the  Longitude  in. 

])  "s  Mer.  Pass.  N.  A.,  April  Uth,  llh  18m     Os  Mean  T.  at  Ship llh  24m   O's  R.  A.  Ih  28m  878  Dif.  9» 

Say  as  360°  is  to  52m  80  is  Lon.  38°_to 5      29    Long.  38°  W.  in  T  ime 2    82  2        6  14b 

Mean  Time  of  Pass,  at  Ship llh  23m  29s  Green.  Date,  April  14th. 

Equation  of   Time Sub.  0      15 


J's  Obs-Alt 62°  41' 


13h56m    O'sR.A.    Ih  30m  488     )126 
#'sR.A.  13    17      228     2^^ 


Apparent  Time  at  Ship llh  23m  14s  Corr Add      12    Mer.  Pass,  of  #  Spica  llh  46m  398 

D  '8  App.  Alt  62°  53'  Sec, 0.3412     D's  App.  Alt. . .  6^53^  -^PP-  T.  of  Obs 11    28     45 


Hor.  Parallax  60'  15"  Pro.  Log 0.4753    ^,^     "  ^j^  o  ,,,  #'s  Dist  fr.  the  Mer.  22m  648— 7-39Y 

Cor.  D '8  Par.  in  Alt  27' 28''=  Pro.  Log.  0.8165    Corr. ..'...  ."Sub. 4  Lat  26°  N.  and  Dec.  10^°  S.  Log.  0.478 

Obs.  Dist.  #  and    5  n^Ar  L.  9°  26'  32"  #'s  App.  Alt 53°    9'  Por.  of  Alt  wanting  -f-  25'  85"=.T87a 

])  '8  Augm.  Semid A<U  16   42    j.g  gen^jj.  jjid.  1 6'  26"  Hor.  Par 60'  17" 

Central   Distance 9   42    14  Augm 16    Cor.  G.  Date.  2 

5  '8  Corr.  for  Par.inAlt. .  Add  27    28  Augm. Semid..  .15' 42"  Hor.  Par "WW' 

D  '8  Declination  N.  A.,  April  14tb,   at  13h 0°  26'  21"  S 

do.  do.      do.  at  14h 0   89   41     S 

Difference  in  1  hour.. 


10° 


Ref.  J  "6  Ap.  Alt  62°  52'. Sub. 


9'  42 
0    29 


10°    9'  13" 
Ref.  *'s  Ap.  Alt  53°  9'-.Add      0   43 


10°    9'  56' 
Por.  of  Alt  wanting  of  Mer.  -\-  25'  35 

True  Dis.  between  #  and  J   9°4T~21" 
m  Spica  Dec.  N.  A.,  Ap.  14,  10°  23'     1" 

Diff  is  the   1)  's  Obs.  Dec.     0°  38   40 
J> '8  Dea  at  13h 0  26    21 

Diff.  between  the  Obs.  and  )  ,      „ 

the  Preceding  DecL.  \        ^^    ^ 


13'  20" 
Then  say  as  13'  20"  is  to  1  hour  so  is  12'  19"  to  a  portion  of  Timl 
Difference  in  1  hour 18'  20"  Pro.  Log.  1.1  SOS 

Arith.  Comp.  8.8697 

Is  to  1  hour Pro.  Log.  0.4771 

g    So  is  the  Diff.  betw.  the  Preced.  and  Obs.  DecL  12'  19"    Pro.  Log.  1.1648 

g      Portion  of  Time  to  be  Added Oh  65m  268     a     0.511* 

Time  of  the  preceding  Declination 13h    0        0 

Grenwich  Mean  Time 13h  55iu  258 

Mean  Time  at  Ship 11     23      29 

Longitude  in 37' 


59'  0"  W.=     2h  31m  568 
The  result  is  a  Diff.  of  only  1'  less  than  that  bv  Cbron.  hnnucht  oii  by  I).  R.  from  Sights  taken  in  the  Aftemomh 


178  NAUTICAL  ASTRONOMY. 

FINDING  THE  LONGITUDE  FROM  THE  MERIDIAN  ALTITUDES  OF  THE  MOON  AND  A  STAR 

The  principle  of  this  method  is  the  same  as  that  in  the  preceding  example,  that  is,  of  finding  the  Moon'* 
Declination  by  observation ;  but  in  the  room  of  measuring  the  Distance  between  the  Moon  and  a  Star,  we 
take  the  Difference  between  their  True  Meridian  Altitudes.  Then  the  Difference  between  this  and  tha 
Star's  Declination  is  the  Moon's  observed  Declination,  which  furnishes  the  Greenwich  Time  as  before. 

In  this  case  it  is  not  necessary  that  the  Altitudes  of  the  Moon  and  Star  should  be  observed  at  the  same 
time,  though  they  necessarily  must  pass  the  Meridian  within  a  short  time  of  each  other,  in  order  to  obviate 
the  necessity  of  making  a  correction  for  the  Ship's  change  of  place,  especially  when  making  much  Northing 
«r  Southing. 

The  Altitudes  should  be  accurately  observed  with  a  Sextant  to  the  nearest  second,  and  at  Twilight^  when 
the  Horizon  is  distinctly  visible.  This  method  is  therefore  seldom  practical  in  the  Night  Time,  as  it  depends 
entirely  on  the  accuracy  of  the  measured  Altitude. 

By  the  method  given  in  the  1st  Example  the  Altitudes  are  not  required  with  precision,  as  its  accuracy 
depends  upon  the  measured  Distance  between  the  Moon  and  the  Star ;  an  ill  defined  Horizon  in  the  Night 
Time  is  therefore  no  detriment  to  the  former  observation. 

THE  OBSERVATION. 
The  Proper  Time  for  Observing  the  Moon's  Altitude. 

1.  The  Limits  are  the  same  as  in  the  preceding  example,  that  is,  the  Time  must  be  chosen  when  the 
Moon's  change  of  Declination  is  at  the  greatest,  and  also  the  day  on  which  the  Moon  will  be  on  the 
Meridian  at  Twilight,  which  can  be  easily  ascertained  by  inspecting  the  Nautical  Almanac,  and  by  inspect- 
ing Table  XVIII,  find  a  Star  which  passes  the  Meridian  about  the  same  time  and  on  the  same  side  of  the 
Zenith. 

Find  the  Mean  Time  of  the  Moon's  Meridian  passage  at  the  Ship,  to  which  apply  the  Equaticu  ->f  Time, 
will  give  the  Apparent  Time,  and  the  Watch  must  be  previously  regulated  to  the  exact  Apparent  Time  at  the 
Ship,  (which  can  be  easily  done  by  an  Altitude  of  the  Sun  before  he  sets,)  because  the  Moon's  Altitude 
must  be  observed  at  the  instant  of  Apparent  Time  by  Watch,  (according  to  computation)  at  which  she  if 
on  the  Meridian  of  the  Ship,  and  the  Time  and  Altitude  observed  noted  down. 

Observing  the  Starts  Altitude. 

2.  Find  the  Star  by  the  rules  given  at  page  106,  No.  3,  and  the  Apparent  Time  of  its  passing  the  Meridian 
oy  Table  XVIII.  Observe  its  Meridian  Altitude  at  this  time,  which  will  be  indicated  by  the  Watch,  either 
before  or  after  the  Meridian  passage  of  the  Moon,  or  according  to  which  of  the  objects  passes  the  Meridian  fiist. 

Correcting  the  Semidiameter  and  Horizontal  Paral^. 

3.  Find  the  Greenwich  Date  as  usual,  and  take  out  the  Moon's  Semidiameter  and  Horizontal  Parallax, 
«orrect  them  to  the  Greenwich  Date,  and  to  the  Semid.  add  the  Moon's  Augmentation. 

To  Find  the  Moon's  Apparent  Altitude. 

4.  If  the  Moon's  Lower  Limb  be  observed  add  the  Aug.  Semidiameter,  if  the  Upper  Limb  suitract  it,  will 
Ijive  the  Central  Altitude.  Take  out  the  Dip  of  the  Horizon  accurately  from  Table  V,  and  Subtract  it 
from  the  Central  Altitude,  will  give  the  Apparent  Altitude. 

To  Find  the  Moon^s  True  Altitude. 

5.  Add  the  Log.  Sec.  of  the  Apparent  Altitude  to  the  Pro.  Log.  of  the  Horizontal  Parallax,  and  their 
Sum  will  be  the  Pro.  Log.  of  the  Moon's  Corr.  for  Parallax  in  Altitude,  which  add  to   the  Apparent  Alt. 

Enter  Table  IV  with  the  Moon's  Apparent  Altitude,  and  take  out  the  Refraction  corresponding  to  it, 
and  which  must  be  subtracted  from  it,  and  the  result  is  the  Moon's  True  Altitude. 

To  Find  the  Star's  True  Altitude. 

6.  Enter  the  same  Table  with  the  Star's  Observed  Altitude,  and  take  out  the  Refraction,  Subtract  both 
Dip  and  Refraction  from  the  Observed  Altitude,  will  give  the  Star's  True  Altitude. 

Having  the  True  Altitudes  to  Find  the  Moon's  Declination. 

7.  From  the  Large  Nautical  Almanac  take  out  the  Star's  correct  Declination  and  mark  it  N.  or  S.  Take 
the  Difference  between  the  Star's  and  the  Moon's  True  Altitudes,  then  the  Difference  between  this  portion 
of  Altitude  and  the  Star's  Declination  is  the  Moon's  Observed  Declination. 

If  the  Difference  of  the  Altitudes  be  greater  than  the  Star's  Declination  the  Moon's  Declination  will  be 
of  a  contrary  name  to  the  Star's.  But  if  the  Difference  of  Altitude  be  less  than  the  Star's  Declination  thf 
Moon's  Declination  will  be  of  the  same  name  as  the  Star's. 

Having  the  Moon's  Observed  Declination  to  Find  the  Greenwich  Mean  Time. 

8.  Find  in  the  Large  Nautical  Almanac  the  two  Declinations  between  which  the  observed  Declination  fallf, 
and  take  their  Difference ;  take  the  Difference  also  between  the  preceding  and  the  observed  Distance  ;  then 
•ay  SM  the  hourly  Difference  is  to  1  hour  so  is  the  Difference  between  the  preceding  and  the  observed  Decli- 
nations to  a  portion  of  Time,  which  Added  to  the  hour  opposite  the  preceding  Declination  will  give  the 
firaeuwich  Mean  Time  at  the  time  of  the  observation 


PINDING  THK  LONGITUDE. 


1751 


RNDING  THE  LONGITUDE  FfiOM  THE  MERIDIAN  ALTITUDES  OF  THE  MOON  AND  A  STAR. 

To  Choose  a  Case. 

Suppose  it  was  required  to  find  the  Longitude  by  this  method,  on  the  evening  of  tlie  6th  of  July,  18&4. 
On  inspecting  the  Nautical  Almanac,  I  find  that  the  Moon's  Declination  changos  at  the  rate  of  123"  in  10 
minutes  of  time  ;  the  Moon  is  also  on  the  Meridian  at  twilight.  And  on  inspecting  Table  XVI 1 1,  I  find 
that  the  Star  Arcturus  will  be  on  the  Meridian  about  the  same  time.  The  case  is,  therefore,  practical, 
and  we  proceed  at  once  to  find  the  Apparent  Time  at  Ship,  and  correct  the  Watch. 

EXAMPLE  2. 

July  6th,  1854.  lu  Latitude  42°  10'  North,  Lougitude  64°  66'  West,  at  6h  47m  78  Apparent  Time  at  Ship  by 
Watch,  the  obseiveil  Meridian  Altitude  of  the  Moon's  Lower  Limb  was  41°  21'  lu",  aud  about  23ra  aftei-warda  th« 
M*-ridian  Altitude  of  the  Star  Aieturus  was  observed  to  be  67°  62'  15  ",  the  elevation  of  the  eye  being  18  feet.  Re- 
quired the  Longitude  in  at  the  Time  of  the  Moon's  Altitude. 

PROJECTION 

Of  the  Meridian  Altitudes  of  the  Moon  and  the  Star  Arcturus. 

Fig.  .32. 


I 


ZENITH 


jRCLE    P;ASS//Wc;    t 


or      '     A  R  CT 


'of  Vecl' 


RATI  ON A  L 


HORIZON 


POfNT 


It  will  be  perceived  by  the  above  Diagram,  that  the  Star's  Declination  (being  North  of  the  Celestial 
Equator)  subtracted  from  the  Difference  between  the  Moon  and  the  Star's  Altitudes,  famishes  at  once  th« 
Aloon's  Declination,  South  of  the  Equator. 

lb  Find  the  Longitude  from  the  Moon's  Observed  Declination. 

I'sMer.  Pass.  N.  A.  July  6th 6h  42m  SOs  M.  T.of  Pass,  at  Ship  6h  51m  SOs   ]) 'sSem.lS' 69"  H.P.SS'Sg" 

Say  as  360°  is  to  50m  so  is  L.  64°  56' W.  to         9       0    Lon.64°  56' W.in  T.    4    19     44    Oor.G.D.  2    Cor.        14 

Mean  Time  of  Pass.  Men  at  Ship 6h  51m  SOs  Gr.  Date,  July  6th,  llh  11m  Us  15'  67"  68^'' 

Equa.  ofTime Sub.  4     23  Augment..        11 

App.  Time  at  Ship 6h  47m    78      Cor.  Eq.  of  Time. .  4m  23s  Augm.  Semi.  16'    8" 


Obs.  Alt.   D  's  Lower  Limb. .  41"  21'  10"  #'s  Obs.  Alt. .  67°  62'  15" 
5  '8  Augm.  Semid Add  16      8     Dip  4'  8"  R.  24"=-     4   32 

Central  Altitude 41°  37'  18"  #'8  True  Alt      67°  47'  43" 

Dipof  theHor.  18  feet 4      8 

D  'b  App.  Alt 41°  33'  10"  App.  Alt     Log.  Sec.  0.1259 

Corr.  for  Par.  in  Alt...  Add  43   43     H.P.  58' 25"  Pro.Log.  0.4887 


Refraction  in  Alt. 


42°  16'  53"  >  'a  C.43'  43"  Pro.Log.  0.6146    Diff.  of  Obs.  and  preced.  Dec. 
.Sub.  1      3 


2>  '8  True  Alt 42*  15'  50" 

%'b  True  Alt 67    47    43 

Diff.  of  Altitudes 25°  31'  58" 

#'8  Dec.  N.  A.,  July  8th. .     19    57   43   N 

D  's  Obs.  Declination 5°  34'  10"  S 

D  's  Dec.  N.  A.,  July  6th,  llh.  5    31    56 

0^ 


2'  14" 


Moon's  True  Altitude 42°  15'  50" 

Bay  as  12'  17"  is  to  Ih  so  is  2'  14"  to  a  portion  of  Time. 

Diff.  Declination. .     12'  17" Pro.  Log 1.1660 

Arith.  Compli 8.8340 

I  hour Pro.Log. 0.4771 

Diff  of  Dec.  2' 14" Pro.Log 1.9063 


T)  '8  Dec.  N.  Al,  July  6th,  llh    5° 
do  at  12h   6 


31' 5C 
44    Itt 

Diff.  of  Dec.  in  1  hour 0°  12'  17" 

Time  of  the  preceding  Declination. ...     llh    Om    0» 

Portion  of  Time  to  be  added 10     64 

Greenwich  Mean  Time llh  10m  54» 

Mean  Time  at  Ship 6    51      30 

Longitude  in 64°  61'  0"  W.=-4h  19m  24fl 


Portion  of  Time  1  Om  548 Pro.  Log. 1.2174 

Degree  of  Dependence. 

Although  the  Altitudes  are  required  to  be  taken  with  much  precision,  to  insure  a  tolerable  degree  of  accuracy  by 
Wiis  method,  still  as  the  errors  in  the  Observation  are  not  multiplied  in  the  computation,  it  may  be  used  with  aavao- 
iHge  in  fine  serene  weather,  when  the  Sea  is  smooth,  and  the  Dip  of  the  Horizon  is  correctly  ascertained,  by  thoM 
persons  who  may  not  have  had  practice  in  the  Lunar  method.  In  this  case  an  error  of  10"  in  computing  the  Moon'a 
Declination,  will  produce  an  error  of  13'  in  the  Longitude  deduced  therefrom  ;  and  an  error  of  1'  m  the  Declination 
will  produce  an  error  of  1°  13'  in  the  Longitude.  "This  method  is  therefore  most  suitable  for  High  Latitudes,  wbflr« 
the  aegrees  of  Longitude  are  small,  and  where  the  actual  error  in  space  (that  is,  Departure)  would  be  small  in  pro- 
portion. It  is,  however,  much  inferior  to  the  Lunar  Tup'^^hod  as  regards  accuracy ;  but  the  Observation  may  be  usalbl 
to  those  who  can  take  Altitudes  accurately  enough,  bu*  who  make  sad  work  at  measuring  a  Lunar  Distance 


180 


MEIHOD  OF  KEEPING  A  SHIPS  RECKONING  AT  SEA; 


AND  THE  MANNER  OF  WRITING  DOWN  THE  SAME  IN  A  LOG  BOOK  OR  JOURNAL 


Description  of  the  Log  Slate  or  Board. 

This  is  ruled  in  the  follo\ring  form,  so  as  to  contain  an  exact  account  of  the  Ship's  progress  during  the 
24  hours  of  a  Sea  Day,  and  which  commences  at  Noon,  that  is,  when  the  Sun  is  on  the  Meridian  of  the 
Ship.  The  hours  are  counted  to  12  at  Midnight,  and  called  the  hours  P.  M.  They  are  then  reckoned 
over  again  in  the  same  manner,  until  the  following  Noon,  and  called  the  hours  A.  M. 

Mode  of  Reckoning  Time. 

The  Sea  Day  begins  12  hours  before  the  Civil  Day,  and  24  hours  before  the  Astronomical  Day.  So 
that  the  end  of  the  Sea  Day,  the  beginning  of  the  Astronomical  Day,  and  the  Middle  or  Noon  of  the  Civil 
Day,  takes  place  at  the  same  period  of  time. 

This  mode  of  reckoning  arises  from  the  custom  of  seamen  dating  their  Day's  Work  for  the  preceding  24 
hours  the  same  as  the  Civil  Day,  so  that  occurrences  which  happen,  for   instance,  on  Tuesday  the  10th  in 
the  afternoon,  are  entered  in  the  Log  marked  Wednesday  the   11th,  P.  M.,  and  occurrences  which  happei 
on  the  following  morning  of  the  Sea  Day,  are  entered  in  the  Log  marked  A.  M.,  and  which  also  corres 
ponds  to  the  same  hours  of  the  Civil  Day 

What  the  Log  Board  should  Contain. 

The  Log  Board  should  contain  a  register  of  the  Courses,  Distances,  Leeway,  and  the  direction  of  th*.,  V^'nA 
tacking  or  wearing  Ship,  making  or  shortening  Sail,  and  other  matters  of  importance  connected  with  tnc  Ship^i» 
way;  and  it  is  the  duty  of  the  officer  of  the  Watch  to  mark  the  same  regularly  on  the  Log  Slate  (whicn  w 
generally  hung  up  in  the  Steerage  for  that  purpose)  at  the  expiration  of  each  Watch,  so  tlia«  the  Chip's 
progress  may  be  ascertained  at  any  given  hour  of  ihe  day. 

When  land  is  in  sight,  the  bearing  and  estimated  distance  of  the  most  prominent  ob'erts,  and  the  time  at 
which  the  bearing  was  taken,  must  be  inserted,  as  also  the  particulars  of  speaking  vea.sels  at  Sea,  and  anT 
ether  memoranda  intended  to  be  inserted  in  the  I  og  Book,  as  a  guard  against  a  tA},  a  the  memory. 

Ruling  of  the  Log  Board. 

The  Log  Board  is  ruled  to  contain  seven  columns ;  the  first  contains  the  hou'a  from  Noon  to  Noon,  bemg 
marked  for  every  hour,  similar  to  a  Civil  Day ;  (or  sometimes  it  is  marked  for  every  two  hours,)  in  the 
second  and  third  columns  are  inserted  the  rate  of  sailing  by  Log  per  hour,  sU  against  the  hour  when  the 
Log  was  hove  ;  the  fourth  column  contains  the  Courses  steered  by  Compass ;  the  fifth,  the  direction  of  the 
Wind;  the  sixth,  the  Leeway;  and  the  seventh  contains  the  transactions,  remarks  on  the  weather,  and 
ther  memoranda. 

Setting  the  Watch  at  Sea. 

When  a  Ship  leaves  a  Port  outward  bound,  the  crew  are  divided  into  two  Watches,  termed  the 
Starboard  and  Larboard  Watches,  and  who  do  duty  4  hours  alternately,  except  between  4  and  8  o'clock  in 
the  evening,  when  each  Watch  does  duty  2  hours  only.  These  are  called  the  Dog  Watches,  and  are  for  the 
purpose  of  changing  the  Night  Watches,  so  that  the  same  party  will  not  be  on  duty  at  the  same  interval  Oi 
time  on  two  follovring  nights;  and  it  is  the  custom  or  rule  for  the  Second  Officer,  who  keeps  the  Captain's, 
or  Starboard  Watch,  to  take  the  first  Watch,  (which  is  from  8  o'clock  in  the  evening  until  midnight.)  on 
leaving  Port  outward  bound ;  and  the  First  Officer,  who  keeps  the  Larboard  Watch  to  take  the  first  Watob 
»n  leaving  Port,  homeward  bound. 


KEEPING  A  Si  HP'S  RECKONING. 


l«l 


THE  LOG  BOARD. 


1.. 

K. 

F. 

COURSES. 

WINDS. 

L.W. 

REMARKS.       TUESDAY,     APRIL    IST,    1854. 

1 

2 

3 
4 

6 

6 

7 

8 

9 

10 

11 

12 

8 
8 
8 
8 
9 
10 
9 
9 
7 
7 
7 
6 

3 
2 
6 

7 
4 

5 

S.  K 

<i 

u 
it 
u 

m 

w.  s.  w. 

tl 
tt 
it 
li 
1( 
tt 
It 

S.  S.  W. 

P.  M.     Smart  breezes  and  cloudy  weather. 

Set  studding-sails,  low  and  aloft. 

Stowed  the  anchors.     Unbent  and  stowed  the  chain  cables  in   the 

lockers. 
Passed  several  vessels  bound  to  the  "Westward. 
At  6h,  very  squally.  In  topgallant-studding-sails,  royals  and  fly 

iug-jib 
At  8h,  wind  hauled  to  the  Southward,  with  heavy  rain.     Took  in 

all  the  studding-sails  and  braced  up  sharp. 

4 

7 

« 
i( 

E.byS, 
East. 

tt 

«t 

S.  by  E. 

S.  S.  E. 

i 

Weather  gloomy  and  threatening. 

At  Midnight,  in  top-gallant-sails,  and  the  first  reefs  of  the  Ujpsails. 

At  2  A   M.  double-reefed  the   topsails.     Strong  gale  and  cloudy 
weather. 

1 
2 

7 

7 

3 

6 

6 

4 

6 

E.N.  E. 

u 

N.  E. 
South, 

Biirom.  292 

(t 

S.  E. 

(t 

E.  S.  E. 

tt 

KS.  3. 

U 

t> 
ti 

0.  Ther.76'' 

1 

H 

2 

At  4h,  sent  down  the  royal  yards,  and  made  all  snug  alofL 

At  6h,  strong  gale  and  a  high  sea  running.  Vessel  shipping  much 
water  on  deck. 

At  Sh,  tacked  ship  to  the  Southward;  more  moderate  weather- 
out  double-reefs  and  set  top-gallmt-sails. 

Spoke  the  ship  Asia,  from  Manilla  to  New  York,  out  85  days  ; 

all  well. 
Noon.  Fresh  gale  and  cloudy.     Sun  obscured. 

Magnetic  variation  1-J^  points  Westerly. 

5 

6 

6 
5 

8 

7 
8 

5 

5 

9 
10 
11 
12 

6 
6 
6 
6 

6 

8 
9 
5 

The  above  form  of  ruling  for  every  hour  is  the  most  accurate  mode,  though  sometimes  another  form  u 
ased,  and  marked  for  every  two  hours,  but  which  is  liable  to  cause  considerable  error  in  the  reckoning, 
in  having  to  double  the  knots  marked  opposite  the  hours,  thereby  doubling  the  error  in  the  distance  sailed. 
Besides,  it  is  inconvenient  for  inserting  the  Course,  when  it  is  changed  between  the  hours  so  marked. 

On  proceeding  to  work  a  Day's  Work,  the  Courses  by  Compass  are  taken  from  the  Log  Board,  and  cor» 
reeled  lor  the  Variation  of  the  Compass  and  for  Leeway,  when  she  makes  any.  This  gives  the  Course 
made  yood  between  the  hours  marked  on  the  Board. 

Cross  off  the  di.stance  below  the  hour  at  which  the  Course  was  changed,  (as  in  the  form  above,)  sum  up 
the  fathoms,  which  divide  by  10*,  the  quotient  is  knots,  and  the  remainder,  if  above  5,  call  1  knot  more, 
but  if  less  than  5,  throw  it  away  ;  carry  the  quotient  to  ihe  column  of  knots,  and  their  sum,  contained 
between  the  hourg  corresponding  to  the  Course,  will  be  the  distance  run  on  that  Course. 

To  Correct  the  Courses  for  Variation. 

RULE.  " 

When  the  Variation  is  \  Westerly,  allow  it  to  the  Left  hand  of  the  Course  steered. 
(  Easterly,  allow  it  to  the  Right  hand  of  the  Course  steered 

To  Correct  the  Courses  for  Leeway. 

RULK 

When  the  Shin  ia    n  the  \  ^tarboard  Tack,  allow  it  to  tiie  Left  hand  of  the  Compass  Course. 


Port  Tack,  allow  it  to  the  Right  hand  of  the  Compass  Course. 
EXAMPLE 


Of  Correcting  the  Courses  and  Finding  the  Distance. 


COMPASS    COURSE    STEERED. 

TARIA. 

L.  WAY. 

WIND. 

ON    WHICH    TACK. 

OOITRSE    MADE    QOOD. 

DI8TAN0K. 

S.  E.  from  Noon  to  Midnight. 

H  pt.  w. 

S.  W. 

Wind  free. 

S.  E.  by  E.  i  K 

100 

E.by  S.  from  Mid  to  2  A.M. 

U                     M 

S.  by  E. 

Starboard  Tack. 

E.  iN. 

14 

East  from  2h  to  4      " 

«<                     11 

ipt. 

S.  S.  E. 

do. 

E.  N  K 

18 

E.  N.  E.      "     4h  to  6      " 

C(                     U 

1       " 

S.  E. 

do. 

N.  K  i  N. 

19 

i*.  E.      -     6h  to  8      " 

u                   tt 

H  " 

E.  S.  £. 

do. 

N.  by  E. 

10 

South        "     Sh  to  Noon. 

tt              u 

2     " 

do. 

Port  Tack. 

S-i  W. 

27 

•  Or,  oonslder  the  Sum  to  be  tenths  of  a  mile,  note  the  unit,  and  carry  the  tens  to  the  next  oolnmn,  in  the  same 
\v  Ml  the  Sums  taken  from  Tables  I  and  U. 


182 


KEEPING   A  SHIPS  RECKONING 


Finditig  the  Variation  of  the  Compass 

The  Variation  of  the  Compass  maybe  found  by  an  Amplitude,  (see  page  116,)  or  by  an  Azimuth,  '■•• 
page  118.)  It  may  also  be  found  by  inspecting  the  Chart,  or  by  the  Variation  Table.  The  Magueti* 
Variation  is  there  laid  down  from  actual  Observation.     (See  Remarks,  page  120.) 

Allowing  for  Leeway. 

Leeway  is  the  effect  of  the  lateral  pressure  of  the  Wind  and  Waves  in  forcing  a  vessel  out  of  the  Courst 
Bhe  is  endeavoring  to  make  when  close-hauled,  and  it  is  the  angle  contained  between  her  wake  and  the 
point  of  the  Compass  right  astern)  It  may  be  ascertained  after  heaving  the  Log,  and  before  the  line  i* 
drawn  in,  by  bringing  it  over  a  Half-Compass,  constructed  for  that  purpose,  on  the  Taffrail,  the  diameter  of 
which  being  at  right  angles  to  the  Ship's  keel,  then  the  angle  between  the  centre  point,  and  the  point  oi 
half  point  over  which  the  line  lies,  will  contain  the  number  of  points  of  Leeway  the  vessel  is  then  making, 
providing  she  has  been  steered  steadily  during  the  time  of  trial.  When  a  Ship  is  laying  to,  the  middl* 
point  between  what  she  comes  up  to,  and  falls  off,  is  taken  as  the  direction  of  her  head  by  Compass.  The 
Leeway  is  then  estimated  from  the  angle  of  her  wake,  as  before. 

As  the  correctness  of  the  Reckoning  in  a  great  measure  depends  upon  a  proper  allowance  for  Leeway, 
the  officer  of  the  Watch  should  be  particular  in  marking  it  on  the  Log  Board,  or  else  in  reckoning  up  th« 
day's  work,  it  will  be  found  difficult  for  a  person  who  has  not  been  on  deck  the  whole  time  to  make  t 
proper  allowance. 

Correcting  the  Course  for  Leeway  and  Variation. 

In  correcting  the  Courses  for  Variation  and  Leeway,  imagine  yourself  to  be  in  the  centre  of  the  CompaM 
and  looking  towards  that  point  which  represents  the  Course  steered. 

EXAMPLES 
Uf  Correcting  the  Courses  Steered  for  the  Effect  of  Leeway  and  Variation. 


OOURBE3    STSEEED. 

WINDS. 

ON    WHICH   TACK. 

LEEWAY. 

VAKIATION. 

OODESES    MADE    GOOD. 

E.  N.  E. 

N.W. 

Wind  free. 

0 

H  pts.  W. 

N.  E.  i  E. 

W.  by  S. 
N.  W.  by  N. 

N.W.  by  N. 

Starboard  Tack. 

1     pt. 

0         » 

W.  s.  w. 

N.  E  bv  N. 

do. 

H 

2       "    W. 

W.  by  N.  i  N. 

South. 

E.  S.  E. 

Port  Tack. 

i 

li     "    E. 

S.  by  W.  i  W. 

N.W. 

W.  S.  W. 

do. 

2 

1       «   W. 

N.  W.  by  N. 

S.  S.  W. 

S.  E. 

do. 

H 

li    "  w. 

S.  S.  W. 

E.  by  N. 

N.  by  E. 

do. 

n 

Oi    "   E. 

S.  E.  by  E  f  K 

West 

N.  N.  W. 

Starboard  TacK. 

5 

1       "   E. 

W.iN. 

In  the  above  Examples,  6  points  of  an  Angle  is  allowed  between  the  Ship's  head  and  the  point  from 
which  the  wind  blows,  this  being  as  near  as  a  square-rigged  vessel  will  lie  to  the  wind  when  close-hauled 
in  smooth  water ;  but  in  blowing  weather  at  Sea,  it  is  the  practice  to  round  in  the  weather-braces,  so  that 
the  Ship's  head,  though  still  close-hauled,  is  about  7  points  from  the  wind,  or  as  it  is  termed  by  seamen, 
on  a  Western  Ocean  bowling,  the  object  being  to  make  greater  speed  and  less  Leeway. 

Fore-and-aft  vessels  generally  lie  within  from  4  to  5  points  of  the  wind,  that  is,  a  point  or  two  higher  or 
nearer  the  wind  than  square-rigged  vessels  do. 

In  allowing  for  Leeway  and  Variation,  when  they  both  go  the  same  way,  it  may  be  done  at  once  by 
allowing  their  Sum  ;  or  when  in  different  ways,  take  their  Difference  and  allow  it  the  same  way  as  that  of 
the  greater  of  the  two,  whether  it  be  Variation  or  Leeway. 

And  the  learner  should  keep  the  figure  of  the  Compass-card  in  view  while  making  these  allowance!, 
which  will  be  found  to  greatly  assist  the  memory. 

Allowing  for  the  Heave  of  the  Sea. 

A  Ship  is  supposed  to  make  Leeway  only  when  she  is  close-hauled  and  a  rough  sea  on.  But  it  some- 
♦icnes  happens  when  the  wind  is  free,  a  heavy  beam-sea  may  be  running,  which  has  the  effect  of  heaving 
tier  to  leeward  of  the  Course  steered.  This  allowance  is  called  the  Heave  of  the  Sea,  and  will  rarely 
xceed  i  point ;  because,  although  the  waves  appear  to  have  a  rolling  motion,  it  is  only  the  crest  of  the 
-vave  which  advances,  the  great  body  of  the  water  remaining  stationary,  rising  and  falling  with  a  motion 
•imilar  to  the  shaking  of  a  sail. 

And  the  greater  the  speed  of  the  vessel  the  less  will  be  the  effect  of  the  waves;  on  the  other  hand,  th« 
less  the  speed  of  the  vessel  the  greater  will  be  the  effect  of  the  waves  in  any  given  distance  sailed  ;  because 
the  fast-sailing  vessel  will  cross  any  given  space  in  a  shorter  time  than  the  slow  one,  and  will  be  subjected 
to  fewer  buffetings. 

So  that  the  allowance  for  the  Heave  of  the  Sea  must  rest  entirely  on  the  judgment  of  the  Navigator 
Keeping  in  view  the  various  circumstances  of  the  case. 

On  allowing  tor  Currents,  (see  page  29,)  and  for  a  description  of  the  Log-Line,  Log-Glasa,  and  inaniiier 
of  using  the  same,  (see  page  6.) 


KREPl^G  A  SHIP'S  RECKONING.  183 

METHOD  OF  KEEPING   A  SHIPS  RECKONING  AT  SEA. 

Allowi?}g  For   Currents. 

Hnving  thuB  found  the  Courses  made  good  and  the  Distance  Sailed  by  the  Log,  they  are  entered  in  the 
traverse  Table,  together  with  the  True  Set  of  the  Current  as  a  Course,  and  its  Drift  as  a  Distance  whea 
the  Current  is  actually  known  to  exist,  otlierwise  much  caution  is  required.     (See  Remarks   at  page  29.) 

Remarks  on  the  First  Day's  Work  after  Leaving  the  Land. 

If  a  departure  has  been  taken  from  the  Land,  the  Variation  must  be  allowed  on  the  Bearng  b 
Compass,  and  the  opposite  point  entered  into  the  Traverse  Table  as  a  Course,  and  the  estimated  distance  o9 
Shore  as  a  Distance,  (see  page  31)  the  Difference  of  Latitude  and  Departure  made  good  is  then  found  by  a 
case  of  Traverse  Sailing ;  then  the  Difference  of  Latitude  made  applied  to  the  Latitude  left,  (or  in  the  case 
of  taking  a  departure  from  the  Land  applied  to  the  Latitude  of  that  place,)  will  give  the  Latitude  of  the 
Ship.  Then  with  the  middle  Latitude  as  a  Course,  found  in  Table  II,  and  the  Departure  made  good  taken 
in  the  Latitude  column,  the  Difference  of  Longitude  corresponding  will  be  found  in  the  Distance  column. 
This  applied  to  the  Longitude  left,  at  the  preceding  Noon,  (or  in  the  case  of  taking  a  Departure  from  the 
Land,  applied  to  the  Longitude  of  that  place,)  will  give  the  Longitude  of  the  Ship. 

Cause  of  the  Errors  in  the  Dead  Reckoning. 

The  Latitude  and  Longitude  thus  calculated  at  Noon  is  called  by  Seamen  the  Dead  Reckoning,  and  it  u 
well  named,  for  it  frequently  happens  that  it  is  dead  enough  as  regards  the  Ship's  true  position.  This  it 
caused  by  many  circumstances,  such  as  bad  steerage,  local  attraction  acting  on  the  Steering  Compa8s,(for 
Remark*  see  page  120,)  unknown  currents,  false  distance  siven  by  the  Log  in  squally  weather,  errors  in  the 
Log-Line  and  Log-Glass,  and  impioper  allowances  for  Leeway  and  Variation. 

Ascertaining  the  Cause  of  the  Error  in  the  Dead  Reckoning. 

When  the  discrepancy  is  great  between  the  Ship's  position  by  Dead  Reckoning  and  that  by  Observation,  a 
careful  Navigator  will  investigate  the  matter,  and  endeavor  to  ascertain  the  cause.  If  the  Log-Line  and 
Glass  have  been  found  correct,  (see  page  6)  examine  the  Steering  Compass  and  see  that  it  is  free  from  Local 
attraction,  and  if  the  Ship  has  been  steered  her  proper  course,  and  the  Log  has  given  her  proper  Distance 
run,  then  the  discrepancy  may  be  set  down  as  the  effect  of  a  Current,  the  direction  and  drift  of  which  may 
be  found  by  the  rules  given  at  page  29,  Case  1st,  and  in  that  case  it  may  be  allowed  for  in  the  next  day's 
work,  as  a  Course  and  Distance  Sailed,  or,  it  may  be  counteracted  by  altering  the  Ship's  course.  (Se« 
method  of  doing  so,  page  30,  Case  3d.) 

Allowing  for  Bad  Steerage. 

When  a  Ship  is  scudding  in  a  Gale  of  wind  some  Navigators  are  in  the  habit  of  allowing  for  the  heave 
of  the  sea,  in  forcing  the  vessel,  as  they  imagine,  ahead  of  the  distance  run  by  Log.  This  allowance  is 
of  very  doubtful  utility.  In  fact,  I  have  always  found  it  the  reverse,  especially  in  a  badly  steered  or  bad 
■teering  Ship,  because  on  account  of  her  yawing  about  she  must  necessarily  waste  a  considerable  portion 
of  her  Distance  run,  and  the  Log  will  be  found  to  give  the  Distance  run  in  excess  of  the  actual  place  o« 
the  Ship  by  observation,  and  it  is  usual  in  some  cases  to  deduct  1  mile  in  10  for  bad  steerage. 

Heaving  the  Log  in  Steam  Vessels. 

In  Steam  Vessels  the  Log  is  found  to  give  too  much  Distance.  This  is  easily  accounted  for,  and  caused 
by  the  action  of  the  paddle-wheels  driving  the  water  astern.  The  Log  in  this  case  should  be  hove  from 
the  paddle-boxes,  outside  of  the  influence  of  this  current  of  water. 

The  Use  of  Keeping  the  Dead  Reckoning. 

Nerertheless,  the  Dead  Reckoning  even  under  all  these  disadvatages  should  not  be  neglected,  as  it  some- 
times is  the  only  mode  we  have  of  detecting  any  very  gross  error  made  in  deducing  the  Ship's  position 
from  Astronomical  observations  and  in  the  detection  of  Currents,  and  otiier  matters. 

When  the  Dead  Reckoning  is  Proved  to  be  Erroneous,  to  take  a  Fresh  Depat  Cure. 

When  theLonuitude  by  Dead  Reckoning  is  proved  to  have  been  erroneous  from  the  Sight  of  Land  or  by  the 
Chron..  the  error  and  rate  of  winch  has  been  recently  found,  or  by  Lunar  Distances  observed  on  both  sides 
of  the  Moon,  il  can  answer  no  useful  purpose  in  carrying  it  on,  and  a  fresh  Departure  and  Longitude  should 
be  adopted  and  then  carried  on  as  before. 

Practice  of  some  Navigators  Regarding  Dead  Reckoning. 

Some  Navigators  carry  the  Longitude  by  Dead  Reckoning  on  from  day  to  day  only,  as  a  means  of  com 
paring  it  with  the  Longitude  made  by  Chronometer.  Others  again  never  keep  any  Dead  Reckoning  at  all 
trusting  entirely  upon  the  Latitude  observed  and  the  Longitude  by  Chronometer. 

Practice  of  Keeping  the  Reckoning  in   Fast  Sailing    Ships. 

In  fast  sailing  Ships  the  Distance  run  is  generally  estimated,  and  the  Log  seldom  or  ever  hove,  and  u 
those  Ships  generally  steer  well,  their  Course  steered  can  be  depended  upon  ;  and  when  the  Difference  of  Lat. 
is  obtain'?d  from  observation,  the  Distance  run  and  the  Departure  made  good,  can  also  be  obtained  by  a 
eas«  in  Plane  Sailing,  and  more  correct  than  if  the  Distance  had  been  measur«^d  in  the  usual  mannvr  b) 
the  Log.     (See  the  following  rules  for  working  Day's  works.) 


184  ■  KEEPING  THE  SHIP'S  RECKONING. 

METHOD  OF  KEEPING  THE  SHIP'S  RECKONING  AT  SEA. 

RULES  FOR  WORKING  A  DAY'S  WORK. 

The  foUovv.ng  rules  have  been  collected  with  the  view  of  simplifing  the  matter,  and  placed  so  as  the) 
4an  be  conveniently  referred  to  by  the  learner. 

Correcting  the  Courses  Sailed 

1.  Correct  ea«h  Course  sailed  for  Variation  and  Lee-way  by  the  rules  (page  182)  already  given;  entef 
them  in  the  Traverse  Table  and  set  against  each  the  Distance  run  on  that  Course.  If  the  Ship  is  in  • 
Current,  the  Set  and  Drift  of  which  is  known,  allow  tiie  Variation  on  its  set,  and  enter  it  in  the  Traverse 
Table  as  a  Course  and  Distance,  but  if  its  Set  and  Drift  is  uncertain,  it  is  better  to  leave  it  out  altogether ; 
•Iso  if  the  ship  has  taken  a  Departure  from  the  Land,  correct  the  Bearing  by  Compass  for  Variation,  and 
enter  the  Table  with  the  Opposite  Point  as  a  Course,  and  the  estimated  Distance  off  as  a  Distance. 

Finding  the    Course  Made  Good. 

2.  Find  the  Difference  of  Latitude  and  Departure  made  good,  with  which  enter  Table  II,  and  find  th« 
Course  and  Distance  made  good,  by  seeking  in  its  columns  until  they  are  found  to  agree,  opposite  to  which 
will  be  found  the  Distance  in  its  column ;  and  if  the  Departure  be  greater  than  the  Difference  of  Latitude,  tha 
Course  is  taken  from  the  bottom  of  the  Table,  but  if  the  departure  be  less  than  the  Difference  of  Lati- 
tude, the  Course  must  be  taken  from  the  top  of  the  Table. 

Finding  the  Latitude  In. 

3.  If  the  Latitude  of  the  place  from  which  the  Ship's  Departure  has  been  taken,  or  yesterday's  Latitude, 
and  the  Diflference  of  Latitude  made  be  both  North  or  both  South,  their  Sum  will  be  the  Latitude  in  of  that 
name  ;  but  if  the  Difference  of  Latitude  be  of  a  contrary  name  to  the  Latitude  left,  their  Difference  will  be 
the  Latitude  in.  of  the  same  name  as  the  greater  of  the  two. 

Finding  the  Difference  of  Longitude. 

4.  Add  together  the  Latitude  observed  yesterday  and  the  Latitude  in  to-day,  and  take  their  Half  Sum  for 
the  middle  Latitude,  then  with  this  middle  Latitude  (taking  the  nearest  Degree)  enter  Table  11,  and  seek 
for  the  Departure  made  good  in  the  Latitude  column,  and  the  Sum  standing  opposite  in  the  Distance  column 
will  be  the  Difference  of  Longitude  made,  which  divided  by  60  will  give  Degrees  and  Minutes,  and  mark  it 
of  the  same  name  as  the  Departure. 

Finding  the  Longitude  In. 

5.  If  the  Longitude  of  the  place  from  which  the  Ship's  Departure  has  be^an  taken,  or  yesterday's  Longi- 
tude, and  the  Difference  of  Longitude  made  be  both  East  or  both  West,  their  Sum  will  be  the  Longitude 
in,  of  that  name  ;  but  if  the  Difference  of  Longitude  be  of  a  contrary  name  to  the  Longitude  left,  their  Dif- 
ference  will  be  the  Longitude  in  of  the  same  name  as  the  greater  of  the  two  ;  but  when  their  Sum  exceeds 
180**  the  Ship  has  crossed  the  opposite  Meridian  to  Greenwich  ;  in  that  case  Subtract  it  from  360",  the  remain- 
der will  be  the  Longitu''':  In,  ^"^d  of  a  different  name  to  the  first. 

Mode  of  Working  the  Day's  Work  when  the  Distance  run  is  Unknown. 

b.  When  the  Distance  run  is  uncertain  or  even   altogether   unknown,  take  the  Difference  of  the  observed 
Latitudes,  and  the  Course  made   good,  with   which  enter   Tables   I  or  II,  as  usual,   and  seek    for  the  ob 
served  Difference  of  Latitude  in  its  column,  and  opposite  to  which  will  be  found  the  corresponding  Distanci 
run  and  the  Departure.     Then  proceed  as  before  by  rule  No.  4,  to  find  the  Longitude  in  by  Dead  Reckoning 

General  Remarks  on  Keeping  a  Ship^s  Reckoning,  Currents,  ^c. 

If  the  Latitude  yesterday  has  been  observed,  the  Difference  of  Latitude  made  is  usually  applied  to  it, 
the  room  of  the  Latitude  by  Dead  Reckoning,  and  it  is  called  the  Latitude  in  by  Dead   Reckoning  at  No(i 
to-day.     Then  if  it  agrees  with  the  Latitude  in  by  observation  to-day,  the  reckoning  is  said  to  be  ju«t,  but 
it  do  not  so  agree  the  Ship  is  said  to  be  the  amount  of  the  Difference  to  the  Northward  or  to  the  Southward  a 
the  Dead  Reckoning.     In  like  manner,  if  the  Longitude  by  Chronometer  or  Lunar  observation  has  been  ob 
served  and  brought  up  to  Noon  yesterday,  and  the  Difference  of  Longitude  made  by  Dead  Reckoning  beinj 
applied  to  it,  then   if  it  agrees   with   similar  observations   for  Longitude   to-day,  brought  up   to  Noon,  tia 
reckoning  is  said  to  be  just,  but  if  they  do  not  so  agree  then  the  Ship  is  said  to  be   the   amount  of  the   D'S- 
ference  to  the  Eastward  or  Westward  of  the  Dead  Reckoning  on  this  day's  work. 

The  errors  of  the  Latitude  and  Longitude  so  found,  furnish  the  means  of  Detecting  the  Set  and  Drift  o/ 
the  Current  (always  providing  that  the  Course  and  Distance  Sailed  are  correctly  given,^  by  taking  the  Mid 
Latitude  a§  a  Course,  and  the  Error  of  the  Longitude  in  the  Distance  column;  then  in  the  Latitude  co)'»ma 
will  stand  the  Departure,  with  the  Departure  and  the  Error  in  the  Latitude  find  the  Course  and  Disiance, 
and  which  will  be  the  true  Set  and  Drift  of  the  Current,  or  in  that  direction  in  which  the  Ship  is  founo  ui 
be  by  observation,  when  compared  with  her  place  as  given  by  the  Dead  Reckoning. 

The  Dead  Reckoning  should  not  be  Altered  on  Slight  Grounds. 
The  Difference  of  Longitude  made  by  Dead  Reckoning  being  applied  daily  to  the  Long,  in  by  Dead  Reckon 
in^  is  carried  on  from  the  commencement  of  taking  a  Departure,  independent  of  that  by  observation,  and 
should  not  be  altered  on  slight  grounds,  because  the  rate  of  the  Chron.  may  change  or  the  Lunar  Distance 
may  be  in  Error,  and  the  Dead  Reckoning  may  thus  be  the  means  of  detecting  it ;  but  wh^n  the  Dead  Reokon< 
tng  has  been  found  to  be  decidedly  in  Error  then  a  fresh  Departure  must  be  taken. 


KEEPING  A  SHIP'S  RECKONING. 


185 


THE  DAY'S  WORK. 


EXAMPLE  1. 


At  1  P.  M^  took  our  Departure  from  Neversink  Light  Houses,  bearing  by  Compaea  W.  N  W.,  distant  9  miles,  an« 
fcave  sailed  until  Noon  this  day  as  per  Lot?  ;  the  Variation  of  the  Compass  being  i  a  point  Westerly,  and  the  Sun'i 
Meridian  Altitude  observed  was  66°  30'  South.  Required  the  Latitude  in  by  Observation,  he  Latitude  and  Longi 
tude  by  Dead  Reckoning,  and  the  Bearing  and  Distance  of  Wreck  Hill,  in  the  Island  of  Bermuda,  at  Noon. 


H. 

K. 

F. 

COURSES. 

WINDS. 

L.W. 

REMARKS    ON    BOARD,    MONDAY,    MAT    IST,    1854. 

1 

West. 

At  1  P.  M.  Neversink  Light-Houses  bore  W,  N.  W.  9  miles,  in  Lati- 

2 

10 

3 

S.  R  by  S. 

t( 

tude  40°  24'  N.,  Long.  73°  59'  W.,  from  which  I  take  my  Dep. 

3 

10 

6 

M 

«« 

Set  the  starboard  studding-sails  low  and  aloft 

4 

11 

M 

44 

Steady  breeze  and  fine  pleasant  weather. 
Stowed  the  anchors  and  secured  the  boats. 

6 
6 

10 
9 

8 
4 

<* 
II 

•i 

7 
8 

10 
10 

5 

U 

m 

At  8h,  squally-like  in  the  South. 

9 

10 

6 

«• 

i< 

At  9h,  wind  hauled  more  to  the  Southward.     In  all  the  studding- 

10 
11 
12 

9 
9 
8 

8 
4 

8.  W. 

sails  and  braced  the  yards  up. 

u 

S.  W.  by  S. 

Midnight     Squally.     Handed  the  Ught  sails. 

1 

7 

S.  K 

S.  S.  W. 

2 
3 

7 
6 

S.Kby  E. 

It 

S.  by  W. 

i 

At  2  A.  M.  in  top-gallant-sails  and  first  reefs  of  the  topsails. 

4 

6 

U 

« 

At  4h,  blowing  fresh  and  a  head  sea. 

6 

6 

4 

E.  S.  K 

South. 

1 

Sun's  Magnetic  Bearing  at  rising  was  observed  to  be  E.  14°  18'  Nn 

6 

7 

6 

5 

6 

«4 

East. 

S.  S.  E. 

2 

which  gives  the  Magnetic  Variation  6°,  or  about  i  pt  Westerly. 

8 

5 

u 

it 

At  8h,  tacked  ship  to  the  Southward  and  set  top-gallant-sails  ; 

9 

6 

6 

South. 

E.  S.  E. 

H 

weather  more  moderate  and  clear. 

10 

6 

6 

** 

t( 

At  lOh,  many  vessels  in  company.    Spoke  the  ship  Jacob  Bell,  from 

11 

6 

6 

S.  E. 

KN.  E 

1 

Boston  to  Australia. 

12 

7 

3 

•' 

»( 

Noon.  do.  weather.     Lat.  Obs.  38°  25'  N.     Varia.  i  pt.  Westerly. 

TVJl VERSE  TABLE. 

DIF.    OF    LAT. 

DEPARTURE. 

COURSES. 

DIST. 

N. 

8. 

E. 

w. 

E.  by  S.  i  S. 

9 

•     •    •    • 

2    -6 

8    -6 

•   •  •   • 

S.  E.  i  S. 

110 

■     •    •    • 

85    -0 

69    -8 

•   .   •   . 

S.  E.  i  E. 

14 

•    •    •     • 

8     9 

10   -8 

•   •   ■   • 

E.  S.  E. 

12 

.     •    •    . 

4    -6 

11    -1 

.   •   .   . 

E.  i  S. 

11 

.     .     . 

1    -1 

10    -9 

•  •  •   ■ 

N.  E.  by  E.  i  E. 

10 

4-7 

•    •  •  • 

8    -8 

•  •  •   • 

S.  by  W. 

13 

.... 

12    -7 

■   •   •  • 

2    -5 

S.  E.  i  S. 

14 

.... 

10    -8 

8    .9 

2    -5 

4  -7 

125    -7  128    -0 

4-7       2-5 

Southing 

DifF.  of  Latitude  made  . 

.      60 

)r21    0 

126   -40 

)fEa8'g. 

2°  r 

3.                           1 

Lat  of  Neversink  L.  Houses         40°  24'  N. 

Lat  in  by  D.  Reckoning  ...         38°  23'  N. 

Sum  of  the  Latitude 78°  47' 

Half  Sum,  or  Mid.  Lat ,39°  23'  taken  as  a  Co., 

and  the  Dep.,   126  '4,  in  the  Lut.  column,  and  in  the 

Dist  Col.  stands  the  Diff.  Lon.  163'  K=  2°  43'  E. 

Long,  of  Neversink  Light-Houses 73    59    W. 

Long,  of  the  Ship  by  D.  Reck. 71°  16'  W. 

Difference  of  Latitude  121,  and  Departui-e  126,  made 

good,  found    togetlier  in  the  Traverse    Table,  gives  the 

Course  made   good  S.   46°  E.,  and   the  Distance  made 

good  175  miles. 

1 

To  Find  the  Variation. 

Lat  by  D.  Reck,  at  Sunrise  about  38|°  N.,  and  Sun's 
Declination  16°  N.,  in  Table  XXXV,  gives  the  true 
Amplitude E.  19°  18'  N. 

Magnetic  Amplitude  at  Rising E.  14    18    N. 

Magnetic  Variation 6°    o'  W 

To  Find  the  Latitude  by  Observation. 

Sun's  Mer.  Altitude  Observed 66°  30'  S. 

Correction,  Table  IX 12 

True  Altitude 66°  42' 

Zenith  Distance 23°  18'  N. 

Sun's  Correct  Declination 15      7    N, 

Latitude  Observed 38°  26'  N 

Summary. 

Course S.  46°  E. 

Distance 175 

Diff.  Latitude 121  S. 

Departure 126  E. 

.    Latitude  by  D.  Reck.  ...  38°  23'  N. 

Latitude  Observed 38    25   N. 

Diff.  Longitude 2    43    K 

Long,  by  D.  Reck 71    16    W. 

Bearing  of  Bermuda   S.  41°  E,  or  S.  E.  J  S,  nead 
fTrue.^     Distuuce  484  miles. 


To  Find  the  Bearing  mid  Distance  of  Bermuda. 


Lat  of  the  Ship  by  Observation . . 
Lat  of  Wreck  Hill,  Bermuda. 

Diff.  of  Latitude  in  miles  366 . . .  = 

Sum     

Middle  Latitude 


38° 
32 


25' 
19 


N. 


=6° 

70 


Long.  7 1 ' 
Lons.  64 


16' 
50 


6' 
44 


6°  26' 

60 


35°  22'  Di£Lon.386 


W.  Middle  Lat  35°,  and  half  the  Diff.  Long.,  193,  i| 
W.  the  Dist  «ol.,  gives  half  the  Dep.,  168,  in  the 
Lat  col.  Then  half  the  Diff.  Lat,  183,  and  Dep, 
158,  gives  the  True  Course  S.  41°  E.,  and  half 
the  Dist.  242,  which  doubled  gives  the  Irue 
Distance  484  miles. 


186 


KEEPING  A  SHIPS  RECKCNING. 


THE  DAY'S  WORK. 


EXAMPLE  2. 


A  Ship  from  Latitude  85°  42'  N.  by  Observation,  and  Longitude  51"  2'  West  by  Chronometer,  yesterday  at  Rood 
has  sailed  until  Noon  this  day  as  per  Log.  The  Sun's  observed  Altitude  iu  the  morning  was  10°  23',  the  Green 
wich  Time  by  Chronometer  llh  Om  28,  or  March  5th,  23h  Om  2s,  and  the  Sun's  Meridian  Altitude  was  46°  32'  S 
Required  the  Latitude  and  Longitude  in,  both  by  Dead  Reckoning  and  Observation,  and  the  Set  and  Drift  of  th» 
Current. 

In  this  Example  the  Fractional  parts  of  the  Knots  are  marked  as  1  half  knot 


H. 

K. 

H.  K. 

COURSES. 

1 

■WINDS.        |L.W. 

TRANSACTIONS    ON    BOARD,    MONDAY,    MA&ZH    6TH,  1854. 

1 

10 

N.  W.  by  N. 

East. 

-■■'■*■  -^ 

P.  M.  Strong  gale  and  squally,  with  hail  anc  sleet.  Vessel  shipping 

2 

lu 

(i 

*t 

much  water  on  deck.     Pumps  carefully  attended. 

3 

9 

1 

i( 

tt 

At  3h,  moie  moderate  and  clear  weather. 

4 

10 

(( 

t( 

At  4h,  out  double  reefs  arc  set  top-gallant-sails. 

5 

10 

(t 

(( 

Signalized  the  ship  Washington,  from  New  York  to  Liverpool,  out 

6 

10 

li 

u 

10  days. 

7 

9 

1 

it 

It 

Observed  the  Sun  to  set  per  Compass  W.  4°  N.,  which  gives  the 
Magnetic  Variation  1 1    30',  or  1  point  Westerly. 

8 

9 

10 

11 

12 

9 

10 

9 

9 
8 

1 

U 

It 

1 

<1 

At  lOh,  passing  squalls,  with  showers  of  haiL 

1 

Sumi 

nary. 

Midnight.     Gale  moderating.     Out   all  reefs  and  set  the  starboabr 

1 

9 

1 

Course. . . . 

...     N.  W. 

foretopmast-studding-sail. 

2 
3 

10 
10 

Distance  .  . 

281 

Diff.  Lat... 

...    163  N. 

4 

9 

1 

Departure 

.  .    163  W. 

At  4  A.  M.  set  top-gallant  and  lower  studding-sails,  royals    and  fly- 

6 

9 

Lat.  D.  R.. 

38°  25'  N. 

ing-jib. 

6 

8 

1 

Lat.  Obs.. . 

38    40    N. 

7 

9 

Diff.  Long... 

3    24    W. 

At  7h,  Longitude  in  by  Chronometer  54'  1'  30"  W 

8 

10 

Long.  D.  R 

.M   26    W. 

9 

10 

Lon.  Chr.  bA 

°  46'  30"V/. 

Unstowed  the  anchors  and  bent  the  cables. 

10 

10 

Bai-om.  30. 

Therm.  42° 

Carpenter  employed  fixing  the  windlass. 

11 

10 

Current  N. 

47°  W.rate 

Fresh  breezes  and  clear  weather.     Variation  1  point  Westerly. 

M2 

10 

of  1  knt  an 

hour,  nearly. 

Noon.    Cape  Sable,  N.  S.,  bore  N.  W.  J-  N.  True,  Distance  750  miles.  , 

The  Ship  has  been  running  on  a  N.  W.  by  N.  Course 
the  whole  24  hours.  The  variation  of  1  point  allowed  to 
the  left,  gives  the  True  Course  N.  W.  The  knots  being 
summed  up  gives  227  miles,  and  the  8  half  knots,  equal 
to  4  whole  ones,  this  added  to  227  gives  the  whole  Dis- 
tance 231. 
Ti  ne  Course  N.  4  pts.  W.  231,  gives  D.  L.  123    Dep.  163 

Diff.  Latitude  made 2°  43'  N. 

Lat.  Observed  yesterday '. .     35   42   N. 

Lat  by  D.  Reckon,  to-day 38°  25'  N. 

Sum )74°    7' 

Middle  Latitude 37°    3'  taken  as  a 

Course,  and  the  Dep.,  163,  in  the  Lat.  column,  the 
DifF.  of  Longitude  is  found  in  the  Distance   column 

to  be  204 3°  24'  W. 

Long,  by  Chron.  yesterday 51      2    W. 

Long,  by  D.  R.  since  yesterday. . . .      54°  26'  W. 

To  Find  the  Set  of  the  Current. 
Lat  Obs.     88°  40'  N.     Long,  by  Chron.  54°  46'  30"  W. 
LatD.  R.   38_25   N.     Long,  by  D.  R.     54   26     0    W. 

Error  in  LaTT^   15'  Error  in  Long.       0°  20'  30" 

With  Latitude  37°  as  a  Course,  and  Difference  of  Lon- 
gitude 20'  30'',  in  the  Dist  column,  opposite  to  which, 
ID  the  Lat.  column,  stands  the  Dep.,  16  .  Then  with  Diff. 
of  Lat  15,  and  Dep.  16,  the  Set  of  the  Current  is  found 
to  have  been  N.  47    W.  (true)  and  its  Drift  22  miles. 


To  Find  the  Magnetic  Variation. 

Diff.  Lat  made  to  Sunset 0°  42'  N. 

Latitude  at  Noon 85    42    N. 

Latitude  at  Sunset 36°  24'  and  th« 

Sun's  Declination  corrected,  5°  54'  South,  found  in  Tab«» 
XXXV,  gives  the  Sun's  True  Amplitude.  W.  7°  30'    a 

Magnetic  Bearing  at  Sunset W.  4     0    N 

Magnetic  Variation 11°  30'   V 


Sights  for  Chronometer  having  been  taken  in  the  mom 
ing  about  7  o'clock,  the  necessary  corrections  are  made 
(see  Example  Ist,  page  140,)  and  the  Meridian  Altitud* 
having  been  observed,  the  Latitude  iu  is  found  to  be  88' 
40'.  This  Latitude  is  then  reduced  back  to  the  time  the 
Sights  were  taken,  ana  tne  Longitude  by  Chronometer 
found,  which  is  then  brought  up  to  Noon  by  the  Dead 
Reckoning,  and  in  this  case  is  64°  46'  80"  W.  {This  will 
be  found  worked  out  at  page  140.) 


Now,  as  there  is  a  considerable  difference  between  th» 
place  of  the  Ship  by  Dead  Reckoning  and  that  by  Ob- 
servation, and  supposing  the  Course  and  Distance  run  to 
have  been  correct,  we  now  proceed  to  find  the  Set  an 
Drift  of  the  Current 


Again  :  Suppose  that  the  Course  steered  could  be  depended  on,  and  the  Distance  run  uncertain.  The  Latitud« 
observed  yesterday  was  86°  42'  N.,  and  to-day  38°  40',  the  Difference  of  Latitude  between  the  Observations  being 
178  miles.  Then,  with  the  Course  N  W.,  and  the  True  Difference  of  Latitude  178,  the  True  Distance  run  is  found 
to  be  262  miles,  and  the  Departure  178.  The  Middle  Latitude  37°,  taken  again  as  a  Course,  and  the  Departurt 
178,  in  the  Latitude  column,  gives  the  correct  Difference  of  Longitude  mivde  223,  in  the  Distance  column,  or  8°  48' 
lliia,  added  to  the  longitude  in  yesterday,  61°  2'  W.,  gives  the  Ij0i>^*ude  in  by  Dead  Reckoning  to  day  64°  46',  anrf 
vhidi  agrees  with  that  given  by  Chronometer,  nearly. 


KEEPING  A  SHIPS  RECKONINK. 
THK  DAY'S  WORK. 


IK1 


EXAMPLE  3. 

A  Ship  from  Latitude  i5*  60'  N.  by  observation,  and  Longitude  by  Chrononoeter  49°  34'  -V.  yesterday  it  Nooi^ 
has  Sailea  until  Noun  this  day  as  per  Log.  An  Altitude  of  the  Sun  in  the  Morning  was  observed  to  be  26°  8',Tiin« 
by  Chronometer  12h  13ni  "ils,  and  which  was  Fast  of  Gieeuwich  this  day  6m  25s.  The  Weather  being  Foggy  at 
Noon  tlie  Meridian  Altitude  of  the  Sun  was  lost  for  the  day,  but  an  Altitude  was  obtained  afterwards,  and  oh. 
•erved  to  be  42°  30',  the  Time  by  Chronometer  being  4h  14ra  21s.  Required  the  Sliip's  position  at  Noon,  both  by 
Dead  Reckoning  and  Observation,  and  the  bearing  and  Distance  of  the  nearest  Laud. 


H. 
1 

K. 

8 

II.    K. 

CO  U  USES. 

"WINDS. 

L.  W. 

\ 

REilARKS,    WEDNESDAY,  MARCH    16tH,    18.54. 

w.  s.  w. 

N.  W 

i 

P.  M.     Steady  breezes  and  due  pleasant  weather,  all  sail  set,  close 

2 

8 

«i 

t( 

hauled. 

3 

8 

tt 

u 

4 

8 

i( 

tt 

At  4h,  Long,  in  by  Chron.  50°  3'  30"  W.,  and  Magnetic  Vari.  as  per 

6 
6 

7 

7 
7 
7 

1 

it 

(t 
tt 

Azimuth  23°  or  2  points  Westerly. 

1 

(( 

ft 

At  7h,  Barom.  filling  lapidly  to  29°  30',  Lee  clouds  appeared  near. 

8 

3 

South. 

W.  s.  W. 

3 

and  of  a  threatening  appearance.     Took  in  all   the   small  sails, 

9 

3 

•i 

tt 

and  double-reefed  the  top-sails,  reefed  the  coursers  and  stowed 

10 

3 

11 

tt 

the  jib  and  S.  M.  Sail. 

11 

2 

1 

4( 

(t 

4 

Wind  very  unsteady  and  blowing  in  gusts. 

12 

2 

(( 

It 

At  Midnight  came  on   to   blow  excessive  hard,  close-reefed  the  top- 

1 

2 

1 

l( 

\           •» 

sails  and  handed  the  foresail,  vessel  laboring  heavy  and  shipping 

2 
3 
4 

2 

2 
2 

1 

11 

11 

<i 

6 

much  water  on  deck ;  pumps  carefully  attended  to. 

1 

tl 

ft 

At  4  A.  M.     The  wind  flew  round   to  the  N.  W.  in   a  heavy  rain 

5 

4 

w.  s.  w. 

N.  W. 

8 

squall,  and   the  weather  clearing  up,  made  sail 

6 

4 

« 

tt 

At  6h,  shook  out  the  close-reefs  and  set  the  jib 

7 

0 

1 

<t 

tt 

2 

At  7h,  passed  several  fishing  vessels  at  anchor. 

8 

6 

1 

U 

it 

At  8h,  out  double-reefs  and  set  the  topgallant-sails 

9 

7 

W.-iN. 

N.  by  N. 

i 

At  9h,  sounded  in  30  fathoms  on  the  Grand  Bank  of  Newfoundland  ; 

10 

8 

It 

tt 

Long,  in  by  Chron.  49°  68'. 

11 

8 

tt 

U 

Noon,  Foggy  weather.  Sun  obscure. 

12 

8 

Cape  Race,  N.  W.  i  W.  True,  or  N.  N.  W.  i  W.  by  Compass  138  miles. 

Variation  2  points  Westerly.           , 

COURSE. 

BIST.I         N. 

S. 

E. 

w. 

S.  W,  i  W. 

54 

it 

34'  -3 

u 

41'  7 

S  E.  bv  E. 

9 

a 

5    0 

7' .5 

<t 

E.  S.  E. 

7 

2   7 

6    5 

E.  by  S. 

1 

1    4 

6    9 

S.  by  W. 

8 

7    8 

a 

1    6 

S.  S.  W. 

12 

11    1 

4    6 

w.  s.  w. 

81 

11    9 

28     6 

1 

D.  LAT. 

81    6 

20'  -6 

69     1 

Diff.  of  Lf 

it  ma 

ide..     1 

L°  22'  S. 

20     9 

Yesterday's  Lat...      45 


Dep.   48    2  W, 


Lat.  in 44°  28'  N. 

Sum )90^18' 

Mid.  Lat.   ""45 

Gives  D.  Lon.  made 


As  no  Meridian  Alt.  has  been  observed  to-day  the  Lat.  must 
be  found  by  the  reduction  to  the  Meridian  of  the  Alt.  Obs.  near 
Noon,  either  by  the  measured  Interval  of  Time  between  th« 
Observations,  which  is  4h  Im,  as  in  the  2d  Example,  given  at 
page  97,  (this  being  the  same  case  worked  out)  gives  Latitude 
44°  32'  N.,  or  it  may  be  found  by  the  method  given  at  page  94, 
that  is,  of  deducing  the  Time  at  the  Ship  from  the  Greenwich 
Time  by  Chron.,  as  follows  : 

Time  by  Chron 4h  14m  2l8  Sun's  Obs.  Alt.  P.M.  42'  80' 

Chron.  Fast 6     25    Corr.  for  Seuiid.  Ac.  11 

8m  568  True  Altitude ^2°1l' 

3    22    48     Sun's  Dec  Cor.  to  the 

Oh  46m  88    Green.  Date 2 


Green.  T.  by  Chron.  4h 
Long.  50°  42'  in  T.. 


M.T.  at  Ship..., 
Equa.  Sub. 


5' 


9'  &  Dep.  48' 
68'=      1°    8W. 
Lon.  by  Chro.  yesterday  Noon    49    84  W. 

Long,  by  D.  R.  to-day "50°  42' 


T.  Past  Noon. .  ._..37m    28=Log.  7-813  )  -pj^yg  -^^y 

Log.  0.293  y 


Summari/.  Lat.  44^°  N Dec.  2°  S 

Course S.  30°  W, 


Dist 94 

Diff.  Lat...  82      S. 

'T    c-    J  /i    n                                 Departure.  48  W. 

To  Find  the  Course.                        ^J,  j^   ^  ^^  2g,  ^^ 

The  Dif.  Lat.  81    6   and  Dep.  48  2,  gives  L^t.  Obs,. .  44  32    N. 

iilie  Course  made  good  S,   31°   W.,  and  the  Djff  Lono-.  1      8    W. 

Distance  94  miles.                                             Long.  D.  R.  60  42   W. 

Lon.^'byCh.  50  34   W. 

Barom 29  90    Ther.  88° 


8106  Corr 0*  44' 

True  Altitude '^3_^\ 

Meridian  Altitude 43~25'  3 

Zenith   Distance 46°  85'  N. 

Declination 2      6  8. 


Latin  at  37  m  past  Noon 44°  30'  S. 

Go's  <fe  Dis.  since  NaW.S.W.5m  D.L.    2   N. 
Lat  in  at  Noon 44°  82'  If. 


Having  the  Correct  Latitude  at  Noon  we  Proceed  now  to  Find  the  Longitude  in  by  Chronometer. 

The  finst  Altitude  observed  was  taken  about  8h  38m  in  the  Morning,  or  3h  22m  before  Noon,  and  in  thai 
Interval  the  Ship  had  made  a  W.  S.  W.  Coursse  good,  and  Distance  by  Log.  27  miles  ;  this  \riU  give  ths 
Diff,  Latitude  10  and  Departure  25;  the  Diff.  Latitude  10  added  to  the  Latitude  at  Noon,  glve.s  the  Lati- 
tude in  at  time  of  the  first  Altitude  44°  42'  N.  The  Apparent  Time  at  Ship  is  thence  found  .o  be  8h  38ra 
64s,  and  the  Mean  Time  8h  48  Os,  the  Difference  between  which  and  the  Greenwich  Time  by  Chronometei 
12h  7m  56s,  is  3h  19m  56s,  or  Longitude  49°  59'  0"  W.  at  the  time  of  the  Sights.  The  Departure  25  turned 
toto  Longitude  is  35'  0",  which  added  to  it  gives  the  Longitude  in  at  Noon  50°  34'  N. 
The  Longitude  by  D.  R.  is  therefore  in  Error  8'  or  3ia>)  of  Time.  The  Time  past  Noon  being  Cor>^etcd 
J7m  34s,  fie  Correction  for  Altitude  is  45',  and  Lat.  at  Noon  Corrected  is  44*  31'  N. 


188  NAVIGATING  THE  SHIP. 

FINDING  THE  LONGITUDE  FROM  THE  OBSERVED  ALTITUDES  OF  A  BODY  ON  THE  PRIM! 
VERTICAL  AT  EQUAL  DISTANCES  IN  TIME  FROM  THE  MERIDIAN. 

On  leaving  any  known  Longitude  take  an  Altitude  of  the  Sun  on  the  Prime  Vertical,  that  is,  when  h« 
bears  True  East  or  West,  which  can  only  be  in  tht,  6ummer  time.  But  a  Star  can  always  be  found  on  the 
Prime  Vertical  at  any  season  of  the  year.  Note  or  find  the  Apparent  Time  by  Watch  when  the  observation 
was  made,  say  in  the  Morning,  and  find  the  Time  before  Noon,  (which  with  the  Sun  is  his  Hour  Angle,) 
Then  observe  another  Altitude  in  the  Afieruoon,  at  the  same  time  past  Noon  by  the  Watch.  Now,  if  the 
Ship  has  not  moved  to  fhe  Eastward  or  Westward,  that  is,  if  she  has  made  no  Departure  during  th« 
Interval,  the  Sun's  Altitude  will  be  the  same  as  in  the  Morning.  But  if  the  Altitudes  do  not  agree,  then 
the  Difference  is  the  number  of  miles  of  Departure  the  Ship  has  made  to  the  Eastward  or  Westward. 

And  in  Sailing  East  the  P.  M.  Altitude  will  be  the  greatest  because  the  Ship  is  meeting  the  Sun,  and  in 
Sailing  West  the  P,  M.  Altitude  will  be   least  because  she  is  leaving  him.     This  Departure,  so  obtamed 
iurned  into  Longitude  by  a  case  of  Middle  Latitude  Sailing,  furnishes  the  Difference  of  Longitude,  whicn 
applied  to  the  Longitude  left  will  give  the  Longitude  in. 

Or  one  Altitude  can  be  observed  on  the  Morning  or  Evening  of  one  day,  (having  the  Apparent  Time  from 
Noon  of  the  observation),  and  exactly  at  the  same  time  on  the  day  following.  The  Difference  between  the 
Altitudes  so  observed  is  the  Departure  made  good  during  the  24  hours,  which  turned  into  Longitude  and  ap- 
plied to  the  Longitude  left  from  day  to  day,  will  furnish  an  excellent  check  on  Gross  Errors  in  the  Dead 
Beckoning  when  there  is  no  Chronometer  on  board. 

The  daily  Variation  of  the  Equation  of  Time  ought  in  strictness  to  be  Added  to  the  Time  from  Noon  by 
Watch,  at  which  the  last  Altitude  should  be  observed,  when  the  Equation  is  Decreasing,  or  Subtracted 
from  it  when  Increasing ;  but  as  this  quantity  amounts  to  only  a  few  seconds,  it  may  be  neglected. 

In  the  case  of  observing  Stars,  3m  56s  should  be  Subtracted  from  the  Time  from  Noon  by  Watch,  at 
which  the  last  Altitude  should  be  observed,  when  P.  M.,  or  Added  to  it  when  A.  M.,  because  the  Stars  are 
that  much  before  the  Apparent  Time  by  the  Sun  every  day, 

EXAMPLE  1. 

Jul  e  10th,  1854.  A  Ship  in  Latitude  40*  0'  N,,  and  Loogitude  45°  0'  W.,  at  8h  2rQ  A.  M.  observed  the  Sum 
Altiti  de  to  be  37°  24',  and  then  Sailed  to  the  "Westward,  until  3h  58m  P,  M.  by  the  same  Watch,  when  the  Sun's 
Alt  \t  %8  Oba.  to  be  3fi°  9',     Required  the  Dep.  made,  the  Diffi  of  Long,  and  the  Long,  in  at  the  Time  of  the  last  Alt 

At  8b  2m  A,  M. Observed  Altitude.. 37°  24'  Departure  75m  -with  Latitude  40°  =  D,  Long )98 

At  8h  58m  P.  M.  Observed  Altitude _36^ 9_  Difference  of  Longitude  made 1°  38' 

1°  15'  Longitude  Left 45 0_ 

^0  Longitude  in 46°  38' 

Departure  made  good .,, .  75  j  at  8h  68m  P.  M. 

EXAMPLE  2.  ^ 

March  SGth,  1854.  A  Ship  took  her  Departure  from  Latitude  40°  43'  N.  and  Longitude  74*  W,,  at  5b  43m  P.  M, 
irhen  the  Sun's  Altitude  was  observed  to  be  6°  6',  and  then  having  Sailed  to  the  Eastward  about  265  miles,  until  tb« 
next  Evening  at  5h  42m  bv  the  same  "Watch,  when  the  Sun's  observed  Altitude  was  10°  16'.  Required  the  Depar- 
ture made,  the  DifFereuce  of  Longitude,  and  the  Longitude  in. 

a  irch  80th,  at  5h  42m  P.  M.  Observed  Altitude .     6°    6'  Departure  250,  Latitude  41°  =  D.  Long )332  _ 

do.    Slst,  at  5h  42m  P,  M.  Observed  Altitude.  10    16    Difference  of  Longitude  made 6°  32' 

4°  10'  Longitude  Left 74     0 

6Q  Longitude  in..,  68°  28' 

Departure  made ....  250 

EXAMPLE  3. 
By  the  Stam. 

April  llth,  1854,  A  Ship  in  Latitude  30°  0'  N.  and  Longitude  65°  O'  "W.,  at  7h  8m  P.  M. observed  the  Altitude  of 
Aldebai<in  to  bj  33°  24'  bearing  True  West.  She  then  Sailed  to  tbe  "Westward  about  196  miles  until  the  following 
Evening  at  7h  tm  48  by  the  same  Watch,  when  the  Star's  Altitude  was  observed  to  be  30°  4'.  Required  tbe  De- 
pfirture  made.  Difference  of  Longitude,  and  Longitude  iu. 

As  tne  Star  is  in  advance  of  App.  T.  3m  56s  it  must  be  Sub.  from  the  Time  by  "Watch  on  the  following  Evening 
April  llth,  at  7h  8m  P,  M.  Star's  Obs.  Altitude. .   33°  24'  Departure  200,  Latitude  8U°  0'  N.,  Diff  of  Loug.  )231 

.io     12th,  at  7h  4m  48  P.  M.  Star's  Obs.  Alt. . . .  ^0 4_  Difference  of  Longitude 3°  61'  "W. 

3°  20'  Longitude  Left 65     0    "W. 

60  Longitude  in 68°  5i'~W 

Departure  made. . . .  200 

NAVIGATING   THE   SHIP. 

in  the  preceding  Days'  works  are  given  the  usual  modes  of  finding  the  Ship's  position  at  Noon  by  the 
L»ead  Reckoning,  and  also  the  Latitude  in  at  or  near  to  Noon  by  tlie  Sun's  Altitude,  and  the  Longitude  by 
Chronometer,  and  providing  the  Chronometer  kept  a  steady  rate,  and  that  those  observations  could  be  ob- 
tained every  day,  nothing  more  would  be  required. 

But  as  the  Sun  is  sometimes  invisible  for  several  days  together  it  is  evident  that  the  Dead  Reckoning  may 
become  very  erroneous  during  that  interval,  and  it  becomes  necessary  as  a  measure  of  precaution  wlien  the 
weather  is  clear  at  Twilight  to  observe  Altitudes  of  the  Planets  or  Stars,  for  at  any  time  during  a  cleai 
night,  Stars  may  be  observed  North  and  South,  on  or  near  the  Meridian,  (see  page  110,)  or  tlie  Moon  eithei 
by  Day  or  Night.  (See  pages  101  and  148.)  The  Latitude  by  observation  and  the  Longitude  by  Cluono 
meter,  (or  by  Lunar  observations,)  may  thence  be  obtained  bv  any  of  these  bodies  in  many  cases  us  cor» 
r«ctly  as  by  the  Sun's  Altitude. 


NAVIGATING  THE  SHIP.  189 

The  Longitude  by  Chronometer  may  also  be  obtained  at  Sunrise  or  Sunset,  (see  page  146.)  or  at  Noon 
from  equ^l  Altitudes  of  the  Sun.    (See  page  147.)     In  the  latter  method  no  Logs,  are  required,  and  will  be 
found  useful  in  delecting  any  gross  Error  committed  in  working  out  the  Time  in  the  usual   manner,  but  is 
best  adapted  for  low  La.titudes.     (See  Remarks,  page  130.) 

When  the  Sun  is  seen  through  watery  clouds,  and  his  Limbs  not  visible,  a  tolerable  observation  for 
Latitude  may  be  obtained  by  observing  his  centre,  (see  Diagram,  page  68,  No.  3,  and  an  Example  of  find- 
ing the  Latitude  by  this  method  at  page  89.) 

An  Altitude  of  any  of  the  heavenly  bodies  having  been  obtained  near  the  Meridian,  the  Latitude  in 
be  found  by  the  Rules  given  in  the  body  of  this  work,  and  although  it  may  probably  be  a  little  in  error 
the  Time  be  not  exactly  known,  it  is  greatly  more  to  be  depended  upon  than  the  Latitude  by  Dead  Recko 
mg,  however  carefully  it  may  have  been  kept. 

An  Error  of  1  point  in  a  Ship's  Course  produces  an  Errpr  in  the  Dead  Reckoning  of  about  20  miles  for 
every  100  miles  run,  whether  produced  by  Local  Attraction,  bad  Steerage,  or  a  Current,  and  it  is  evident  that 
in  Ships  of  the  present  day,  many  of  which  are  constructed  to  sail  twice  as  fast  as  the  old  ones,  that  an 
Error  in  their  Course  steered  will  produce  twice  the  Error  in  their  Dead  Reckoning  in  one  day's  run,  than 
would  be  the  case  in  a  slower  sailing  vessel ;  and  in  that  case  it  would  require  greater  vigilance  on  the  part 
of  the  commander  of  those  vessels  to  ascertain  their  True  Position  as  often  as  possible  both  by  day  and 
eight,  especially  in  the  vicinity  of  Land  or  a  danger.     The  following  remarks  may  be  found  useful. 

On   Commencing  the  Voyage,  ^c. 

The  first  and  most  important  matter  is  to  examine  the  Binnacle  and  to  see  that  no  foreign  articles   sue' 
as  iron,  are  deposited  therein,  and  whether   the   steerage  Compass  is  free  from  local  attraction,  (by  the  Rulck 
given  at  page  120.)     At  the  time  of  taking  a  Departure  from  the  Land,  if  possible,  a  set  of  Altitudes  of 
the  Sun  should  be  taken  for  Chronometer  to  find  its  Error  on  Greenwich   Mean  Time,  (see  page  155  )  and 
always  to  use  the  same  Sextant  in  observing  Altitudes  for  rating  the  Chronometer. 

It  is  the  common  practice  at  Sea  to  observe  a  set  of  Altitudes  of  the  Sun  at  about  8  or  o  o'clock  in  the 
Mcrning.  ami  to  make  all  the  necessary  corrections  ready  for  use,  as  at  page  140,  and  as  soon  as  the  Latitude 
is  observed  at  Noon,  the  Latitude  in  at  the  time  of  the  Sights  can  be  deduced,  and  thence  the  Longitude  by 
Chronometer.  Or  the  Sights  can  be  worked  out  at  once,  using  the  Latitude  by  Dead  Reckoning  from  the 
preceding  Noon ;  then  if  it  appears  there  is  an  Error  in  the  Latitude  by  Dead  Reckoning,  the  Longitude  by 
Chronometer  thus  found  may  be  corrected  by  Table  XXX,  (see  pages  144  and  145,)  which  saves  the  labor 
and  time  of  working  it  over  again.  In  either  case  tiie  Longitude  in  by  Chronometer  at  the  time  of  the 
Sights  is  brought  up  to  Noon  by  the  Dead  Reckoning,  and  as  before  observed,  if  this  could  be  done  dail 
nothing  more  would  be  required  for  the  safe  navigation  of  a  Ship  on  the  open  Sea,  or  in  the  fine  seren 
weather  in  the  Tropics  ;  but  when  a  Ship  is  approaching  Land,  or  in  high  Latitudes,  where  uncertaii. 
weather  prevails,  the  heavenly  bodies  are  frequently  obscured  for  several  days  together,  it  is  necessary  t« 
take  an  Altitude  of  the  first  object  that  becomes  visible,  and  to  note  the  time  by  Chronometer  •  if'^  bearing 
is  near  the  True  North  or  South  the  Latitude  may  at  once  be  found,  (by  any  of  the  Rules  which  are  appro- 
priated to  the  Object  observed,  and  will  be  found  in  the  body  of  this  work,)  and  if  the  Altitude  of  another 
Object  can  be  obtained  at  a  sufficient  Distance  East  or  West  of  the  Meridian,  the  Longitude  by  Chrono- 
meter may  be  found.  If  the  object  be  a  Star  and  not  known,  see  the  method  of  finding  the  Stars  at  page 
136,  or  a  Planet,  at  page  134,  and  as  before  observed,  Twilight  is  the  proper  time  to  observe  Altitudes  of 
the  Stars.  An  Altitude  of  the  Sun  or  Moon  also,  taken  at  any  time  they  are  visible,  and  the  time  noted 
by  the  Chronometer,  is  an  observation  of  great  importance  to  a  Ship  in  the  vicinity  of  the  Land,  and  by 
which  either  the  Latitude  or  the  Longitude  may  be  obtained,  many  Examples  of  which  will  be  found  in 
this  work,  or  the  Ship's  postion  may  be  determined  by  Sumner's  Method,  an  Example  of  which  is  given  at 
page  152;  but  as  some  of  the  Altitudes  may  have  been  observed  in  stormy  weather,  when  the  horizon  was 
ill  defined,  and  used  only  because  no  better  coUld  be  obtained,  the  Navigator  will  place  that  degree  of 
dependence  in  the  result  which  the  circumstances  of  the  case  would  seem  to  warrant,  and  if  doubtful  they 
may  be  confirmed  or  rejected,  as  the  case  may  be,  by  another  observation  made  under  more  favorable  cir- 
cumstances, or  as  in  the  case  of  finding  the  Latitude  by  the  Stars  N.  and  S.  and  taking  the  Mean  of  the 
two  Latitudes.  The  Longitude  by  Chronometer  may  also  be  found  by  the  Altitudes  of  Stars  E.  and  W., 
and  the  Mean  of  the  two  Longitudes  taken  as  the  true  one. 

When  Altitudes  of  the  Sun  have  been  taken  in  the  Forenoon,  as  a  reserve  in  case  of  losing  the  Meridian 
Altitude,  that  one  should  be  used  which  is  the  nearest  to  the  Meridian  to  find  the  Latitude  by.  and  the  one 
farthest  from  the  Meridian  to  find  the  Longitude  by  Chronometer.  And  when  the  Meridian  Altitude  of  the 
Sun  has  been  observed  the  Latitude  is  usually  deduced  therefrom  in  preference  to  all  the  other  observationi 
for  Latitude 

When  a  Departure  is  taken  fro^  the  Land,  the  Course  is  shaped  on  the  Chart  by  the  Rules  given  at  pase 
48,  and  which  is  the  True  Course.  The  Variation  of  the  Compass  being  then  allowed  for  as  directed  will 
give  the  Compass  Course  required  to  steer ;  the  amount  of  this  Variation  is  generally  given  on  all  Charts,  but 
it  should  be  verified  by  observing  the  Variation  with  the  Ship's  head  in  different  directions.     (Seepage  120.^ 

Verifying  the  Chronometer. 

When  the  Ship  is  [lassing  near  any  Island  or  Headland,  the  position  of  which  is  well  known  by  Sight- 
ing It  and  bringing  it  to  bear  true  North  or  South  at  the  time  of  taking  a  set  of  Altitudes,  the  Sea  Erroi 
and  Rate  of  the  Chronometer  may  be  found.  See  the  method  of  rating  Chronometer  at  Sea.  (page  155^} 
and  Remarks  on  Chronometer  (at  page  79.) 

But  if  no  land  has  been  seen  for  many  days  it  may  be  verified  within   certain  limits   by  Lunar  obseiva 
UoM  taken  East  and  West  of  the  Moon,  and  using  the  Mean  of  the  two  Longitudes  so  found.     'Sw  page  1  (  fc^ 


190  NAVIGATING  TtjiL  SHIP 

Indications  of  Stormy  Weather. 

The  height  of  the  Barometer  should  be  frequently  noted  when  on  the  Southern  limits  of  the  S  L    Trade 
Wind,  or  on  the  Northern   limits  of  the  N.  E.  Trade,  or  in  high   Latitudes,  where  stormy  weather  may 
expected.     See  Remarks  on  Hurricanes,  (page  41,)  and   the  uses  of  the   Barometer  and  Thermometer 
^ages  82  and  83.) 

Falling  in  with  Icebergs. 

An  Iceberg  should  always  be  passed  to  Windward,  if  possible,  in  the  night  time,  because  of  the  loose 
agments  which  drift  faster  than  the   body  of  the   berg,  and  stream  out  to  leeward  of  it,  and  which  may 
•eriously  injure  a  vessel, 

Discovery  of  a  Danger. 

When  a  Ship  is  going  free  and  suddenly  discovers  she  is  runnmg  into  danger,  the  best  means  of  avoiding 
it  is  to  haul  to  the  wind  on  that  tack  on  which  she  will  most  rapidly  increase  her  distance  from  it ;  by 
doing  so  she  will  gain  time  in  order  to  prepare  for  Tacking  Ship.  If  the  water  should  continue  to  shoal, 
and  if  in  the  night  time,  the  proper  way  to  extricate  herself  would  be  to  steer  out  on  the  opposite  course  to 
which  she  was  steering  on  its  discovery  ;  but  if  that  cannot  be  done  on  account  of  the  wind,  to  work  to  Wmd- 
ward  so  as  to  make  that  Course  good. 

If  the  danger  is  a  new  discovery,  its  position  should  be  ascertained  by  a  set  of  observations  taken  as  soon 
as  possible  afterwards,  and  its  place  deduced  from  the  place  of  the  Ship  by  Cross  Bearings,  or  by  two  Bear- 
ings and  the  Distance  sailed  between  them,  by  the  Rules  given  (at  page  32.)  Soundings  should  also  be 
taken,  and  the  quality  of  the  ground  2Lscertained,  which,  with  the  particulars,  must  be  entered  in  the  Ship's 

Log-Book. 

While  it  is  necessary  to  be  on  the  look  out  for  Coral  Reefs  and  other  dangers  which  may  grow  up,  or  be 
thrown  up  by  Seaquakes,  where  none  formerly  existed,  it  is  no  less  so  to  guard  against  false  alarms,  for  it 
is  easy  to  imagine  you  see  breakers  when  on  the  look  out  for  them.  For  instance,  in  Moonlight  nights,  when 
the  clouds  are  flying,  a  stray  moonbeam  falling  on  the  crest  of  a  broken  wave,  has  really  all  the  appear- 
ance of  a  breaker  ;  but  if  the  bearing  of  it  be  taken  it  will  be  found  not  to  appear  again  in  the  same  place 
Clouds  and  Fog-banks  on  the  horizon  often  resemble  land,  though  the  experienced  eye  of  the  Seaman  can 
usually  tell  the  difference.  Whales  and  other  large  animals  are  frequently  seen  asleep  on  the  surface  of 
the  ocean  and  mistaken  for  rocks  ;  and  in  some  parts  of  the  ocean  the  surface  is  covered  with  a  kind  of  fish- 
spawn  of  yellowish-grey  color,  which  at  a  distance  looks  like  a  sand-bank.  On  the  Coast  of  Africa,  also, 
about  the  Meridian  of  Greenwich,  a  very  alarming  appearance  of  breakers  is  caused  by  a  multitude  of 
Phosphorus  Fish,  and  the  Ship  seems  to  be  approaching  a  Sea  of  fire,  ajjd  so  great  is  the  light  from  this 
eause  that  a  book  may  be  read  on  deck  in  the  darkest  night. 

RULES  TO  PREVENT  COLLISION  ON  SHIPS  MEETING  AT  SEA. 

Two  Ships  approaching  each  other  on  opposite  tacks,  close-hauled,  and  it  is  doubtful  which  will  weather 
the  other,  the  Rule  is  that  the  one  on  the  Starboard  Tack  keep  her  reach,  while  the  one  on  the  Pork  Tack 
must  bear  up  and  go\  under  the  stern  of  the  other;  but  if  through  ignorance  or  stupidity  the  one  on  the  Port 
Tack  continues  to  keep  her  reach,  and  a  collision  is  unavoidable,  then  both  vessels  should  instantly  put  theii 
helms  a-lee,  by  which  means  they  will  be  thrown  in  Stays,  and  the  shock  of  collision,  if  it  should  take 
place,  will  be  very  much  lessened.  ¥ 

Two  Ships  meeting  each  other  right  ahead,  and  steering  opposite  courses,  both  having  the  wind  free,  the 
rule  is  that  both  vessels  Port  their  helms  so  as  to  pass  each  other  on  the  Port  side,  or  if  one  of  them  should 
be  close-hauled,  then  it  is  the  duty  of  the  other,  which  is  going   free,  to  give  way  and  pass  under  her  stern. 

This  rule  should  not  be  too  hastily  adopted  in  the  night  time,  when  a  vessel  or  her  light  is  suddenly  seen 
near  to  on  the  Starboard  bow,  because,  in  this  case,  were  each  to  Port  their  helms  they  would  run  on  board 
of  each  other. 

This  rule  is  therefore  only  applicable  when  vessels  meet  each  other  right  ahead  or  a  little  on  the  Port  bow 
and  steam  vessels,  which  are  always  supposed  to  be  under  the  command  of  their   helms,  are  deemed  to  be 
^ssels  going  free. 

The  commanders  of  steam  vessels  say  that  if  sailing  vessels  would  keep  their  proper  course  on  the  ap- 
proach  of  a  steamer  towards  them,  the  officer  in  charge  of  those  vessels  would  then  see  exactly  the  state  of 
the  case  and  steer  so  as  to  clear  the  sailing  vessel,  and  thereby  prevent  collision  ;  but  it  frequently  happens 
that  those  on  board  the  sailing  vessel  become  alarmed  and  keep  changing  their  course  without  any  fixed 
principle,  and  thereby  mutually  deceiving  each  other  as  to  their  intentions. 

Ships  meeting  each  other  at  sea  in  a  dark,  stormy  night,  or  in  foggy  weather,  the  utmost  vigilance  and 
presei^je  of  mind  on  the  part  of  the  officer  of  the  watch  is  required  to  prevent  collision,  many  melancholy 
instances  of  which  frequently  take  place. 

On  a  vessel  or  her  light  being  reported  as  seen  ahead,  or  on  either  bow,  the  officer  of  the  watch  should 
immediately  ascertain  in  which  direction  the  other  vessel  is  steering  ;  if  that  cannot  be  done  on  account  of 
the  darkness  of  the  night,  take  her  bearing  by  the  Compass  ;  then  her  change  of  bearing  in  a  short  time 
will  point  out  the  direction  in  wliich  she  is  steering,  but  if  the  bearing  does  not  seem  to  change  the  vessel 
must  either  be  coming  directly  towards  you  or  you  are  coming  up  with  her.  If  you  are,  a  running  Ship, 
and  the  vessel  ahead  about  to  cross  your  bow,  if  there  is  a  doubt  of  her  doing  so  in  time,  it  is  your  duty  to 
bear  up  and  pass  astern  of  her.  ' 

In  the  case  of  the  vessel  coming  towards  you,  if  she  is  on  the  Starboard  bow  and  too  near,  Starboard 
your  heim  ;  but  if  seen  right  ahead  or  a  little  on  the  Port  bow.  Port  your  helm  ;  and  were  each  to  obey 
this  rule  a  collision  would  be  impossible.  It  is  only  when  the  one  Starboards  and  the  other  Ports  her  helm 
at  the  same  time  that  such  takes  place.  The  intention  of  one  vessel  should  be  made  manifest  to  the  other  by 
a  broad  sheer  in  the  direction  in  which  she  intends  to  pass ;  this  will  save  some  anxiety  of  mind  on  the  subieot 


I 


inAVIGATING  the  SHiP.  191 

All  vessels  in  foggy  weather  should  sound  an  alarm  either  by  bell,  gong,  or  steam-whistle,  at  intervals  of 
two  01  three  minutes,  and  that  the  alarm  should  be  promptly  responded  to  by  ail  vessels  withing  hearing 
distance.  If  the  sound  of  the  alarm  be  heard  on  the  Starboard  bow  both  vessels  should  instantly  Starboard 
their  helms.  But  if  it  is  heard  from  right  ahead  or  on  the  Port  bow,  both  vessels  should  in.stantiy  Port 
»neir  helms,  and  by  doing  so  a  collision  would  be  impossible.  Slacking  a  vessel's  speed  will  not  always 
prevent  collision  ;  the  only  remedy  is  the  helm,  and  the  promptness  with  which  it  is  turned  in  the  same 
direction  as  above  by  both  vessels.  But  to  make  this  effectual  we  must  have  a  universal  Law,  to  be 
adopted  by  Ships  of  all  nations. 

Error  in  the  Course  of  a  Scudding  Ship. 

When  the  Ship  is  scudding  in  a  Gale  and  a  high  Sea  running,  with  the  wind  on  the  quarter,  she  is  gene- 
rally found  to  have  been  runoff  to  the  leeward  of  the  course  intended  to  have  been  steered.  This  is  some- 
times unavoidable  to  prevent  the  sea  falling  on  board,  but;  more  frequently  caused  by  bad  steerage,  thai  is, 
by  the  helmsman  hanging  on  his  weather  helm  when  the  Ship  is  on  the  top  of  a  Sea,  in  the  room  of  easing 
it,  as  he  ought  to  do,  the  consequence  of  which  is,  that  the  Ship  is  yawed  off  nearly  before  the  wind,  and 
r^uns  for  some  time  so  before  she  can  be  brought  up  to  her  course  again.  In  this  case  the  officer  of  the 
Watch  should  mark  on  the  Log-Board  th*^  course  the  vessel  is  supposed  to  have  made  good  by  Compass  ; 
this  will  seldom  amount  to  more  than  .^e  point  to  leeward  of  the  given  course,  unless  the  vessel  has  been 
wretchedly  steered,  because  we  ma}  suppose  she  has  been  kept  some  part  of  the  time  at  or  even  to  wind- 
ward of  the  given  course.  When  the  vessel  is  running  in  a  narrow  channel  or  in  the  vicinity  of  a  danger, 
it  becomes  of  the  utmost  importance  that  this  yawing  off  should  be  guarded  against,  by  steering  a  point,  or 
whatever  allowance  may  be  deemed  sufficient,  to  windward  of  the  given  course,  or  by  yawing  her  to  wind 
ward  as  much  as  she  has  been  run  off,  so  as  to  make  the  course  good.  This  yawing  of  the  vessel  about 
necessarily  cuts  off  a  considerable  portion  of  the  Distance  she  would  have  run  on  a  straight  course,  hence  an 
allowance  of  about  1  mile  in  10  is  deducted  from  the  Distance  run  by  Log.,  and  as  before  observed,  an 
Error  of  1  point  in  the  Course  steered  will  produce  an  Error  in  this  case  of  20  miles  for  every  hundred 
miles  of  distance  run,  which  the  Ship  will  be  to  leeward  of  her  course. 

The  Proper  Tack  to  Lay  To  On. 

In  the  Remarks  on  Hurricanes,  at  pages  42  and  43,  rules  are  given  for  Laying  To  on  the  Proper  Tack 
in  those  cases ;  but  as  the  Storms  in  Higher  Latitudes  revolve  in  a  contrary  direction  to  what  the  regular- 
built  Hurricanes  do — for  instance,  in  the  North  Atlantic  Ocean  they  commence  generally  at  S.  E.  or 
South,  with  rain,  and  veer  gradually  round  by  the  West  to  N.  W.  and  North  when  the  rain  ceases,  but 
the  most  danger  is  to  be  apprehended  from  a  sudden  shift,  which  frequently  takes  place  after  a  heavy  fall 
of  rain  from  S.  W.  to  N.  W. ;  in  that  case  it  is  evident  that  the  Starboard  Tack  is  the  proper  one  to  be  on. 
In  a  high  South  Latitude,  in  the  South  Atlantic  Ocean,  Storms  commence  at  N.  E.  and  North,  with  rain, 
as  in  the  former  case,  and  veer  round  by  the  West  to  S.  W.  and  South  when  the  rain  ceases :  sudden 
changes  take  place  in  the  same  manner  from  N.  W.  to  S.  W.  The  Port  Tack  is  therefore  the  proper  one  to 
Lay  To  on  in  the  latter  case.     (See  the  Acting  of  the  Barometer  in  these  cases,  at  page  83.) 

Laying  To  under  a  Drag. 

When  a  Ship  has  the  misfortune  to  be  dismasted,  and  totally  unmanageable,  an  endeavor  should  be 
made  to  keep  her  Head  to  the  Sea.  This  can  be  effected  (circumstances  permitting)  by  constructing  a 
•^rag,  as  follows  : — 

Lay  across  the  Gunwale  any  useless  spars  and   lumber,  so  that  after  being  lashed  together  they  mav 

^e  easily  launched  overboard,  to  which  attach  as  much  of  the  wreck   and  heavy  articles  as  possible,  so  as 

■,  sink  the  spars  and  lumber  square  with  the  surface:  to  each  end  of  the  spars  attach  the  ends  of  a  piec« 

.  chain  or  rope  in  the  form  of  a  span  or  bridle  ;  now  pass  the  end  of  a  hawser  or  stream-chain  out  through 

-  jB  hawse-holes,  and  bend  it  on  to  the  middle  of  the  span,  and  launch  the  whole  concern  overboard,  and  it 

will  be  found  that  the  Ship  will  ride  by  this  Drag  nearly  head  on  to  the  Sea,  because  by  the  wind  acting  on 

the  hull  of  the  vessel,  she  will  drift  faster  than  the  Drag  will  allow  her,  consequently  her  head  is  kept  up 

to  the  Wind  and  Sea.     In  the  meantime  the  crew  will  be  enabled  to  work  more  easily  in  the  fixing  up  ana 

rigging  Jury-Masts,  in  consequence  of  the  vessel  having  now  less  rolling  motion. 

To  Construct  a  Temporary  Rudder  at  Sea. 

When  a  Ship  has  lost  her  Rudder  at  Sea,  a  temporary  one  may  be  made  out  of  a  thick  spar,  shaped  into 
a  Rudder-stock,  and  if  it  is  made  several  feet  shorter  than  the  old  one,  it  can  be  better  secured  below 
water.  Make  the  Rudder  with  what  materials  are  at  hand,  and  if  the  upper  part  of  the  old  stock  hat 
oeen  saved,  transfer  the  pintles.  &c.,  to  the  new  one,  placing  the  pintles  at  the  same  distance  as  before, 
and  prepare  the  Rudder-head  for  receiving  the  tiller  as  soon  as  it  is  shipped.  Now  take  a  piece  of  chain, 
of  a  sufficient  length  for  guys,  middle  i'  exactly,  and  mark  both  parts  of  it  at  intervals  with  exactly 
corresponding  marks,  take  a  round  turn  with  the  middle  of  this  chain  round  the  foot  of  the  Rudder-stock, 
and  cross  the  guy  on  the  fore  part  of  the  Rudder,  and  secure  it  fro'ii  slipping  off. 

Then,  when  the  guy-lines,  and  the  purchase  for  shipping  it,  are  all  prepared,  launch  it  overboard,  enter 
the  head  of  the  Rudder  in  the  trunk,  the  guys  having  been  previously  passed  round,  one  on  each  quarter 
(taking  care  that  the  crossing  has  been  retained,)  and  passed  forward,  are  hauled  taught  abreast  of  the 
main  rigging,  and  the  corresponding  marks  on  the  chain  are  then  placed  at  an  equal  distance  frcm  the  rails 
on  each  side.  After  the  pintles  of  the  rudder  are  shipped,  then  clap  tackles  on  the  guys  and  haul  thera 
laoght,  which  will  bind  the  lower  part  of  the  Rudder  to  the  Ship's  stern-post,  and  at  the  same  time  allow 
I*  to  EUJt  freely. 


192  -lAVIGATING  THE  SHIP. 

The  guys  should  be  elected  to  the  Ship's  side  on  the  first  calm  day,  to  prevent  them  chafing  about  u  tka 
trash  of  the  Sea. 

The  reason  why  the  Rudder  is  not  required  the  whole  length  is,  that  the  lower  part  of  it,  is  of  no  use  to 
Jhe  Ship  for  steering  purposes,  and  it  is  only  the  upper  part  of  it  that  is  'acted  upon  by  the  water,  and 
which  lias  been  proved  in  cases  where  a  Ship,  having  had  the  lower  part  of  her  Rudder  broken  ofi"  at  the 
lower  gudgeon,  has  been  steered  as  well  as  if  nothing  had  been  amiss  with  it. 

This  can  be  easily  accounted  for,  when  we  consider  the  immense  pressure  of  the  Ship  on  the  water,  and 
that  as  she  advances,  this  water,  being  set  free  from  under  her,  rushes  up  her  run  at  an  angle  of  about  45°, 
and  must  necessarily  strike  the  upper  part  of  her  rudder  with  a  force  greater  than  the  actual  velocity  ' 
which  she  is  going  through  the  water. 

Making  the  Land. 

This  is  generally  a  time  of  much  anxiety,  especially  in  tempestuous  weather,  when  no  observations  have 
been  recently  obtained,  because  of  the  uncertainty  in  the  Reckoning,  in  consequence  of  the  Ship  having 
been  probably  under  the  influence  of  Currents  which  generally  prevail  near  the  land,  and  great  caution  is 
.heieiore  required  in  approaching  it.  When  Soundings  can  be  obtained  they  should  never  be  neglected. 
(See  Remarks  on  Sounding,  at  page  52.) 

When  the  Reckoning  is  doubtful,  the  usual  practice  is  to  get  into  the  parallel  of  Latitude  of  the  place 
the  Ship  intends  to  make,  and  then  steer  true  East  or  West,  as  the  case  may  be,  proceeding  cautiously  uiilil 
tlie  land  is  seen,  but  care  must  be  taken  that  the  Ship  is  not  too  far  ahead  of  her  reckoning  before  falling 
into  its  parallel ;  as  in  tlie  case  of  making  an  island,  for  instance,  laying  West  of  the  ship,  she  must  be 
sure  that  she  is  to  the  Eastward  of  it  before  falling  into  its  parallel.  It  is  therefore  safest,  if  there  is  no 
Chronometer  on  board,  to  keep  well  to  the  Eastward  before  failing  into  its  parallel,  and  then  to  steer  dut 
W^est.     She  will  make  it  ahead. 

When  a  Ship  is  bound  to  a  Port  on  a  Coast  which  trends  North  and  South,  the  Land  should  be  made  at 
some  point  to  windward  of  it,  and  which  has  a  high  and  bold  shore;  thou  by  running  down  the  Coast  the 
Latitude  by  Observation  will  point  out  her  Port  of  Destination. 

When  Observations  for  Latitude  and  the  Chronometer  can  be  depended  on,  they  should  be  continued  up 
to  the  latest  period  at  which  the  land  is  expected  to  be  seen,  because  of  the  currents  or  tides  near  the  land, 
and  which  affect  the  Ship's  Landfall.  The  Observations  should  be  verified  by  sounding  at  least  once,  even 
when  the  weather  is  clear,  and  compared  witJi  that  laid  down  on  the  large  Chart  of  the  Coast,  at  or  near 
to  the  Ship's  Position  by  Observation,  the  bearing  and  distance  of  any  part  of  the  Coast  can  then  be 
ascertained,  and  a  Course  shaped  accordingly.  It  is  usual  to  make  some  prominent  headland  or  lighthouse 
in  the  daytime,  or  some  well  known  light  by  night.  If  the  Navigator  is  a  stranger  to  the  Coast,  he  will 
naturally  consult  the  Sailing  Directions,  so  as  to  form  some  idea  beforehand  of  its  appearance,  or  the 
character  of  the  lights  he  may  expect  to  see,  so  that  when  the  Land  is  seen  he  may  compare  it  with  the 
description  given  of  it,  and  also  its  outline  on  the  Chart.  But  to  remove  all  doubt  the  Bearing  of  three 
Objects  on  Shore  should  be  taken,  and  a  cast  of  the  Lead  ;  then  if  those  Bearings  laid  off  on  the  Chart 
meet  at  a  point  as  a  common  centre,  and  the  Soundings  also  agree,  there  can  be  no  farther  doubt  but  that 
the  Landtall  is  correct.  This  sometimes  is  a  matter  of  much  importance  to  a  stranger  in  making  the 
Land,  because  by  mistaking  the  Land  or  a  Light  for  some  other  on  the  same  Coast,  fatal  errors  have  been 
otten  commuted.  It  is  therefore  prudent  to  test  it  as  above  mentioned,  before  shaping  a  Course  to  any  other 
part  of  the  Coast. 

A  Sliip  on  approaching  a  Coast  in  thick  bfowing  weather,  where  shoals  lay  off  some  distance,  would 
naturally  keep  sounding  as  she  stood  in,  but  by  mistaking  the  Soundings  so  obtained  for  those  outside  of 
the  Slioals  when  they  were  in  fact  those  near  the  Beach,  and  in  standing  off  has  run  aground  on  the  inside 
of  the  Shoals.  This  is  of  frequent  occurrence,  and  caused  by  an  error  in  the  Reckoning  ;  and  the  only 
remedy  to  guard  against  such  an  accident  is  to  keep  the  Lead  going  until  the  Ship  has  made  an  offing  equal 
to  the  Distance  at  whicli  the  Shoals  lay  off  from  the  Shore. 

When  a  Ship  is  caught  by  thick  weather  in  a  narrow  channel,  between  Shoals,  and  it  is  not  considered 
prudent  to  anchor,  she  is  put  under  easy  sail,  and  tacked  or  wore  round  every  hour  or  half  hour,  as  the 
circumstances  of  the  case  require,  until  the  weather  clears  up,  and  she  can  extricate  herself. 

Signs  of  Land. 

There  are  some  Signs  whereby  it  may  be  known  when  a  Ship  is  approaching  Land — the  most  infallible 
is  that  of  the  change  in  the  color  of  the  Sea  from  a  deep  blue  to  a  pea  green,  (a  sure  indication  of  being  on 
Soundings,)  and  from  that  to  a  muddy  color  as  she  approaches  the  Coast,  where  tree-roots  and  other  drift- 
wood may  be  met  with  floating  about,  and  the  coasting  and  fishing  vessels  of  tlie  country.  The  Bearing  of 
the  Land  may  also  be  known  from  the  direction  in  which  a  flock  of  Sea-birda  are  seen  flying  at  Sunset. 
Ducks,  and  other  kinds  of  diving-birds,  which  do  not  fly  far,  are  a  sign  of  being  near  the  land. 

Land  is  seen  at  the  greatest  distance  off  at  Sunrise  or  Sunset,  before  the  vapors  begin  to  collect  around 
;t,  iu  the  for.m  of  clouds,  which  frequently  hide  it  from  view  in  the  daytime.  Tl  is  is  called  by  seamen  the 
Leoir  if  the  Land. 


1  ;>;-5 


METHOD  OF  KEEPING  THE  LOG-BOOK. 


The  Log-Book  is  an  official  Journal  or  Record  of  all  the  transactions  which  occur  during  the  T?oyage  of  • 
Ship,  from  the  time  of  her  sailing  from  a  port  in  the  country  to  wliich  she  belongs,  until  her  returu  lo  • 
aome  port  again,  and  her  cargo  discharged ;  although  it  is  usual  to  consider  the  voyage  at  an  end  when  she 
u  safely  moored  in  that  port,  so  far  as  regards  the  engagements  with  seamen. 

It  should,  therefore,  contain  a  true  and  faithful  account  of  all  matters  connected  with  the  duty  of  the  Ship, 
of  daily  occurrence,  both  at  Sea  and  in  port.  Accidents,  or  loss  in  the  Ship's  material  sustained,  and  also 
the  misconduct  of  either  the  crew  or  officers,  should  all  be  entered  distinctly,  and  in  as  few  words  as 
possible. 

While  the  Ship  is  in  port,  the  Harbor  Log,  as  it  is  called,  is  kept  in  the  common,  or  Civil  Time  at  the 
place,  the  Day  beginning  at  midnight  and  ending  at  midnight.  It  contains  an  account  of  the  wind  and 
weather,  the  number  of  packages  received  or  discharged,  as  per  Cargo  Book,  the  quantity  of  stores  received 
on  board  or  discharged,  the  number  of  hired  laborers  employed,  and  the  general  employment  of  the  crew 
and  when  leave  is  granted  to  a  portion  of  them  to  go  on  shore,  to  return  again  at  a  stated  time,  if  they  do 
not  so  return,  the  fact  should  be  entered  in  the  Log-Book,  and  the  length  of  time  they  were  absent  without 
leave  also.  Any  occurrence  which  may  have  a  bearing  upon  the  discipline  of  the  Ship  should  be  taken 
notice  of  and  noted  down;  because,  m  the  case 'of  trouble  wit  li  the  crew,  the  Log-Book  is  received  as 
evidence  of  the  facts  of  the  case  in  a  Court  of  Justice.  These  entries  should  all  be  made  in  the  evening  of 
the  day  on  which  they  occur,  or  on  the  morning  of  the  following  day,  while  the  circumstances  are  fresh  in 
the  memory  of  the  officer  whose  duty  it  is  to  record  them.  The  Log-Book  is  kept  by  the  1st  officer;  but 
in  the  event  of  sickness,  or  in  having  been  put  off  duty  for  misconduct,  whoever  is  appointed  in  his  room 
by  the  Captain)  must  keep  the  Log.  Sometimes  the  Captain  writes  it  himself.  This  is  legal  enough, 
providing  nothing  but  the  truth  is  recorded. 

This  18  mentioned  merely  to  show  that  the  Chief  Mate  of  a  Ship  is  not  justified  in  retaining  the  Log- 
Book  after  its  being  demanded  from  him  by  the  Captain,  as  some  Mates  seem  to  imagine  they  have  a  right 
to  do.     The  Book  belongs  to  the  Ship  and  to  her  commander. 

The  Sea  Log  may  be  kept  in  Common  or  Apparent  Civil  Time,  if  required.  (See  the  Example  following.) 
The  entries  comaience  at  midnight,  and  are  continued  nntil  the  following  midnight,  liaviug  the  Noon  of  the 
Sea  Day  in  the  middle  of  it.  The  Log  Board  is  carried  on  from  Noon  to  Noon,  as  usual,  the  preceding  12 
hours  work  on  the  Board,  that  is,  from  the  preceding  Noon  to  midnight,  and  the  following  12  hours,  from 
midnight  to  Noon,  constitute  the  day's  work,  as  before ;  the  Ship's  reckoning  up  to  Noon,  in  this  case, 
appearing  in  the  middle  of  the  Log.  This  method  is  very  convenient  in  case  of  referring  back  to  dates, 
and  is  perfectly  easy  in  practice,  because  we  have  only  to  copy  off  from  the  Log  Board  as  above  stated. 

The  old-  method  is  still,  however,  generally  used,  through  the  force  of  habit,  and  which  is  an  exact  copy 
of  the  form  used  on  the  Log  Board.     (See  page  180.) 

The  Log-Book  commences,  as  before  observed,  when  the  Ship  is  unmoored,  or  breaks  ground,  under 
charge  of  the  Pilot;  and  the  time  at  which  he  leaves  the  vessel  is  noted,  and  the  bearing  and  distance  of 
the  land  taken  as  a  Departure.  Suppose  the  Ship  to  have  sailed  in  the  morning  of  the  5th  of  June,  and  a 
Departure  taken  at  6  A.  M.,  in  writing  the  Log  up  to  Noon,  we  would  say,  this  day's  work  ends  with  12 
hours,  (being  the  end  of  the  Sea  Day  of  June  5th,)  to  begin  the  Sea  Log.  The  Course  and  Distance  sailed 
is  then  reckoned  up.  and  the  Ship's  position  found  at  Noon.  The  Log  for  the  afternoon  is  then  dated  the 
6th  of  June. 

Suppose  the  Ship  to  sail  and  take  her  Departure  in  the  afternoon  at  6  P.  M.,  we  would  commence  the 
Sea  Day  in  like  manner,  noting  that  the  last  Harbor  Log  contains  only  12  hours. 

On  the  other  hand,  when  a  Ship  goes  into  port  in  the  morning,  the  Sea  Date  of  the  Log  and  the  Civil 
Date  of  the  place  being  the  same,  the  entries  are  continued  until  midnight,  and  we  say,  this  day  contains  36 
hours,  to  begin  the  Harbor  Log. 

And  when  she  goes  into  port  in  the  afternoon,  the  entries  are  continued  under  the  same  date  until  the 
following  midnight,  when  the  same  remark  ia  made,  tha'  this  day  «uds  with  36  hours,  to  begin  the  Harbor 
Log. 


ipi 


KEEPING  THE  LOG-BOOK 


METHOD  OF  KEEPING  A  SHIPS  LOG-BOOK  IN  CIVIL  TIME. 


We  shall  now  proceed  to  give  a  few  Examples  of  writing  the  Harbor  Log,  and  the  Log  at  Sea,  by  Civil 
Time,  and  conclude  this  work  with  a  short  Journal  of  a  voyage,  or  rather  a  passage,  of  a  Ship  from  Santa 
Cruz  to  St.  John's,  N.  F. 

The  Harbor  Log. 


DAT    OF   THE    MONTH. 

WINDS. 

EEMAEKS    ON    BOAED    THE    C.  S.    DAUNTLESS,    LYING    AT   SANTA    OEUZ. 

Monday, 
March  18th,  1854. 

Barom.  30.00 

N.  K 
Therm.  80* 

Throughout  this  day  fresh  breezes,  with  passing  showers. 

Crew  and  3  laborers  employed  taking  in  cargo,  (as  oer  Cargo  Book,) 

bending  light  sails,  and  other  duty. 
James  CoUius  off  duty,  sick. 

Tuesday, 
March  14th. 

Barom.  29.85 

N.  K  E. 
Therm.  79° 

First  part  of  this  day  fresh  trade,  and  fine,  middle  and  latter  parts. 

Strong  wind  and  rain  squalls.     3  laborers  employed. 
Finished  taking  on  board  cargo.     Hoisted  in  the  longboat  and  cleared 

up  the  decks.     J.  Collins  returned  to  bis  duty. 

Wednesday, 
March  15th, 

Barom.  80.05 

E.  N.  E. 
Therm.  81" 

Throughout  this  day  moderate  and   fine  weather.     Employed  filling 
fresh  water,  bending  sails,  and   taking  in  Ship's  stores,  and  in  the 
evcLiug  got  the  Ship  ready  for  Sea,  and  at  6  P.  M.  unmoored,  and 
hove  up  the  starboard   bower  anchor,  and   hove  in  to  30  fathoms. 
Shackle  on  tlie  small  bowei-.     Discharged  the  laborers. 

The  Clipper  Ship  Dauntless,  W.  Griffen,  Commander,  from  Santa  Cruz  to  St.  John's,  N.  F. 

Thursday, 
March  16th. 

Barom.  31.00 

N.  E. 
Therm.  82* 

At  6  A.  M.  the  Pilot  came  on  board.     Hove  short  and  made  sail.     At 
5h    80m    Weighed    from   the    anchorage    at  Santa   Cruz  and    pro- 
ceeded to  Sea.     Light  baffling  wind  and  cloudy. 

At  7  A.  M.  discharged  the    Pilot  and  made  all  possible  sail.     The 
steady  Tiade  set  in,  with  fine  pleasant  weather. 

kt  Noon,  the  N.  E.  end  of  St.  Anthony  Island,  one  of  the  Cape  Verde 
Islands,  bore  West  by  Compass,  3  or  4  miles  distant 

Lat.  Obs.  17°  9'  N.     Magnetic  Varia.  1|  points  Westerly. 

H. 

E. 

H.  K. 

oouasE& 

WINDS. 

L  .W. 

Log  Kept  in  Civil  Time. 

1 

2 
3 
4 
5 
6 
1 
8 
9 
10 

n 

5 

5 
6 

8 
9 

10 
10 
11 

1-2 
IS 
1?. 
13 

1 
1 

N.  W.  by  N. 

it 

a 

N.  N.  W 

tt 
M 
U 
U 

u 
tt 

it 
a 

N.  E.  by  N. 

it 
it 

N.  E.  by  K 

ti 
u 

E.  N.  E. 

tt 
U 

Kby  N. 

u 

i'.  M.     Fresh  Trade  and  fine  weather. 

Stowed  the  anchors,  unbent  the  cables  and  put  them  below. 

At  3h,  the  N.  W.  end  of  St.  Anthony  bore  S.  17"  80'  W.,  distant 

15  miles,  from  which  the  Dep.  is  taken  in  Lat.  17°  12'  N,  Long. 

25°  19'  W.     At  5h,  set  the  starboard  studding-sails. 
At  6h,  the  Mag.  Vai-iation  at  sunset  was  17°  30'  Westerly. 
Passed  several  vessels  bound  West 
A  t  8h,  increasing  breezes  and  smooth  water. 
Light  squalls  from  passing  clouds. 
At  lOh,  in  sky-sails  and  rounded  in  the  weather  braces. 

Midnight.     Fresh  Trade  and  clear  weather. 

The  Departure  is  taken  from  theNorth  West  end  of  the  Island  of  S  .  Anthony,  bearing  S.  17°  80'  West, 
and  the  Variation  17°  30'  West  allowed,  gives  the  true  bearing  South  ;  the  Ship  is,  therefore,  on  the 
Meridian  of  that  point,  distant  15  miles  to  the  N^rth  of  it.  Sights  being  taken  for  Chronometer,  its  error 
on  Greenwich  Mean  Time  is  found  to  be  OL  .Oin  39s  too  fast,  and  the  Rate  since  last  Observation,  taken 
in  a  similar  manner,  2  sec.  5-lOth  gaining.  We  have  thence  the  Sea  rror  and  Rate  of  it  obtained.  (See 
the  Rules  and  Examples  given  at  page  155.) 

To  shape  a  Course  in  this  case,  we  lay  the  ruler  over  the  place  of  th  Ship  and  Cape  St.  John,  N.  F,  and 
find  the  true  Course  to  be  N.  W.  J  N.,  the  Variation  allowed  to  tho  right  gives  the  Compass  Course 
required  to  steer  N.  by  W.  J  W.  TJie  distance  off  at  present  is  immaterial,  but  both  Bearing  and  Distance 
may  be  found  by  a  case  in  Middle  Latitude  or  Mercator's  Sailing. 

In  Ships  of  great  speed,  when  working  up  the  day's  work,  it  will  be  found  more  corrrct  to  turn  the 
Coarse  steered  into  degrees,  and  apply  the  Variation,  (also  in  degrees,) to  it,  and  thenca  find  the  Difference 
•(  Latitude  and  Departure. 


KKEPING  THE  LOG-BOOK. 


195 


KEEPING  THE  LOG-BOOK  IN  CIVIL  TIME. 


The  tipper  Ship  Dauntless,  W.  Griffen,  Commander,  from  Santa  Crm  towards  St.  Johns 


a. 

1 

K. 

\3 

H.  K. 

'7 

COURSES. 

WINDS. 

L.  w. 

EKMARKS,    FEIDAY,   MARCH    17tH,    1854. 

N   N.  W 

E.  by  N. 

t4 

A.  M.     Fresh  W-eeze  and  clear  weather. 

2 

14 

tt 

" 

" 

At  2h,  squared  the  ya'  Is  and  set  the  lower  studding-sail.     Set  up 
and  secured  the  boom  braces,  and  preventer   breast  and  back 

3 

15 

t( 

East. 

i( 

4 

14 

1 

(t 

" 

t( 

stays. 

6 

I  a 

it 

it 

1* 

6 

14 
15 
14 

1 

9 
4 

4t 

it 

At  6h,  The  Magnetic  Variation  at  Sunrise  was    20'  Westerly. 

8 

1 

(4 

At  8h,  Longitude  in  by  Chronometer  was  27°  57'  30"  W. 

9 

15 

M 

U 

u 

Watch  employed  about  the  rigging  fixing  chafing  gear. 

10 

15 

ti 

(( 

"        Carpenler  I'epairin^  the  longboat. 

11 

15 

W 

ti 

(1 

Pumps  carefully  attended. 

12 

15 
itioD 

u 

a 

(4 

Noon.     Strong  steady  Trade  wind                                                              , 

Varii 

Course 

Dist 

D.  LaL 

Dep. 

Lat.  DR.  20°  52'N.  Lon.  D.R.28°  34'W.|Lon.Chr.  28°40'W.|Bar.  80  00 

19° 

W. 

N.40°W. 

287 

220  N. 

185  W. 

LatObs.  20    60  N. 

Dif.  Lon.    3    15  W.  D.  R.  since  yester- 

Ther.    79° 

Iday 28   34 

I 

15 

N 

N.  W. 

East. 

W 

P.  M.     do.     weather.     All  possible  sail  set. 

2 

15 

u 

t< 

U 

Signalized  the  Ship  Shannon  from  Havre,  bound  to  New  Orleans, 

3 

15 

(C 

M 

4* 

out  30  days. 

4 

15 

(t 

U 

44 

At  4h,  Long,  in  by  Chronometer  29°  26'  "W. 

6 

15 

i< 

t« 

4i 

At  5h,  Carried    away    the    top-gallant  studding-sail  booms.     Made 

6 

14 

w 

M 

44 

up  the  sails  and  sent  the  booms  down  on  deck. 

7 

15 

a 

U 

(4 

At  Sunset  the  Magnetic  Var.  was  Obs.  to  be  20°  Westerly. 

8 

15 

t4 

u 

44 

At  8h,  squally-like   clouds  in   the  N.  W.  and  the  Barometer  falling. 

9 

15 

u 

u 

(( 

Ship  approaching  the  Northern  hmit  of  the  N.  E.  Trade  wind. 

10 

15 

(4 

n 

41 

Hautled  all  the  small  sails. 

11 

15 

M 

M 

44 

At  Mid.     The  wind  heading  the  Ship   off,  in   all  studding-sails,  and 

12 

H. 

15 

u 

U 

braced  forward  the  yards. 

K. 

H.    K. 

cotrasK. 

WINDS. 

L.  W. 

REMARKS,  SATUaOAY,  MARCH   1  8tH,   1854. 

1 

10 

N.  W. 

N.  K  by  N. 

41 

A.  M.     Very  squally  weather,  with  heavy  rain ;  handed  the  stay- 

2 

10 

it 

K 

11 

sails  ami  flying-jib. 

3 

10 

M 

i( 

44 

4 
6 

6 

7 

10 
10 
10 
10 
10 

Ct 

ti 
It 

Heavy  ground  swell  from  the  N.  W. 

« 

(1 

<4 

At  Sunrise  the  Magnetic  Varia.  was  Oba.  to  be  19'  30'  W. 

8 

W.  by  N. 

North. 

At  8h,  lu  first  reef  of  the   top-sails  and   set  top-gallant-sails  over 

9 

10 

1 

t4 

t( 

l( 

them. 

10 

10 

1 

u 

U 

i( 

No  observations,  Sun  obscure. 

11 

10 

1 

l( 

n 

l< 

Noon.     Strong  gale  and  a  high  topping  sea. 

12 

10 

1 

ti 

'•    '    In  tdo-srallant-sails  aud  dduble-ieefecl  tlie  top-snils.                                | 

Va.i 

ition 

Course 

Dist. 

D.  Lat. 

Dep.      Lat.  D.R.23°  26'N.|Lon.  D.R.  32M6'W. 

Long.  Cliro.  0°  0' 

Bur.  29.50 

19° 

W. 

N.56'W. 

280 

166  N 

234  W.    Lat.  Ob Dif.  Lon.     4    12  W. 

D.  R.  since  yes- 

Ther.  78° 

'             1 

tenlav  S2°52'W.                        ( 

As  sufficient  examples  of  working  a  Day's  work  have  been  already  given  worked  out,  it  is  considered 
unnecessary  to  work  out  those  in  this  Journal,  the  result  only  being  given,  that  is,  a  summary  of  the  whole, 
including  the  Latitude  by  Observation,  and  Lonizitude  by  Chronometer  at  Noon,  the  Longitude  by  Dead 
Reckoning  being  carried  on  from  day  to  day  by  it-self.  The  Difference  of  Longitude  made  is  also  applied 
to  the  Longitude  by  Chronometer  on  the  preceding  day,  and  placed  under  the  Longitude  by  Chronometer 
to-day.  This  affords  a  means  of  comparison.  In  like  manner  the  Latitude  by  Dead  lieckoning  and  that  by 
Observation  are  placed  under  each  other,  which  will  show  at  any  time  the  effect  of  a  Current  or  the  Error» 
in  the  reckonins. 

The  Variation  ob.served  agreeing  with  that  laid  down  on  the  Chart,  we  conclude  there  is  no  Local  Attrac- 
traction  on  board.  The  Courses  steered  by  Compas.s  ni  the  above  Days'  works  are  turned  info  Degrees 
and  Minutes,  the  Variation  applied  gives  the  True  Course  in  Degrees;  fo'  in.stance,  N.  N.  W.  is  N  23°  W. 
nearly,  and  as  the  Variation  has  increased  in  the  rirsl  Day's  work  from  1V°  30'  to  20°,  we  take  the  Mean, 
or  19°,  as  the  f 'oper  Variation  to  be  allowed  on  the  whole  Day's  work  ;  this  added  to  N.  23°  W.  by  Com- 
pass, gives  the  ^rue  Course  N.  42°  W.,  with  which  and  the  Distance  run,  gives  the  D  Latitude  and 
Departure. 


19G 


KKh:PING  a  SHIP'S  log  B(X)K. 


METHOD  OF  KEEPING  A  SHIP'S  LOG-BOOK  IN  SEA  TIME. 

Hanng  thus  given  Examples  of  Keeping  the  Harbor  and  also  the  Sea  Logs,  in  Civil  Time  in  the  com 
mencement  of  this  Journal,  the  remainder  of  it  will  be  kept  in  Sea  Time,  that  is,  in  the  usual  mannei 
adopted  on  board  merchant  vessels. 

The  Clipper  Ship  Dauntless^  W.  Griffen^  Commander. 


H. 

K. 

a.  K. 

COURSES. 

WINDS. 

L.  W. 

REMARKS,  SUNDAY,  MARCH  19tH,  1854.                                            • 

1 

2 
8 

4 
6 

« 

7 
8 

9 
9 

9 
9 

10 
10 
10 
10 

1 
1 
1 

West. 

4i 

N.  by 

W. 

1 

(1 

P.  M.     Strong  gale  and  rainy  weather. 

Sent  down  the  royal-yardf"  and  rigged  iu  the  flying-jib-boom. 

W.  iS. 

u 
(t 

(1 

u 

t 

41 

1 
a 

U 

• 

At  4h,  eased  the  Ship  by  cheeking  in  the  weather  braces  and  keep- 
ing clean  full-and-by,  the  object   being   to  tjet  well   to  the  West- 
ward before  a  change  of  wind  takes  place,  wbieb,  by  the   falling 
of  the  Barometer  to   29.40  would  seem  to  indicate. 

9 

10 

10 

12 

1 

2 

10 

10 
10 
10 
10 
10 

4i 
u 

« 
u 

tt 

U 

u 
u 
u 
u 

(t 
M 
M 
i( 

U 
(1 

At  lOh,  do.  weather. 

Midnight.     Strong  gale  and  a  high  sea.     Pumps  carefully  attended 
Ship  keeping  perfectly  tight. 

8 

4 
5 
6 

7 
8 

10 
10 
9 
9 
10 
10 
10 
10 
10 
10 

1 
1 

1 

K 

u 
u 
(( 
u 

u 

u 

M 

u 
(< 
u 

u 

(4 

44 
tt 
It 

U 

At  4^ A.  M.     Gale  increasing,  reefed  the  coursers  and  spanker  and 
eased  the  jib-half-boom  in. 

At  6h,  the  Magnetic  Varia.  at  Sunrise,  aa  near  as   it  could   be  ob- 
served, appeared  to  be  14°  or  IJ  points  Westerly. 

At  8h,  observed  an  Alt.  of  the  Suu.     Long,  in  by  Chron.  36°  0'  W. 

9 
10 
11 
12 

u 

(( 
41 

It 

• 

At  lib  45m,  another  Alt  of  the  Sun  gave,  Lat.  in  21"  9'  N. 

Noon.     Stormy  weather.     Sun.  obscure. 

Varif 
17' 

ition 
W. 

Course 
S.57°W. 

Dist. 
237 

D.  Lat. 
129  S. 

Dep. 
198  W. 

Lat.D.R.21''17'N. 
Lat  Obs.  21      7 

Dif.  LoD.    3°  34' 
Lou.  D.R.36    20 W. 

Long.  Chr.  36°  36' 
D.  R.  since  yester- 
day     36°  26' 

Bar.  29.36 
Ther.  78° 

In  'he  above  Day's  work  it  appears  that  the  Magnetic  Variation  has  changed  from  19*  30'  to  14°,  durmg 
the  run  to  the  Westward  since  yesterday  evening  at  Sunset,  we  therefore  use  the  mean  of  the  two,  which  is 
17*  or  li  points,  *;n  correct  the  Compass  Course. 

An  Altitude  oi  the  Sun  having  been  obtained  at  about  8  o'clock  ft)r  Chronometer,  and  another  for  the 
Latitude  near  Noon,  the  time  by  Chronometer  being  noted  at  the  time  of  each  observation,  the  Latitude  is 
thence  found  by  the  method  given  at  page  94,  and  the  Longitude  by  Chronometer  is  found  by  the  method 
given  at  page  140.  This  is  the  simple  case  ;  or  the  Latitude  may  be  found  from  the  two  Altitudes  having 
the  measured  interval  of  Time  between  the  observations  by  the  method  given  at  page  96.  As  the  Ship  haa 
plenty  of  sea-room  it  is  not  necessary  to  resort  to  the  method  given  at  page  144  in  this  case  ;  besides  the  1st 
Altitude  was  observed  at  a  proper  distance  from  the  Meridian,  and  any  Error  in  the  Latitude  by  Dead 
Reckoning  would  not  affect  the  Time  much,  nor  the  Longitude  by  Chronometer,  because  the  Ship  is  in  a 
lo\v  Latitude. 

One  point  of  Leeway  and  li  points  of  Variation  being  allowed  to  the  left  of  the  Course  by  Compass, 
gives  the  True  Courses,  which,  with  the  Distance  run  on  each,  gives  the  Difference  of  Latitude  and  Depar- 
ture made  good,  and  thence  the  Latitude  and  Longitude  by  Dead  Reckoning.  Then  the  Difference  of  Lon- 
gitude made  by  Dead  Reckoning  applied  to  the  Longitude  by  Chronometer  yesterday,  gives  the  Longitude 
iji  by  Dead  Reckoning  since  yesterday.  This  compared  with  the  Longitude  by  Chronometer  to-day  shows 
the  Ship  to  be  10'  of  Lon-jitude  to  the  Westward  of  the  Dead  Reckoning.  In  like  manner  the  Difference 
between  the  Latiiude  by  Dead  Reckoning  and  that  by  observation  shows  the  Ship  to  be  10'  to  the  South- 
ward of  the  Dead  Reckoning.  This  may  be  accounted  for  in  two  ways,  that  is,  she  must  either  have  gone 
more  distance  than  the  Log  has  given  her,  or  there  may  have  been  a  Current  setting  in  the  direction  of  her 
Course.  It  is  evident  it  could  not  have  been  caused  by  an  Error  in  the  Course,  because  the  Error  in  the 
Latitude  is  to  the  Southward  of  the  Dead  Reckoning,  and  the  Error  in  the  Longitude  is  to  the  West  of  the 
Dead  Reckoning,  or  in  excess ;  but  had  the  Longitude  by  Chronometer  been  to  the  Eastward  of  the  Deacf 
Reckoning,  or  less  than  it,  it  would  then  have  been  concluded  that  the  Error  was  due  to  the  Courie  having 
been  more  to  the  Southward  than  that  given  by  Log 


JOURNAL. 


191 


JOURNAL  OF  A  VOYAGE 
From  Santa  Cruz,  {Cape  Verdes,)  towards  St.  John's,  Newfoundland. 


B. 


1 

2 
3 
4 
6 
6 
7 

b 

9 
10 

11 

12 
1 
2 
3 
4 
6 
6 
7 
8 
9 

10 

U 

12 


10 


8 

8 

8 

7 

7 

8 

8 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

9 

9 

9 

9 


H.  K.       COUE8KS. 


WINDS. 


W.  S.  W. 

N.  E.  by  N. 
N.  N.  E. 


N.W.  by  N 
N.  W. 

N.W.  by  W. 


L.  W. 


H 
H 


aElIAEES,    HONDA T,  MABOH    20tH,  1864. 


At  1  p.  M.  the  wind  hauled  more  to  the  Westward.  Wore  ship 
to  the  North  Eastward. 

At  4h,  strong  gale  and  rainy  weather. 

At  6h  SOm,  the  sky  cleared  up  to  the  Southward.  ObserTcd  the 
Meridian  Altitude  of  the  star  Siriu8,(a  goodobserration,)  which 
gave  Lat  in  21*  42'  N.     Lat  by  D.  R.  at  same  time  21*  86'  N. 

At  lOh,  more  moderate  weather.     Out  double  reefi  of  tha  topsailr 

and  set  top-gallaut-sails  over  them. 
Midnight     Fresh  breeze  and  clear  weather. 

At  2  A.  M.,  weather  moderating,  and  the  head  tea  going  down. 

At  4h,  out  reefs  of  the   courses  and  spanker 

At  5h  SOm,  Lat  by  the  Moon  23°  26'  N.,  D    A.  gave  28*  17'  N. 

At  Sunrise,  the  Magnetic  Variation  observ*  d  was  18*  0'  W. 

At  8h,  Long,  in  by  Chronometer  35°  26'  "W. 
Watch  on  deck  employed  repairing  chafing  gear. 
Carpenter  repairing  the  Longboat 

Noon.     Cloudy  weather  ;  Sun  obscure. 


Varia. 
13°  W. 


Course. 
N.  23°  E. 


DistlD.  Lat 

198  1182  N. 


Dep.  ILatD.R.  24°  23' N. 
76  KLatObs.   24   38  N. 


DiflLong.  1°23'E. 
Lon.  D.R.34  57  W. 


Lon.  Chro.      85*    8'  W.j  Baro.  29.80 
D.R.sin.ye8t  36    13  W.I  Therm.  77° 


To  Correct  the  Courses  Steered  in  Degrees. 

Comp.  Course  W.  S.W.  or  S.  67°  30'  W.  N.  E.  by  N.  or  N.  38°  46'  K  N.  N.  E.  or  N.  22'  30'  R  N.  N  E.  or  N.  22°  80'  E 
8ub.L.W.ll'15'4Va.l3°— 24   16  Add  the  DifiE: . . .   8   62        AddDiff.....  3   52        Sub.  Diff....     2     0 


Course  made  good S.  43°  16'  W. 


N.  37°  37'  E. 


N.  26°  22'  E. 


N.  20°  80'  E, 


The  Courses  being  corrected  in  the  above  manner,  and  entered  into  the  Traverse  Tab'e,  with  their 
respective  distances,  as  usual,  the  nearest  degree  being  then  taken  as  the  Course  to  find  the  Difference  oi 
Latitude  and  Departure. 

This  is  a  very  important  matter,  and  should  be  attended  to  in  a  fast-sailing  vessel ;  because  an  omis 
•ion  of,  say  2°,  in  the  variation  allowed  on  the  Course  steered,  when  the  distance  run  is  great,  will  cause 
a  considerable  error  in  the  Dead  Reckoning.     When   the   Course  is  near  the  Meridian,  or  near  a  Parallel 
of  Latitude,  this  error  will  amount  to  4'  in  every  100  miles  distance ;    when  near  45°  the  error  will  be  2' 
in  every  100  miles. 

In  looking  over  this  day's  work,  we  find  that  at  6h  SOm  the  Latitude  found  by  the  Meridian  Altitude  of 
the  Star  Sirius.  made  the  Ship  7'  to  the  Northward  of  the  Dead  Reckoning,  and  at  5h  30'  A.  M.,  by  the 
Meridian  Altitude  of  the  Moon,  she  was  9'  to  the  Northward  of  the  Dead  Reckoning. 

And  that  the  Longitude  by  Clironometer  made  her  5'  of  Longitude  to  the  Eastward  of  the  Dead  Reck 
OKxng.  She  has,  therefore,  made  less  Leeway  than  has  been  allowed  her,  and  gone  more  Distance  than 
the  Log  gives  her  ;  it  is  therefore  proper  to  examine  the  Log-line  ;  and  which,  on  being  examined,  we  find 
to  be  5  feet  too  long  at  the  5  knot  mark,  which  would  be  equivalent  to  an  error  of  nearly  i  a  knot  in  using 
the  14  sec.  or  Short  Glass,  giving  the  Distance  too  small.  The  proper  length  between  the  knots  should  b« 
45  feet,  whereas  the  line  was  found  to  be  46  feet,  or  one  foot  too  long  on  each  knot.  A  measured  space 
of  say  22  feet  6  inches,  the  length  of  the  half-knot,  should  be  marked  off  on  the  deck,  and  a  copper  nail 
driven  in  at  each  end  of  it,  as  a  permanent  measure,  whereby  the  line  may  be  verified  occasionally  ;  becaasa 
It  is  liable  to  shrink  up  as  well  as  to  stretch,  when  new.  In  fitting  a  new  line,  it  should  be  well  stretched 
and  then  thoroughly  wetted,  before  it  is  measure'!  and  marked. 


IM 


JOURNAL. 


JOURNAL  OF  A  VOYAGE. 


The  Clipper  Ship  Dauntless,  W.  Griffen.,  Commander. 


H. 

K. 

H.  K. 

COCESES. 

WINDS. 

L.  w. 

REMARKS,   TUESDAY,  MARCH    21sT,    1854. 

1 

9 

N.byE.  iE. 

N.W.  by  W. 

i 

At  28m  past  Noou,  Lat.  Obs.  24°  43'  N. 

2 

10 

(( 

N.w.byw.^w 

At  2  P.  M.,  out  all  leefs.     Seiit  up  the  royal  yai-ds,  rigged  out  the 

8 

10 

•* 

" 

flying-jib-boom,  aud  set  the  sails. 

4 

10 

u 

ii 

At  4h,  the  Long,  iu  bv  Chronometer  35°  0'  W. 

6 

10 

u 

i( 

Steady  breeze  and  fine  weather. 

6 

10 

li 

it 

Suiisft,  Magnetic  Variation  Obs.  12°  Westerly. 

At  7h  20m,  Mer.  Alt. #  Castor.  Latin  25°  66' N.  D.  R.  25°  64' N. 

7 
8 
9 

10 
10 

10 

44 
4t 

u 

44 

At  9h,  set  the  stay -sails,  fore  and  aft 

10 

11 

M 

44 

11 

10 

U 

" 

12 

11 

w 

« 

Midnight     Steady  breeze  and  fine  clear  weather. 

1 

10 

u 

it 

i 

2 

11 

tt 

(t 

A.  M.     Do.  weather.     All  possible  sail  set. 

3 

10 

a 

(( 

4 

11 

u 

4< 

At  4h  20m,  Mer.  Alt.  *  Antares.  Lat.  in  27°  25'  N.  D.  R.  27°  27'  N. 

6 

10 

t« 

it 

6 

11 

u 

U 

At  6h  3&m,  Mer.  Alt  (  Lat  in  27°  54'  N.     D.  R.  27°  63'  N. 

7 

10 

it 

4( 

8 

11 

u 

tc 

At  8h,  Long,  in  by  Chronometer   34°  28'  W.      An  Azimuth  taken 

9 

10 

a 

u 

same  time  gave  the  Magnetic  Variation  14'  Westerly. 

lu 

11 

u 

4( 

Employed  painting  the  boats,  <fec. 

11 

10 

u 

it 

Carpenter  caulking  on  deck. 

12 

11 

" 

u 

Noon.     Island  of  Payal  (Azores)  N.  26°  E.,  650  miles. 

Varia.       ( 

Dours 

e.      Dist. 

D.  Lat. 

Dep. 

Lat.D 

R.  28°  48'  N. 

Dif.  Long.    0°  42'   E. 

Long.  Chro.    34°  22'  W. 

Bar.  29.80 

13°  W.  N. 

8°3C 

'  E.  253 

250  N. 

37  E. 

Lat.  0 

bs.  28    50  N. 

Lou.  D.  R.  34    15  W. 

D.R.  siny est.  34   26  W. 

Ther.  76° 

As  the  Meridian  Altitude  of  the  Sun  was  not  obtained  yesterday,  an  Altitude  was  taken  in  the  after- 
noon, and  the  Time  noted  by  Chronometer,  by  which  means  the  Apparent  Time  at  the  Ship  was  found  to 
se  28m  past  Noon.  The  Latitude  being  then  worked  out,  (by  the  method  given  at  page  94,)  is  found  as 
ibove.  The  Ship  has  made  5'  of  Difference  of  Latitude  to  the  Northward  since  N00.1,  which  subtracted 
'rem  it,  gives  the  Latitude  in  at  Noon  yesterday. 

The  Magnetic  Variation  having  changed  from  12°  to  14°  during  the  day's  run,  the  INlean  of  which,  13°, 
oeing  applied  to  the  left  hand  of  the  Courses  by  Compass,  after  being  corrected  for  Leeway,  as  shown  in 
/^esterday's  work,  will  give  the  True  Courses. 

The  Difference  between  the  Dead  Reckoning  and  Observations  to-day  is  much  less  than  heretofore,  being 
mly  2'  of  Latitude  to  the  Northward,  and  4'  of  Longitude  to  the  Eastward. 

The  Variation  was  found  this  morning  by  an  Azimuth,  and  by  the  same  Altitude  which  was  used  for 
.'hronometer.     (See  the  method  of  doing  this  at  page  150.) 

By  inspecting  Table  XVIII,  against  the  Day  of  the  Month,  the  Times  of  the  Meridian  Passages  of  the 
A(.ars  Sirius  and  Antares  will  be  found  as  above.  Then  their  computed  Altitudes  furnish  the  means  of 
inding  them.  (See  page  106,  No.  3.)  The  Latitudes  so  found,  and  that  by  the  Dead  Reckoning  since 
Noon,  on  being  compared  are  found  to  agree,  nearly. 

By  reference  to  the  Nautical  Almanace,  in  the  case  of  the  Moon,  the  Mean  Time  of  her  passing  the 
Meridian  at  Greenwich  is  found  and  reduced  to  the  Meridian  of  the  Ship.  Then  the  Equation  of  Tims 
lubtracted,  gives  the  Apparent  Time  as  above.  (See  page  101.)  The  Latitude  Observed  and  Dead  Recfc 
ining  agree,  nearly. 

The  Ship's  position  being  laid  down  on  the  Chart  each  day  at  Noon,  as  directed  at  page  48,  and  joined 
together  with  a  pencil  line,  produces  her  track.  When  out  on  the  open  Sea,  it  is  not  necessary  to  note 
the  bearing  of  the  Land  daily,  but  in  the  case  of  having  to  pass  near  to  certain  land,  it  is  prudent  to  note 
its  Bearing  aud  Distance  at  Noon,  as  we  approach  it.  As  in  this  case  the  Ship  is  heading  towards  the 
Azores  Islands,  we  therefore  find  the  Bearing  and  Distance  of  the  nearest.  Fayal  bears  N  N.  E.  i  E, 
True,  or  N.  E.  i  N.  by  Compass,  distant  65Q  miles  ;  and  Flores,  which  lies  West  of  it,  bears  N  bv  E  i  E. 
or  N.  N.  E.  t  E.  by  Compass,  distant  660  miles.  The  same  may  found  bv  the  Rule  in  Casn  2d  in  Mid- 
dle Latiiode  or  Mercator's  Sailings 


XWRNAL. 


199 


JOURNAL  OF  A    VOYAGE 
From  Santa  Cruz  (Cape  Verdes.)  towards  St.  Johns,  Newfoundland. 


II. 

1 

K 

U.    K.        CODR8HS. 

WINDS. 

L.  w. 

atlMARKS,  WKDNKSDAT,  MARCH  22d,   1854. 

1  j 

1    N.byE.iE. 

N.W.b.W.^W. 

i 

P.  M.     A  fresh,  steady  breeze  ;  all  possible  sail  set     Signalized 

.. 

U 

M 

11 

the  Sliip  South  Carolina,  from   Liverpool,  bound  to  Austra- 

M 

U 

t( 

lia,  out  15  days. 

4 

U 

u 

u 

At  4h,  Long,  in  by  Chron.  34°  22'  W.,  and  an  Azimuth  Obe.  at 

t'l 

1 

*4 

M 
U 

u 

the  same  time  gave  the  Magnetic  Varia.  20°  W 

h 

U 
*• 

U 

u 

At  8h,  Squally  ;  handed  the  stay-sails. 

1" 

U 

« 

w 

At  1  Oh  6m,  Alt.  Pl't  Mars  S.  gave  Lat  30*  86'  N.  )  ,;r        o^.  ^ ,  / «. 
do.         Alt.  Polar  #  N.  gave  Lat.  30°  46'  N.  \  ^^*"'  ^^  "^^  ^ 

11 

w 

u 

(i 

1^ 

1 

N.K 

N.  W.  by  W. 

0 

Tlie  Lat.  by  D.  R.  since  Noon  same  time 30°  S9'  N. 

1 

U 

u 

Clear  stailight   night  and  smooth  water ;  set  all  the  stay-sails, 

-* 

H 

" 

" 

fore  and  aft. 

M 

« 

- 

a 

I 

XV 

1 

u 

M 

w 

At  4  A.  M.     Fresh  breeze  and  showery  weather. 

5 

(4 

1 

At  Sunrise  the  Mag.  Varia.  observed  was  25°  Westerly. 

6 

U 

1      .. 

At  Ih  40m,  Mer.  Alt. of  the  ])   Lat.  m  32°  16'  N,  D.  R.32'  17'  N. 

7 

u 

u 

u 

Long,  in  by  Chron.  same  time  33°  42'  W. 

8 

u 

u 

u 

Employed  reeving  new  running  rigging  and   setting  up  the  jib- 

10 

u 

u 

M 

guys  and  top-gallant  backstays. 

11 

u 

M 

t( 

Steady  breeze  and  pleasant  weather. 

12 

t( 

u 

« 

Noon.     Island  of  F  ores.  (Azores)  N.  15°  E.,  Disi.  404  miles. 

Vari 

atjon 

Course 

Dist 

D.  Lat. 

Dep. 

LatD 

R.  33°  2'N. 

Dif.Lou.    1°    4'E. 

Lon.  Chr.         33° 'id' W.  Bar.  29.80 

22°  8 

O'W. 

N.]'2=E. 

260 

2.V2   N. 

55     E.I  Lat.  01 

38.  33    1  N. 

Lon.  D.R.33    11  W. 

D.  R.  sin.  yest.  33°  1 8'  W.  Tli^r.    7f 

The  Magnetic  Variation  has  changed  considerably  since  yesterday  morning,  at  whicli  irme  it  W3.» 
observed  to  be  14°.  At  4  P.  M.  it  had  increa.sed  to  20°,  and  this  morning  it  was  found  to  be  25°.  We 
therefore  take  the  Mean  of  the  two  Variations  last  found,  which  is  22°  30',  or  2  points  Westerly,  as  thv 
proper  Variation  to  be  allowed  on  the  Courses  steered. 

As  the  Ship's  position  by  Dead  Reckoning  agrees  very  nearly  with  that  by  observations  to-day,  w<"  there- 
fore conclude  that  the  Log  is  correct. 

At  about  10  P.  M.  the  Altitude  of  the  Planet  Mars,  observed  to  the  Southward,  gave  the  Latitude  a» 
above,  but  the  night  being  dark  and  the  horizon  doubtful,  an  Altitude  of  the  Polar  Star  was  observed  to 
the  Northward,  the  Latitude  by  which  difiered  10'  from  that  by  the  Altitude  of  Mara,  but  the  Mean  of  the 
two  agrees  nearly  with  that  by  Dead  Reckoning.      (See  Remarks,  page  110.) 

The  Moon  being  on  the  Meridian  at  7h  40m,  Apparent  Time  in  the  morning,  ner  Meridian  Altitude  wa» 
observed,  and  at  the  same  time  Altitudes  of  tiie  Sun  were  taken  for  the  Chronometer,  which  gave  the  Lati« 
tude  and  Longitude  of  the  Ship  at  that  tune,  as  above. 

The  Longitude  by  Chronometer  at  Noon  was  found  to-day  by  equal  Altitudes  of  the  Sun,  and  agree* 
with  that  brought  up  to  Noon  by  the  Dead  Reckoning  since  the  morning  Sights  were  tjiken.  The  first  equal 
Altitude  was  taken  at  7  bells,  and  the  time  noted  by  Chronometer.  The  Index  of  the  instrument  was 
then  screwed  back  10',  equal  to  the  Difference  of  Latitude  made  to  the  Northward  in  1  hour,  and  when  the 
Sun's  Lower  Limb  fell  to  that  Altitude,  the  Time  by  Chronometer  was  noted  again.  This  method  is  fully 
explained  in  the  Note  at  page  147. 

The  Bearing  and  Distance  of  the  adjacent  Land,  or  that  which  the  Ship  is  approaching,  is  again  noted  at 
Nt)on  to-day.  The  Island  of  Fayal  bears  N.  E.  by  N.  True,  or  N.  E.  by  E. ;  by  Compass  (Variation  S 
points  W.)  Distant  400  miles;  and  the  Island  of  Flores  bears  N  by  E.  i  E.  "rrue,  or  N.  E.  }  N.  ;  by 
Compass  Distant  404  miles.  That  is,  I  of  a  point  on  the  Weather  or  Port  bow  of  the  Ship.  These  bear* 
ingg  are  from  the  Chart.  But  if  a  Chart  is  not  at  hand,  the  Bearing  and  Distance  of  any  of  the  Islands  may 
be  worked  out  by  the  Rules  given  in  Case  2d,  of  Middle  Latitude  or  Mercator  Sailing.  The  Latitudes  and 
Longitudes  of  the  several  Islands  are  given  in  the  Table  of  Positioos  at  the  end  of  the  work 


too 


JOURNAL. 


JOURNAL  OF  A  VOYAGE. 

The  Clipper  Ship  Dauntless,  W.   Grijffen,   Commander 


H. 

K. 

1 

11 

2 

11 

•i 

11 

4 

11 

6 

11 

6 

11 

7 

10 

8 

10 

9 

10 

10 

10 

11 

9 

12 

9 

1 

8 

2 

8 

8 

8 

4 

8 

6 

8 

6 

8 

7 

8 

8 

8 

» 

8 

10 

8 

11 

8 

12 

8 

H.   K.      OODS8SS. 


N.  E. 

«4 

N.  E.  by  N. 


N.N.KiK 


WINDS. 


N.  W.  by W 
N.  W. 


N.  W.  i  W 


L.    W. 


REMARKS,  THURSDAY,    MAROB    23d,  1864. 


P.  M.     Fresb  breeze  and  clear  weather. 

People  employed  repairing  sails,  <fec. 

Carpenter  making  a  top-gallant  studding-sail-boom 

Several  vessels  in  sight,  bound  West. 

At  Sunset  the  Long,  by  Chron.  was  32°  52'  W. 

The  Dead  Reck,  at  the  same  time    32    59    W. 

Ampli.  gave  the  Mag.  Varia.  23°  Westerly. 

And  an  Altitude  of  #  Sirius  near  the  Mer.  gave  Lat  ia  84'  4'  N. 

The  Dead  Reckoning  since  Noon  was 84    6    N. 

Midnight     Cloudy  weather. 

At  2  A.  M.     Less  wind  and  hazy  weather. 

At  4h.  Mer.  Alt  of  #  Antares  gave  Lat  35°  26'  N. )  The  Mean 
and  an  Alt  of  the  Polar  #  gave  Lat  36°  37'       )  36*  31'  N. 
At  Sunrise,  Mag.  Varia.  Obs.  23°  W.     D.  R.  gave  Lat  35*  84'  N. 
Steady  breeze  and  fine  clear  weather. 

At  8h  40m.   D  's  Mer.  Alt  gave   Lat  in  36°  5'  N.,  D.  R.  86°  9'  N. 
Sun's  Alt  gave  Long.  Chron.  32°  3'  W.     The  D.  R.  was  82°  29'  W. 
Azimuth  Obs.  same  time  gave  Mag.  Varia.  23°  W. 
Watch  on  deck  repairing  sails,  &o. 

Noon.     The  Island  of  Flores  (Azores)  N.  10°  E.  (True)  182  miles. 
Current  to-day  E.  by  S.  (True)  1  mile  an  hour. 


Vari'n 
2ptW. 


N, 


Course 
12°3n'E. 


Dist 
223 


D.  Lat. 

217  N. 


Dep. 

48'  E. 


Lat 

Lat 


D.  R.  36°  38'N. 
Obs.  36   33  N. 


Dif.  Lon.     0°  58'  E. 
Lon.  D.R.  32   13  W. 


Long.  Chron.  31°  52'W.IBar.29.80 
D.R.  sin.  yest  82   22  W.lTher.  70° 


The  Magnetic  Variation  having  continued  the  same  throughout  this  day,  that  is  23*  or  2  points  Westerly, 
we  allow  that  quantity  on  the  Courses  by  Compass. 

The  Ship's  position  by  observation  being  to  the  East  of  that  by  the  Dead  Reckoning,  it  is  evident  there 
-must  have  been  a  Current  setting  her  in  that  direction. 

At  Sunset  the  Longitude  by  Chronometer  was  observed  as  above,  (see  the  Method  of  doing  this  at  page 
128,)  and  which  was  7'  of  Longitude  to  the  Eastward  of  that  by  Dead  Reckoning  since  Noon;  and  at  8h 
40m  A.  M.  the  Longitude  by  Chronometer  was  26'  to  the  Eastward  of  the  Dead  Reckoning  since  Noon. 

The  Latitude  observed  by  the  Star  Sirius  at  Sunset  was  1'  to  the  Southward  of  the  Dead  Reckoning; 
and  at  8h  40m  A.  M.  the  Meridian  Altitude  of  the  Moon  gave  the  Latitude  4'  to  the  Southward  of  the 
Dead  Reckoning.  Now,  by  the  Method  given  at  page  29,  of  finding  the  Current,  we  ascertain  that  in  15 
liours,  that  is,  from  Sunset  until,  say  9  o'clock  next  morning,  the  Current  has  set  S.  79°  E.,  E.  by  S.  True, 
or  S.  E.  by  E.  by  the  Compass,  and  the  Drift  15  miles,  or  at  the  rate  of  1  mile  per  hour. 

Equal  Altitudes  taken  near  Noon  in  the  same  manner  as  was  done  yesterday,  corroborates  the  Long,  in  by 
Chronometer  at  Noon  as  above.  The  whole  Error  in  the  Longitude,  from  Noon  to  Noon,  caused  by  the  Cur- 
rent,  amounts  to  30'  E.,  and  the  whole  Error  in  the' Latitude  in  like  manner,  amounts  to  5'  S.  From  this 
data  we  find,  as  before,  that  the  Current  has  .set  E.  by  S.  True,  or  S.  E.  by  E.  by  Compass,  24  miles  in  24 
hours,  or  at  the  rate  of  I  mile  per  hour. 

This  Current  is  supposed  to  be  a  continuation  of  the  Gulf  Stream,  which,  after  pursuing  its  course  along 
the  Coast  of  America,  branches  off  in  the  direction  of  the  Azores  Islands,  and  after  striking  the  Coast  of 
Africa  turns  South,  passing  to  the  East  of  the  Cape  Verde  Islands,  it  joins  the  great  Guinea  Current  on 
the  S.  W.  Coast  of  Africa.     (See  the  llemarks  on  Currents  at  page  39.) 

The  Bearing  and  Distance  of  the  Isle  of  Flores,  at  Noon  to-day,  is  N.  by  E.  nearly,  or  N.  E.  by  N.  by 
Compass,  Distant  182  miles.  And  suppose  it  was  required  to  shape  a  Course  so  as  to  keep  the  Island  oa 
the  same  bearing,  and  allow  for  the  effect  of  the  Current,  we  would  proceed  as  follows:  The  Curren 
being  found  to  run  nearly  at  right  angles  to  the  bearing  of  the  Island,  we  take  the  Sum  of  the  bearing  N. 
10°  E.,  and  the  Set  of  the  Current  S.  79°  E.  =  89°  as  a  Course,  and  its  rate  1  knot  as  a  Distance  gives  the 
Departure  1',  the  Ship's  rate  of  Sailing  8  knots,  and  Departure  1,  gives  the  Course  7°,  which  subtracted 
from  N.  10°  E.  gives  the  True  Course  N.  3°  E.,  and  the  Variation  being  allowed  gives  the  Compass  Cours* 
N.  N   E,  i  E.     (Se^  Method  of  doing  this  at  page  3),  Case  3d.) 


JOURNAL. 


201 


JOURNAL  OF  A  VOYAGE 
From  Santa  Cruz,  (Cape  Verdes,)  towards  St.  J)hn^s,  Newfoundland. 


H. 

K.      H.  K. 

COURSES. 

WINDS. 

L.W. 
i 

REMAINS,    FRIDAY,    MARCH    24TH,    1854. 

I 
2 
8 
4 
6 

0 

7 
8 

8 

8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
7 
8 
7 
8 
8 
8 
8 
8 
6 
6 
6 
6 

N.by  E.  J  E. 

u 
u 

N.  W.  by  W. 

44 

14 

P.  M.     Steady  breeze  and  fiue  clear  -weather. 
Employed  as  yesterday. 

u 
u 
u 
t« 

44 

4( 

44 
U 
44 
(4 
44 

At4h,  Longitude   iu   by  Chrouometer  81'  45' W.      Deaa  Reck. 
31°  50'  W.  An  Azimuth  Obs.  same  time  gave  the  Var.  23°  W, 
and  at  Sunset  an  Amplitude  gave  the  Var.  23°  30' W. 

At  7h,  Gbs.Mer.  Alt  #  Castor.  Lat  in  37°  28'  N,  D.  R.  37°  29'  N. 
Obs.  Alt  of  the  Polar  #.     Lat  in  37°  28'  N. 

9 

10 

11 

12 

1 

2 

3 

4 

5 

6 

7 

8 

1     » 
•   10 

11 

12 

1 
1 

1 

1 

U 
M 
U 

U 

n 

u 
u 

At  1  Oh,  sky  overcast,  with  rain.    Haudad  the  staysails,  royals,  and 

flying-jib. 
Midnight     Squally,  with  showers  of  raio. 

U 

44 

At  2  A.  M.,  weather  cleared  up.     Set  the  light  sails  again. 

u 

44 

NJ!f .  E.  i  E. 

<4 

<( 

N.byE.  }E. 

44 
ti 
44 

44 
U 

N.W.i  W. 

M 
«4 

N.  W.  by  W. 

(( 
44 
(4 

1 

i 

At  4h  9m,  Obs.  M.  Alt.  #  Antares.  Lat  38°  35'  N.  Mean  88°  38'  N. 

Obs.  Alt  of  the  Polar  %.     Lat  38°  41'  K     D.  R.  38°  41'  N. 
At  Sunrise,  Mag.  Vai'ia.  Obs.  23°  W.,  and    the  Long,  in  by  Chron 

same  time  was  31°  20'  W.     D.  Reckon.  31°  42'  W. 
At  8h,  Long,  in    by   Chron.  31°  12'  W.,  and  at   the  same   time 

the  Isle  of  Flores  was  seen  bearing  N.  23°  E.  distant  24  miles. 
Took  Sights  to  verify  the  rate  of  the  Chronometer. 
Noon.     Light  winds  and  fiue.  The  North  end  of  the  Isle  of  Flores 

bore  W.  N.  W.  by  Compass,  distant  7  miles. 

Current  E.  by  S.  (true,)  1  mile  an  hour 

Varit 
28"V 

I.       Course. 
7.  N.  4°  30'  E. 

Dist 

184 

D.  Lat. 
188  N. 

Dep.  Li 
14  E.  Li 

it  D.  R.  39°  36'  N. 
it  Obs.  39    31  N. 

Dif  Long.    0°  18'  E.  Long.  Chro.   31°    4'  W. 
Lon.  D.  R.  31    55   W.  D.Rsin.yest  31    34  W. 

Bar.  29.50 
Ther.  69° 

The  Course  was  shaped,  or  rather  the  Ship  lay  up,  N.  by  E.  I  E.,  and  allowing  J-  a  point  of  Leeway, 
she  made  good  the  Course  N.  N.  E.  i  E.,  as  computed  at  the  end  of  the  last  day's  work,  in  order  to  coun- 
teract the  effect  of  the  current  and  to  keep  the  Island  on  the  same  bearing;  and  had  she  been  continued 
on  that  Course  until  Noon,  she  would  have  closed  with  the  Island  on  the  above  bearing.  But  between 
the  hours  of  5  and  8  A.  M.  she  was  kept  off  1  point,  so  as  to  be  on  its  Meridian  at  8  o'clock,  with  the  view 
of  verifying  the  Chronometer  when  the  Island  was  seen.  At  8  A.  M.  the  Island  was  seen  accordingly 
bearing  N.  23°  E.,  distant  24  miles,  and  which  placed  the  Ship  exactly  on  its  Meridian  ;  sights  for  Chro 
nometer  being  then  taken,  in  the  manner  as  recommended  at  page  155  for  rating  the  Chronometer.  Ii, 
this  case,  the  error  of  the  Chronometer  on  Greenwich  Mean  Time  was  found  to  be  Oh  10m  59s.  Its  error 
Dn  leaving  the  Cape  Verdes.  8  days  ago,  was  Oh  10m  39s.  ;  consequently  it  has  gained  20  sec.  in  8  days, 
and  its  daily  rate,  2  sec.  5-lOth  gaining,  (its  previous  rate,)  confirmed. 

From  the  above  method  of  allowing  for  Currents,  it  will  be  perceived  that  if  the  Set  and  Drift  of  a 
Current  be  known,  it  is  eaay  to  compute  beforehand  the  precise  effect  it  will  have  on  the  Ship's  Course, 
according  to  her  rate  of  sailing,  so  that  the  land  may  be  made  on  any  given  bearing.  But  it  must  b« 
remembered,  that  if  her  rate  of  sailing  changes,  the  Course  must  again  be  computed  to  this  change. 

As  before  observed,  the  Ship  had  been  kept  off  1  point  for  three  hours,  with  the  view  of  placing  her  on 
(h«  Meridian  of  the  Island,  in  consequence  of  which  she  did  not  fetch  it  in,  but  was  on  its  parallel  of  Lat- 
itude at  Noon,  and  she  passed  7  miles  to  the  Eastward  of  its  Meridian. 

In  working  up  the  above  day's  work,  23°  of  Variation  is  allowed  on  all  the  Courses,  after  being  corrected 
for  Leeway,  and  which  being  entered  in  the  Traverse  Table,  together  with  the  true  Set  and  Drift  of  the 
Current,  that  is,  E.  by  S.  1  knot  an  hour,  the  Dead  Reckoning  and  the  Observations  taken  at  varioiu 
times  during  the  day,  will  be  found  to  agree,  as  also  the  Dead  Reckoning  and  the  Observations  at  Noon. 

The  Longitude  by  Dead  Reckoning,  carried  on  from  day  to  day  since  leaving  the  Cape  Verdes,  is  found 
to  be  in  error  51'  too  far  Westerly.  Consequently  a  fresh  Depa.-ture  is  taken  to-day  at  Noon,  from  the 
North  end  of  the  I.^land  of  Flores,  bearing  W.  N.  W.,  distant  7  niles,  the  poe ition  of  which  is  Latitude 
W  32'  N.,  Longitude  31°  12' W. 


loi 


JOURNAi.. 


JOURNAL  OF  A  VOYAGE. 


ITu  Clipper  Ship  Dauntless,  W.  Griffen,  Commander. 


fl. 

K. 

H.  K. 

1 

5 

2 

5 

8 

8 

4 

2 

6 

) 

6 

7 

C 

aim. 

8 

9 

ID 

5 

11 

16 

12 

15 

1 

15 

2 

16 

S 

16 

4 

16 

5 

15 

6 

15 

1 

7 

15 

8 

15 

9 

16 

10 

15 

11 

15 

1 

12 

15 

OODR6E8. 


N.  bj  E. 


N.  W.  I  N. 


•WTNDS. 


N.  W.  byW, 


L.  W. 


South. 


REMARKS,    SATURDAY,  MARCH    25tH,    1854. 


Took  a  fresb  Departure  at  Noon  yesterday,  from  the  N.  end  of  the 
Isle  of  Flores  bearing  W.  N.  W.  by  CompaBB,  distant  7  miles. 

At  3  P.  M.,  light  winds,  inclining  to  calm. 

The  Isles  of  Flores  and  Corva  in  sight  to  the  S.  W.,  12  miles. 

At  6h,  calm.  Heavy  threatening  clouds  rising  in  the  South,  indi- 
cating a  storm.     Barom.  fallen  to  29.20. 

Handed  all  the  light  sails,  sent  down  the  royal  yards,  and  made  all 
snug  for  a  gale.     Mag.  Varia.  Obs.  25°  W. 

At  9h,  a  breeze  sprung  up  from  the  Southward,  with  rain,  which 
rapidly  increased  to  a  gale  of  wind. 

At  llh,  in  top-gallant-sails  and  double-reefed  the  topsails. 

At  Midnight,  handed  the  S.  M.  sail  and  spanker. 

At  2  A.  M.,  gale  increasing  and  a  heavy  sea  running. 

At  4h,  close-reefed  the  topsails  and  foresail  and  furled  the  mizzen 

topsail. 
Passed  several  vessels  lying  to. 

At  8  A  M.,  blowing   excessively  hard,  and  thick  with  heavy  rain. 

Vessel  shipping  much  water  on  deck. 
Pumps  carefully  attended. 
Rigged  in  the  flying-jib-boom. 
Noon.     Co.  weather.     Sun  obscure. 

Bearing  and  Distance  of  St.  John's,  N.  63°  W.,  (true,)  830  miles. 


Varia. 
|2ipt.W 


Course.  DistlD.  Lat. 


N.  60°  W 


213  1108  N 


Dep. 
184W 


Lat.D.R.41' 
Lat  Obs.  " 


19' N. 


Dif.  Long.  4° 
Lon.  D.R.35 


O'W. 
12  W. 


Lon.  Chro.         "      "        I  Baro.  29.10 
D.R.  sin.  yest.  35°  12'W.I  Therm.  65° 


No  Observations  have  been  obtained  to-day,  except  at  Sunset,  when  an  Amplitude  gave  the  Magnetic 
Variation  25°,  or  2i  points  Westerly. 

In  working  up  this  day's  work,  we  allow  for  the  Set  of  tho  Current  E.  by  S.  (true)  1  knot  an  hour,  from 
Noon  antil  9  P.  M.,  at  which  time  the  wind  came  out  from  the  Southward,  and  increased  into  a  gale, 
consequently,  the  Ship  would  soon  run  to  the  North  Westward,  where  she  would  be  out  of  its  influence. 

There  is  reason  to  apprehend  that  the  Ship  has  been  run  off  to  the  Northward  of  her  Course  to-day,  as 
the  Sea  broke  heavily  on  the  weather  quarter ;  and  also  from  the  fault  of  the  helmsman  hanging  on  his 
weather  helm  when  the  Ship  was  on  the  top  of  a  Sea,  thereby  causing  her  to  yaw  off.  But  as  there  i» 
plenty  of  Sea-room,  it  is  not  deemed  necessary  to  make  any  allowance  for  that  in  this  day's  work.  (See 
the  Remarks  on  this  subject  at  page  190.) 

When  the  wind  came  fair  last  night  the  Course  was  shaped  as  above,  from  the  position  of  the  Ship  at 
that  time,  in  Latitude  39'  44'  N.,  and  Longitude  30°  56'  W.  Then  a  ruler  placed  over  the  Ship's  place 
an  the  Chart  and  over  that  of  St.  John's,  gives  the  True  Course  N.  W.  by  W.  i  W.,  and  allowing  2i  points 
Variation  to  the  right,  gives  the  Compass  Course  required  to  steer  N.  W.  i  N.,  and  the  Distance  1050 
miles;  or  the  same  may  be  found  by  Case  2d,  in  Middle  Latitude  or  Mercator's  Sailings  In  Ihis  case, 
the  Latitude  in  at  9  P.  M.  being  39°  44'  N.,  and  Longitude  30°  56'  W. 

In  the  Table  of  Positions  is  found  St.  John's,  Latitude  47°  34'  N.,  Longitude  52°  45'  W.  This  gives  the 
True  Bearing  N.  64  W.,  or  N.  W.  by  W.  f  W.,  nearly,  and  the  Distance  1050,  same  as  the  Chart. 

In  like  manner,  the  Bearing  and  Distance  is  found  to-day  at  Noon  to  h>e  N.  63'  W.,  or  N.  W.  by  W.f  W, 
nearly,  by  Compass,  Distance  830  miles. 


JOURNAL. 


203 


JOURNAL  OF  A  VOYAGE 
F\rom  Santa  Cruz,  (Cape  Verdes.)  towards  St.  John's,  Newfoundland. 


B. 

K. 

B.  K. 

OODBSKfi. 

WINDS.          L.W. 

REUAEES,    SDNDAT,   MABOH    26TH,  1864. 

1 

2 

15 

15 

S.  by  W. 

P.  M.     Heavy  Southerly  gale  and  a  high  topping  Bea  running. 

S 

4 
6 

6 

15 
15 
16 
16 

a 

u 
« 

S.  W.  by  S. 

At  4h,  more  moderate  ;  wind  inclining  to  "Westerly 
Set  the  reefed  S.  M.  sail  and  mizen  topsail 

7 

8 

9 

10 

11 

12 

1 

2 

16 
16 
16 
16 
16 
16 
16 
16 

u 
u 
u 

u 
u 
u 

At  8h,  the  rain  ceased,  and  the  weather  made  an  attempt  to  clear  up. 

M 

u 
« 
a 
u 

u 
a 

a 
u 
u 

At  9h  40ra  Mer.Alt  #  Regulus.  Lat  in  42'  59'  N.  )  Mean  43°    5'N. 
Same  time  the  Alt.  of  Pole  #.     Lat  in  48*  1 1'  N.  J  D.  R.  42°  25'N. 
Midnight.     Blowing  bard  ;  vessel  shipping  much  water  on  deck  ; 
pumps  carefully  attended  every  4  nours. 

3 
4 
5 
6 

7 

8 

9 

10 

11 

12 

16 
16 
16 
16 
16 
15 
15 
15 
15 
15 

« 
u 
u 
u 
u 
u 
u 
u 
u 
u 

u 
u 
u 
u 

M 

u 
u 

C( 

u 
u 

At  4  A.M.,  Mer.  Alt.  #  Antares.  Lat  in  43°  46'  N.  )  Mean  48°  53'N. 
Same  time  the  Alt  of  Polar  #,     Latin  44°    0'  K  )  D.  R.  43°    8'N. 
At  6h,  gale  moderating  and  the  sea  falling.    Out  close  reefs  of  the 

topsails  and  set  the  jib. 
At  8h.  obs.  au  Alt  of  the  Sun.     Long,  in  by  Chron.  41°  12'  W. 
Weather  set  in  thick  again,  with  mizzling  rain. 
The  temperature   of  the  Sea-water  at  Noon  was  found  to  be  the 

same  as  that  of  the  air,  56°. 
Noon.     Do.  weather.     Suu  obscure. 

True  bearing  of  St  John's,  N.  69°  W.     Distance  468  miles. 

Variation  I  Course 
gipta.W.lN.65°W 


Dist 
878 


D.  Latj 
162  N. 


Dep. 

342W. 


Lat  D.  R.  44°  I'N.IDif.  Lon.    7°  46'W. 
Lat  Ohs.  44  46  N.|Lon.  D.R.  42  68W. 


Lon.  Chr.         42°  27'W. 
D.R.Biaye8t  42°  68'W. 


Bar.  29.06 
Ther.  55" 


The  Variation  allowed  on  this  day's  v/ork  is  2^  points  Westerly. 

At  9h  40m  P.  M.,  the  Meridian  Altitude  of  the  Star  Regulus  was  observed  to  the  Southward,  and  at 
the  same  time  an  Altitude  of  the  Polar  Star  was  observed  to  the  Northward.  The  Mean  of  the  two  Lati- 
tudes so  found,  compared  with  that  by  the  Dead  Reckoningj  places  the  Ship  40'  to  the  Northward  of  th« 
,  Dead  Reckoning 

And  at  4  A.  M.,  the  Meridian  Altitude  of  Antares  was  observed  to  the  Southward,  at  the  same  time  the 
Altitude  of  the  Pole  Star  was  observed  to  the  Northward.  The  Mean  of  the  two  Latitudes  places  the 
Ship  45'  to  the  Northward  of  the  Dead  Reckoning.  These  Observatioas  may  not  be  very  accurate,  on 
account  of  the  obscurity  of  the  horizon  and  the  heavy  sea  running,  together  with  the  difficulty  of  making 
the  Observations,  but  are  sufficiently  near  to  act  as  a  warning  that  the  Dead  Reckoning  is  in  error,  and  by 
taking  Stars  North  and  South  of  the  Meridian  the  errors  in  the  Observation  are  very  much  diminished. 
For  instance,  the  Difference  in  the  two  Latitudes  given  by  Altitudes  of  Antares  and  the  Pole  Star  is  1 4', 
but  the  Mean  of  the  two  Latitudes  is  taken. 

The  Sun's  Altitude  was  also  obtained  about  8  o'clock  in  the  morning,  and  by  using  the  corrected  Lati- 
tude in  finding  the  Time,  we  get  the  Longitude  by  Chronometer  as  above,  and  which  places  the  Ship  33' 
of  Longitude  to  the  Eastward  of  the  Dead  Reckoning.  These  errors  in  the  Latitude  and  Longitude  so 
found,  shows  that  the  Ship's  Course  made  good  is  about  1  point  further  to  the  Northward  than  the  Course 
by  Compass  makes  her;  she  has,  therefore,  been  run  off. 

The  Barometer  having  fallen  to  29.5,  and  the  weather  at  Noon  assumed  a  very  threatening  appearance, 
we  may  look  for  a  continuance  of  the  gale. 

The  Ship  is  now  approaching  the  Eastern  edge  of  the  Polar  Current,  in  which  we  may  expect  to  find 
large  masses  of  Ice,  brought  down  by  it  from  the  Polar  regions.  On  a  Ship  entering  this  current  the  temper- 
ature of  the  Sea  water  will  be  found  to  fall  about  20",  and  may  be  easily  ascertained  by  drawing  a  bucket 
of  water  from  alongside  and  plunging  the  Thermometer  into  it.  (See  the  Remarks  on  Currents  and  tho 
Use  of  the  Thermometer,  at  page  82.) 

The  position  of  the  Ship  by  Observation  being  laid  off  on  the  Chart,  the  bearing  of  St.  John's  is  found 
to  be  W.  by  N.  }  N.  ;  2i  points  Variation  allowed  on  that  gives  the  bearing  by  Compan  N.  W.,  Distanst 
468  miles. 


904 


JOURNAL. 


JOURNAL  OF  A  VOYAGE. 


The  Clipper  Ship  Dauntless,  W.  Grtffen,  Commander. 


2 
8 

4 
6 
6 
1 
8 
9 

10 

11 

12 

1 

2 

S 

4 

6 

6 

7 

8 

9 

10 

11 

12 


16 

16 

17 

17 

17 

17 

10 

10 

10 

10 

9 

8 

8 

8 

8 

8 

12 

16 

16 

16 

16 

17 

17 

17 


H.K. 


COUBSKS. 


N.N.WiW, 


WINDS. 


South. 


L.  W. 


s.  s.  w. 


Ourrent  Sontb  by  Compass  1^  knots. 


REMARKS,  MONDAY,  MARCH  27tH,  1854. 


At  1  P.  M.,  temperature  of  the  Sea-water  50*,  Air  52*. 

Wind  backed  into  the  Southward,  and  the  gale  mcreased. 

At  Ih  30m,  temperature  of  the  Sea-water  40°,  Air  42°.  ' 

At  4h,  it  fell   to  35°.      Ship  was  then  in  the  strength  of  the 

Polar  Current. 
At  6h,  blowing   excessively  hard.     Close-reefed  the  topsails  and 

handed  the  courses  and  jib. 
At  8h,  the  temperature  fell  to  33°  in  the  water,  and  at  the  same 

time  an  Iceberg  was  seen  ahead  of  the  Ship.      Hauled  up  and 

passed  to  wmdward  of  it. 
At  llh,  furled  the  mizen  topsail. 
Midnight.     Ship   running  under  easy  sail,  and    a  bright  lookout 

kept  for  ice. 
At  2  A.  M.,  passed  another  large  berg. 

At  4h,  weather  more  clear.    Set  the  reefed  foresail 

At  6h,  out  close  reefs  and  set  the  reefed  mainsail,  jib  and  mizen- 

topsail. 
Ship  passing  a  great  many  Icebergs. 

Noon.  Thick  fog  and  heavy  rain.  Close-reefed  the  topsails  and 
furled  the  courses.  Passed  several  fields  and  detached  pieces 
of  ice. 

St.  John's  S.  89°  W.,  (true,)  or  W.  N.  W.  by  Comp.,  dist.  194  miles 


Variation 
2pt8.  W. 


Course 
N.  54°W 


Dist. 
290 


D.LaL 

171  N. 


Dep.    ILat.  D.R.47°  87'N.|Dif  Lon.     5°  36' W. 
234  W.   Lat.  Ob Lon.  D.R.  48  34  W, 


Long.  Cliro. ' 
D.  R.  since  yes- 
terday48°3'W. 


Bar.  29.10 
Ther.  34° 


The  Magnetic  Variation  not  having  been  observed  to-day,  it  is  taken  from  the  Chart,  which  gives  2 
points  Westerly. 

By  the  decrease  in  the  temperature  of  the  Sea-water,  as  noted  above,  the  Ship  evidently  entered  the 
Polar  Current  soon  after  mid-day,  the  Set  of  which  is  about  South  by  the  Compass,  or  S.  S.  E.  (true,)  and 
its  Drift  H  knots  an  hour.  It  being  desirable  to  get  to  the  Northward  of  the  Parallel  of  Latitude  of  St. 
John's  jbefore  the  wind  shifts  to  the  Northward,  a  Course  must  be  shaped  for  that  purpose.  By  reference 
to  the  Ship's  place  on  the  Chart,  a  N.  W.  f  W.  True  Course,  and  Distance  300  miles,  would  place  her  to- 
morrow at  Noon  near  the  Eastern  edge  of  the  Great  Bank,  in  the  Parallel  of  Latitude  required.  But  to 
make  this  Course  good,  we  must  allow  for  the  Set  and  Drift  of  the  Current  as  follows :  The  Set  of  the 
Current  being  nearly  in  a  contrary  direction  to  the  required  Course,  we  take  their  Difference,  2|  points,  as 
a  Course,  and  the  Drift,  H  knots,  as  a  Distance,  which  gives  the  Departure,  7-tenths.  Then  the  average 
rate  of  sailing,  say  13  knots  an  hour,  (which  the  vessel  is  expected  to  make  next  24  hours,)  as  a  Distance, 
and  "vrith  7-tenths  as  a  Departure,  find  the  Course,  3°,  or  i  of  a  point,  which  subtracted  from  the  given 
Course,  N.  W.  }  W.,  gives  the  required  Course  N.W.  i  W. ;  the  Variation,  2  points  W.,  allowed,  gives  the 
Compass  Course  required  to  steer  N.  N.  W.  ^  W.     (See  the  Rule  in  Current  Sailing,  page  30,  Case  3d.) 

The  Ship  has  passed  many  Icebergs  to-day,  and  on  her  approach  to  them  the  Thermometer  was  fourJ 
to  fall  to  32°,  nearly,  but  rose  3°  after  having  passed  them.  The  Mean  temperature  of  the  Sea-water  in 
the  Polar  Current  appeared  to  be  35°. 

The  wind  having  backed  into  the  Southward  again,  an  omen  of  bad  weather,  the  sail  on  the  Ship  was  re- 
duced to  the  close-reefed  topsails  before  night-fall,  and  a  vigilant  lookout  kept  during  the  night  for  Icebergs, 
as  they  can  be  seen  at  a  considerable  distance  in  dark  weather,  if  a  good  lookout  is  kept  for  the  glare  oi 
reflection,  which  is  a  peculiar  kind  of  phosphorus  light  which  surrounds  them. 

At  Noon,  a  dense  fog  with  heavy  rain  came  on,  and  as  the  Barometer  is  rising,  it  indicates  a  shift  of 
wind  to  the  Northward.  It  was,  therefore,  deemed  prudent  to  put  the  Ship  under  low  canvas,  in  case  of 
a  sudden  shift;  besides,  according  to  the  Dead  Reckoning,  she  is  to  the  Northward  of  the  Parallel  of 
Latitude  of  the  intended  port. 

The  Bearing  of  St.  John's  at  Noon  to-day  is  S.  89*  W.,  or  W.  N.  W.  by  Compass,  nearly,  distant  194 
Biles 


JOURNAL. 


lOl^,NAL  OF  A  VOYAGE 
Prom  Santa  Cruz,  (Cape  Verdes,)  towards  St.  John's,  Newfoundland. 


1 

2 
3 
4 
6 

6 

7 

8 

9 

10 

11 

12 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 


11 
11 
10 
10 
10 
10 
2 

2 

2 

2 

2 

2 

2 

5 

7 

14 

16 

16 

15 

15 

16 

15 

15 


S.K. 


OODKSES. 


N.W.byN.   W.  S.  "W 


WINDS. 


Lying  to. 
Up  S.  b  W, 
OS  S.  by  E. 

W.  N.  W. 


N.w.byw.^w, 


uvr. 


W.  S.  W. 

North. 

U 
M 
•I 

N.  by  E. 


12      15 

Current  South  Dy  Compass  1^  knots. 


BEMABKS,  TUESDAT,  MABOB  28Ta,  1864. 


P.  M.     Dense  fog,  with  mizzling  rain.      Wind  inclining  to  Wft** 

erly.     No  ice  visible. 
Bent  the  cables  and  got  the  anchors  on  the  gunwale. 

At  4h,  sounded  in  60  fathoms.     Temperature  of  the  3ea-wat«r  84" 
Air  36°. 

At  6h,  blowing  excessive  hard  and  heavy  sea  on. 

Wore  ship  with  her  head  to  the  Southward.     Furled  the  fore  and 
mizen  topsails,  and  hove  to  under  the  main-topaail. 

At  9h,  less  wind  and  a  heavy  fall  of  rain. 

At  lOh,  the  wind  cbanged  suddenly  to  the  Northward,  ia  a  tre- 
mendous rain  squall. 

At  Midnight,  blowing  hard,  but  the  weather  clearing  up. 

At  1  A.  M.,  set  the  fore  and  mizen  topsails. 

At  2h,  set  the  reefed  courses  and  spanker. 

At  3h,  out  doable  reefs  and  set  top-gallant-sails  andjiK 

At  4h,  Mer.  Alt  of  #  An  tares.     Lat  in  47°  29'  )  Mean  47*  84'  N. 

Same  time  Alt.  of  Polar  #.         Lat.  in  47"  39'  J  D.  R.  47*  86'  N. 

At  Sunrise,  Mag.  Varia.  Obs.  was  23°  Westerly. 

Out  all  reefs  and  checked  in  the  weather  braces. 

At  8  A.  M.,  Long,  in  by  Chron.  51°  18'  W.     D.  R.  50°  58'  W. 

St.  John's  harbor  bears  W.  N.  W.  by  Compass,  distant  60  milea. 

At  lOh,  the  land  was  seen  in  that  directioa 

At  llh,  made  out  Signal  Hill,  bearing  W.  N.  W,  distant  5  leaguei. 

Noon.     Ship  close  in  with    Fort  Amherst.      Received  on  board  a 
Pilot,  and  proceeded  into  port. 


Vari'n 
«ptW. 


Course 
S.  89°  W. 


Dist 
177 


D.  Lat. 
3'  S. 


Dep. 

177  W. 


Lat 
Lat 


D.R.47' 
Obs.  47 


34'N. 
34  N. 


Dif.  Lon.     4' 
Lon.  D.R.  52 


'25' 
59  W. 


Long.  Chron.  62" 
D.R.  sin.  yest  52 


48'W.|Bar.28.90 
28  W.lTher.46' 


At  1  P.  M.  came  to  with  the  small  bower  anchor  in  8  fathoms  water,  abreast  of  the  town  of  St  John's.  Furled 
lails  and  moored  ship,  with  45  fathoms  cable  on  each  bower  anchor,  and  sent  down  top-gallant  yards.  Midnight. 
Heavy  rain  squalls  from  the  N.  W.  This  day's  work  ends  with  and  contains  36  hours,  in  order  to  oommence  th« 
Harbor  Log. 

On  referring  to  the  above  Log,  it  will  be  noticed  that  the  Ship  ran  to  the  N.  W.  by  N.  until  4  P.  M., 
when  soundings  were  obtained  in  60  fathoms  water,  on  the  North  Eastern  edge  of  the  Great  Bank  of  New- 
foundland, and  at  6  P.  M.  she  was  wore  round  with  her  head  to  the  Southward,  and  hove  to  under  the 
elose-reefed  main-topsail  for  the  night,  on  account  of  the  dense  fog  which  prevailed,  in  case  of  meeting 
with  ice ;  and  also  with  the  view  of  being  on  the  proper  tack  should  a  sudden  shift  of  wind  from  the 
Northward  take  place  during  the  night  time. 

At  9  P.  M.  the  gale  began  to  moderate,  and  heavy  showers  of  rain  fell,  the  usual  precursor  of  a  violent 
and  sudden  shift  of  wind.  The  Barometer  now  began  to  rise  rapidly,  and  at  10,  a  squall  from  the  North- 
ward struck  the  Ship,  and  blew  with  great  fury  for  about  two  hours,  and  she  luffed  up  to  the  wind  on  the 
same  tack,  and  sail  was  made  as  the  wind  moderated. 

The  sky  having  now  cleared  up,  the  opportunity  was  taken  of  finding  the  Latitude  by  Observation  ut  4 
A.  M.,  from  the  Meridian  Altitude  of  Antares  to  the  Southward,  and  the  Altitude  of  the  Polar  Star  to  the 
Northward.  The  Mean  of  the  two  Latitudes  so  found  agrees  with  that  by  Dead  Reckoning,  and  places 
the  Ship  in  the  parallel  of  Latitude  of  the  intended  port,  47°  34'  N.  ;  consequently,  it  bears  W.  N.  W.  by 
Compass,  but  we  must  steer  i  a  point  more  to  the  Northward,  in  order  to  make  the  necessary  allowanw 
for  Leeway  and  Currents. 

At  Sunrise,  the  Magnetic  Variation  was  observed  to  be  23°  W.,  and  at  8  A.  M.  the  Longitude  by  Chre- 
Bometer,  as  above,  is  found  to  be  20'  to  the  Westward  of  that  by  Dead  Reckoning  since  last  Observation, 
and  by  a  case  of  Parallel  Sailing,  or  by  the  Chart,  St.  John's  is  found  to  bear  true  West,  or  W.  N.  W.  by 
Ccmpass,  distant  60  miles. 

At  10  A.  M.,  High  Land  was  discovered  ahead,  and  at  11  the  buildings  on  Signal  Hill,  and  Fort 
Amherst,  at  the  entrance  of  St.  John's  Harbor,  were  distinctly  made  out,  and  at  Noon  she  closed  with  th« 
entrance  of  the  Harbor,  and  took  a  Pilot  on  board.  Thus  making  the  Pass»ge  from  Port  to  Port  in  18 
days  6  hours,  and  sailed  a  distance  of  2977  miles. 

In  working  up  this  day's  work,  the  allowance  for  the  Set  and  Drift  cf  the  Current,  as  above,  (S.  S.  K. 
irue,  36  miles  in  24  hours,)  must  be  inserted  in  the  Traverse  Tabk,  aloa«  irith  the  other  Courses 
Distanoea,  and  the  result  of  the  day's  work  will  be  fou.nd  as  abo^e. 


306 


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TABLES. 


TABLE  ] 

.—  DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  i  POINT. 

1 

North  i  East. 

North ; 

:  West        South  J  East        South  J  "West 

Dist. 

Lut 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist.   Lat 

Dep. 

Dist 

liat 

Dep. 

1 

01.0 

00.0 

61 

60.9 

03.0 

121 

120.9 

05.9 

181  180.8 

08.9 

241 

240.7 

11.8 

2 

02.0 

00.1 

62 

61.9 

03.0 

122 

121.9 

06.0 

182 

181.8 

08.9 

242 

241.7 

11.9 

3 

03.0 

00.1 

63 

62.9 

03.1 

123 

122.9 

06.0 

183 

182.8 

09.0 

243 

242.7 

11.9 

4 

04.0 

00.2 

64 

63.9 

03.1 

124 

123.9 

06.1 

184 

183.8 

09.0 

244  243.7 

12.0 

5 

05.0 

00.2 

65 

64.9 

03.2 

125 

124.8 

06.1 

185 

184.8 

09.1 

245 

244.7 

12.0 

6 

06.0 

00.3 

Q6 

65.9 

03.2 

126 

125.8 

06.2 

186 

185.8 

09.1 

246 

245.7 

12.1 

7 

07.0 

00.3 

67 

66.9 

03.3 

127 

126.8 

06.2 

187 

186.8 

09.2 

247 

246.7 

12.1 

8 

08.0 

00.4 

68 

67.9 

03.3 

128 

127.8 

06.3 

188 

187.8 

09.2 

248 

247.7 

12.2 

9 

09.0 

00.4 

69 

68.9 

03.4 

129 

128.8 

06.3 

189 

188.8 

09.3 

249 

248.7 

12.2 

10 

10.0 

00.5 

70 

69.9 

03.4 

130 

129.8 

06.4 

190 

189.8 

09.3 

250 

249.7 

12.3 

11 

11.0 

00.5 

71 

70.9 

03.5 

131 

130.8 

06.4 

191 

190.8 

09.4 

251 

250.7 

12.3 

12 

12.0 

00.6 

72 

71.9 

03.5 

132 

131.8 

06.5 

192 

191.8 

09.4 

252 

251.7 

12.4 

13 

13.0 

00.6 

73 

72.9 

03.6 

133 

132.8 

06.5 

193 

192.8 

09.5 

253 

252.7 

124 

14 

14.0 

00.7 

74 

73.9 

03.6 

134 

133.8 

06.6 

194 

1938 

09.5 

254 

253.7 

125 

15 

15.0 

00.7 

75 

74.9 

03.7 

135 

134.8 

06.6 

195 

194.8 

09.6 

255 

254.7 

12.5 

16 

16.0 

00.8 

76 

75.9 

03.7 

136 

135.8 

06.7 

196 

195.8 

09.6 

256 

255.7 

12.6 

17 

17.0 

00.8 

77 

76.9 

03.8 

137 

136.8 

06.7 

197 

196.8 

09.7 

257 

256.7 

12.6 

18 

18.0 

00.9 

78 

77.9 

03.8 

138 

137.8 

06.8 

198 

197.8 

09.7 

258 

257.7 

12.7 

19 

19.0 

00.9 

79 

78.9 

03.9 

139 

138.8 

06.8 

199 

198.8 

09.8 

259 

258.7 

12.7 

20 

20.0 

01.0 

80 

79.9 

03.9 

140 

139.8 

06.9 

200 

199.8 

09.8 

260 

259.7 

12.8 

21 

21.0 

01.0 

81 

80.9 

04.0 

141 

140.8 

06.9 

201 

200.8 

09.9 

261 

260.7 

12.8 

22 

22.0 

01.0 

82 

81.9 

04.0 

142 

141.8 

07.0 

202 

201.8 

09.9 

262 

261.7 

12.9 

23 

23.0 

01.1 

83 

82.9 

04.1 

143 

142.8 

07.0 

203 

202.8 

10.0 

263 

262.7 

12.9 

24 

24.0 

01.2 

84 

83.9 

04.1 

144 

143.8 

07.1 

204 

203.8 

10.0 

264 

263.7 

13.0 

25 

25.0 

01.2 

85 

84.9 

04.2 

145 

144.8 

07.1 

205 

204.8 

10.1 

265 

264.7 

13.0 

26 

26.0 

01.3 

86 

85.9 

04.2 

146 

145.8 

07.2 

206 

205.8 

10.1 

266 

265.7 

13.1 

27 

27.0 

01.3 

87 

86.9 

04.3 

147 

146.8 

07.2 

207 

206.8 

10.2 

267 

266.7 

13.1 

28 

28.0 

01.4 

88 

87.9 

04.3 

148 

147.8 

07.3 

208 

207.7 

10.2 

268 

267.7 

13.2 

29 

29.0 

01.4 

89 

88.9 

04.4 

149 

148.8 

07.3 

209 ;  208.7 

10.3 

269 

268.7 

13.2 

30 
31 

30,0 

01.5 

90 

89.9 

04.4 

150 

149.8 

07.4 

210 

209.7  1 10.3 

270 

269.7 

13.2 

31.0 

01.5 

91 

90.9 

04.5 

151 

150.8 

07.4 

211 

210.7,10.4 

271 

270.7 

13.3 

32 

32.0 

01.6 

92 

91.9 

04.5 

152 

151.8 

07.5 

212 

211.7 

10.4 

272 

271.7 

13.3 

33 

33.0 

01.6 

93 

92.9 

04.6 

153 

152.8 

07.5 

213 

212.7 

10.5 

273 

272.7 

13.4 

34 

34.0 

01.7 

94 

93.9 

04.6 

154 

153.8 

07.6 

214 

213.7 

10.5 

274 

273.7 

13.4 

35 

35.0 

01.7 

95 

94.9 

04.7 

155 

154.8 

07.6 

215 

214.7 

10.5 

275 

274.7 

13.5 

36 

36.0 

01.8 

96 

95.9 

04.7 

156 

155.8 

07.7 

216 

215.7 

10.6 

276 

275.7 

13.5 

37 

37.0 

01.8 

97 

96.9 

04.8 

157 

156.8 

07.7 

217 

216.7 

10.6 

277 

276.7 

13.6 

38 

38.0 

01.9 

98 

97.9 

04.8 

158 

157.8 

07.8 

218 

217.7 

10.7 

278 

277.7 

13.6 

39 

39.0 

01.9 

99 

98.9 

04.9 

159 

158.8 

07.8 

219 

218.7 

10.7 

279 

278.7 

13.7 

40 

41 

40.0 

02.0 

100 

99.9 

04.9 

160 

159.8 

07.9 

220 

219.7 

10.8 

280 

279.7 

13.7 

41.0 

02.0 

101 

100.9 

05.0 

161 

160.8 

07.9 

221 

220.7 

10.8 

281 

280.7 

13.8 

42 

41.9 

02.1 

102 

101.9 

05.0 

162 

161.8 

07.9 

222 

221.7 

10.9 

282 

281.7 

13.8 

43 

42.9 

02.1 

103 

102.9 

05.1 

163 

162.8 

08.0 

223 

222.7 

10.9 

283 

282.7 

13.9 

44 

43.9 

02.2 

104 

103.9 

05.1 

164 

163.8 

08.0 

224 

223.7 

11.0 

284 

283.7 

13.9 

45 

44.9 

02.2 

105 

104.9 

05.2 

165 

164.8 

08.1 

225 

224.7 

11.0 

285 

284.7 

14.0 

46 

45.i> 

02.3 

106 

105.9 

05.2 

166 

165.8 

08.1 

226 

225.7 

11.1 

286 

285.7 

14.0 

47 

46.9 

02.3 

107 

106.9 

05.3 

167 

166.8 

08.2 

227 

226.7 

11.1 

287 

286.7 

14.1 

48 

47.9 

02.4 

108 

107.9 

05.3 

168 

1G7.8 

08.2 

228 

227.7 

11.2 

288 

287.7 

14.1 

49 

48.9 

02.4 

109 

108.9 

05.3 

169 

168.8 

08.3 

229 

228.7 

11.2 

289 

288.7 

14.2 

50 

49.9 

02.5 

110 

109.9 

05.4 

170 

169.8 

08.3 

230 

229.7 

11.3 

290 

289.7 

14.2 

51 

50.9 

02.5 

111 

110.9 

05.4 

171 

170.8 

08.4 

231 

230.7 

11.3 

291 

290.6 

14.3 

52 

51.9 

02.6 

112 

111.9 

05.5 

172 

171.8 

08.4 

232 

231.7 

11.4 

292 

291.6 

14.3 

53 

52.9 

02.6 

113 

112.9 

05.5 

173 

172.8 

08.5 

233 

232.7 

11.4  293 

292.6 

14.4 

54 

53.9 

02.6 

114 

113.9 

05.6 

174 

173.8 

08.5 

234 

233.7 

11.5  294 

293.6 

14.4 

55 

54.9 

02.7 

115 

114.9 

05.6 

175 

174.8  !  08.6 

235 

234.7 

11.5 

295 

294.6 

14.5 

56 

55.9 

02.7 

116 

115.9 

05.7 

176 

175.8  08.6 

236 

235.7 

11.6 

296 

295.6 

14.5 

57 

56.9 

02.8 

117 

116.9 

05.7 

177 

176.8 

08.7 

237 

236.7 

11.6 

297 

296.6 

14.6 

58 

57.9 

02.8 

118 

117.9 

05.8 

17S 

177.8 

08.7 

238 

237.7 

11.7 

298 

2;t7.6 

14.6 

59 

58.9 

02.9 

119 

118.9 

05.8 

179 

178.8 

08.8 

239 

238.7 

11.7 

299 

29S.6 

14.7 

60 

59.9 

02.9 

120 

119.9 

05.9 

180 

179.8 

08.8 

240 

239.7 

11.8 

300 

299.6 

14.7 

Dist 

Dep. 

Lat 

Dist 

Dep. 

Lat 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist  Dep. 

Lat 

El«t  J  North. 

Ka 

.St  t  South. 

[ 

ForTJ-Pts.]          Wpst  i  .North      West  J  South. 

8    TABLE  I.— DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  i   POINT 

North  i  East        North  |We«t.        South  i  East.        South  i  West. 

Dist. 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat. 

Dep. 

1 

01.0 

00.1 

61 

60.7 

06.0 

121 

120.4 

11.9 

181 

180.1 

17.7 

241 

239.8 

23.6 

') 

02.0 

00.2 

62 

61.7 

06.1 

122 

121.4 

12.0 

182 

181.1 

17.8 

242 

240.8 

23.7 

3 

03.0 

00.3 

63 

62.7 

06.2 

123 

122.4 

12.1 

183 

182.1 

17.9 

243 

241.8 

23.8 

4 

04  0 

00.4 

64 

63.7 

06.3 

124 

123.4 

12.2 

184 

183.1 

18.0 

244 

242.8 

23.9 

5 

05.0 

00.5 

65 

64.7 

06.4 

125 

124.4 

12.3 

185 

184.1 

18.1 

245 

243.8  24.0  1 

6 

06.0 

00.6 

66 

65.7 

06.5 

126 

125.4  12.4 

186 

185.1 

18.2 

246 

244.8\  24.1  \ 

7 

07.0 

00.7 

67 

66.7 

06.6 

127 

126.4  12.4 

187 

186.1 

18.3 

247 

245.8 

24.2 

8 

08.0 

00.8 

68 

67.7 

06.7 

128 

127.4  12.5 

188 

187.1 

18.4 

248 

246.8 

24.3 

9 

09.0 

00.9 

69 

68.7 

06.8 

129 

128.4 

12.6 

189 

188.1 

18.5 

249 

247.8 

24.4 

10 

10.0 

01.0 

70 

69.7 

06.9 

130 

129.4 

12.7 

190 

189.1 

18.6 

250 

248.8 

24.5 

11 

10.9 

01.1 

71 

70.7 

07  0 

131 

130.4 

12.8 

191 

190.1 

18.7 

251 

249.8 

24.6 

12 

11.9 

01.2 

72 

71.7 

07.1 

132 

131.4 

12.9 

192 

191.1 

18.8 

252 

250.8 

24.7 

13 

12.9 

01.3 

73 

72.6 

07.2 

133 

132.4 

13.0 

193 

192.1 

18.9 

253 

251.8 

24.8 

14 

13.9 

01.4 

74 

73.6 

07.3 

134 

133.4 

13.1 

194 

193.1 

19.0 

254 

252.8 

24.9 

15 

14.9 

01.5 

75 

74.6 

07.4 

135 

134.3 

13.2 

195 

194.1 

19.1 

255 

253.8 

25.0 

16 

15.9 

01.6 

76 

75.6 

07.4 

136 

135.3 

13.3 

196 

195.1 

19.2 

256 

254.8 

25.1 

17 

16.9 

01.7 

77 

76.6 

07.5 

137 

136.3 

13.4 

197 

196.1 

19.3 

257 

255.8 

25.2 

18 

17.9 

01.8 

78 

77.6 

07.6 

138 

137.3 

13.5 

198 

197.0 

19.4 

258 

256.8 

25.3 

19 

18.9 

01.9 

79 

78.6 

07.7 

139 

138.3 

13.6 

199 

198.0 

19.5 

259 

257.8 

25.4 

20 
21 

19.9 

02.0 

80 

79.6 

07.8 

140 

139.3 

13.7 

200 

199.0 

19.6 
19.7 

260 

258.7 

25.5 

20.9 

02.1 

81 

80.6 

07.9 

141 

140.3 

13.8 

201 

200.0 

261 

259.7 

25.6 

22 

21.9 

02.2 

82 

81.6 

08.0 

142 

141.3 

13.9 

202 

201.0 

19.8 

262 

260.7 

25.7 

23 

22.9 

02.3 

83 

82.6 

08.1 

143 

142.3 

14.0 

203 

202.0 

19.9 

263 

261.7 

25.8 

24 

23.9 

02.4 

84 

83.6 

08.2 

144 

143.3 

14.1 

204 

203.0 

20.0 

264 

262.7 

25.9 

25 

24.9 

02.5 

85 

84.6 

08.3 

145 

144.3 

14.2 

205 

204.0 

20.1 

265 

263.7 

26.0 

2t) 

25.9 

02.5 

86 

85.6 

08.4 

146 

145.3 

14.3 

206 

205.0 

20.2 

266 

264.7 

26.1 

27 

26.9 

02.6' 

87 

86.6 

08.5 

147 

146.3 

14.4 

207 

206.0 

20.3 

267 

265.7 

26.2 

28 

27.9 

02.7 

88 

87.6 

08.6 

148 

147.3 

14.5 

208 

207.0 

20.4 

268 

266.7 

ie,  ^ 

29 

28.9 

02.8 

89 

88.6 

08.7 

149 

148.3 

14.6 

209 

208.0 

20.5 

269 

267.7 

26.4 

30 

29.9 

02.9 
03.0 

90 

89.6 

08.8 

150 

149.3 

14.7 

210 

209.0 

20.6 

270 

268.7 
269.7 

26.5 

31 

30.9 

91 

90.6 

08.9 

151 

150.3  14.8 

211 

210.0 

20.7 

271 

26.6 

32 

31.8 

03.x 

92 

91.6 

09.0 

152 

151.3] 

14.9 

212 

211.0 

20.8 

272 

270.7 

26.7 

33 

32.8 

03.2 

93 

92.6 

09.1 

153 

152.3 

15.0 

213 

212.0 

20.9 

273 

271.7 

26.8 

34 

33.8 

03.3 

94 

93.5 

09.2 

154 

153.3 

15.1 

214 

213.0 

21.0 

274 

272.7 

26.9 

35 

34.8 

03.4 

95 

94.5 

09.3 

155 

154.3 

15.2 

215 

214.0 

21.1 

275 

273.7 

27.0 

36 

35.8 

03.5 

96 

95.5 

09.4 

156 

155.2 

15.3 

216 

215.0 

21.2 

276 

274.7 

27.1 

37 

36.8 

03.6 

97 

96.5 

09.5 

157 

156.2 

15.4 

217 

216.0 

21.3 

277 

275.7 

27.2 

38 

37.8 

03.7 

98 

97.5 

09.6 

158 

157.2 

15.5 

218 

217.0 

21.4 

278 

276.7 

27.2 

39 

38.8 

03.8 

99 

98.5 

09.7 

159 

158.2 

15.6 

219 

217.9 

21.5 

279 

277.7 

27.3 

40 
41 

39.8 

03.9 

100 

99.5 

09.8 

160 

159.2 

15.7 

220 

218.9 

21.6 

280 

278.7 

27.4 

40.8 

04.0 

101 

100.5 

09.9 

161 

160.2 

15.8 

221 

219.9 

21.7 

281 

279.6 

27.5 

42 

41.8 

04.1 

102 

101.5 

10.0 

162 

161.2 

15.9 

222 

220.9 

21.8 

282 

280.6 

27.6 

,  43 
44 

42.8 

04.2 

103 

102.5 

10.1 

163 

162.2 

16.0 

223 

221.9 

21.9 

283 

281.6 

27.7 

43.8 

04.3 

104 

103.5 

10.2 

164 

163.2 

16.1 

224 

222.9 

22.0 

284 

282.6 

27.8 

45 

44.8 

04.4 

105 

104.5 

10.3 

165 

164.2 

16.2 

225 

223.9 

22.1 

285 

283.6 

27.9 

46 

45.8 

04.5 

106 

105.5 

10.4 

166 

165.2 

16.3 

226 

224.9 

22.2 

286 

284.6 

28.0 

'  47 

46.8 

04.6 

107 

106.5 

10.5 

167 

166.2 

16.4 

227 

225.9 

22.2 

287 

285.6 

28.1 

48 

47.8 

04.7 

108 

107.5 

10.6 

168 

167.2 

16.5 

228 

226.9 

22.3 

288 

286.6 

28.2 

49 

48.8 

04.8 

109 

108.6 

10.7 

169 

168.2 

16.6 

229 

227.9 

22.4 

289 

287.6 

28.3 

;     50 
51 

49.8 

04.9 

110 

109.5 

10.8 
10.9 

170 

169.2 

16.7 

230 

228.9 

22.5 

290 

288.6 

28.4 

50.8 

05.0 

HI 

110.5 

171 

170.2 

16.8 

231 

229.9 

22.6 

291 

289.6 

28.5 

52 

51.7 

05.1 

112 

111.5 

11.0 

172 

171.2 

16.9 

232 

230.9 

22.7 

292 

290.6 

28.6 

53 

52.7 

05.2 

113 

112.5 

11.1 

173 

172.2 

17.0 

233 

231.9 

22.8 

293 

291.6 

28.7 

54 

53.7 

05.3 

114 

113.5 

11.2 

174 

173.2 

17.1 

234 

232.9 

22.9 

294 

292.6 

28.8 

55 

54.7 

05.4 

115 

114.4 

11.3 

175 

174.2 

17.2 

235 

233.9 

23.0 

295 

293.6 

28.9 

56 

55.7 

05.5 

116 

115.4 

11.4 

176 

175.2 

17.3 

236 

234.9 

23.1 

296 

294.6 

29.0 

57 

56.7 

05.6 

117 

116.4 

11.5 

177 

176.1 

17.3 

237 

235.9 

23.2 

297 

295.6 

29.1 

58 '  57.7 

05.7 

118 

117.4 

11.6 

178 

177.1 

17.4 

238 

236.9 

23.3 

298 

296.6 

29.2 

59  58.7 

05.8 

119 

118.4 

11.7 

179 

178.1 

17.5 

239 

237.8 

23.4 

299 

297.6  '29.3 

60  59.7 

05.9 

120 

119.4 

11.8 

180 

179.1 

17.6 

Lat. 

240 

238.8 

23.5 

300 

298.6  29.4 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat 

Dist 

Dep. 

Dist 

Dep. 

Lat 

Dist. 

Dep.  1  Lat 

Eart  i  North.     Emrt  i  Sonth.          tF"''  7*  Pte-I          West  i  North      West  i  Sentk 

} 

TABLE  I 

Nortli  J  Ef 

.—DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  J  POINT.    8  | 

ist. 

North  i  West. 

South  i  East         South  f  West.       1 

Dist. 

1 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat.   Dep. 

01.0 

00.1 

61 

60.3 

09.0 

121 

119.7 

17.8 

181 

179.0 

26.6 

241 

23S.4  35.4 

2 

02.0 

00.3 

62 

61.3 

09.1 

122 

120.7 

17.9 

182 

180.0 

26.7 

242.239.4  35.5  | 

3 

03.0 

00.4 

63 

62.3 

09.2 

123 

121.7 

18.0 

183 

181.0 

26.9 

243  ;  240.4 

35.7 

4 

04.0 

00.6 

64 

DO.O 

09.4 

124 

122.7 

18.2 

184 

182.0 

27.0 

244  241.4 

35.8 

5 

04.9 

00.7 

65 

64.3 

09.5 

125 

123.6 

18.3 

185 

183.0 

27.1 

245  242.3 

35.9 

6 

05.9 

00.9 

66 

65.3 

09.7 

126 

124.6 

18.5 

186 

184.0 

27.3 

246  1 243.3 

36.1 

7 

06.9 

OI.O 

67 

66.3 

09.8 

127 

125.6 

18.6 

187 

185.0 

27.4 

247  1 244.3 

36.2 

8 

07.9 

01.2 

68 

67.3 

10.0 

128 

126.6 

18.8 

188 

186.0 

27.6 

248  245.3 

36.4 

9 

08.9 

01.3 

69 

68.3 

10.1 

129 

127.6 

18.9 

189 

187.0 

27.7 

249 

246.3 

36.5 

10 

09.9 

01.5 

70 

69.2 

10.3 

130 

128.6 

19.1 

190 

187.9 

27.9 

250 

247.3 

36.7 

11 

10.9 

01.6 

71 

70.2 

10.4 

131 

129.6 

19.2 

191 

188.9 

28.0 

251 

248.3  36.8  1 

12 

11.9 

01.8 

72 

71.2 

10.6 

1-32 

130.6 

19.4 

192 

189.9 

28.2 

252 

249.3  i  37.0  1 

13 

12.9 

01.9 

73 

72.2 

10.7 

133 

131.6 

19.5 

193 

190.9 

28.3 

253 

250.3 

37.1 

14 

13.8 

02.1 

74 

73.2 

10.9 

134 

132.5 

19.7 

194 

191.9 

28.5 

254 

251.3 

37.3 

15 

14.8 

02.2 

75 

74.2 

11.0 

135 

133.5 

19.8 

195 

192.9 

28.6 

255 

252.2 

37.4 

16 

15.8 

Oi.3 

76 

75.2 

11.2 

136 

134.5 

20.0 

196 

193.9 

28.8 

256 

253.2 

37.6 

17 

16.8 

02.5 

77 

76.2 

11.3 

137 

135.5 

20.1 

197 

194.9 

28.9 

257 

254.2 

37.7 

18 

17.8 

02.6 

78 

77.2 

11.4 

138 

136.5 

20.2 

198 

195.9 

29.1 

258 

255.2 

37.9 

19 

18.8 

02.8 

79 

78.1 

11.6 

139 

137.5 

20.4 

199 

196.8 

29.2 

259 

256.2 

38.0 

20 

19.8 

02.9 

80 

79.1 

11.7 

140 

138.5 

20.5 

200 

197.8 

29.3 

260 

257.2 

38.1 

21 

20.8 

03.1 

81 

80.1 

11.9 

141 

139.5 

20.7 

201 

198.8 

29.5 

261 

258.2 

38.3 

22 

21.8 

03.2 

82 

81.1 

12.0 

142 

140.5 

20.8 

202 

199.8 

29.6 

262 

259.2 

38.4 

23 

22.8 

03.4 

83 

82.1 

12.2 

143 

141.5 

21.0 

203 

200.8 

29.8 

263 

260.2 

38.6 

24 

23.7 

03.5 

84 

83.1 

12.3 

144 

142.4 

21.1 

204 

201.8 

29.9 

264  261.1 

38.7 

25 

24.7 

03.7 

85 

84.1 

12.5 

145 

143.4 

21.3 

205 

202.8 

30.1 

265 

262.1 

38.9 

26 

25.7 

03.8 

86 

85.1 

12.6 

146 

144.4 

21.4 

206 

203.8 

30.2 

266 

263.1 

39.0 

27 

26.7 

04.0 

87 

86.1 

12.8 

147 

145.4 

21.6 

207 

204.8 

30.4 

267 

264.1 

39.2 

28 

27.7 

04.1 

88 

87.0 

12.9 

148 

146.4 

21.7 

208 

205.7 

30.5 

268 

265.1 

39.3 

29 

28.7 

04.3 

89 

88.0 

13.1 

149 

147.4 

21.9 

209 

206.7 

30.7 

269 

266.1 

39.5 

30 
31 

29.7 

04.4 

90 

89.0 

13.2 

150 

148.4 

22.0 

210 

207.7 

30.8 

270 

,267.1 

39.6 

30.7 

04.5 

91 

90.0 

13.4 

151 

149.4 

22.2 

211 

208.7  31.0 

271  ;  268. 1,39.8  | 

32 

31.7 

04.7 

92 

91.0 

13.5 

152 

150.4 

22.3 

212 

209.7 

31.1 

272 

269.1 

39.9 

33 

32.0 

04.8 

93 

92.0 

13.6 

153 

151.3 

22.4 

213 

210.7 

31.3 

273 

270.0 

40.1 

34 

33.6 

05.0 

94 

93.0 

13.8 

154 

152.3 

22.6 

214 

211.7 

31.4 

274 

271.0 

40.2 

35 

34.6 

05.1 

95 

94.0 

13.9 

155 

153.3 

22.7 

215 

212.7 

31.5 

275 

272.0 

40.4 

36 

35.6 

05.3 

96 

95.0 

14.1 

156 

154.3 

22.9 

216 

213.7 

31.7 

276 

273.0 

40.5 

37 

36.6 

05.4 

97 

96.0 

14.2 

157 

155.3 

23.0 

217 

214.7 

31.8 

277 

274.0 

40.6 

38 

37.6 

05.6 

98- 

96.9  I  14.4 

158 

156.3 

23.2 

218 

215.6 

32.0 

278 

275.0 

40.8 

39 

38.6 

05.7 

99 

97.9  i  14.5 

159 

157.3 

23.3 

219 

216.6 

32.1 

279 

276.0,40.9  1 

40 
41 

39.6 

05.9 

100 

98.9  i  14.7 

160 

158.3 

23.5 

220 

217.6 

32.3 

280 

277.0 

41.1 

40.6 

06.0 

101 

99.9  14.8 

161 

159.3 

23.6 

221 

218.6 

32.4 

281 

278.0 

41.2 

42 

41.5 

06.2 

102 

100.9,15.0 

162 

160.2 

23.8 

222 

219.6 

32.6 

282 

278.9 

41.4 

43 

42.5 

06.3 

103 

101.9 

15.1 

163 

161.2 

23.9 

223 

220.6 

32.7 

283  ,  279.9 

41.5 

44 

43.5 

06.5 

104 

102.9 

15.3 

164 

162.2 

24.1 

224 

221.6 

32.9 

284 

280.9 

41.7 

45 

44  5 

06.6 

105 

103.9 

15.4 

165 

163.2 

24.2 

225 

222.6 

33.0 

285 

281.9 

41.8 

46 

45.5 

06.7 

106 

104.9 

15.6 

166 

164.2 

24.4 

226 

223.6 

33.2 

286 

282.9 

42.0 

47 

46.5 

06.9 

107 

105.8 

15.7 

167 

165.2 

24.5 

227 

224.5 

33.3 

287 

283.9 

42.1 

48 

47.5 

07.0 

108 

106.8 

15.8 

168 

166.2 

24.7 

228 

225.5 

33.5 

288 

284.9 

42.3 

49 

48.5 

07.2 

109 

107.8 

16.0 

169 

167.2 

24.8 

229 

226.5 

33.6 

289 

285.9 

42.4 

50 

49.5 

07.3 

110 

108.8 

16.1 

170 

168.2 

24.9 

230 

227.5 

33.7 

290 

286.9 

42.6 

51 

50.4 

07.5 

111 

109.8 

16.3 

171 

169.1 

25.1 

231 

228.5 

33.9 

291 

287.9 

42.7 

52 

51.4 

07.6 

112 

110.8 

16.4 

172 

170.1 

25.2 

232 

229.5 

34.0 

292 

288.8 

42.8 

53 

52.4 

07.8 

113 

111.8 

16.6 

173 

171.1 

25.4 

233 

230.5 

34.2 

293 

289.8 

43.0 

54 

53.4 

07.9 

114 

112.8 

16.7 

174 

172.1 

25.5 

234 

231.5 

34.3 

294 

290.8 

43.3 

55 

54.4 

08.1 

115 

113.8 

16.9 

175 

173.1 

25.7 

235 

232.5 

34.5 

295 

291.8,43.3  1 

5ti 

55.4 

0«.2 

116 

1147!  17.0 

176 

174.1 

25.8 

236 

233.4 

34.6 

296 

292.8 

43.4 

57 

56.4 

08.4 

117 

1157 

17.2 

177 

175.1 

26.0 

237 

234.4  '  34.8 

297  293.8 

43.6 

58 

57.4 

08.5 

118 

116.7 

17.3 

17S 

176.1 

26.1 

238  235.4 

34.9 

298  294.8 

43  7 

59 

58.4 

08.7 

119 

117.7 

17.5 

179 

177.1  26.3 

239 

236.4 

35.1 

299  ;  295.8 

43.9 

60 

59.4 

08.8 

120 

118.7 

17.6 

180 

178.1 

26.4 

240 

237.4 

35.2 

300 

296.8 

44.0 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist 

Dep. 

Lat 

Dist 

Dep. 

Lat 

Dist 

Dep. 

Lat 

East  1  North. 

E 

ast  1  South. 

rForTJPts.]          West  J  North.     West  J  South        | 

4    TABLE  I.— DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  1  POINT.      | 

North  b.  Ea«t        North  b.  West. 

South  h.  East        South  b.  We«t.       1 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

Dist. 

Lat   Dep. 

Dist 

Lat 

Dep. 

1 

01.0 

00.2 

61 

59.8 

11.9 

121 

118.7 

23.6 

181 

177.5  35.3 

241 

236.4 

47.0 

2 

02.0 

00.4 

62 

60.8  12.1 

122 

119.7 

23.8 

182 

178.5 

35.5 

242 

237.4 

47.2 

3 

02.9 

00.6 

63 

61.8 

12.3 

123 

120.6 

24.0 

183 

179.5 

35.7 

243 

238.3 

47.4 

4 

03.9 

00.8 

64 

62.8 

12.5 

124 

121.6 

24.2 

184 

180.5 

35.9 

244 

239.3 

47.6 

5 

04.9 

01.0 

65 

63.8 

12.7 

125 

122.6  24.4 

185 

181.4 

36.1 

245 

240.3 

47.8 

6 

05.9 

01.2 

66 

.64.7 

12.9 

126 

123.6  24.6 

186 

182.4 

36.3 

246 

241.3 

48.0 

7 

06.9 

01.4 

67 

65.7 

13.1 

127 

124.6 

24.8 

187 

183.4 

36.5 

247 

242.3 

48.2 

8 

07.8 

01.6 

68 

66.7 

13.3 

128 

125.5 

25.0 

188 

184.4 

36.7 

248 

243.2 

48.4 

9 

08.8 

01.8 

69 

67.7 

13.5 

129 

126.5 

25.2 

189 

185.4 

36.9 

249 

244.2 

48.6 

10 

09.8 

02.0 

70 

68.7 

13.7 

130 

127.5 

25.4 

190 
191' 

186.3 
187.3 

37.1 

250 

245.2 

48.8 

11 

lO.S 

02.1 

71 

69.6 

13.9 

131 

128.5 

25.6 

37.3 

251 

246.2 

49.0 

12 

11.8 

02.3 

72 

70.6 

14.0 

132 

129.5 

25.8 

192 

188.3 

37.5 

252 

247.2 

49.2 

13 

12.8 

02.5 

73 

71.6 

14.2 

J  33 

130.4 

25.9 

193 

189.3 

37.7 

253 

24^.1 

49.4 

14 

13.7 

02.7 

74 

72.6 

14.4 

134 

131.4 

26.1 

194 

190.3 

37.8 

254 

249.1 

49.6 

15 

14.7 

02.9 

75 

73.6 

14.6 

135 

132.4 

26.3 

195 

191.3 

38.0 

255 

250.1 

49.7 

16 

15.7 

03.1 

76 

74.5 

14.8 

136 

133.4 

26.5 

196 

192.2 

38.2 

256 

251.1 

49.9 

17 

16.7 

03.3 

77 

75.5 

15.0 

137 

134.4 

26.7 

197 

193.2 

38.4 

257 

252.1 

50.1 

18 

17.7 

03.5 

78 

76.5 

15.2 

138 

135.3 

26.9 

198 

194.2 

38.6 

258 

253.0 

50.3 

19 

18.6 

03.7 

79 

77.5 

15.4 

139 

136.3 

27.1 

199 

195.2 

38.8 

259 

254.0 

50.5 

20 

19.6 

03.9 

80 

78.5 

15.6 

140 

137.3 

27.3 

■200 

196.2 

39.0 

260 

255.0 

50.7 

21 

20.6 

04.1 

81 

79.4 

15.8 

141 

138.3 

27.5 

201 

197.1 

39.2 

261 

256  0 

50.9 

22 

21.6 

04.3 

82 

80.4 

16.0 

142 

139.3 

27.7 

202 

198.1 

39.4 

262 

257  0 

51.1 

23 

22.6 

04.5 

83 

81.4 

16.2 

143 

140.3 

27.9 

203 

199.1 

39.6 

263 

257  9  151.3  1 

24 

23.5 

04.7 

84 

82.4 

16.4 

144 

141.2 

28.1 

204 

200.1 

39.8 

264 

258.9 

51.5 

25 

24.5 

04.9 

85 

83.4 

16.6 

145 

142.2 

28.3 

205 

201.1 

40.0 

265 

259.9 

51.7 

26 

25.5 

05.1 

86 

84.3 

16.8 

146 

143.2 

28.5 

206 

202.0 

40.2 

266 

260.9 

51.9 

27 

26.5 

05.3 

87 

^  85.3 

17.0 

147 

144.2 

28.7 

207 

203.0 

40.4 

267 

261.9 

52.1 

28 

27.5 

05.5 

88 

86.3 

17.2 

148 

145.2 

28.9 

208 

204.0 

40.6 

268 

262.9 

52.3 

29 

28.4 

05.7 

89 

87.3 

17.4 

149 

146.1  29.1 

209 

205.0  I  40.8 

269 

263.8 

52.5 

30 
31 

29.4 
30.4 

05.9 

90 

88.3 

17.6 

150 

147.1 

29.3 

210 

206.0 !  41.0 

270 

264.8 

52.7 

06.0 

91 

89.3 

17.8 

151 

148.1 

29.5 

211 

206.9 

41.2 

271 

265.8 

52.9 

32 

31.4 

06.2 

92 

90.2 

17.9 

152 

149.1 

29.7 

212 

207.9 

41.4 

272 

266.8 

53.1 

33 

32.4 

06.4 

93 

91.2 

18.1 

153 

150.1 

29.8 

213 

208.9 

41.6 

273 

267.8 

53.3 

34 

33.3 

06.6 

94 

92.2 

18.3 

154 

151.0 

30.0 

214 

209.9 

41.7 

274 

268.7 

53.5 

35 

34.3 

Ob.8 

95 

93.2 

18.5 

155 

152.0 

30.2 

215 

210.9 

41.9 

275  269.7 

53.6 

36 

35.3 

07.0 

96 

94.2 

18.7 

156 

153.0  30.4 

216 

211.8 

42.1 

276  ;  270.7 

53.8 

37 

36.3 

07.2 

97 

95.1 

18.9 

157 

154.0 

30.6 

217 

212.8 

42.3 

277  271.7 

54.0 

38 

37.3 

07.4 

98 

96.1 

19.1 

158 

155.0 

30.8 

218 

213.8 

42.5 

278  .  272.7 

54.2 

39 

38.3 

07.6 

99 

97.1 

19.3 

159 

155.9 

31.0 

219 

214.8 

42.7 

279  273.6 

54.4 

40 

39.2 

07.8 

100 

98.1 

19.5 

160 

156.9 

31.2 

220 

215.8 

42.9 

280  i  274.6 

54.6 

41 

40.2 

08.0 

101 

99.1 

19.7 

161 

157.9 

31.4 

221 

216.8 

43.1 

281 

275.6 

54.8 

42 

41.2 

08.2 

102 

100.0 ;  19.9 

162 

158.9 

31.6 

222 '  217.7 

43.3 

282 

276.6 

55.0 

43 

42.2 

08.4 

103 

101.0 

20.1 

163 

159.9 

31.8 

223 

218.7 

43.5 

283 

277.6 

55.2 

44 

43.2 

08.6 

104 

102.0 

20.3 

164 

160.8 

32.0 

224 

219.7 

43.7 

284  :■  278.5 

55.4 

45 

44.1 

08.8 

105 

103.0 

20.5 

165 

161.8 

32.2 

225 

220.7 

43.9 

285 

279.5 

55.6 

46 

45.1 

09.0 

106 

104.0 

20.7 

166 

162.8 

32.4 

226 

221.7 

44.1 

286 

280.5 

55.8 

47 

46.1 

09.2 

107 

104.9 

20.9 

167 

163.8 

32.6 

227 

222.6 

44.3 

287 

281.5 

56.0 

48 

47.1 

09.4 

108 

105.9 

21.1 

168 

164.8 

32.8 

228 

223.6 

44.5 

288 

282.5 

56.2 

49 

48.1 

09.6 

109 

106.9 

21.3 

169 

165.8 

33.0 

229 

224.6 

44.7 

289 

283.4 

56.4 

50 

49.0 

09.8 

110 

107.9 

21.5 

170 

166.7 

33.2 

230 
231 

225.6 

44.9 

290 

284.4 

56.6 

51 

50.0 

09.9 

111 

108.9 

21.7 

171 

167.7 

33.4 

226.6 '45.1 

291 

285.4 

56.8 

52 

51.0 

10.1 

112 

109.8 

21.9 

172 

168.7 

33.6 

232 

227.5 

45.3 

292 

286.4 

57.0  - 

53 

52.0 

10.3 

113 

110.8 

22  0 

173 

169.7 

33.8 

233 

228.5 

45.5 

293 

287.4 

57.2 

54 

53.0 

10.5 

114 

111.8 

22.2 

174 

170.7 

33.9 

234 

229.5 

45.7 

294 

288.4 

57.4 

55 

53.9 

10.7 

llf) 

112.8 

22.4 

175 

171.6 

34.1 

235  230.5 

45.8 

295 

289.3  :  57.6 

56 

54.9 

10.9 

116 

113.8 

22.6 

176 

172.6 

34.3 

236 

231.5 

46.0 

296 

290.3  57.7 

57 

55.9 

11.1 

117 

114.8 

22.8 

177 

173.6 

34.5 

237 

232.4 

46.2 

297 

291.3  57.9 

58 

56.9 

11.3 

118 

115.7 

23.0 

178 

174.6 

34.7 

238 

233.4 

46.4 

298 

292.3 

58.1 

59 

57.9 

11.5 

119 

116.7 

23.2 

179 

175.6 

34.9 

239 

234.4 

46.6 

299 

293.3 

58.3 

60 

58.8 

11.7 

120 

117.7 

23.4 

180 

176.5 

35.1 

240 

235.4 

46.8 

300 

294.2 

58.5 

Dial. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist 

Dpp.   Lat  Dist 

Dep. 

Lat 

Dist 

Dep.  t  Lat  1 

East  ».  North.      East  b.  Sonth. 

Tor  7  Pts.]          Wpst  A.  North.      West  b.   South.        | 

TABLE  I.— DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  IJ  POINTS.         6     | 

North  b.  East  i  East. 

North  b.  West  i  Wost            South  b.  East  i  East            South  b.  West  *  "West.  1 

Dist. 

Lat. 

Dep.    Dist.  1 

Lilt 

Dep. 

Dist 

Lilt 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep.   1 

1 

01.0 

00.2 

61 

59.2 

14.8 

121 

117.4 

29.4 

181 

175.6 

44.0 

241 

233.8 

58.6 

2 

01.9 

00.5 

62 

60.1 

15.1 

122 

118.3 

29.6 

182 

176.5 

44.2 

234.7 

58.8 

3 

02.9 

00.7 

63 

61.1 

15.3 

123 

119.3 

29.9 

183 

177.5 

44.5 

243 

235.7 

59.0   1 

4 

03.9 

01.0 

64 

«2.1 

15.6 

124 

1 20.3 

30.1 

184 

178.5 

44.7 

244 

236.7 

59.3 

5 

04.9 

01.2 

65 

d3.1 

15.8 

125 

121.3 

30.4 

185 

179.5 

45.0 

245 

237.7 

59.5 

6 

05.8 

01.5 

66 

64.0 

16.0 

126 

122.2 

30.6 

186 

180.4 

45.2 

246 

238.6 

59.8 

7 

06.8 

01.7 

67 

65.0 

16.3 

127 

123.2 

30.9 

187 

181.4 

45.4 

247 

239.6 

60.0 

>=;  07.8 

01.9 

68 

66.0 

16.5 

128 

124.2 

3>.l 

188 

182.4 

45.7 

248 

240.6 

60.3 

9 

08.7 

02.2 

69 

66.9 

16.8 

129 

125.1 

31.3 

189 

183.3 

45.9 

249 

241.5 

60.5 

10 

11 

09.7 

02.4 

70 

67.9 

17.0 

130 

126.1 

31.6 

190 

184.3 

46.2 

250 

242.5 

60.7 

10.7 

02.7 

71 

68.9 

17.3 

131 

127.1 

31.8 

191 

18.5.3 

46.4 

251 

243.5 

61.0 

12 

11.6 

02.9 

72 

69.8 

17.5 

132 

128.0 

32.1 

192 

186.2 

46.7 

252 

244.4 

61.2 

13 

12.6 

03.2 

73 

70.8 

17.7 

133 

129.0 

32.3 

193 

187.2 

46.9 

253 

245.4 

61.5 

14 

13.6 

03.4 

74 

71.8 

18.0 

134 

130.0 

32.6 

194 

188.2 

47.1 

254 

246.4 

61.7 

15 

14.6 

03.6 

75 

72.8 

18.2 

135 

131.0 

32.8 

195 

189.2 

47.4 

255 

247.4 

62.0 

16 

15.5 

03.9 

76 

73.7 

18.5 

136 

131.9 

33.0 

196 

190.1 

47.6 

256 

248.3 

62.2 

17 

16.5 

04.1 

77 

74.7 

18.7 

137 

132.9 

33.3 

197 

191.1 

47.9 

257 

249.3 

62.4 

IS 

17.5 

04.4 

78 

75.7 

19.0 

138 

133.9 

33.5 

198 

192.1 

48.1 

258 

250.3 

62.7 

19 

18.4 

04.6 

79 

76.6 

19.2 

139 

134.8 

33.8 

199 

193.0 

48.4 

259 

251.2 

62.9 

20 

21 

19.4 
20.4 

04.9 

80 

77.6 

19.4 

140 

135.8 

34.0 

200 

194.0 

48.6 

260 

2.52.2 

63.2 

05.1 

81 

78.6 

19.7 

141 

136  8 

34.3 

201 

195.0 

48.8 

261 

253.2 

63.4 

22 

21.3 

05.3 

82 

79.5 

19.9 

142 

137.7 

34.5 

202 

195.9 

49.1 

262 

254.1 

63.7 

23 

22.3 

05.6 

83 

80.5 

20.2 

143 

138.7 

34.7 

203 

196.9 

49.3 

263 

255.1 

63.9 

24 

23.3 

05.8 

84 

81.5 

20.4 

144 

139.7 

35.0 

204 

197.9 

49.6 

264 

256.1 

64.1 

25 

24.3 

06.1 

85 

82.5 

20.7 

145 

140.7 

35.2 

205 

198.9 

49.8 

265 

257.1 

64.4 

2t) 

25.2 

06.3 

86 

83.4 

20.9 

146 

141.6 

35.5 

206 

199.8 

50.1 

266 

258.0 

64.6 

27 

26.2 

06.6 

87 

84.4 

21.1 

147 

142.6 

35.7 

207 

200.8 

50.3 

267 

259.0 

64.9 

28 

27.2 

06.8 

88 

85.4 

21.4 

148 

143.6 

36.0 

208 

201.8 

50.5 

268 

260.0 

65.1 

29 

28.1 

07.0 

89 

86.3 

21.6 

149 

144.5 

36.2 

209 

202.7 

50.8 

269 

260.9 

65.4 

30 

29.1 

07.3 

90 

87.3 

21.9 

150 

145.5 

36.4 

210 

203.7 

51.0 

270 
271 

261.9 

65.6 

31 

30.1 

07.5 

91 

88.3 

22.1 

151 

146.5 

36.7 

211 

204.7 

51.3 

262.9 

65.8 

36 

31.0 

07.8 

92 

89.2 

22.4 

152 

147.4 

36.9 

212 

205.6 

51.5 

272 

263.8 

66.1 

33 

32.0 

08.0 

93 

90.2 

22.6 

153 

148.4 

37.2 

213 

206.6 

51.8 

273 

264.8 

66.3 

34 

33.0 

08.3 

94 

91.2 

22.8 

154 

149.4 

37.4 

214 

zv7.6 

52.0 

274 

265.8 

66.6 

35 

34.0 

08.5 

95 

92.2 

23.1 

155 

150.4 

37.7 

215 

208.6 

o'^  2  '275 

266.8 

66.8 

36 

34.9 

08.7 

96 

93.1 

23.3 

156 

151.3 

37.9 

216 

209.5 

52.5 

276 

267.7 

67.1 

37 

35.9 

09.0 

97 

94.1 

23.6 

157 

152.3 

38.1 

217 

210.5 

52.7 

277 

268.7 

67.3 

38 

36.9 

09.2 

98 

95.1 

23.8 

158 

153.3 

38.4 

218 

211.5 

53.0 

278 

269.7 

67.5 

39 

37.8 

09.5 

99 

96.0 

24.1 

159 

154.2 

38.6 

219 

212.4 

53.2 

279 

270.6 

67.8 

40 

38.8 

09.7 

100 

97.0 

24.3 

160 

155.2 

38.9 

220 

213.4 

53.5 

280 

271.6 

68.0 

41 

39.8 

10.0 

101 

98.0 

24.5 

161 

156.2 

39.1 

221 

214.4 

53.7 

281 

272.6 

68.3 

42 

40.7 

10.2 

102 

98.9 

24.8 

162 

157.1 

39.4 

222 

215.3 

53.9 

282 

273.5 

68.5 

43 

41.7 

10.4 

103 

99.9 

25.0 

163 

158.1 

39.6 

223 

216.3 

54.2 

283 

274.5 

68.8 

44 

42.7 

10.7 

104 

100.9 

25.3 

164 

159.1 

39.8 

224 

217.3 

54.4 

284 

275.5 

69.0 

45 

43.7 

10.9 

105 

101.9 

25.5 

165 

160.1 

40.1 

225 

218.3 

54.7 

285 

276.5 

69.2 

46 

44.6 

11.2 

106 

102.8 

25.8 

166 

161.0 

40.3 

226 

21S.2 

54.9 

286 

277.4 

69.5 

47 

45.6 

11.4 

107 

103.8 

26.0 

167 

162.0 

40.6 

227 

220.2 

55.2 

287 

278.4 

69.7 

48 

46.6 

11.7 

108 

104.8 

26.2 

168 

163.0 

40.8 

228 

221.2 

55.4 

288 

279.4 

70.0 

49 

47.5 

11.9 

109 

105.7 

26.5 

169 

163.9 

41.1 

229 

222.1 

55.6 

289 

280.3 

70.2 

50 
51 

48.5 

12.1 

110 

106.7 

26.7 
27.0 

170 

164.9 

41.3 
41.5 

230 
231 

223.1 

55.9 

290 

281.3 

70.5 

49.5 

12.4 

111 

107.7 

171 

165.9 

224.1 

56.1 

291 

282.3 

70.7 

52 

50.4 

12.6 

112 

108.6 

27.2 

172 

166.8 

41.8 

232 

225.0 

56.4 

292 

283.2 

71.0 

53 

51.4 

12.9 

113 

109.6 

27.5 

173 

167.8 

42.0 

233 

226.0 

56.6 

293 

284.2 

71.2 

54 

52.4 

13.1 

114 

110.6 

•^7.7 

174 

168.8 

42.3 

•234 

227.0 

56.9 

294 

285.2 

71.4 

55 

53.4 

13.4 

115 

111.6 

27.9 

175 

169.8 

42.5 

235 

228.0 

57.1 

295 

286.2 

71.7 

56 

54.3 

13.6 

116 

112.5 

28.2 

170 

170.7 

42.8 

236 

228.9 

57.3 

296 

287.1 

71.9 

57 

55.3 

13.8 

117 

113.5 

•28.4 

177 

171.7 

43.0 

237 

229.9 

57.6 

297 

288.1 

72.2 

58 

56.3 

14.1 

118 

114.5 

28.7 

178 

172.7 

43.3 

238 

230.9 

57.8 

298 

289.1 

72.4 

59 

57.2 

14.3 

119 

115.4 

28.9 

179 

173.6 

43.5 

239 

231.8 

58.1 

299 

290.0 

72.7 

60 

58.2 
Dep. 

14.6 

120 

116.4 

29.2 

180 

174.6 

43.7 

Lat. 

240 

232.8 

58.8 

300 

291.0 

72.9 

Dist 

Lat 

Dist 

Dep. 

Lat 

Dist 

Dep. 

Dist 

Dep. 

Lat 

Dist 

Dep. 

Lat 

Eut  North  East  f  East.     Ej 

«t  South  East  }  Eist.     [For  6f  Pts.]     Weit  North  West  J  West.     West  South  West  f  Wmi.    | 

^-        . 

*■ 

• — '__ 

1    6        TABLE  I— DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  U  POINTS.            | 

North  b.  East  \  E  ist. 

North  h.  West  J-  West             South  h.  East  ^  East             South  h.  West  \  West.    1 

Dist 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

Dist 

Lat 

Dep. 

1 

01.0 

00.3 

61 

58.4 

17.7 

121 

115.8 

35.1 

181 

173.2 

52.5 

241 

230.6 

70.0 

2 

01.9 

00.6 

62 

59.3 

18.0 

122 

116.7 

35.4 

182 

174.2 

52.8 

242 

231.6 

70.2 

3 

02.9 

00.9 

63 

60.3 

18.3 

123 

117.7 

35.7 

183 

175.1 

53.1 

243 

232.5  70.5    1 

4 

03.8 

01.2 

64 

61.2 

18.6 

1-24 

118.7 

36.0 

184 

176.1 

53.4 

244 

233.5   70.8    1 

5 

04.8 

01.5 

65 

62.2 

18.9 

125 

119.6 

36.3 

185 

177.0 

53.7 

245 

234.5 

71.1 

6 

05.7 

01.7 

66 

63.2 

19.2 

126 

120.6 

36.6 

186 

178.0 

54.0 

246 

235.4 

71.4 

7 

06.7 

02.0 

07 

64.1 

19.4 

127 

121.5 

36.9 

187 

178.9 

54.3 

247 

236.4 

71.7 

8 

07.7 

02.3 

68 

65.1 

19.7 

128 

122.5 

37.2 

188 

179.9 

54.6 

248 

237.3 

72.0 

9 

08.6 

02.6 

69 

66.0 

20.0 

129 

123.4 

37.4 

189 

180.9 

54.9 

249 

238.3 

72.3 

10 
11 

09.6 

02.9 

70 

67.0 

20.3 

130 

124.4 

37.7 

190 

181.8 

55.2 

250 

239.2 

72.6 

10.5 

03.2 

71 

67.9 

20.6 

131 

125.4 

38.0 

191 

182.8 

55.4 

251 

240.2 

72.9 

12 

11.5 

03.5 

72 

68.9 

20.9 

132 

126.3 

38.3 

192 

183.7 

55.7 

252 

241.1 

73.2 

13 

12.4 

03.8 

73 

69.9 

21.2 

133 

127.3 

38.6 

193 

184.7 

56.0 

253 

242.1 

73.4 

14 

13.4 

04.1 

74 

70.8 

21.5 

134 

128.2 

38.9 

194 

185.6 

56.3 

254 

243.1 

73.7 

15 

14.4 

04.4 

75 

71.8 

21.8 

135 

129.2 

39.2 

195 

186.6 

56.6 

-255 

244.0 

74.0 

16 

15.3 

04.6 

76 

72.7 

22.1 

136 

130.1 

39.5 

196 

187.6 

56.9 

256 

245.0 

74.3 

17 

16.3 

04.9 

77 

73.7 

22.4 

137 

131.1 

39.8 

197 

188.5 

57.2 

257 

245.9 

74.6 

18 

17.2 

05.2 

78 

74.6 

22.6 

138 

13-2.1 

40.1 

198 

189.5 

57.5 

258 

246.9 

74.9 

19 

18.2 

05.5 

79 

75.6 

22.9 

139 

133.0 

40.3 

199 

190.4 

57.8 

259 

247.8 

75.2 

20 

19.1 

05.8 

80 

76.6 

23.2 

140 

134.0 

40.6 

200 

191.4 

58.1 

260 

248.8 '75.5   1 

21 

•20.1 

06.1 

81 

77.5 

23.5 

141 

134.9 

40.9 

201 

192.3 

58.3 

261 

249.8 

75.8 

22 

21.1 

06.4 

82 

7S.5 

23.8 

142 

135.9 

41.2 

202 

193.3 

58.6 

262 

250.7 

76.1 

23 

22.0 

06.7 

83 

79.4 

24.1 

143 

136.8 

41.5 

203 

194.3 

58.9 

'263 

251.7 

76.3 

24 

23.0 

07.0 

84 

80.4 

24.4 

144 

137.8 

41.8 

204 

195.2 

59.2 

264 

252.6 

76.6 

25 

•23.9 

07.3 

85 

81.3 

24.7 

145 

138.8 

42.1 

205 

196.2 

59.5 

265 

253.6 

76.9 

26 

24.9 

07.5 

86 

82.3 

25.0 

146 

139.7 

42.4 

206 

197.1 

59.8 

266 

254.5  '  77.2 

27 

25.8 

07.8 

87 

83.3 

25.3 

147 

140.7 

42.7 

207 

198.1 

60.1 

267 

255.5  i  77.5 

28 

26.8 

08.1 

88 

84.2 

25.5 

148 

141.6 

43.0 

208 

199.0 

60.4 

268 

256.5 

77.8 

29 

27.8 

08.4 

89 

85.2 

25.8 

149 

142.6 

43.3 

209 

200.0 

60.7 

269  1 257.4 

78.1 

30 
31 

28.7 

08.7 

90 

86.1,26.1 

150 

143.5 

43.5 

210 

201.0 

61.0 

270 

258.4 

78.4 

29.7 

09.0 

91 

87.1 

26.4 

151 

144.5 

43.8 

211 

201.9 

61.3 

271 

259.3 

78.7 

32 

30.6 

09.3 

92 

88.0 

26.7 

152 

145.5 

44.1 

212 

202.9 

61.5 

272 

260.3 

79.0 

33 

31.6 

09.6 

93 

89.0 

27.0 

153 

146.4 

44.4 

213 

203.8 

61.8 

273 

261.2 

79.2 

34 

32.5 

09.9 

94 

90.0 

27.3 

154 

147.4 

44.7 

214 

204.8 

62.1 

274 

262.2 

79.5 

35 

33.5 

10.2 

95 

90.9 

27.6 

155 

148.3 

45.0 

215 

205.7 

62.4 

275 

263.2 

79.8 

36 

34.4 

10.5 

96 

91.9 

27.9 

156 

149.3 

45.3 

216 

206.7 

62.7 

276 

264.1 

80.1 

37 

35.4 

10.7 

97 

92.8 

28.2 

157 

150.2 

45.6 

217 

207.7 

63.0 

277 

265.1 

80.4 

38 

36.4 

11.0 

98 

93.8 

28.4 

158 

151.2 

45.9 

218 

208.6 

63.3 

278 

266.0 

80.7 

39 

37.3 

11.3 

99 

94.7 

28.7 

159 

152.2 

46.2 

219 

-209.6 

63.6 

279 

267.0 

81.0 

40 

38.3 

11.6 

100 

95.7 

29.0 

160 

153.1 

46.4 

220 

210.5 

63.9 

280 

267.9 

81.3 

41 

39.2 

11.9 

101 

96.7 

29.3 

161 

154.1 

46.7 

221 

211.5 

64.2 

281 

268.9 

81.6 

42 

40.2 

12.2 

102 

97.6 

29.6 

162 

155.0 

47.0 

222 

212.4 

64.4 

282 

269.9 

81.9 

43 

41.1 

12.5 

103 

98.6 

29.9 

163 

156.0 

47.3 

223 

213.4 

64.7 

•283 

270.8 

82.2 

44 

4-2.1 

12.8 

104 

99.5 

30.2 

164 

156.9 

47.6 

224 

214.4 

65.0 

284 

271.8 

8-2.4 

45 

43.1 

13.1 

105 

100.5 

30.5 

165 

157.9 

47.9 

225 

215.3 

65.3 

285 

272.7 

82.7 

46 

44.0 

13.4 

106 

101.4 

30.8 

166 

158.9 

48.2 

226 

216.3 

65.6 

286 

273.7 

83.0 

47 

45.0 

13.6 

107 

102.4 

31.1 

167 

159.8 

48.5 

227 

217.2 

65.9 

287 

274.6 

83.3 

48 

45.9 

13.9 

108 

103.3 

31.4 

168 

160.8 

48.8 

228 

218.2 

66.2 

288 

275.6 

83.6 

49 

46.9 

14.2 

109 

104.3 

31.6 

169 

161.7 

49.1 

229 

219.1 

66.5 

289 

276.6 

83.9 

50 

47.8 

14.5 

110 

105.3 

31.9 

170 

162.7 

49.3 

230 

220.1 

66.8 

290 

277.5 

84.2 

51 

48.8 

14.8 

111 

106.2 

32.2 

171 

163.6 

49.6 

231 

221.1 

67.1 

291 

278.5 

84.5 

52 

49.8 

15.1 

112 

107.2 

32.5 

172 

164.6 

49.9 

232 

222.0 

67.3 

292 

279.4 

84.8 

53 

50.7 

15.4 

113 

108.1 

32.8 

173 

165.6 

50.2 

233 

-223.0 

67.6 

293 

280.4 

85.1 

54 

517 

15.7      14 

109.1 

33.1 

174 

166.5 

50.5 

234 

223.9 

67.9 

294 

281.3 

85.3 

55 

52.6 

16.0 

115 

1 10.0 

33.4 

175 

167.5 

50.8 

235 

224.9 

68.2 

295 

282.3 

85.6 

56 

53.6 

16.3 

116 

111.0 

33.7 

176 

168.4 

51.1 

236 

2-25.8 

68.5 

296 

283.3 

85.9 

57 

54.5 

16.5 

117 

112.0 

34.0 

177 

169.4 

51.4 

•237 

226.8 

68.8 

297 

284.2 

86.2 

58 

55.5 

16.8 

118 

112.9 

»34.3 

178 

170.3 

51.7 

-238 

2-27.8 

69.1 

298   285.2] 

86.5 

59 

56.5 

17.1 

119 

113.9 

34.5 

179 

171.3 

52.0 

239   228.7 

69.4 

299   286.1  1 

86.8 

_60 

57.4 

17.4 

120 

114.8 

34.8 

180 

172.2 

52.3 

•240 '  229.7 

69.7 

300 

287.1  1 

87.1 

Dist 

Dep.     Lat 

Dist 

Dep. 

Lat 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat 

Dist 

Dep.   ;  Lat     | 

EMt  North  Eart  i  Eart.     E* 

«t  Sonth  Eaat  ♦  E«t.     fForSif^ts]     West  North  West  J  Wpst.     West  Sonth  West  i  "Weit.  | 

TABLE  I.- 

•DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  If  POINTS. 

7     i 

Noith  b.  East  *  Ei 

I8t. 

Nurtli  b.  We><t  J  West.             Soutli  b.  East  j  East.             South  *.  West  »  West  [ 

Dist. 
1 

Lat. 

Dep. 

Dist. 

61 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Di»t      Lat 

Dep. 

Dist 

Lat 

Dep. 

00.9 

00.3 

57.4 

20.6 

121 

113.9 

40.8 

181 

170.4 

61.0 

241 

226.9 

81.2 

2 

01.9 

00.7 

62 

58.4 

20.9 

122 

114.9 

41.1 

182 

171.4 

61.3 

242 

227.9 

81.5 

3 

02.8 

01.0 

63 

59.3 

21.2 

123 

115.8 

41.4 

183 

172.3 

61.7 

243 

228.8 

81.9 

4 

03.8 

01.3 

64 

60.3 

21.6 

124 

116.8 

41.8 

184 

173.2 

62.0 

244 

229.7 

82.2 

5 

04.7 

01.7 

65 

61.2 

21.9 

125 

117.7 

42.1 

185 

174.2 

62.3 

245 

230.7 

82.5 

6 

05.6 

02.0 

66 

62.1 

22.2 

126 

118.6 

42.4 

186 

175.1 

62.7 

246 

231.6 

82.9 

7 

06.6 

02.4 

67 

63.1 

22.6 

127 

119.6 

42.S 

187 

176.1 

63.0 

247 

232.6 

83.2 

8 

07.5 

02.7 

68 

64.0 

22.9 

128 

120.5 

43.1 

188 

177.0 

63.3 

248 

233.5 

83.5 

9 

08.5 

03.0 

69 

65.0 

23.2 

129 

121.5 

43.5 

189 

178.0 

63.7 

249 

234.4 

83.9 

10 

09.4 

03.4 

70 

65.9 

23.6 

130 

122.4 

43.8 

190 

178.9 

64.0 

250 

235.4 

84.2 

11 

10.4 

03.7 

71 

66.8 

23.9 

131 

123.3 

44.1 

191 

179.8 

64.3 

251 

236.3 

84.6 

12 

11.3 

04.0 

72 

67.8 

24.3 

132 

124.3 

44.5 

192 

180.8 

64.7 

252 

237.3 

84.9 

13 

12.2 

04.4 

73 

68.7 

24.6 

133 

125.2 

44.8 

193 

181.7 

65.0 

253 

238.2 

85.2 

14 

13.2 

04.7 

74 

69.7 

24.9 

134 

126.2 

4.5.1 

194 

182.7 

65.4 

254 

239.2 

85.6 

15 

14.1 

05.1 

75 

70.6 

25.3 

135 

127.1 

45.5 

195 

183.6 

65.7 

255 

240.1 

85.9 

16 

15.1 

05.4 

76 

71.6 

25.6 

136 

128.0 

45.8 

196 

184.5 

66.0 

256 

241.0 

86.2 

17 

16.0 

05.7 

77 

72.5 

25.9 

137 

129.0 

46.2 

197 

185.5 

66.4 

257 

242.0 

86.6 

18 

16.9 

06.1 

78 

73.4 

26.3 

138 

129.9 

46.5 

198 

186.4 

66.7 

258 

242.9 

86.9 

19 

17.9 

06.4 

79 

74.4 

26.6 

139 

130.9 

46.8 

199 

187.4 

67.0 

259 

243.9 

87.3 

20 
21 

18.8 

06.7 

80 

75.3 

27.0 

140 

131.8 

47.2 

200 

188.3 

67.4 

260 

244.8 

87.6 

19.8 

07.1 

81 

76.3 

27.3 

141 

132.8 

47.5 

201 

189.3 

67.7 

261 

245.7 

87.9 

22 

20.7 

07.4 

82 

77.2 

27.6 

142 

133.7 

47.8 

202 

190.2 

68.1 

262 

246.7 

88.3 

23 

21.7 

07.7 

83 

78.1 

28.0 

143 

134.6 

'48.2 

203 

191.1 

68.4 

263 

247.6 

88.6 

24 

22.6 

08.1 

84 

79.1 

28.3 

144 

135.6 

48.5 

204 

192.1 

68.7 

264 

248.6 

88.9 

25 

23.5 

08.4 

85 

80.0 

28.6 

145 

136.5 

48.8 

205 

193.0 

69.1 

265 

249.5 

89.3 

2() 

24.5 

08.8 

86 

81.0 

29.0 

146 

137.5 

49.2 

206 

194.0 

69.4 

266 

250.5 

89.6 

27 

25.4 

09.1 

87 

81.9 

29.3 

147 

138.4 

49.5 

207 

194.9 

69.7 

267 

251.4 

89.9 

28 

26.4 

09.4 

88 

82.9 

29.6 

148 

139.3 

49.9 

208 

195.8 

70.1 

268 

252.3 

90.3 

29 

27.3 

09.8 

89 

83.8 

30.0 

149 

140.3 

50.2 

209 

196.8 

70.4 

269 

253.3 

90.6 

30 
31 

28.2 

10.1 

90 

84.7 

30.3 

150 

141.2 

50.5 

210 

197.7 

70.7 
71.1 

270 
271 

2.54.2 

91.0 

29.2 

10.4 

91 

85.7 

30.7 

151 

142.2 

50.9 

211 

198.7 

255.2 

91.3 

32 

30.1 

10.8 

92 

86.6 

31.0 

152 

143.1 

51.2 

212 

199.6 

71.4 

272 

256.1 

91.6 

33 

31.1 

11.1 

93 

87.6 

31.3 

153 

144.1 

51.5 

213 

200.5 

71.8 

273 

257.0 

92.0 

34 

32.0 

11.5 

94 

88.5 

31.7 

154 

145.0 

51.9 

214 

201.5 

72.1 

274 

258.0 

92.3 

35 

33.0 

11.8 

95 

89.4 

32.0 

155 

145.9 

52.2 

215 

202.4 

72.4 

275 

258.9 

92.6 

36 

33.9 

12.1 

96 

90.4 

32.3 

156 

146.9 

52.6 

216 

203.4 

72.8 

276 

259.9 

93.0 

37 

34.8 

12.5 

97 

91.3 

32.7 

157 

147.8 

52.9 

217 

204.3 

73.1 

277 

260.8 

93.3 

38 

35.8 

12.8 

98 

92.3 

33.0 

158 

148.8 

53.2 

218 

205.3 

73.4 

278 

261.7 

93.7 

39 

36.7 

13.1 

99 

93.2 

33.4 

159 

149.7 

53.6 

219 

206.2 

73.8 

279 

262.7 

94.0 

40 

37.7 

13.5 

100 

94.2 

33.7 

160 

150.6 

53.9 

220 

207.1 

74.1 

280 

263.6 

94.3 

41 

38.6 

13.8 

101 

95.1 

34.0 

161 

151.6 

54.2 

208.1 

74.5 

281 

264.6 

94.7 

42 

39.5 

14.1 

102 

96.0 

34.4 

162 

152.5 

54.6 

222 

209.0 

74.8 

282 

265.5 

95.0 

43 

40.5 

14.5 

103 

97.0 

34.7 

163 

153.5 

54.9 

223 

210.0 

75.1 

283 

266.5 

95.3 

44 

41.4 

14.8 

104 

97.9 

35.0 

164 

154.4 

55.2 

224 

210.9 

75.5 

284 

267.4 

95.7 

45 

42.4 

15.2 

105 

98.9 

354 

165 

155.4 

55.6 

225 

211.8 

75.8 

285 

268.3 

96.0 

46 

43.3 

15.5 

106 

99.8 

35.7 

166 

156.3 

55.9 

226 

212.8 

76.1 

286 

269.3 

96.4 

47 

44.3 

15.8 

107 

100.7 

36.0 

167 

157.2 

56.3 

227 

213.7 

76.5 

287 

270.2 

96.7 

48 

45.2 

16.2 

108 

101.7 

36.4 

168 

158.2 

56.6 

228 

214.7 

76.8 

288 

271.2 

97.0 

49 

46.1 

16.5 

109 

102.6 

36.7 

169 

159.1 

56.9 

229 

215.6 

77.1 

289 

272.1 

97.4 

50 
51 

47.1 

16.8 

110 

103.6 

37.1 
37.4 

170 

160.1 

57.3 
57.6 

230 

216.6 

77.5 

290 

273.0 

97.7 

48.0 

17.2 

HI 

104.5 

171 

161.0 

231 

217.5 

77.8 

291 

274.0 

98.0 

52 

49.0 

17.5 

1  12 

105.5 

37.7 

172 

161.9 

57.9 

232 

218.4 

78.2 

292 

274.9 

98.4 

53 

49.9 

17.9 

113 

106.4 

38.1 

173 

162.9 

58.3 

233 

219.4 

78.5 

293 

275.9 

98.7 

54 

50.8 

18.2 

114 

107.3 

38.4 

174 

163.8 

58.6 

234 

220.3 

78.8 

294 

276.8 

99.0 

55 

51.8 

18.5 

115 

108.3 

38.7 

175 

164.8 

.59.0 

235 

221.3 

79.2 

295 

277.8 

99.4 

56 

52.7 

18.9 

116 

109.2 

39.1 

176 

165.7 

59.3 

236 

222.2 

79.5 

296 

278.7 

99.7 

57 

53.7 

19.2 

117 

110.2 

39.4 

177 

166.7 

59.6 

237 

223.1 

79.8 

297 

279.6 

100.1 

58 

54.6 

19.5 

118 

111.1 

39.8 

178 

167.6 

60.0 

238 

224.1 

80.2 

298 

280.6 

100.4 

59 

55.6 

19.9 

119 

112.0 

40.1 

179 

168.5 

60.3 

239 

225.0 

80.5 

299 

281.5 

100.7 

60 

56.5 

20.2 

120 

113.0 

40.4 

180 

169.5 

60.6 
Lnt. 

240 

226.0 

80.9 

300 
Dist 

282.5 

101.1 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Dist 

Dep. 

Lat 

Dep. 

Lat 

East  North  East  i  F, 

ist.     Ee 

Lst  South   Ea.st  t  E'lst.     [Por  Sifts]     West  North  Wflst  J  West     West  South  «Vost 

iWert. 

8    TABLE  L— DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  2  POINTS. 

1 

North  Nurth  East. 

North  North  West.     '  South  South  East.     South  South  West.    1 

Dist. 

Lat 

Dep. 

Disf. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

Dist 

Lat. 

Dep. 

1 

00.9 

00.4 

61 

56.4 

23.3 

121 

111.8 

46.3 

181 

W57.2 

69.3 

241 

222.7 

92.2 

2 

01.8 

00.8 

62 

57.3 

23.7 

122 

112.7 

46.7 

182 

168.1 

69.6 

242 

223.6 

92.6. 

3 

02.8 

01.1 

63 

58.2 

24.1 

123 

113.6 

47.1 

183 

169.1 

70.0 

243 

224.5 

93.0 

4 

03.7 

01.5 

64 

59.1 

24.5 

124 

114.6 

47.5 

184 

170.0 

70.4 

244  r25.4 

93.4 

5 

04.6 

01.9 

65 

60.1 

24.9 

125 

115.5 

47.8 

185 

170.9 

70.8 

245 

226.4 

93.8 

6 

05.5 

02.3 

66 

61.0 

25.3 

126 

116.4 

48.2 

186 

171.8 

71.2 

246 

227.3 

94.1 

7 

06.5 

02.7 

67 

61.9 

25.6 

127 

117.3 

48.6 

187 

172.8 

71.6 

247 

228.2 

94.5 

8 

07.4 

03.1 

68 

62.8 

26.0 

128 

118.3 

49.0 

188 

173.7 

71.9 

248 

229.1 

94.9 

9 

08.3 

03.4 

69 

63.7 

26.4 

129 

119.2 

49.4 

189 

174.6 

72.3 

249 

230.0 

95.3 

10 

09.2 

03.8 

70 

64.7 

26.8 

130 

120.1 

49.7 

190 

175.5 

72.7 

250 

231.0 

95.7 

11 

10.2 

04.2 

71 

65.6 

27.2 

131 

121.0 

50.1 

191 

176.5 

73.1 

251 

231.9 

96.1 

12 

11.1 

04.6 

72 

66.5 

27.6 

132 

122.0 

50.5 

192 

177.4 

73.5 

252 

232.8 

96.4 

13 

12.0 

05.0 

73 

67.4 

27.9 

133 

122.9 

50.9 

193 

178.3 

73.9 

253 

233.7 

96.8 

14 

12.9 

05.4 

74 

68.4 

28.3 

134 

123.8 

51.3 

194 

179.2 

74.2 

254 

234.7 

97.2 

15 

13.9 

05.7 

75 

69.3 

28.7 

135 

124.7 

51.7 

195 

180.2 

74.6 

255 

235.6 

97.6 

16 

14.8 

06.1 

76 

70.2 

29.1 

136 

125.6 

52.0 

196 

181.1 

75.0 

256 

236.5 

98.0 

17 

15.7 

06.5 

77 

71.1 

29.5 

137 

126.6 

52.4 

197 

182.0 

75.4 

257 

237.4 

98.3 

18 

16.6 

06.9 

78 

72.1 

29.8 

138 

127.5 

52.8 

198 

182.9 

75.8 

258 

238.4 

98.7 

19 

17.6 

07.3 

79 

73.0 

30.2 

139 

128.4 

53.2 

199 

183.9 

76.2 

259 

239.3 

99.1 

20 

18.5 

07.7 

80 

73.9 

30.6 

140 

129.3 

53.6 

200 

184.8 

76.5 

260 

240.2 

99.5 

21 

19.4 

08.0 

81 

74.8 

31.0 

141 

130.3 

54.0 

201 

185.7 

76.9 

261 

241.1 

99.9 

22 

20.3 

08.4 

82 

75.8 

31.4 

142 

131.2 

54.3 

202 

186.6 

77.3 

262 

242.1 

100.3 

23 

21.2 

08.8 

83 

76.7 

31.8 

143 

132.1 

54.7 

203 

187.5 

77.7 

263 

243.0 

100.6 

24 

22.2 

09.2 

84 

77.6 

32.1 

144 

133.0 

55.1 

204 

188.5 

78.1 

264 

243.9 

101.0 

25 

23.1 

09.6 

85 

78.5 

32.5 

145 

134.0 

55.5 

205 

189.4 

78.5 

265 

244.8 

101.4 

26 

24.0 

09.9 

86 

79.5 

32.9 

146 

134.9 

55.9 

206 

190.3 

78.8 

266 

245.8 

101.8 

27 

24.9 

10.3 

87 

80.4 

33.3 

147 

135.8 

56.3 

207 

191.2 

79.2 

267 

246.7 

102.2 

28 

25.9 

10.7 

88 

81.3 

33.7 

148 

136.7 

56.6 

208 

192.2 

79.6 

268 

247.6 

102.6 

29 

26.8 

11.1 

89 

82.2 

34.1 

149 

137.7 

57.0 

209 

193.1 

80.0 

269 

248.5 

102.9 

30 

27.7 

11.5 

90 

83.1 

34.4 

150 

138.6 
139.5 

57.4 

210 

194.0 

80.4 

270 

249.4 

103.3 

31 

28.6 

11.9 

91 

84.1 

34.8 

151 

57.8 

211 

194.9 

80.7 

271 

250.4 

103.7 

32 

29.6 

12.2 

92 

85.0 

35.2 

152 

140.4 

58.2 

212 

195.9 

81.1 

272 

251.3 

104.1 

33 

30.5 

12.6 

93 

85.9 

35.6 

153 

141.4 

58.6 

213 

196.8 

81.5 

273 

252.2 

104.5 

34 

31.4 

13.0 

94 

86.8 

36.0 

154 

142.3 

58.9 

214 

197.7 

81.9 

274 

253.1 

104.9 

35 

32.3 

13.4 

95 

87.8 

36.4 

155 

143.2 

59.3 

215 

198.6 

82.3 

275 

254.1 

105.2 

36 

33.3 

13.8 

96 

88.7 

36.7 

156 

144.1 

59.7 

216 

199.6 

82.7 

276 

255.0 

105.6 

37 

34.2 

14.2 

97 

89.6 

37.1 

157 

145.0 

60.1 

217 

200.5 

83.0 

277 

255.9 

106.0 

38 

35.1 

14.5 

98 

90.5 

37.5 

158 

146.0 

60.5 

218 

201.4 

83.4 

278 

256.8 

106.4 

39 

36.0 

14.9 

99 

91.5 

37.9 

159 

146.9 

60.8 

219 

202.3 

83.8 

279 

257.8 

106.8 

40 
41 

37.0 

15.3 

100 

92.4 

38.3 

160 

147.8 

61.2 

220 

203.3 

84.2 

280 

258.7 

107.2 

37.9 

15.7 

101 

93.3 

38.7 

161 

148.7  61.6 

221 

204.2 

84.6 

281 

259.6 

107.5 

42 

38.8 

16  1 

102 

94.2 

39.0 

162 

149.7 

62.0 

222 

205.1 

85.0 

282 

260.5 

107.9 

43 

39.7 

16.5 

103 

95.2 

39.4 

163 

150.6 

62.4 

223 

206.0 

85.3 

283 

261.5 

108.3 

44 

40.7 

16.8 

104 

96.1 

39.8 

164 

151.5 

62.8 

224 

206.9 

85.7 

284 

262.4 

108.7 

45 

41.6 

17.2 

105 

97.0 

40.2 

165 

152.4 

63.1 

225 

207.9 

86.1 

285 

263.3 

109.1 

46 

42.5 

17.6 

106 

97.9 

40.6 

166 

153.4 

63.5 

226 

208.8 

86.5 

286 

264.2 

109.4 

47 

43.4 

18.0 

107 

98.9 

40.9 

167 

154.3 

63.9 

227 

209.7 

86.9 

287 

265.2 

109.8 

48 

44.3 

18.4 

108 

99.8 

41.3 

168 

155.2 

64.3 

228 

210.6 

87.3 

288 

266.1 

110.2 

49 

45.3 

18.8 

109 

100.7 

41.7 

169 

156.1 

64.7 

229 

211.6 

87.6 

289 

267.0 

110.6 

50 

46.2 

19.1 

110 

101.6 

42.1 

170 

157.1 

65.1 

230 

212.5 

88.0 

290 

267.9 

111.0 

51 

47.1 

19.5 

111 

102.6 

42.5 

171 

158.0 

65.4 

231 

213.4  88.4 

291 

268.8 

111.4 

52 

48.0 

19.9 

112 

103.5 

42.9 

172 

158.9 

65.8 

232 

214.3 

88.8 

292 

269.8 

111.7 

53 

49.0 

20.3 

113 

104.4 

43.2 

173 

159.8 

66.2 

233 

215.3 

89.2 

293 

270.7 

112.1 

54 

49.9 

20.7 

114 

105.3 

43.6 

174 

160.8 

66.6 

234 

216.2 

89.5 

294 

271.6 

112.5 

55 

50.8 

21.0 

115 

106.2 

44.0 

175 

161.7 

67.0 

235 

217.1 

89.9 

295 

272.5 

112.9 

56 

51.7 

21.4 

116 

107.2 

44.4 

176 

162.6 

67.4 

236 

218.0 

90.3 

296 

273.5 

113.3 

57 

52.7 

21.8 

117 

108.1 

44.8 

177 

163.5 

67.7 

237 

219.0 

90.7 

297 

274.4 

113.7 

58 

53.6 

22.2 

118 

109.0 

45.2 

17S 

164.5 

68.1 

238 

219.9 

91.1 

298 

275.3 

114.0 

59 

54  5 

22.6 

119 

109.9 

45.5 

179 

165.4 

68.5 

239 

220.8 

91.5 

299 

276.2 

114.4 

60 
Dili 

55.4 
Dep. 

23.0 

120 

110.9 

45.9 

18C 

166.3 

68.9 

240 

221.7 

91.8 

300 

277.2 

114.8 

Lat.  Dist. 

Dep.   Lat 

Dist. 

Dep. 

Lat  Dist 

Dep. 

Lat 

Dist 

Dep. 

Lat 

Eut  North  Eart.     I 

,Mt  Sonth  East.       [^"'■ePts.]       West  North  Went.     West! 

South  W* 

It 

TABLE  I.— DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  2i  POINTS.    9  1 

North  North  East  i  East. 

Nortli  North  West  i  West,  i 

South  South  East  i  East  SoutL  South  West  i  West.  1 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

LaL 

Dep. 

Dist. 
181 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

00.4 

61 

55.1 

26.1 

121 

109.4 

51.7 

103.6 

77.4 

241 

217.9 

103.0 

2 

01.8 

00.9 

62 

50.0 

26.5 

122 

110.3 

52.2 

182 

104.5 

77.8 

242 

218.8 

103.5 

3 

02.7 

01.3 

63 

57.0 

26.9 

123 

111.2 

52.6 

183 

165.4 

78.2 

243 

219.7 

103.9 

4 

03.6 

01.7 

64 

57.9 

27.4 

124 

112.1 

53.0 

184 

166.3 

78.7 

244 

220.6 

104.3 

5 

04.5 

02.1 

65 

58.8 

27.8 

125 

113.0 

53.4 

185 

167.2 

79.1 

245 

221.5 

104.8 
105.2 
105.6 

6 

05.4 

02.6 

66 

59.7 

28.2 

126 

113.9 

53.9 

186 

168.1 

79.5 

246 

222.4 

7 

06.3 

03.0 

67 

60.6 

28.6 

127 

114.8 

54.3 

187 

169.0 

80.0 

247 

223.3 

8 

07.2 

03.4 

68 

61.5 

29.1 

128 

115.7 

54.7 

188 

169.9 

80.4 

248 

224.2 

106.0 

9 

08.1 

03.8 

69 

62.4 

29.5 

129 

116.6 

55.2 

189 

170.9 

80.8 

249 

225.1 

106.5 

10 
11 

09.0 

04.3 

70 

63.3 

29.9 

130 

117.5 

55.6 

190 

171.8 

81.2 

250 

226.0 

106.9 

09.9 

04.7 

71 

64.2 

30.4 

131 

118.4 

56.0 

191 

172.7 

81.7 

251 

226.9 

107.3 

12 

10.8 

05.1 

72 

65.1 

30.8 

132 

119.3 

56.4 

192 

173.6 

82.1 

252 

227.8 

107.7 

13 

11.8 

05.6 

73 

66.0 

31.2 

133 

120.2 

56.9 

193 

174.5^  82.5 

253 

228.7 

108.2 

14 

12.7 

06.0 

74 

66.9 

31.6 

134 

121.1 

57.3 

194 

175.4 

82.9 

254 

229.6 

108.6 

15 

13.6 

06.4 

75 

67.8 

32.1 

135 

122.0 

57.7 

195 

176.3 

83.4 

255 

230.5 

109.0 

10 

14.5 

06.8 

70 

68.7 

32.5 

136 

122.9 

58.1 

196 

177.2 

83.8 

256 

231.4 

109.5 

17 

15.4 

07.3 

77 

69.6 

32.9 

137 

123.8 

58.6 

197 

178.1 

84.2 

257 

232.3 

109.9 

18 

16.3 

07.7 

78 

70.5 

33.3 

138 

124.8 

59.0 

198 

179.0 

84.7 

258 

233.2 

110.3 

19 

17.2 

08.1 

79 

71.4 

33.8 

139 

125.7 

59.4 

199 

179.9 

85.1 

259 

234.1 

110.7 

20 
21 

18.1 
19.0 

08.6 
09.0 

80 

72.3 

34.2 

140 

126.6 

59.9 

200 

180.8 

85.5 

260 

235.0 

111.2 

81 

73.2 

34.6 

141 

127.5 

60.3 

201 

181.7 

85.9 

201 

235.9 

111.6 

22 

19.9 

09.4 

82 

74.1 

35.1 

142 

128.4 

60.7 

202 

182.6 

86.4 

262 

236.8 

112.0 

23 

20.8 

09.8 

83 

75.0 

35.5 

143 

129.3 

61.1 

203 

183.5 

86.8 

203 

237.7 

112.4 

24 

21.7 

10.3 

84 

75.9 

35.9 

144 

130.2 

61.6 

204 

184.4 

87.2 

264 

238.7 

112.9 

25 

22.6 

10.7 

85 

76.8 

36.3 

145 

131.1 

62.0 

205 

185.3 

87.6 

265 

239.6 

113.8 

26 

23.5 

11.1 

86 

77.7 

36.8 

146 

132.0 

62.4 

206 

186.2 

88.1 

266 

240.5 

113.7 

27 

24.4 

11.5 

87 

78.6 

37.2 

147 

132.9 

62.9 

207 

187.1 

88.5 

267 

241.4 

114.2 

28 

25.3 

12.0 

88 

79.6 

37.6 

148 

133.8 

63.3 

208 

188.0 

88.9 

268 

242.3 

114.6 

29 

26.2 

12.4 

89 

80.5 

38.1 

149 

134.7 

63.7 

209 

188.9 

89.4 

209 

243.2 

115.0 

30 

27.1 

12.8 

90 

81.4 

38.5 

150 

135.6 

64.1 

210 

189.8 

89.8 

270 
271 

244.1 

115.4 

31 

28.0 

13.3 

91 

82.3 

38.9 

151 

136.5 

64.6 

211 

190.7 

90.2 

245.0 

115.9 

32 

28.9 

13.7 

92 

83.2 

39.3 

152 

137.4 

65.0 

212 

191.6 

90.6 

272 

245.9 

116.3 

33 

29.8 

14.1 

93 

84.1 

39.8 

153 

138.3 

05.4 

213 

192.5 

91.1 

273 

246.8 

116.7 

34 

30.7 

14.5 

94 

85.0 

40.2 

154 

139.2 

65.8 

214 

193.5 

91.5 

274 

247.7 

117.2 

35 

31.6 

15.0 

95 

85.9 

40.6 

155 

140.1 

66.3 

215 

194.4 

91.9 

275 

248.6 

117.6 

36 

32.5 

15.4 

96 

86.8 

41.0 

156 

141.0 

66.7 

216 

195.3 

92.4 

276 

249.5 

118.0 

37 

33.4 

15.8 

97 

87.7 

41.5 

157 

141.9 

67.1 

217 

196.2 

92.8 

277 

250.4 

118.4 

38 

34.4 

16.2 

98 

88.6 

41.9 

158 

142.8 

67.6 

218 

197.1 

93.2 

278 

251.3 

118.9 

39 

35.3 

16.7 

99 

89.5 

42.3 

159 

143.7 

08.0 

219 

198.0 

93.6 

279 

252.2 

119.3 

40 
41 

36.2 

17.1 

100 

90.4 

42.8 

100 

144.6 

68.4 

220 

198.9 

94.1 

280 

253.1 

119.7 

37.1 

17.5 

101 

91.3 

43.2 

161 

145.5 

68.8 

221 

199.8 

94.5 

281 

254.0 

120.1 

42 

38.0 

18.0 

102 

92.2 

43.0 

162 

146.4 

69.3 

222 

200.7 

94.9 

282 

254.9 

120.6 

43 

38.9 

18.4 

103 

93.1 

44.0 

163 

147.4 

69.7 

223 

201.6 

95.3 

283 

255.8 

121.0 

44 

39.8 

18.8 

104 

94.0 

44  5 

104 

148.3 

70.1 

224 

202.5 

95.8 

284 

256.7 

121.4 

45 

40.7 

19.2 

105 

94.9 

44.9 

105 

149.2 

70.5 

225 

203.4 

96.2 

285 

257.6 

121.9 

40 

41.6 

19.7 

106 

95.8 

45.3 

166 

150.1 

71.0 

226 

204.3 

90.0 

286 

258.5 

122.3 

47 

42.5 

20.1 

107 

96.7 

45.7 

167 

151.0 

71.4 

227 

205.2 

97.1 

287 

259.4 

122.7 

48 

43.4 

20.5 

108 

97.6 

46.2 

168 

151.9 

71.8 

228 

206.1 

97.5 

288 

200.3 

123.1 

49 

44.3 

21.0 

109 

98.5 

40.6 

109 

152.8 

72.3 

229 

207.0 

97.9 

289 

261.3 

123.6 

50 

45.2 

21.4 

110 

99.4 

47.0 
47.5 

170 

153.7 

72.7 
73.1 

230 

207  9 

98.3 

290 

262.2 

124.0 

51 

46.1 

21.8 

111 

100.3 

171 

154.6 

231 

208.8 

98.8 

291 

263.1 

124.4 

52 

47.0  22.2 

112 

101.2 

47.9 

172 

155.5 

73.5 

232 

209.7 

99.2 

292 

264.0 

124.8 

53 

47.9  22.7 

113 

102.2 

48.3 

173 

156.4 

74.0 

233 

210.6 

99.0 

293 

204.9 

125.3 

54 

48.8 

23.1 

114 

103.1 

48.7 

174 

157.3 

74.4 

234 

211.5 

100.0 

294 

205.8 

125.7 

55 

49.7 

23.5 

115 

104.0 

49.2 

175 

158.2 

74.8 

235 

212.4 

100.5 

295 

206.7 

120.1 

50 

50.6 

23.9 

116 

104.9 

49.0 

176 

159.1 

75.2 

230 

213.3 

100.9 

290 

207.6 

126.6 

57 

51.5 

24.4 

117 

105.8 

50.0 

177 

100.0 

75.7 

237 

214.2 

101.3 

297 

208.5 

127.0 

58 

52.4 

24.8 

118 

106.7 

50.5 

178 

100.9 

70.1 

238 

215.1 

101.8 

298 

209.4 

127.4 

59 

53.3 

25.2 

119 

107.6 

50.9 

179 

101.8 

70.5 

239 

216.1 

102.2 

299 

270.3 

127.8 

60 

54.2 

25.7 

120 

108.5 

51.3 

180 

102.7 

77.0 
Lat. 

240 

Dist. 

217.0 

102.0 

300 

271.2 

128.3 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Nirth  East*.  Eaat^  East,  f 

?outh  East*  East  f  Bh  St.  [For  5f  Pts  ]  \orth  Wen  A.  West }  West.  South  West  *,  West  f  We«t  J 

4 

7 ABLE  I 

—DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  2j  POINTS 

1 

North  North  East  i  East 

.  North  No.  th  West  i  "West.  South  South  East  i  East  South  South  West  i  West.  [ 

Dist 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist 

1  Lat 

Dep. 

Dist 

Lat 

Dep. 

1 

00.9 

00.5 

61 

53.8 

28.8 

121 

106.7 

57.0 

181 

159.6 

85.3 

241 

212.5 

113.6 

2 

01.8 

00.9 

62 

54.7 

29.2 

122 

107.6 

57.5 

182!  160.5 

85.8 

242 

213.4 

114.1 

3 

02.6 

01.4 

63 

55.6 

29.7 

123 

108.5 

58.0 

183!  161.4 

86.3 

243 

214.3 

114.5 

4 

03.5 

01.9 

64 

56.4 

30.2 

124 

109.4 

58.5 

184  162.3 

86.7 

244 

215.2 

115.0 

5 

04.4 

02.4 

65 

57.3 

30.6 

125 

110.2 

58.9 

185  163.2 

87.2 

245 

216.1 

115.5 

6 

05.3 

02.8 

66 

58.2 

31.1 

126 

111.1 

59.4 

186  164.0 

87.7 

246 

217.0 

116.0 

7 

06.2 

03.3 

67 

59.1 

31.6 

127 

J  12.0 

59.9 

187 

164.9 

88.2 

247 '217.8 '116.41 

8 

07.1 

03.8 

68 

60.0 

32.1 

128 

112.9 

60.3 

188 

165.8 

88.6 

248,218.7;  116.91 

9 

07.9 

04.2 

69 

60.9 

32.5 

129 

113.8 

60.8 

189 

166.7 

89.1 

249 

219.6 

117.4 

10 
11 

08.8 

04.7 

70 

61.7 

33.0 

130 

114.6 

61.3 

190 

167,6 

89.6 

250 

220.5 

117.8 

09.7 

05.2 

71 

62.6 

33.5 

131 

115.5 

61.8 

191 

168.4 

90.0 

251 

221.4 

118.3 

12 

10.6 

05.7 

72 

63.5 

33.9 

132 

116.4 

62.2 

192 

169.3 

90.5 

252 

222.2 

118.8 

13 

11.5 

06.1 

73 

64.4 

34.4 

133 

117.3 

62.7 

193 

170.2 

91.0 

253 

223.1 

119.3 

14 

12.3 

06.6 

74 

65.3 

34.9 

134 

118.2 

63.2' 194 

171.1 

91.5 

254 

224.0 

119.7 

15 

13.2 

07.1 

75 

66.1 

35.4 

135 

119.1 

63.6  195 

172.0 

91.9 

255 

224.9 

120.2 

16 

14.1 

07.5 

76 

67.0 

35.8 

136 

119.9 

64.1  196 

172.9 

92.4 

256 

225.8 

120.7 

17 

15.0 

08.0 

77 

67.9 

36.3 

137 

120.8;  64.6  197 '173.7 

92.9 

257 

226.7 

121.1 

18 

15.9 

08.5 

78 

68.8 

36.8 

138 

121.7 

65.1  198  1174.6 

93.3 

258 

227.5 

121.6 

19 

16.8 

09.0 

79 

69.7 

37.2 

139 

122.6 

65.5  1991175.5 

93.8 

259 

228.4 

122.1 

20 

17.6 

09.4 

80 

70.6 

37.7 

140 

123.5 

66.0  2001176.4 

1 

94.3 

260 

229.3 

122.6 

21 

18.5 

09.9 

81 

71.4 

38.2 

141 

124.4 

66.5 

201  1 177.3 

94.8 

261 

230.2 

123.0 

22 

19.4 

10.4 

82 

72.3 

38.7 

142 

125.2 

66.9 

202 

178.1 

95.2 

262 

231.1 

123.5 

23 

20.3 

10.8 

83 

73.2 

39.1 

143 

126.1 

67.4 

203 

179.0 

95.7 

263 

231.9 

124.0 

24 

21.2 

11.3 

84 

74.1 

39.6 

144 

127.0  67.9 

204 

179.9 

96.2 

264 

232.8 

124.4 

25 

22.0 

11.8 

85 

75.0 

40.1 

145 

127.9  68.4 

205 

180.8 

96.6 

265 

233.7 

124.9 

26 

22.9 

12.3 

86 

75.8 

40.5 

146 

128.8 

68.8 

206 

181.7 

97.1 

266 

234.6 

125.4 

27 

23.8 

12.7 

87 

76.7 

41.0 

147 

129.6 

69.3 

207 

182.6 

97.6 

267 

235.5 

125.9 

28 

24.7 

13.2 

88 

77.6141.5 

148 

130.5 

69.8 

208 

183.4 

98.1 

268  236.4 

126.3 

29  ;  25.6 

13.7 

89 

78.5,42.0 

149 

131.4 

70.2 

209 

184.3 

98.5 

269  237.2 

126.8 

30 
31 

26.5 

14.1 

90 

79.4 

42.4 

150 

132.3 

70.7 

210 

185.2 

99.0 

270,238.1 

127.3 

27.3 

14.6 

91 

80.3 

42.9 

151 

133.2 

71.2 

211 

186.1 

99.5 

271 

239.0 

127.7 

32 

28.2 

15.1 

92 

81.1 

43.4 

152 

134.1 

71.7 

212 

187.0 

99.9 

272 

239.9 

128.2 

33 

29.1 

15.6 

93 

82.0 

43.8 

153 

134.9 

72.1 

213 

187.8 

100.4 

273 

240.8 

128.7 

34 

30.0 

16.0 

94 

82.9 

44.3 

154 

135.8  ,  72.6 

214 

188.7 

100.9 

274 

241.6 

129.2 

35 

30.9 

16.5 

95 

83.8 

44.8 

155 

136.7  73.1 

215 

189.6 

101.4 

275 

242.5 

129.6 

36 

31.7 

17.0 

96 

84.7 

45.3 

156 

137.6  73.5 

216 

190.5 

101.8 

276 

243.4 

130.1 

37 

32.6 

17.4 

97 

85.5 

45.7 

157 

138.5 

74.0 

217 

191.4 

102.3 

277 

244.3 

130.6 

38 

33.5 

17.9 

98 

86.4 

46.2 

158 

139.3 

74.5 

218 

192.3 

102.8 

278 

245.2 

131.0 

39 

34.4 

18.4 

99 

87.3 

46.7 

159 

140.2 

75.0 

219 

193.1 

103.2 

279 

246.1 

131.5 

40 

35.3 

18.9 

100 

88.2 

47.1 

160 

141.1 

75.4 

220 

194.0 

103.7 

280 

246.9 

132.0 

41 

36.2 

19.3 

101 

89.1 

47.6 

161 

142.0 

75.9 

221 

194.9 

104.2 

281 

247.8 

132.5 

42 

37.0 

19.8 

102 

90.0 

48.1 

162 

142.9 

76.4 

222 

195.8 

104.7 

282 

248.7 

132.9 

43 

37.9 

20.3 

103 

90.8 

48.6 

163 

143.8 

76.8 

223 

196.7 

105.1 

283 

249.6 

133.4 

44 

38.8 

20.7 

104 

91.7 

49.0 

164 

144.6 

77.3 

224 

197.6 

105.6 

284 

250.5 

133.9 

45 

39.7 

21.2 

105 

92.6 

49.5 

165 

145.5 

77.8 

225 

198.4 

106.1 

285 

251.3 

134.3 

46 

40.6 

21.7 

106 

93.5 

50.0 

166 

146.4 

78.3 

226 

199.3 

106.5 

286 

252.2 

134.8 

47 

41.5 

22.2 

107 

94.4 

50.4 

167 

147.3 

78.7 

227 

200.2 

107.0 

287 

253.1 

135.3 

48 

42.3 

22.6 

108 

95.2 

50.9 

1()8 

148.2 

79.2 

228 

201.1 

107.5 

288 

254.0 

135.8 

49 

43.2 

23.1 

109 

96.1 

51.4 

169 

149.0 

79.7 

229 

202.0 

107.9 

289 

254.9 

136.2 

50 

44.1 

23.6 

110 

97.0 

51.9 

170 

149.9  80.1 

230 

202.8 

108.4 

290 

255.8 

136.7 

51 

45.0 

24.0 

111 

97.9 

52.3 

171 

150.8  '  80.6 

231 

203.7 

108.9 

291 

256.6 

137.2 

52 

45.9 

24.5 

112 

98.8 

52.8 

172 

151.7'81.1 

232 

204.6 

109.4 

292 

257.5 

137.6 

53 

46.7 

25.0 

113 

99.7  53.3 

173 

152.6 

81.6 

233 

205.5 

109.8 

293 

258.4  138.1 

54 

47.6 

25.5 

114 

100.5 

53.7 

174 

153.5 

82.0 

234 

206.4 

110.3 

294 

259.3  1 138.6 

55 

48.5 

25.9 

115 

101.4 

54.2 

175 

154.3 

82.5 

235 

207.3 

110.8 

295 

260.2.139.1 

56 

49.4 

20.4 

116 

102.3 

54.7 

176 

155.2 

83.0 

236 

208.1 

111.2 

296 

261.0  1139.5 

57 

50.3 

26.9 

117 

103.2 

55.2 

177 

156.1 

83.4 

237 

209.0 

111.7 

297 

261.91140.0 

58 

51.2 

27.3 

118 

104.1 

55.6 

17S 

157.0 

83.9 

238 

209.9 

112.2 

298 

262.8  1 140.5 

59 

52.0 

27.8 

119 

104.9 

56.1 

179 

157.9 

84.4 

239  210.8 

112.7 

299 

263.7 

140.9 

60 

Dist 

52.9 

28.3 

120 

Dist 

105.8 

56.6 

180 

158.7 

84.9 

240 

211.7 

113.1 

300 

264.6 

141.4 

Dep.   Lat. 

Dep. 

Lat. 

Dist   Dep. 

Lat. 

Dist 

Dep.   Lat  | 

Dist  Dep.  j 

Lat. 

Wort 

Il  Ra.st  b.  East  )  East.  P 

outh  East*.  Easti  East.  [ForJHPts.;!  North  Wen  ft.  Wast  J  West.  South  West  A.  Was 

t  i  We»t. 

TABLE  I.- 

-DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  2i  POINTS. 

a  1 

North  North  East* East. 

North  Northwest  IWest.  South  South  East  »  East.  South  SouthWest  *  West.  1 

Oist 

1 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

00.9 

00.5 

61 

52.3 

31.4 

121 

103.8 

62.2 

181 

155.2 

93.1 

241 

206.7 

123.9 

2 

01.7 

01.0 

62 

53.2 

31.9 

122 

104.6 

62.7 

182 

156.1 

93.6 

242 

207.6 

124.4 

3 

02.6 

01.5 

63 

54.0 

32.4 

123 

105.5 

63.2 

183 

157.0 

94.1 

243 

208.4 

124.9 

4 

03.4 

02.1 

64 

54.9 

32.9 

124 

106.4 

63.7 

184 

157.8 

94.6 

244 

209.3 

125.4 

5 

04.3 

02.6 

65 

55.8 

33.4 

125 

107.2 

64.3 

185 

158.7 

95.1 

245 

210.1 

126.0 

6 

05.1 

03.1 

66 

56.6 

33.9 

126 

108.1 

64.8 

186 

159.5 

95.6 

246 

211.0 

126.5 

7 

06.0 

03.6 

67 

57.5 

34.4 

127 

108.9 

65.3 

187 

160.4 

96.1 

247 

211.9 

127.0 

8 

06.9 

04.1 

68 

58.3 

35.0 

128 

109.8 

65.8 

188 

161.3 

96.7 

248 

212.7 

127.5 

9 

07.7 

04.6 

69 

59.2 

35.5 

129 

110.6 

66.3 

189 

162.1 

97.2 

249 

213.6 

128.0 

10 

08.6 

05.1 

70 

60.0 

36.0 
36.5 

130 

111.5 

66.8 

190 

163.0 

97.7 

250 
251 

214.4 

128.5 

11 

09.4 

05.7 

71 

60.9 

131 

112.4 

67.3 

191 

163.8 

98.2 

215.3 

129.0 

12 

10.3 

06.2 

72 

61.8 

37.0 

132 

113.2 

67.9 

192 

164.7 

98.7 

252 

216.1 

129.6 

13^ 

11.2 

06.7 

73 

62.6 

37.5 

133 

114.1 

68.4 

193 

165.5 

99.2 

253 

217.0 

130.1 

14 

12.0 

07.2 

74 

63.5 

38.0 

134 

114.9 

68.9 

194 

166.4 

99.7 

254 

217.9 

130.6 

15 

12.9 

07.7 

75 

64.3 

38.6 

135 

115.8 

69.4 

195 

167.3 

100.3 

255 

218.7 

131.1 

16 

13.7 

08.2 

76 

65.2 

39.1 

136 

116.7 

69.9 

196 

168.1 

100.8 

256 

219.6 

131.6 

17 

14.6 

08.7 

77 

66.0 

39.6 

137 

117.5 

70.4 

197 

169.0 

101.3 

257 

220.4 

132.1 

18 

15.4 

09.3 

78 

66.9 

40.1 

138 

118.4 

70.9 

198 

169.8 

101.8 

258 

221.3 

132.6 

19 

16.3 

09.8 

79 

67.8 

40.6 

139 

119.2 

71.5 

199 

170.7 

102.3 

259 

222.2 

133.2 

20 
21 

17.2 
18.0 

10.3 

80 

68.6 

41.1 

140 

120.1 

72.0 

200 

171.5 

102.8 

260 

223.0 

133.7 

10.8 

81 

69.5 

41.6 

141 

120.9 

72.5 

201 

172.4 

103.3 

261 

223.9 

134.2 

22 

18.9 

11.3 

82 

70.3 

42.2 

142 

121.8 

73.0 

202 

173.3 

103.8 

262 

224.7 

134.7 

23 

19.7 

11.8 

83 

71.2 

42.7 

143 

122.7 

73.5 

203 

174.1 

104.4 

263 

225.6 

135.2 

24 

20.6 

12.3 

84 

72.0 

43.2 

144 

123.5 

74.0 

204 

175.0 

104.9 

264 

226.4 

135.7 

25 

21.4 

12.9 

85 

72.9 

43.7 

145 

124.4 

74.5 

205 

175.8 

105.4 

265 

227.3 

136.2 

20 

22.3 

13.4 

86 

73.8 

44.2 

146 

125.2 

75.1 

206 

176.7 

105.9 

266 

228.2 

136.8 

27 

23.2 

13.9 

87 

74.6 

44.7 

147 

126.1 

75.6 

207 

177.5 

106.4 

267 

229.0 

137.3 

28 

24.0 

14.4 

88 

75.5 

45.2 

148 

126.9 

76.1 

208 

178.4 

106.9 

268 

^29.9 

137.8 

29 

24.9 

14.9 

89 

76.3 

45.8 

149 

127.8 

76.6 

209 

179.3 

107.4 

269 

230.7 

138.3 

30 

25.7 

15.4 

90 

77.2 

46.3 

150 

128.7 

77.1 

210 

180.1 

108.0 

270 
271 

231.6 

138.8 

31 

26.6 

15.9 

91 

78.1 

46.8 

151 

129.5 

77.6 

211 

181.0 

108.5 

232.4 

139.3 

32 

27.4 

16.5 

92 

78.9 

47.3 

152 

130.4 

78.1 

212 

181.8 

109.0 

272 

233.3 

139.8 

33 

28.3 

17.0 

93 

79.8 

47.8 

153 

131.2 

78.7 

213 

182.7 

109.5 

273 

234.2 

140.4 

34 

29.2 

17.5 

94 

80.6 

48.3 

154 

132.1 

79.2 

214 

183.6 

110.0 

274 

235.0 

140.9 

35 

30.0 

18.0 

95 

81.5 

48.8 

155 

132.9 

79.7 

215 

184.4 

110.5 

275 

235.9 

141.4 

36 

30.9 

18.5 

96 

82.3 

49.4 

156 

133.8 

80.2 

216 

185.3 

111.0 

276 

236.7 

141.9 

37 

31.7 

19.0 

97 

83.2 

49.9 

157 

134.7 

80.7 

217 

186.1 

111.6 

277 

237.6 

142.4 

38 

32.6 

19.5 

98 

84.1 

50.4 

158 

135.5 

81.2 

218 

187.0 

112.1 

278 

238.4 

142.9 

39 

33.5 

20.1 

99 

84.9 

50.9 

159 

136.4 

81.7 

219 

187.8 

112.6 

279 

239.3 

143.4 

40 

34.3 

20.6 

100 

85.8 

51.4 

160 

137.2 

82.3 

220 

188.7 

113.1 

280 

240.2 

143.9 

41 

35.2 

21.1 

101 

86.6 

51.9 

161 

138.1 

82.8 

221 

189.6 

113.6 

281 

241.0 

144.5 

42 

36.0 

21.6 

102 

87.5 

52.4 

162 

139.0 

83.3 

222 

190.4 

114.1 

282 

241.9 

145.0 

43 

36.9 

22.1 

103 

88.3 

53.0 

163 

139.8 

83.8 

223 

191.3 

114.6 

283 

242.7 

145.5 

44 

37.7 

22.6 

104 

89.2 

53.5 

164 

140.7 

84.3 

224 

192.1 

115.2 

284 

243.6 

146.0 

45 

38.6 

23.1 

105 

90.1 

54.0 

165 

141.5 

84.8 

225 

193.0 

115.7 

285 

244.5 

146.5 

46 

39.5 

23.6 

106 

90.9 

54.5 

166 

142.4 

85.3 

226 

193.8 

116.2 

286 

245.3 

147.0 

47 

40.3 

24.2 

107 

91.8 

55.0 

167 

143.2 

85.9 

227 

194.7 

116.7 

287 

246.2 

147.5 

48 

41.2 

24.7 

108 

92.6 

55.5 

168 

144.1 

86.4 

228 

195.6 

117.2 

288 

247.0 

148.1 

49 

42.0 

25.2 

109 

93.5 

56.0 

169 

145.0 

86.9 

229 

196.4 

117.7 

289 

247.9 

148.6 

50 
51 

42.9 
43.7 

25.7 
26.2 

110 

94.4 

56.6 
57.1 

170 

145.8 

87.4 
87.9 

230 

197.3 

118.2 

290 

248.7 

149.1 
149.6 

111 

95.2 

171 

146.7 

231 

198.1 

118.8 

291 

249.6 

52 

44.6 

26.7 

112 

96.1 

57.6 

172 

147.5 

88.4 

232 

199.0 

119.3 

292 

250.5 

150.1 

53 

45.5 

27.2 

113 

96.9 

58.1 

173 

148.4 

88.9 

233 

199.9 

119.8 

293 

251.3 

150.6 

54 

46.3 

27.8 

114 

97.8 

58.6 

174 

149.2 

89.5 

234 

200.7 

120.3 

294 

252.2 

151.1 

55 

47.2 

28.3 

115 

98.6 

59.1 

175 

150.1 

90.0 

235 

201.6 

120.8 

295 

253.0 

151.7 

56 

48.0 

28.8 

116 

99.5 

59.6 

176 

151.0 

90.5 

236 

202.4 

121.3 

296 

253.9 

152.2 

57 

48.9 

29.3 

117 

100.4 

60.2 

177 

151.8 

91.0 

237 

203.3 

121.8 

297 

254.7 

152.7 

58 

49.7 

29.8 

118 

101.2 

60.7 

178 

152.7 

91.5 

238 

204.1 

122.4 

298 

255.6 

153.2 

59  50.6 

30.3 

119 

102.1 

61.2 

179 

153.5 

92.0 

239 

205.0 

122.9 

299 

256.5 

153.7 

60  51.5 

30.8 

120 

102.9 

61.7 

180 

154.4 

92.5 

240 

205.9 

123.4 

300 

257.3 

154.2 

Dist.  Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat 

North  Ewt  b.  East  t  Eart. 

South  East*.  East  A  F:Hst.  [ForgiPts]  North  West  4.  West  i  West  South  West  *.  We 

St  i  W«rt 

n   TABLE  I.— DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  8  ] 

POINTS. 

K ..rth  East  b.  North.     North  West  b.  North.     South  East  b.  South.     South  West  b.  South. 

Dist 

Lat 

Dep. 

Dist 

Lat 

50.7 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

pep. 

1 

00.8 

00.6 

61 

33.9 

121 

100.6 

67.2 

181 

150.5 

100.6 

241 

200.4 

133.9 

2 

01.7 

01.1 

62 

51.6 

34.4 

122 

101.4 

67.8 

182 

151.3 

101.1 

242 

201.2 

134.4 

3 

02. 5 

01.7 

63 

52.4 

35.0 

123 

102.3 

68.3 

183 

152.2 

101.7 

243 

202.0 

135.0 

4 

03.3 

02.2 

64 

53.2 

35.6 

124 

103.1 

68.9 

184 

153.0 

102.2 

244 

202.9 

135.6 

5 

04.2 

02.8 

65 

54.0 

36.1 

125 

103.9 

69.4 

185 

153.8 

102.8 

245 

203.7 

136.1 

6 

05.0 

03.3 

66 

54.9 

36.7 

126 

104.8 

70.0 

186 

154.7 

103.3 

246 

204.5 

136.7 

7 

05.8 

03.9 

67 

55.7 

37.2 

127 

105.6 

70.6 

187 

155.5 

103.9 

247  i  205.4 

1  137.2 

8 

06.7 

04.4 

68 

56.5 

37.8 

128 

106.4 

71.1 

188 

156.3 

104.4 

248  ,  206.2 

137.8 

9 

07.5 

05.0 

69 

57.4 

38.3 

129 

107.3 

71.7 

189 

157.1 

105.0 

249 

207.0 

138.3 

10 
11 

08.3 

05.6 

70 

58.2 

38.9 

i;50 

108.1 

72.2 

190 

158.0 

105.6 

250 

207.9 

138.9 

09.1 

06.1 

71 

59.0 

39.4 

131 

108.9 

72.8 

191 

158.8 

106.1 

251 

208.7 !  139.4 

12 

10.0 

06.7 

72 

59.9 

40.0 

132 

109.8 

73.3 

192 

159.6  106.7 

252 '  209.5 

140.0 

13 

10.8 

07.2 

73 

60.7 

40.6 

133 

110.6 

73.9 

193 

160.5  107.2 

253 

210.4 

140.6 

14 

11.6 

07.8 

74 

61.5 

41.1 

134 

111.4 

74.4 

194 

161.3 

107.8 

254 

211.2 

141.1 

15 

12.5 

08.3 

75 

62.4 

41.7 

135 

112.2 

75.0 

195 

162.1 

108.3 

255 

212.0 

141.7 

16 

13.3 

08.9 

76 

63.2 

42.2 

136 

113.1 

75.6 

196 

163.0 

108.9 

256 

212.9 

142.2 

17 

14.1 

09.4 

77 

64.0 

42.8 

137 

113.9 

76.1 

197 

163.8 

109.4 

257 

213.7 

142.8 

18 

15.0 

10.0 

78 

64.9 

43.3 

138 

114.7 

76.7 

198 

164.6 

110.0 

258 

214.5 

143.3 

19 

15.8 

10.6 

79 

65.7 

43.9 

139 

115.6 

77.2 

199 

165.5 

110.6 

259 

215.4 

143.9 

•20 

16.6 

11.1 
11.7 

80 

66.5 

44.4 

140 

116.4 

77.8 

200 

166.3 

111.1 

260 

216.2 

144.4 

21 

17.5 

81 

67.3 

45.0 

141 

117.2 

78.3 

201 

167.1 

111.7 

261 

217.0 

145.0 

22 

18.3 

12.2 

82 

68.2 

45.6 

142 

118.1 

78.9 

202 

168.0 

112.2 

262 

217.8 

145.6 

23 

19.1 

12.8 

83 

69.0 

46.1 

143 

118.9 

79.4 

203 

168.8 

112.8 

263 

218.7 

146.1 

24 

20.0 

13.3 

84 

69.8 

46.7 

144 

119.7 

80.0 

204 

169.6 

113.3 

264 

219.5 

146.7 

25 

20.8 

13.9 

85 

70.7 

47.2 

145 

120.6 

80.6 

205 

170.5 

113.9 

265 

220.3  147.2 

26 

21.6 

14.4 

86 

71.5 

47.8 

146 

121.4 

81.1 

206 

171.3 

114.4 

266 

221.2 '147.8 

27 

22.4 

15.Q 

87 

72.3 

48.3 

147 

122.2 

81.7 

207 

172.1 

115.0 

267 

222.0  1 148.3 

2S 

23.3 

15.6 

88 

73.2 

48.9 

148 

123.1 

82.2 

208 

172.9 

115.6 

268 

222.8  148.9] 

29 

24.1 

16.1 

89 

74.0 

49.4 

149 

123.9 

82.8 

209 

173.8 

116.1 

269 

223.7  149.4( 

30 

24.9 

16.7 

90 

74.8 
75.7 

50.0 

150 

124.7 

83.3 

210 

174.6 

116.7 

270 '224.5  150.C 

31 

25.8 

17.2 

91 

50.6 

151 

125.6 

83.9 

211 

175.4 

117.2 

271  .  225.3  il5C.6 

:^2 

26.6 

17.8 

92 

76.5 

51.1 

152 

126.4 

84.4 

212 

176.3 

117.8 

272  I  226.2 

Ifyl.l 

33 

27.4 

18.3 

93 

77.3 

51.7 

153 

127.2 

85.0 

213 

177.1 

118.3 

273  !  227.0 

151.7 

34 

28.3 

18.9 

94 

78.2 

52.2 

154 

128.0 

85.0 

214 

177.9 

118.9 

274 

227.8 

152.2 

35 

29.1 

19.4 

95 

79.0 

52.8 

155 

128.9 

86.1 

215 

178.8 

119.4 

275 

228.7 

152.8 

36 

2Q.9 

20.0 

96 

79.8 

53.3 

156 

129.7 

86.7 

216 

179.6 

120.0 

276 

229.5 

153.3 

37 

30.8 

20.6 

97 

80.7 

53.9 

157 

130.5 

87.2 

217 

180.4 

120.6 

277 

230.3 

153.9 

38 

31.6 

21.1 

98 

81.5 

54.4 

158 

131.4 

87.8 

218 

181.3 

121.1 

278 

231.1 

154.4 

39 

32.4 

21.7 

99 

82.3 

55.0 

159 

132.2  88.3 

219 

182.1 

121.7 

279 

232.0 

155.0 

40 

33.3 
34.1 

22.2 

22.8 

100 

83.1 

55.6 

160 

133.0  !  88.9 

220 

182.9 

122.2 

280 

232.8 

155.6 

41 

101 

84.0 

56.1 

161 

133.91  89.4 

221 

183.8 

122.8 

281 

233.6 

156.1 

i>\ 

34.9 

23.3 

102 

84.8 

56.7 

162 

134.7 

90.0 

222 

184.6 

123.3 

282 

234.5 

156.7 

43 

35.8 

23.9 

103 

85.6 

57.2 

163 

135.5 

90.6 

223 

185.4 

123.9 

283 

235.3 

157.2 

44 

36.6 

24.4 

104 

86.5 

57.8 

164 

136.4  1 

91.1 

224 

186.2 

124.4 

284 

236.1 

157.8 

45 

37.4 

25.0 

105 

87.3 

58.3 

165 

137.21 

91.7 

225 

187.1 

125.0 

285 

237.0 

158.3 

46 

38.2 

25.6 

106 

88.1 

58.9 

166 

138.0 

92.2 

226 

187.9 

125.6 

286 

237.8 

158.9 

47 

39.1 

26.1 

107 

89.0 

59.4 

167 

138.9 

92  8 

227 

188.7 

126.1 

287 

238.6 

159.4 

48 

39.9 

26.7 

108 

89.8 

60.0 

1'-^ 

139.7 

93.3 

228 

189.6 

126.7 

288 

239.5 

160.0 

49 

40.7 

27.2 

109 

90.6 

60.6 

169 

140.5 

93.9 

229 

190.4 

127.2 

289 

240.3 

160.6 

50 

41.6 

27.8 

110 

91.5 

61.1 

170 

141.3 

94.4 

230 

191.2 

127.8 

290 

241.1  161.1 1 

51 

42.4 

28.3 

111 

92.3 

61.7 

171 

142.2 

95.0 

231 

192.1 

128.3 

291  242.01 

161.7 

52 

43.2 

28.9 

112 

93.1 

62.2 

172 

143.0 

95.6 

232 

192.9 

128.9 

292 

242.8 

162.2 

53 

44.1 

29.4 

113 

94.0 

62.8 

173 

143.8 

96.1 

233 

193.7 

129.4 

293 

243.6 

162.8 

54 

44.9 

30.0 

114 

94.8  63.3 

174 

144.7 

96.7 

234 

194.6 

130.0 

294 

244.5 

163.3 

55 

45.7 

30.6 

lUy 

95.6  63.9 

175 

145.5 

97.2 

235 

195.4 

130.6 

295 

245.3 

163.9 

56 

46.6 

31.1 

116 

96.5 

64.4 

176 

146.3 

97.8 

236 

196.2 

131.1 

296 

24().l 

164.4 

57 

47.4 

31.7 

117 

97.3 

65.0 

177 

147.2 

98.3 

237 

197.1 

131.7 

297 

246  9 

165.0 

58  4S.2 

32.2 

118 

98.1 

65.6 

17S 

148.0 

98.9 

238 

197.9 

132.2 

298 

247.8 

165.6 

59  49.1 

32.8 

119 

98.9 

66.1 

179 

148.8 

99.4 

239 

198.7 

132.8 

299 

24S.6 

166.1 

60 
Dist. 

49.9 

33.3 

120 

99.8 

66.7 

180 

149.7 

100.0 

240 

199.6 

133.3 

300 

249.4 

166.7 

Dep.   Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

D(MT 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep.  j  Lat.  | 

N 

iith  Satt  b.  Eaa1 

t.    S 

outh  Ea 

St  b.  East.      fPor  6  Pts  ]      North  West  h.   West.     South  West  *.  Wert.    | 

TABLE  I.- 

-DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  3*  POINTS.   13  1 

North  East  *  North.      North  West  *  North.      South  East »  South. 

South  West  t  South.   1 

Diat. 
1 

Lat. 

Dep. 

Dist. 

Lat. 
49.0 

Dep. 

Dist 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

00.8 

00.6 

61 

36.3 

121 

97.2 

72.1 

181 

145.4 

107.8 

241 

193.6 

143.6 

01.6 

01.2 

62 

49.8 

36.9 

122 

98.0 

72.7 

182 

146.2 

108.4 

242 

194.4 

144.2 

3 

024 

01.8 

63 

50.6 

37.5 

123 

98.8 

73.3 

183 

147.0 

109.0  243  195.2 

144.8 

4 

03.2 

02.4 

64 

51.4 

38.1 

124  99.6' 

73.9 

184 

147.8 

109.r  244  196.0 

145.4 

5 

04.0 

03.0 

65 

52.2 

38.7 

125  100.4  74.5 1 

185 

148.6 

110.2  245  196.8 

145.9 

6 

04.8 

03.6 

66 

53.0 

39.3 

126  101.2 

75.1 

186 

149.4 

110.8 

246 

197.6 

146.5 

7  05.6 

04.2 

67 

53.8 

39.9 

127 

102.0 

75.7 

187 

150.2 

111.4 

247 

198.4 

147.1 

8  06.4 

04.8 

68 

54.6 

40.5 

128 

102.8 

W.2 

188 

151.0 

112.0 

248 

199.2 

147.7 

9\ 

07.2 

05.4 

69 

55.4 

41.1 

129 

103.6 

76.8 

189 

151.8 

11^.6 

249 

200.0 

148.3 

iO 

11 

08.0 

06.0 

70 

56.2 

41.7 

130 

104.4 

77.4 
78.0 

190 

152.6 

113.2 

250 

200.8 

148.9 

08.8 

06.6 

71 

57.0 

42.3 

131 

105.2 

191 

153.4 

113.8 

251 

201.6 

149.5 

12 

09.6 

07.1 

72 

57.8 

42.9 

132 

106.0 

78.6 

192 

154.2 

114.4 

252 

202.4 

150.1 

13 

10.4 

07.7 

73 

58.6 

43.5 

133 

106.8 

79.2 

193 

155.0 

115.0 

253 

203.2 

150.7 

14 

11.2 

08.3 

74 

59.4 

44.1 

134 

107.6 

79.8 

194 

155.8 

115.6 

254 

204.0 

151.3 

15 

12.0 

08.9 

75 

60.2 

44.7 

135 

108.4 

80.4 

195 

156.6 

116.2 

255 

204.8 

151.9 

10 

12.9 

09.5 

76 

61.0 

45.3 

136 

109.2 

81.0 

196 

157.4 

116.8 

256 

205.6 

152.5 

17 

13.7 

10.1 

77 

61.8 

45.9 

137 

110.0 

81.6 

197 

1,58.2 

117.4 

257 

206.4 

153.1 

18 

14.5 

10.7 

78 

62.7 

46.5 

138 

110.8 

82  2 

198 

159.0 

117.9 

258 

207.2 

153.7 

19 

15.3 

11.3 

79 

63.5 

47.1 

139 

111.6 

82.8 

199 

159.8 

118.5 

259 

208.0 

154.3 

21 

16.1 
16.9 

11.9 
12.5 

80 

64.3 

47.7 

140 

112.4 

83.4 

200 

160.6 

119.1 

260 

208.8 

154.9 

81 

65.1 

48.3 

141 

113.3 

84.0 

201 

161.4 

119.7 

261 

209.6 

155.5 

22 

17.7 

13.1 

82 

65.9 

48.8 

142 

114.1 

84.6 

202 

162.2 

120.3 

262 

210.4 

156.1 

23 

18.5 

13.7 

83 

66.7 

49.4 

143 

114.9 

85.2 

203 

163.1 

120.9 

263 

211.2 

156.7 

24 

19.3 

14.3 

84 

67.5 

50.0 

144 

115.7 

85.8 

204 

163.9 

121.5 

264 

212.0 

157.3 

25 

20.1 

14.9 

85 

68.3 

50.6 

145 

116.5 

86.4 

205 

164.7 

122.1 

265  212.8 

157.9 

2f. 

20.9 

15.5 

86 

69.1 

51.2 

146 

117.3 

87.0 

206 

165.5 

122.7 

266  213.7 

158.5 

27 

21.7 

16.1 

87 

69.9 

51.8 

147 

118.1 

87.6 

207 

166.3 

123.3 

267  214.5 

159.1 

28 

22.5 

16.7 

88 

70.7 

52.4 

148 

118.9 

88.2 

208 

167.1 

123.9 

268  215.3 

159.6 

2'J 

23.3 

17.3 

89 

71.5 

53.0 

149 

119.7 

88.8 

209 

167.9 

124.5 

269  216.1 

160.2 

30 

24.1 

17.9 

90 

72.3 

53.6 
54.2 

150 
151 

120.5 

89.4 

210 

168.7 

125.1 

270 

216.9 

160.8 

31 

24.9 

18.5 

91 

73.1 

121.3 

90.0 

211 

169.5 

125.7 

271 

217.7 

161.4 

32 

25.7 

19.1 

92 

73.9 

54.8 

152 

122.1 

90.5 

212 

170.3 

126.3 

272 

218.5 

162.0 

33 

26.5 

19.7 

93 

74.7 

55.4 

153 

122.9 

91.1 

213 

171.1 

126.9 

273 

219.3 

162.6 

34 

27.3 

20.3 

94 

75.5 

56.0 

154 

123.7 

91.7 

214 

171.9 

127.5 

274 

220.1 

163.2 

35 

28.1 

20.8 

95 

76.3 

56.6 

155 

124.5 

92.3 

215 

172.7 

1281 

275 

220.9 

163.8 

36 

28.9 

21.4 

96 

77.1 

57.2 

156 

125.3 

92.9 

216 

173.5 

128.7 

276 

221.7 

164.4 

37 

29.7 

22.0 

97 

77.9 

57.8 

157 

126.1 

93.5 

217 

174.3 

129.3 

277 

222.5 

165.0 

38 

30.5 

22.6 

98 

78.7 

58.4 

158 

156.9 

94.1 

218 

175.1 

129.9 

278 

223.3 

165.6 

39 

31.3 

23.2 

99 

79.5 

59.0 

159 

127.7 

94.7 

219 

175.9 

130.5 

279 

224.1 

166.2 

40 
41 

32.1 

23.8 

100 

80.3 

59.6 

160 

128.5 

95.3 

220 

176.7 
177.5 

131.1 

280 

224.9 

166.8 

32.9 

24.4 

101 

81.1 

60.2 

161 

129.3 

95.9 

221 

131.6 

281 

225.7 

167.4 

42 

o3.7 

25.0 

102 

81.9 

60.8 

162 

130.1 

96.5 

222 

178.3 

132.2 

282 

226.5 

168.0 

43 

34.5 

25.6 

103 

82.7 

61.4 

163 

130.9 

97.1 

223 

179.1 

132.8 

283 

227.3 

168.6 

44 

35.3 

26.2 

104 

83.5 

62.0 

164 

131.7 

97.7 

224 

179.9 

133.4 

284 

228.1 

169.2 

45 

36.1 

26.8 

105 

84.3 

62.5 

165 

132.5 

98.3 

225 

180.7 

134.0 

285 

228.9 

169.8 

46 

36.9 

27.4 

106 

85.1 

63.1 

166 

133.3 

98.9 

226 

181.5 

134.6 

286  '  229.7 

170.4 

47 

37.8 

28.0 

107 

85.9 

63.7 

167 

134.1 

99.5 

227 

182.3 

135.2 

287  230.5 

171.0 

48 

38.6 

28.6 

108 

86.7 

64.3 

168 

134.9 

100.1 

228 

183.1 

135.8 

288  231.3 

171.6 

49 

39.4 

29.2 

109 

87.5 

64.9 

1(>9 

135.7 

100.7 

229 

183.9 

136.4 

289  232.1 

172.2 

50 
51 

40.2 

29.8 

110 
111 

88.4 
89.2 

65.5 
66.1 

170 

136.5 

101.3 

230 
231 

184.7 

137.0 

290  232.9 

172.8 

41.0 

30.4 

171 

137.3 

101.9 

185.5 

137.6 

291  233.7 

173.3 

52 

41.8 

31.0 

112 

90.0 

66.7 

172 

138.2 

102.5 

232 

186.3 

138.2 

292  234.5 

173.9 

53 

42.6 

31.6 

113 

90.8 

67.3 

173 

139.0 

103.1 

233 

187.1 

138.8 

293 

235.3 

174.5 

54 

43.4 

32.2 

114 

91.6 

67.9 

174 

139.8 

103.7 

234 

188.0 

139.4 

294 

236.1 

175.1 

55 

44.2 

32.8 

115 

92.4 

68.5 

175 

140.6 

104.2 

235 

188.8 

140.0 

295 

236.9 

175.7 

56 

45.0 

33.4 

116 

93.2 

69.1 

176 

141.4 

104.8 

236 

189.6 

140.6 

296 

237.7 

176.3 

57 

45.8 

34.0 

117 

94.0 

69.7 

177 

142.2 

105.4 

237 

190.4 

141.2 

297 

238.6 

176.9 

58 

46.6 

34.6 

118 

94.8 

70.3 

178 

143.0 

106.0 

238 

191.2 

141.8 

298 

239.4 

177.5 

59 

47.4 

35.1 

119 

95.6 

70.9 

179 

143.8 

106.6 

239 

192.0 

142.4 

299 

240.2 

178.1 

60 

48.2 

35.7 

120 

96.4 

71.5 

Lat 

180 

144.6 

107.2 

240 

192.8 

143.0 

300 

241.0 

178.7 

Dist 

.  Dep. 

Lat. 

Dist. 

Dep. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.   Lat  1 

1   North  Eiut  f  Eii 

<t.      South  East  }  East       [For  4f  Pts]      North  \\  e>t  J 

Wesi.      South  V\'est  J  West.    | 

14  TABLE  I.— DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  8^  POINTS.     | 

North  East  i  North.      North  West  i  North. 

South  Eist  i  South.     South  West  i  South.   1 

Diflt 

Lat 

Dep. 

Dist 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

1 

00.8 

00.6 

61 

47.2 

38.7 

121 

93.5 

76.8 

181 

139.9 

114.8 

241 

186.3 

152.9 

2 

01.5 

01.3 

62 

47.9 

39.3 

122 

94.3 

77.4 

1«2 

140.7 

115.5 

242 

187.1 

153.5 

3 

02.3 

01.9 

63 

48.7 

40.0 

123 

95.1 

78.0 

183 

141.5 

116.1 

243 

187.8  154.2 1 

4 

03.1 

02.5 

64 

49.5 

40.6 

124 

95.9 

78.7 

184 

142.2 

116.7 

244 

188.6  154.81 

5 

03.9 

03.2 

65 

50.2 

41.2 

125 

96.6 

79.3 

185 

143.0 

1 17.4 

245 

189.4 

155.4 

6 

04.6 

0M.8 

66 

51.0 

41.9 

126 

97.4 

79.9 

186 

143.8 

118.0 

246 

190.2 

156.1 

7 

05.4 

04.4 

67 

51.8 

42.5 

127 

98.2 

80.6 

187 

144.6 

118.6 

247 

190.9 

156.7 

8 

06.2 

05.1 

68 

52.6 

43.1 

128 

98.9 

81.2 

188 

145.3 

119.3 

248 

191.7  I57.3| 

9 

07.0 

05.7 

69 

53.3 

43.8 

129 

99.7 

81.8 

189 

146.1 

119.9 

249 

192.5  158.0  1 

10 
11 

07.7 

06.3 

70 

54.1 

44.4 

130 

100.5 

82.5 

190 

146.9  120.5 

250 

193.3 

158.6 

08.5 

07.0 

71 

54.9 

45.0 

131 

101.3 

83.1 

191 

147.6 

121.2 

251 

194.0 

159.2 

12 

09.3 

07.6 

72 

55.7 

45.7 

132 

102.0 

83.7 

192 

148.4 

121.8 

252 

194.8 

159,9 

13 

10.0 

08.2 

73 

56.4 

46.3 

133 

102.8 

84.4 

193 

149.2 

122.4 

253 

195.6 

160.5 

14 

10.8 

08.9 

74 

57.2 

46.9 

134 

103.6 

85.0 

194 

150.0 

123.1 

254 

196.3 

161.1 

15 

11.6 

09.5 

75 

58.0 

47.6 

135 

104.4 

85.6 

195 

150.7 

123.7 

255 

197.1 

161.8 

16 

12.4 

10.2 

76 

58.7 

48.2 

136 

105.1 

86.3 

196 

151.5 

124.3 

256 

197.9 

162.4 

17 

13.1 

10.8 

77 

59.5 

48.8 

137 

105.9 

86.9 

197 

152.3 

125.0 

257 

198.7 

163.0 

18 

13.9 

11.4 

78 

60.3 

49.5 

138 

106.7 

87.5 

198 

153.1 

125.6 

258 

199.4 

163.7 

19 

14.7 

12.1 

79 

61.1 

50.1 

139 

107.4 

88.2 

199 

153.8 

126.2 

259 

200.2 

164.3 

20 

15.5 

12.7 
13.3 

80 

61.8 

50.8 

140 

108.2 

88.8 

200 

154.6 

126.9 

260 

201.0 

164.9 

21 

16.2 

81 

62.6 

51.4 

141 

109.0 

89.4 

201 

155.4 

127.5 

261 

201.8 

165.6 

22 

17.0 

14.0 

82 

63.4 

52.0 

142 

109.8 

90.1 

202 

156.1 

128.1 

262 

202.5 

166.2 

23 

17.8 

14.6 

83 

64.2 

52.7 

143 

110.5 

90.7 

203 

156.9 

128.8 

263 

203.3 

166.8 

24 

18.6 

15.2 

84 

64.9 

53.3 

144 

111.3 

91.4 

204 

157.7 

129.4 

264 

204.1 

167.5 

25 

19.3 

15.9 

85 

65.7 

53.9 

145 

112.1 

92.0 

205 

158.5 

130.1 

265 

204.8 

168.1 

26 

20.1 

16.5 

86 

66,5 

54.6 

146 

112.9 

92.6 

206 

159.2 

130.7 

266 

205.6 

168.7 

27 

20.9 

17.1 

87 

67.3 

55.2 

147 

113.6 

93.3 

207 

160.0 

131.3 

267  206.4 

169.4 

28 

21,6 

17.8 

88 

68.0 '  55.8 

148 

114.4 

93.9 

208 

160.8 

132.0 

268  207.2 

170.0 

29 

22.4 

18.4 

89 

68.8 

56.5 

149 

115.2 

94.5 

209 

161.6,132.6 

269  ,  207.9 

170.7 

30 

23.2 

19j0 

90 

69.6 
70.3 

57.1 

150 

116.0 

95.2 

210 

162.3 

133.2 

270 

208.7 

171.3 

31 

24.0 

19.7 

91 

57.7 

151 

116.7 

95.8 

211 

163.1 

133.9 

271 

209.5 

171.9 

32 

24.7 

20.3 

92 

71.1 

58.4 

152 

117.5 

96.4 

212 

163.9 

134.5 

272 

210.3 

172.6 

33 

25.5 

20.9 

93 

71.9 

59.0 

153 

118.3 

97.1 

213 

164.7 

135.1 

273 

211.0 

173.2 

34 

26.3 

21.6 

94 

72.7 

59.6 

154 

119.0 

97.7 

214 

165.4 

135.8 

274 

211.8 

173.8 

35 

27.1 

22.2 

95 

73.4 

60.3 

155 

119.8 

98.3 

215 

166.2 

136.4 

275 

212.6 

174.5 

36 

27.8 

22.8 

96 

74.2 

60.9 

156 

120.6 

99.0 

216 

167.0 

137.0 

276 

213.4 

175.1 

37 

28.6 

23.5 

97 

75.0 

61.5 

157 

121.4 

99.6 

217 

167.7 

137.7 

277 

214.1 

175.7 

38 

29.4 

24.1 

98 

75.8 

62.2 

158 

122.1 

100.2 

218 

168.5 

138.3 

278 

214.9 

176.1 

39 

30.1 

24,7 

99 

76.5 

62.8 

159 

122.9 

100.9 

219 

169.3 

138.9 

279 

215.7 

177.0 

40 

30.9 

25.4 

100 

77.3 

63.4 

160 

123.7 

101.5 

220 

170.1 

139.6 

280 

216.4 

177.6 

41 

31.7 

26.0 

101 

78.1 

64.1 

161 

124.5 

102.1 

221 

170.8 

140.2 

281  '217.2 

178.3 

42 

32.5 

26.6 

102 

78.8 

64.7 

162 

125.2 

102.8 

222 

171.6 

140.8 

282 

218.0 

178.9 

43 

33.2 

27.3 

103 

79.6 

65.3 

163 

126.0 

103.4 

223 

172.4 

141.5 

283 

218.8 

179.5 

44 

34.0 

27.9 

104 

80.4 

66.0 

164 

126.8 

104.0 

224 

173.2 

142.1 

284 

219.5 

180.2 

45 

34.8 

28.5 

105 

81.2 

66.6 

165 

127.5 

104.7 

225 

173.9 

142.7 

285 

220.3 

180.8 

46 

35.6 

29.2 

106 

81.9 

67.2 

166 

128.3 

105.3 

226 

174.7 

143.4 

286 

221.1 

181.4 

47 

36.3 

29.8 

107 

82.7 

67.9 

167 

129.1 

105.9 

227 

175.5 

144.0 

287 

221.9 

182.1 

48 

37.1 

30.5 

108 

83.5 

68.5 

168 

129.9 

106.6 

228 

176.2 

144.6 

288 

222.6 

182.7 

49 

37.9 

31.1 

109 

84.3 

69.1 

169 

130.6 

107.2 

229 

177.0 

145.3 

289  i  223.4 

183.3 

50 

38.7 

31.7 

110 

85.0 

69.8 

170 

131.4 

107.8 

230 

177.8 

145.9 

290 

224.2  184.0 1 

51 

39.4 

32.4 

111 

85.8 

70.4  171 

132.2 

108.5 

231 

178.6 

146.5 

291 

224.9 

184.6 

52 

40.2 

33.0 

112 

86.6 

71.1  172 

133.0 

109.1 

232 

179.3 

147.2 

292 

225.7 

185.2 

53 

41.0 

33.6 

113 

87.4 

71.7 

173 

133.7 

109.8 

233 

180.1 

147.8 

293 

226.5 

185.9 

54 

41.7 

34.3 

114 

88.1 

72.3 

174 

134.5 

110.4 

234 

180.9 

148.4 

294 

227.3 

186.5 

55 

42.5 

34.9 

115 

88.9 

73.0 

175 

135.3 

111.0 

235 

181.7 

149.1 

295 

228.0 

187.1 

56 

43.3 

35.5 

116 

89.7 

73.6 

176 

136.0 

111.7 

236 

182.4 

149.7 

296 

228.8 

187,8 

57 

44.1 

36.2 

117 

90.4 

74.2 

177 

136.8 

112.3 

237 

183.2 

1.^0.4 

297 

229.6 

188.4 

58 

44.8 

36.8 

118 

91.2 

74.9 

178 

137.6 

112.9 

238 

184.0 

151.0 

298 

230.4 

189,0 

59 

45.6 

37.4 

119 

92.0 

75.5 

179 

138.4 

113.6 

239 

184.7 

151.6 

299 

231.1  1 189.7  1 

60 
DiaL 

46.4 

38.1 

120 

92.8 

76.1 

180 

139.1 

114.2 

240 

185.5 

152.3 

300 

231.9 

190.3 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat 

North  Es*t  i  East.     South  East  ♦  East.     [For  4i 

Pts.]     North  Wpst  i  West.     8ou»h  Wesv  #  Witt.         | 

TABLE  I.— DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  81  POINTS.   15 

North  East  i  North.     North  West  i  North.     South  East  i  South,      South  We»  t*  South. 

Dist 
1 

Lat. 

Dep. 

Dist. 

Lat  Dep. 

Diat. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Disi. 

Lat.    Dep.  1 

00.7 

00.7 

61 

45.2  41.0 

121 

89.7 

81.3 

181 

134.1 

121.6 

241 

178.6 

161.8 

2 

01.5 

01.3 

62 

45.9  41.6 

122 

90.4 

81.9 

182 

134.9 

122.2 

242 

179.3 

162.5 

8 

02.2 

02.0 

63 

46.7 

42.3 

123 

91.!   82.6 

183 

135.6 

122.9 

243 

180.1 

163.2 

4 

03.0 

02.7 

64 

47.4 

43.0 

124 

91.9 

8:i3 

184 

136.3 

123.6 

244 

180.8 

163.9 

5 

03.7 

03.4 

65 

48.2 

43.7 

L25 

92.6 

83.9 

185 

137.1 

124.2 

245  181.5  1 

164.5 

6 

04.4 

04.0 

66 

48.9 

44.3 

126 

93.4 

84.6 

186 

137.8 

124.9 

246  182.3 

165.2 

7 

05.2 

04.7 

67 

49.6 

45.0 

127 

94.1 

85.3 

187 

138.6 

125.6 

247 

183.0 

165.9 

8 

05.9 

05.4 

68 

50.4 

45.7 

128 

94.8 

86.0 

188 

139.3 

126.3 

248 

183.8 

166.5 

9 

06.7 

06.0 

69 

51.1 

46.3 

129 

95.6 

86.6 

189 

140.0 

126.9 

249 

184.5 

167.2 

10 
11 

07.4 

06.7 

70 

51.9 

47.0 

130 

96.3 

87.3 
88.0 

190 

140.8 

127.6 

250 
251 

185.2 

186.0 

167.9 

08.2 

07.4 

71 

52.6 

47.7 

131 

97.1 

191 

141.5 

128.3 

168.6 

12 

08.9 

08.1 

72 

53.3 

48.4 

132 

97.8 

88.6 

192 

142.3 

128.9 

252 

186.7 

169.2 

13 

09.6 

08.7 

73 

54.1 

49.0 

133 

98.5 

89.3 

193 

143.0 

129.6 

253 

187.5 

169.9 

14 

10.4 

09.4 

74 

54.8 

49.7 

134 

99.3 

90.0 

194 

143.7 

130.3 

254 

188.2 

170.6 

15 

11.1 

10.1 

75 

55.6 

50.4 

135 

100.0 

90.7 

195 

144.5 

131.0 

255 

188.9 

171.2 

l(i 

11.9 

10.7 

76 

56.3 

51.0 

136 

100.8 

91.3 

196 

145.2 

131.6 

256 

189.7 

171.9 

17 

12.6 

11.4 

77 

57.1 

51.7 

137 

101.5 

92.0 

197 

146.0 

132.3 

257 

190.4 

172.6 

18 

13.3 

12.1 

78 

57.8 

52.4 

138 

102.3 

92.7 

198 

146.7 

133.0 

258 

191.2 

1733 

19 

14.1 

12.8 

79 

58.5 

53.1 

139 

103.0 

93.3 

199 

147.4 

133.6 

259 

191.9 

173.9 

^0 
21 

14.8 
15.6 

13.4 
14.1 

80 

59.3 

53.7 

140 

103.7 

94.0 

200 

148.2 

134.3 

260 

192.6 

174.6 

81 

60.0 

54.4 

141 

104.5 

94.7 

201 

148.9 

135.0 

261 

193.4 

175.3 

22 

16.3 

14.8 

82 

60.8 

55.1 

142 

105.2 

95.4 

202 

149.7 

135.7 

262 

194.1 

175.9 

23 

17.0 

15.4 

83 

61.5 

55.7 

143 

106.0 

96.0 

203 

150.4 

136.3 

263 

194.9 

176.6 

24 

17.8 

16.1 

84 

62.2 

56.4 

144 

106.7 

96.7 

204 

151.2 

137.0 

264 

195.6 

177.3 

25 

18.5 

16.8 

85 

63.0 

57.1 

145 

107.4 

97.4 

205 

151.9 

137.7 

265 

196.4 

178.0 

2t> 

19.3 

17.5 

86 

63.7 

57.8 

146 

108.2 

98.0 

206 

152.6 

138.3 

266 

197.1 

178.6 

27 

20.0 

18.1 

87 

64.5 

58.4 

147 

108.9 

98.7 

207 

153.4 

139.0 

267 

197.8 

179.3 

28 

20.7 

18.8 

88 

65.2 

59.1 

148 

109.7 

99.4 

208 

154.1 

139.7 

268 

198.6 

180.0 

29 

21.5 

19.5 

89 

65.9 

59.8 

149 

110.4 

100.1 

209 

154.9 

140.4 

269 

199.3 

180.6 

30 
31 

22.2 
23.0 

20.1 

90 

66.7 

60.4 

150 

111.1 

100.7 

210 

155.6 

141.0 

270 
271 

200.1 

181.3 

20.8 

91 

67.4 

61.1 

151 

111.9 

101.4 

211 

156.3 

141.7 

200.8 

182.0 

32 

23.7 

21.5 

92 

68.2 

61.8 

152 

112.6 

102.1 

212 

157.1 

142.4 

272 

201.5 

182.7 

33 

24.5 

22.2 

93 

68.9 

62.5 

153 

113.4 

102.7:213 

157.8 

143.0 

273 

202.3 

183.3 

34 

25.2  22.8 

94 

69.6 

63.1 

154 

114.1 

103.4 

214 

158.6 

143.7 

274 

203.0 

184.0 

35 

25.9 

23.5 

95 

70.4 

63.8 

155 

114.8 

104.1 

215 

159.3 

144.4 

275 

203.8 

184.7 

36 

26.7 

24.2 

96 

71.1 

64.5 

156 

115.6 

104.8 

216 

160.0 

145.1 

276 

204.5 

185.4 

37 

27.4 

24.8 

97 

71.9 

65.1 

157 

116.3 

105.4 

217 

160.8 

145.7 

277 

205.2 

186.0 

38 

28.2 

25.5 

98 

72.6 

65.8 

158 

117.1 

106.1 

218 

161.5 

146.4 

278 

206.0 

186.7 

39 

28.9 

26.2 

99 

73.4 

66.5 

159 

117.8 

106.8 

219 

162.3 

147.1 

279 

206.7 

187.4 

40 

29.6 

26.9 

100 

74.1 

67.2 

160 

118.6 

107.4 

220 

163.0 

147.7 

280 

207.5 

188.0 

41 

30.4 

27.5 

101 

74.8 

67.8 

161 

119.3 

108.1 

221 

163.8 

148.4 

281 

208.2 

188.7 

42 

31.1 

28.2 

102 

75.6 

68.5 

162 

120.0 

108.8 

222 

164.5 

149.1 

282 

208.9 

189.4 

43 

31.9 

28.9 

103 

76.3 

69.2 

163 

120.8 

109.5 

223 

165.2 

149.8 

283 

209.7 

190.1 

44 

32.6 

29.5 

104 

77.1 

69.8 

164 

121.5 

110.1 

224 

166.0 

150.4 

284 

210.4 

190.7 

45 

33.3 

30.2 

105 

77.8 

70.5 

165 

122.3 

110.8 

225 

166.7 

151.1 

285 

211.2 

191.4 

46 

34.1 

30.9 

'106 

78.5 

71.2 

166 

123.0 

111.5 

226 

167.5 

151.8 

286 

211.9 

192.1 

47 

34.8 

31.6 

107 

79.3 

71.9 

167 

123.7 

112.2 

227 

168.2 

152.4 

287 

212.7 

192.7 

48 

35.6 

32.2 

108 

80.0 

72.5 

168 

124.5 

112.8 

228 

168.9 

153.1 

288 

213.4 

193.4 

49 

36.3 

32.9 

109 

80.8 

73.2 

169 

125.2 

113.5 

229 

169.7 

153.8 

289 

214.1 

194.1 

50 
51 

37.0 

33.6 

110 

81.5 

73.9 
74.5 

170 

126.0 

114.2 

230 
231 

170.4 

154.5 

290 

214.9 

194.8 

37.8 

34.2 

111 

82.2 

171 

126.7 

114.8 

171.2 

155.1 

291 

215.6 

195.4 

52 

38.5 

34.9 

112 

83.0 

75.2 

172 

127.4 

115.5 

232 

171.9 

155.8 

292 

216.4 

196.1 

53 

39.3 

35.6 

113 

83.7 

75.9 

173 

128.2 

116.2 

233 

172.6 

156.5 

293 

217.1 

196.8 

54 

40.0 

36.3 

114 

84.5 

76.6 

174 

128.9 

116.9 

234 

173.4 

157.1 

294 

217.8 

197.4 

55 

40.8 

36.9 

115 

85.2 

77.2 

175 

129.7 

117.5 

235 

174.1 

157.8 

295 

218.6 

198.1 

56 

41.5 

37.6 

116 

86.0 

77.9 

176 

130.4 

118.2 

236 

174.9 

158.5 

296 

219.3 

198.8 

57 

42.2 

38.3 

117 

86.7 

78.6 

177 

131.1 

118.9 

237 

175.6 

159.2 

297 

220.1 

199.5 

58 

43.0 

39.0 

118 

87.4 

79.2 

178 

131.9 

119.5 

238 

176.3 

159.8 

298 

220.8 

200.1 

59 

43.7 

39.6 

119 

88.2 

79.9 

179 

132.6 

120.2 

239 

177.1 

160.5 

299 

221.5 

200.8 

60 

44.5 

40.3 

120 

88.9 

80.6 

180 

133.4 

120.9 

240 

177.8 

161.2 

300 

222.3 

201.5 

Oifit 

.  Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.  iDist 

Dep. 

Lat 

Dist. 

Dep.   Lat. 

North  East  i  East.     South  Kast  i  Eait.     [For  4i  Pts.J     North  West  i  West.     South  West  i  Wert. 

1  16   TABLE  I.— DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  4  POINTS. 

North  East.         North  West.         South  East         South  West.       1 

Dist 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist   Lat 

Dep.  1 

1 

00.7 

00.7 

61 

43.1 

43.1 

121 

85.6 

85.6 

181 

128.0 

128.0 

241 

170.4 

170.4' 

2 

01.4 

01.4 

62 

43.8 

43.8 

122 

86.3 

86.3 

182 

128.7 

128.7 

242 

171.1 

171.1 

8 

02.1 

02.1 

63 

44.5 

44.5 

123 

87.0 

87.0 

183 

129.4 

129.4 

243 

171.8 

171.8 

4 

02.8 

02.8 

64 

453 

45.3 

124 

87.7 

87.7 

184 

130.1 

130.1 

244 

172.5 

172.5 

5 

03.5 

03.5 

65 

46.0 

46.0 

125 

88.4 

88.4 

185 

130.8 

130.8 

245 

173.2 

173.2 

6 

04.2 

04.2 

66 

46.7 

46.7 

126 

89.1 

89.1 

186 

131.5 

131.5 

246 

173.9 

173.9 

7 

04.9 

04.9 

67 

47.4 

47.4 

127 

b9.8 

89.8 

187 

132.2 

132.2 

247 

174.7 

174.7 

s 

05.7 

05.7 

68 

48.1 

48.1 

128 

90.5 

90.5 

188 

132.9 

132.9 

248 

175.4 

175.4 

9 

06.4 

06.4 

69 

48.8 

48.8 

129 

91.2 

91.2 

189 

133.6 

133.6 

249 

176.1 

176.1 

10 
11 

07.1 

07.1 

70 

49.5 

49.5 

130 

91.9 

91.9 
92.6 

190 

134.4 
135.1 

134.4 

250 
251 

176.8 

176.8 

07.8 

07.8 

71 

50.2 

50.2 

131 

92.6 

191 

135.1 

177.5  177.5 1 

12 

08.5 

08.5 

72 

50.9 

50.9 

132 

93.3 

93.3 

192 

135.8 

135.8 

252 

178.2 

178.2 

13 

09.2 

09.2 

73 

51.6 

51.6 

133 

94.0 

94.0 

193 

136.5 

136.5 

253 

178.9 

178.9 

14 

09.9 

09.9 

74 

52.3 

52.3 

134 

94.8 

94.8 

194 

137.2 

137.2 

254 

179.6 

179.6 

15 

10.6 

10.6 

75 

53.0 

53.0 

135 

95.5 

95.5 

195 

137.9 

137.9 

255 

180.3 

1<0.3 

16 

11.3 

11.3 

76 

53.7 

53.7 

136 

96.2 

96.2 

196 

138.6 

138.6 

256 

181.0 

181.0 

17 

12.0 

12.0 

77 

54.4 

54.4 

137 

96.9 

96.9 

197 

139.3 

139.3 

257 

181.7 

181.7 

18 

12.7 

12.7 

78 

55.2 

55.2 

138 

97.6 

97.6 

198 

140.0 

140.0 

258 

182.4 

182.4 

19 

13.4 

13.4 

79 

55.9 

55.9 

139 

98.3 

98.3 

199 

140.7 

140.7 

259 

183.1 

183.1 

20 

21 

14.1 

14.8 

14.1 

14.8 

80 

56.6 

56.6 

140 

99.0 

99.0 

200 

141.4 

141.4 

260 

183.8 

183.8 

81 

57.3 

57.3 

141 

99.7 

99.7 

201 

142.1 

142.1 

261 

184.6 

184.6 

22 

15.6 

15.6 

82 

58.0 

58.0 

142 

100.4 

100.4 

202 

142.8 

142.8 

262 

185.3 

185.3 

23 

16.3 

16.3 

83 

58.7 

58.7 

143 

101.1 

101.1 

203 

143.5 

143.5 

263 

186.0 

186.0 

24 

17.0 

17.0 

84 

59.4 

59.4 

144 

101.8 

101.8 

204 

144.2 

144.2 

264 

186.7 

186.7 

25 

17.7 

17.7 

85 

60.1 

60.1 

145 

102.5 

102.5 

205 

145.0 

145.0 

265 

187.4 

187.4 

2t) 

18.4 

18.4 

86 

60.8 

60.8 

146 

103.2 

103.2 

206 

145.7 

145.7 

266 

188.1 

188.1 

27 

19.1 

19.1 

87 

61.5 

61.5 

147 

103.9 

103.9 

207 

146.4 

146.4 

267 

188.8 

188.8 

28 

19.8 

19.8 

88 

62.2 

62.2 

148 

104.7 

104.7 

208 

147.1 

147.1 

268 

189.5 

189.5 

29 

20.5 

20.5 

89 

62.9 

62.9 

149 

105.4 

105.4 

209 

147.8 

147.8 

269 

190.2 

190.2 

30 
31 

21.2 
21.9 

21.2 

90 

63.6 

63.6 

150 

106.1 

106.1 

210 

148.5 

148.5 

270 
271 

190.9 

190.9 

21.9 

91 

64.3 

64.3 

151 

106.8 

106.8 

211 

149.2 

149.2 

191.6 

191.6 

32 

22.6 

22.6 

92 

65.1 

65.1 

152 

107.5 

107.5 

212 

149.9 

149.9 

272 

192.3 

192.3 

33 

23.3 

23.3 

93 

65.8 

65.8 

153 

108.2 

108.2 

213 

150.6 

150.6 

273 

193.0 

193.0 

34 

24.0 

24.0 

94 

66.5 

66.5 

154 

108.9 

108.9 

214 

151.3 

151.3 

274 

193.7 

193.7  • 

35 

24.7 

24.7 

95 

67.2 

67.2 

155 

109.6 

109.6 

215 

152.0 

152.0 

275 

194.5 

194.5 

36 

25.5 

25.5 

96 

67.9 

67.9 

156 

110.3 

110.3 

216 

152.7 

152.7 

276 

195.2 

195.2 

37 

26:2 

26.2 

97 

68.6 

68.6 

157 

111.0 

111.0 

217 

153.4 

153.4 

277 

195.9 

195.9 

38 

26.9 

26.9 

98 

69.3 

69.3 

158 

111.7 

111.7 

218 

154.1 

154.1 

278 

196.6 

196.6 

39 

27.6 

27.6 

99 

70.0 

70.0 

159 

112.4 

112.4 

219 

154.9 

154.9 

279 

197.3 

197.3 

40 
41 

28.3 

28.3 

100 

70.7 

70.7 

160 

113.1 

113.1 

220 

155.6 

155.6 

280 

198.0 

198.0 

29.0 

29.0 

101 

71.4 

71.4 

161 

113.8 

113.8 

221 

156.3 

156.3 

281 

198.7 

198.7 

42 

29.7 

29.7 

102 

72.1 

72.1 

162 

114.6 

114.6 

222 

157.0 

157.0 

282 

199.4 

199.4 

43 

30.4 

30.4 

103 

72.8 

72.8 

163 

115.3 

115.3 

223 

157.7 

157.7 

283 

200.1 

200.1 

44 

31.1 

31.1 

104 

73.5 

73.5 

164 

116.0 

116.0 

224 

158.4 

158.4 

284 

200.8 

200.8 

45 

31.8 

31.8 

105 

74.2 

74.2 

165 

116.7 

116.7 

225 

159.1 

159.1 

285 

201.5 

201.5 

46 

32.5 

32.5 

106 

75.0 

75.0 

166 

117.4 

117.4 

226 

159.8 

159.8 

286 

202.2 

202.2 

47 

33.2 

33.2 

107 

75.7 

75.7 

167 

118.1 

118.1 

227 

160.5 

160.5 

287 

202.9 

202.9 

48 

33.9 

33.9 

108 

76.4 

76.4 

168 

118.8 

118.8 

228 

161.2 

161.2 

288 

203.6 

203.6 

49 

34.6 

34.6 

109 

77.1 

77.1 

169 

119.5 

119.5 

229 

161.9 

161.9 

289 

204.4 

204.4 

50 

35.4 

35.4 

110 

77.8 

77.8 
78.5 

170 

120.2 

120.2 

230 
231 

162.6 

162.6 

290 

205.1 

205.1 

51 

36.1 

36.1 

111 

78.5 

171 

120.9 

120.9 

163.3 

163.3 

291 

205.8 

205.8 

52 '  36.8 

36.8 

112 

79.2 

79.2 

172 

121.6 

121.6 

232 

164.0 

164.0 

292 

206.5 

206.5 

53  37.5 

37.5 

113 

79.9 

79.9 

173 

122.3 

122.3 

233 

164.8 

164.8 

293 

207.2 

207.2 

54 

38.2 

38.2 

114 

80.6 

80.6 

174 

123.0 

123.0 

234 

165.5 

165.5 

294 

207.9 

207.9 

55 

38.9 

38.9 

115 

81.3 

81.3 

175 

123.7 

123.7 

235 

166.2 

166.2 

295 

208.6 

208.6 

56 

39.6 

39.6 

116 

82.0 

82.0 

176 

124.5 

124.5 

236 

166.9 

166.9 

296 

209.3 

209.3 

57 

40.3 

40.3 

117 

82.7 

82.7 

177 

125.2 

125.2 

237 

167.6 

167.6 

297 

210.0 

210.0 

58 

41.0 

41.0 

118 

83.4 

83.4 

178 

125.9 

125.9 

238 

168.3 

168.3 

298 

210.7 

210.7 

59 

41.7 

41.7 

119 

84.1 

84.1 

179 

126.6 

126.6 

239 

169.0 

169.0 

299 

211.4 

211.4 

t)0 

42.4 

42.4 

120 

84.9 

84.9 

180 

127.3 

127.3 

240 

169.7 

169.7 

300 

212.1 

212.1 

Dist 

.  Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist 

Dep.  1  Lat 

N»rth  Eajst.        North  West       [F'or  4  Pf]       .«oiith  Rast.         Sonth  Wert. 

TABLE  U. 

n  1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  1  DEGREE.    Oh  4m.  1 

Dist 

.  Lat. 

Dep. 

Di^t. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat.  i  Dep. 

1 

01.0 

00.0 

61 

61.0 

01.1 

121 

121.0 

02.1 

181 

181.0 

03.2 

241 

241.0^04.2 

2 

02.0 

00.0 

62 

62.0 

01.1 

122 

122.0 

02.1 

KS2 

182.0 

03.2 

242 

242.0 

04.2 

3 

03.0 

00.1 

63 

63.0 

01.1 

123 

123.0 

02.1 

183 

183.0 

03.2 

243 

243.0 

04.2 

4 

04.0 

00.1 

64 

64.0 

01.1 

124 

124.0 

02.2 

184 

184.0 

03.2 

244 

244.0 

04.3 

5 

05.0 

00.1 

65 

65.0 

01.1 

125 

125.0 

02.2 

185  185.0 

03.2 

245 

245.0 

04.3 

6 

06.0 

00.1 

66 

66.0 

01.2 

126 

126.0 

02.2 

186,186.0 

03.2 

246 

246  0 

04.3 

7 

07.0 

00.1 

67 

67.0 

01.2 

127 

127.0 

02.2 

187 

187.0 

03.3 

247 

247.0 

04.3 

8 

08.0 

00.1 

68 

68.0 

01.2 

128 

128.0 

0'2.2 

188 

188.0 

03.3 

248 

248.0 

04.3 

9 

09.0 

00.2 

69 

69.0 

01.2 

129 

129.0 

02.3 

189 

1 89.0 

03.3 

249 

249.0 

04.3 

10 
11 

10.0 

00.2 

70 

70.0 

01.2 

l.SO 

130.0 

02.3 

190 

190.0 

03.3 

250 

250.0 

04.4 

11.0 

00.2 

71 

71.0 

01.2 

131 

131.0 

02.3 

191 

191.0 

03.3 

251 

251.0 

04.4 

12 

12.0 

00.2 

72 

72.0 

01.3 

132 

132.0 

02.3 

192 

192.0 

03.4 

2:.2 

252.0 

04.4 

13 

13.0 

00.2 

73 

73.0 

01.3 

133 

133.0 

02.3 

193 

193.0 

03.4 

253 

253.0 

04.4 

14 

14.0 

00.2 

74 

74.0 

01.3 

134 

134.0 

02.3 

194 

194.0 

03.4 

254 

254.0 

04.4 

15 

15.0 

00.3 

75 

75.0 

01.3 

135 

135.0 

02.4 

195 

195.0 

03.4 

255 

255.0 

04.5 

16 

16.0 

00.3 

76 

76.0 

01.3 

136 

136.0 

02.4 

196 

196.0 

03.4 

256 

256.0 

04.5 

17 

17.0 

00.3 

77 

77.0 

01.3 

137 

137.0 

02.4 

197 

197.0 

03.4 

2.^7 

257.0 

04.5 

18 

18.0 

00.3 

78 

78.0 

01.4 

138 

138.0 

02.4 

198 

198.0 

03.5 

258 

258.0 

04.5 

19 

19.0 

00.3 

79 

79.0 

01.4 

139 

139.0 

02.4 

199 

199.0 

03.5 

259 

259.0 

04.5 

20 

20.0 

00.3 

80 

80.0 

01.4 

140 

140.0 

02.4 

200 

200.0 

03.5 

260 

260.0 

04.5 

21 

21.0 

00.4 

81 

81.0 

01.4 

141 

141.0 

02.5 

201 

201.0 

03.5 

261 

261.0 

04.6 

22 

22.0 

00.4 

82 

82.0 

01.4 

142 

142.0 

02.5 

202 

202.0 

03.5 

262 

262.0 

04.6 

23 

23.0 

00.4 

83 

83.0 

01.4 

143 

143.0 

02.5 

203 

203.0 

03.5 

263 

2(i3.0 

04.6 

24 

24.0 

00.4 

84 

84.0 

01.5 

144 

144.0 

02.5 

204 

204.0 

03.6 

264 

264.0 

04.0 

25 

25.0 

00.4 

85 

85.0 

01.5 

145 

145.0 

02.5 

205 

205.0 

03.6 

265 

265.0 

04.6 

26 

26.0 

00.5 

86 

86.0 

01.5 

146 

146.0 

02.5 

206 

206.0 

03.6 

266 

266.0 

04.6 

27 

27.0 

00.5 

87 

87.0 

01.5 

147 

147.0 

02.6 

207 

207.0 

03.6 

267  '  267.0 

04.7 

28 

28.0 

00.5 

88 

88.0 

01.5 

148 

148.0 

02.6 

208 

208.0 

03.6 

268  .  268.0 

04.7 

29 

29.0 

00.5 

89 

89.0 

01.6 

149 

149.0 

02.6 

209 

209.0 

03.6 

269 '269.0  04.7  1 

30 

30.0 

00.5 

90 

90.0 

01.6 
01.6 

150 

150.0 

02.6 

210 

210.0 

03.7 

270 

270.0  04.7  1 

31 

31.0 

00.5 

91 

91.0 

151 

151.0 

02.6 

211 

211.0 

03.7 

271 

271.0 

04.7 

32 

32.0 

00.6 

92 

92.0 

01.6 

152 

152.0 

02.7 

212 

212.0 

03.7 

272 

272.0 

04.7 

33 

33.0 

00.6 

93 

93.0 

01.6 

153 

153.0 

02.7 

213 

213.0 

03.7 

273 

273.0 

04.8 

34 

34.0 

00.6 

94 

94.0 

01.6 

154 

154.0 

02.7 

214 

214.0 

03.7 

274 

274.0 

04.8 

35 

35.0 

00.6 

95 

95.0 

01.7 

155 

155.0 

02.7 

215 

215.0 

03.8 

275 

275.0 

04.8 

36 

36.0 

00.6 

96 

96.0 

01.7 

156 

156.0 

02.7 

216 

216.0 

03.8 

276 

276.0 

04.8 

37 

37.0 

00.6 

97 

97.0 

01.7 

157 

157.0 

02.7 

217  217.0 

03.8 

277 

277.0 

04.8 

38 

38.0 

00.7 

98 

98.0 

01.7 

158 

158.0 

02.8 

218 

218.0 

03.8 

278 

278.0 

04.9 

39 

39.0 

00.7 

99 

99.0 

01.7 

159 

159.0 

02.8 

219 

219.0 

03.8 

279 

279.0 

04.9 

40 

40.0 

00.7 

100 

100.0 

01.7 

160 

160.0 

02.8 

220 

220.0 

03.8 

280 

280.0 

04.9 

41 

41.0 

00.7 

101 

101.0 

01.8 

161 

161.0 

02.8 

221 

221.0 

03.9 

281 

281.0 

04.9 

42 

42.0 

00.7 

102 

102.0 

01.8 

162 

162.0 

02.8 

222 

222.0 

03.9 

282 

282.0 

04.9 

43 

43.0 

00.8 

103 

103.0 

01.8 

163 

163.0 

02.8 

223 

223.0 

03.9 

283 

283.0 

04.9 

44 

44.0 

00.8 

104 

104.0 

01.8 

164 

164.0 

02.9 

224 

224.0 

03.9 

284 

284.0 

05.0 

45 

45.0 

00.8 

105 

105.0 

01.8 

165 

165.0 

02.9 

225 

225.0 

03.9 

285 

285.0 

05.0 

46 

46.0 

m.8 

106 

106.0 

01.8 

166 

166.0 

02.9 

226 

226.0 

03.9 

280 

286.0  05.0 

47 

47.0 

00.8 

107 

107.0 

01.9 

167 

167.0 

02.9 

227 

227.0 

04.0 

287 

287.0 '  05.0 

48 

48.0 

00.8 

108 

108.0 

01.9 

1()8 

168.0 

02.9 

2-28 

228.0 

04.0 

288 

288.0 

05.0 

49 

49.0 

00.9 

109 

109.0 

01.9 

169 

169.0 

02.9 

229 

229.0 

04.0 

289 

289.0 

05.0 

50 

50.0 

00.9 

110 

110.0 

01.9 

170 

170.0 

03.0 

230 

230.0 

04.0 

290 

290.0 

05.1 

51 

51.0 

00.9 

111 

111.0 

01.9 

171 

171.0 

03.0 

231 

231.0 

04.0 

291 

291.0 

05.1 

52 

52.0 

00.9 

112 

112.0 

02.0 

172 

172.0 

03.0 

232 

232.0 

04.0 

292 

292.0 

05.1 

53 

53.0 

00.9 

113 

113.0 

02.0 

173 

173.0 

03.0 

233 

233.0 

04.1 

293 

293.0 

05.1 

54 

54.0 

00.9 

114 

114.0 

02.0 

174 

174.0 

03.0 

234 

234.0 

04.1 

294 

294.0 

05.1 

55 

550 

01.0 

115 

115.0 

02.0 

175 

175.0 

03.1 

235 

235.0 

04.1 

295 

295.0 

05.1 

56 

56.0 

01.0 

116 

116.0 

02.0 

176 

176.0 

03.1 

236 

236.0 

04.1 

296 

296.0  05.2  r 

57 

57.0 

01.0 

117 

117.0 

02.0 

177 

177.0 

03.1 

237 

237.0 

04.1 

297 

297.0  05  21 

58 

58.0 

01.0 

118 

118.0 

02.1 

178 

178.0 

03.1 

238 

238.0 

04.2 

298 

298.0 

05.2 

59 

59.0 

01.0 

119 

119.0 

02.1 

179 

179.0 

03.1 

239 

239.0 

04.2 

299 

299.0 

05.2 

60 

Dist. 

60.0 

01.0 

120 

120.0 

02.1 

180 

180.0 

03.1 

240 

240.0  04.2 

300  300.0 

05.2 

] 

Dep.  Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep.    Lat.  | 

Dist. 

Dep.  ,  Lat. 

Dist.  I  Dep. 

Lat 

1 

F..r  89  Dei,'ree*. 

5*1  6 

Em. 

18                   TABLE  11. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  2  DEGREES.    Oh  8»n. 

Wat. 

1 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep.( 

01.0 

00.0 

61 

61.0 

02.1 

121 

120.9 

04.2 

181 

180.9 

06.3 

241 

240.9 

08.4 

o 

02.0 

00.1 

62 

62.0 

02.2 

122 

121.9 

04.3 

182 

181.9 

06.4 

242 

241.9 

08.4 

3 

03.0 

00.1 

63 

63.0 

02.2 

123 

122.9 

04.3 

183 

182.9 

06.4 

243 

242.9 

08.5 

4 

04.0 

00.1 

64 

64.0 

02.2 

124 

123.9 

04.3 

184 

183.9 

06.4 

244 

243.9 

08.5 

5  05.0 

00.2 

65 

65.0 

02.3 

125 

124.9 

04.4 

185 

184.9 

06.5 

245 

244.9 

08.6 

6  06.0 

00.2 

66 

66.0 

02.3 

126 

125.9 

04.4 

186 

185.9 

06.5 

246 

245.9 

08.6 

7  07.0 

00.2 

67 

67.0 

02.3 

127 

126.9 

04.4 

187 

186.9 

06.5 

247 

246.8 

08.6 

8 

08.0 

00.3 

68 

68.0 

02.4 

128 

127.9 

04.5 

188 

187.9 

06.6 

248 

247.8 

08.7 

9 

09.0 

00.3 

69 

69.0 

02.4 

129 

128.9 

04.5 

189 

188.9 

06.6 

249 

248.8 

08.7 

10 

10.0 

00.3 

70 

70.0 

02.4 

130 

129.9 

04.5 
04.6 

190 
191 

189.9 

06.6 

250 
251 

249.8 
250.8 

08.7 
08.6 

11 

11.0 

00.4 

71 

71.0 

02.5 

131 

130.9 

190.9 

06.7 

12 

12.0 

00.4 

72 

72.0 

02.5 

132 

131.9 

04.6 

192 

191.9 

06.7 

252 

251.8 

08.8 

13 

13.0 

00.5 

73 

73.0 

02.5 

133 

132.9 

04.6 

193 

192.9 

06.7 

253 

252.8 

08.8 

14 

14.0 

00.5 

74 

74.0 

02.6 

134 

133.9 

04.7 

194 

193.9 

06.8 

254 

253.8 

08.9 

15 

15.0 

00.5 

75 

75.0 

02.6 

135 

134.9 

04.7 

195 

194.9 

06.8 

255 

254.8 

08.9 

16 

16.0 

00.6 

76 

76.0 

02.7 

136 

135.9 

04.7 

196 

195.9 

06.8 

256 

255.8 

08.9 

17 

17.0 

00.6 

77 

77.0 

02.7 

137 

136.9 

04.8 

197 

196.9 

06.9 

257 

256.8 

09.0 

18 

18.0 

00.6 

78 

78.0 

02.7 

138 

137.9 

04.8 

198 

197.9 

06.9 

258 

257.8 

09.0 

19 

19.0 

00.7 

79 

79.0 

02.8 

139 

138.9 

04.9 

199 

198.9 

06.9 

259 

258.8 

09.0 

20 

20.0 

00.7 

80 

80.0 

02.8 

140 

139.9 

04.9 

200 

199.9 

07.0 

260 

259.8 

09.1 

21 

21.0 

00.7 

81 

81.0 

02.8 

141 

140.9 

04.9 

201 

200.9 

07.0 

261 

260.8 

09.1 

22 

22.0 

00.8 

82 

82.0 

02.9 

142 

141.9 

05.0 

202 

201.9 

07.0 

262 

261.8 

09.1 

23 

23.0 

00.8 

83 

82.9 

02.9 

143 

142.9 

05.0 

203 

202.9 

07.1 

263 

262.8 

09.2 

24 

24.0 

00.8 

84 

83.9 

02.9 

144 

143.9 

05.0 

204 

203.9 

07.1 

264 

263.8 

09.2 

25 

25.0 

00.9 

85 

84.9 

03.0 

145 

144.9 

05.1 

205 

204.9 

07.2 

265 

264.8 

09.2 

26 

26.0 

00.9 

86 

85.9 

03.0 

146 

145.9 

05.1 

206 

205.9 

07.2 

266 

265.8 

09.3 

27 

27.0 

00.9 

87 

86.9 

03.0 

147 

146.9 

05.1 

207 

206.9 

07.2 

267 

266.8 

09.3 

28 

28.0 

01.0 

88 

87.9 

03.1 

148 

147.9 

05.2 

208 

207.9 

07.3 

268 

267.8 

09.4 

29  29.0 

01.0 

89 

88.9 

03.1 

149 

148.9 

05.2 

209 

208.9 

07.3 

269 

268.8 

09.4 

30 

30.0 

01.0 

90 

89.9 

03.1 

150 

149.9 

05.2 

210 

209.9 

07.3 

270 
271 

269.8 

09.4 

31 

31.0 

01.1 

91 

90.9 

03.2 

151 

150.9 

05.3 

211 

210.9 

07.4 

270.8 

09.5 

32 

32.0 

01.1 

92 

91.9 

03.2 

152 

151.9 

05.3 

212 

211.9 

07.4 

272 

271.8 

09.5 

33 

33.0 

01.2 

93 

92.9 

03.2 

153 

152.9 

05.3 

213 

212.9 

07.4 

273 

272.8 

09.5 

34 

34.0 

01.2 

94 

93.9 

03.3 

154 

153.9 

05.4 

214 

213.9 

07.5 

274 

273.8 

09.6 

35  35.0 

01.2 

95 

94.9 

03.3 

155 

154.9 

05.4 

215 

214.9 

07.5 

275 

274.8 

09.6 

36 

36.0 

01.3 

96 

95.9 

03.4 

156 

155.9 

05.4 

216 

215.9 

07.5 

276 

275.8 

09.6 

37 

37.0 

01.3 

97 

96.9 

03.4 

157 

156.9 

05.5 

217 

216.9 

07.6 

277 

276.8 

09.7 

38 

38.0 

01.3 

98 

97.9 

03.4 

158 

157.9 

05.5 

218 

217.9 

07.6 

278 

277.8 

09.7 

39 

39.0 

01.4 

99 

98.9 

03.5 

159 

158.9 

05.5 

219 

218.9 

07.6 

279 

278.8 

09.7 

40 

40.0 

01.4 

100 

99.9 

03.5 

160 

159.9 

05.6 

220 

219.9 

07.7 

280 

279.8 

09.8 

41 

41.0 

01.4 

101 

100.9 

03.5 

161 

160.9 

05.6 

221 

220.9 

07.7 

281 

280.8 

09.8 

42 

42.0 

01.5 

102 

101.9 

03.6 

162 

161.9 

05.7 

222 

221.9 

07.7 

282 

281.8 

09.8 

43 

43.0 

01.5 

103 

102.9 

03.6 

163 

162.9 

05.7 

223 

222.9 

07.8 

283 

282.8 

09.9 

44 

44.0 

01.5 

104 

103.9 

03.6 

164 

163.9 

05.7 

224 

223.9 

07.8 

284 

283.8 

09.9 

45 

45.0 

01.6 

105 

104.9 

03.7 

105 

164.9 

05.8 

225 

224.9 

07.9 

285 

284.8 

09.9 

46 

46.0 

01.6 

106 

105.9 

03.7 

166 

165.9 

05.8 

226 

225.9 

07.9 

286 

285.8 

10.0 

47 

47.0 

01.6 

107 

106.9 

03.7 

167 

166.9 

05.8 

227 

226.9 

07.9 

287 

286.8 

10.0 

48 

48.0 

01.7 

108 

107.9 

03.8 

168 

167.9 

05.9 

228 

227.9 

08.0 

288 

287.8 

10.1 

49 

49.0 

01.7 

109 

108.9 

03.8 

169 

168.9 

05.9 

229 

228.9 

08.0 

289 

288.8 

10.1 

50 

50.0 

01.7 

110 

109.9 

03.8 

170 

169.9 

05.9 

230 

229.9 

08.0 

290 

289.8 

10.1 

51 

51.0 

01.8  111 

110.9 

03.9 

171 

170.9 

06.0 

231 

230.9 

08.1 

291 

290.8 

10.2 

52 

52.0 

01.8 

112 

111.9 

03.9 

172 

171.9 

06.0 

232 

231.9 

08.1 

292 

291.8 

10.2 

53 

53.0 

01.8 

113 

112.9 

03.9 

173 

172.9 

06.0 

233 

232.9 

08.1 

293 

292.8 

10.2 

54 

54.0 

01.9 

114 

113.9 

04.0 

174 

173.9 

06.1 

234 

233.9 

08.2 

294 

293.8 

10.3 

55 

55.0 

01.9 

115 

114.9 

04.0 

175 

174.9 

06.1 

235 

234.9 

08.2 

295 

294.8 

10.3 

56 

56.0 

02.0 

116 

115.9 

04.0 

176 

175.9 

06.1 

236 

235.9 

08.2 

296 

295.8 

10.3 

57 

57.0 

02.0 

117 

116.9 

04.1 

177 

176.9 

06.2 

237 

236.9 

08.3 

297 

296.8 

10.4 

58 

58.0 

02.0 

118 

117.9 

04.1 

178 

177.9 

06.2 

238 

237.9 

08.3 

298 

297.8 

10.4 

59 

59.0 

02.1 

119 

118.9 

04.2 

179 

178.9 

06.2 

239 

238.9 

08.3 

299 

298.8 

10.4 

60 

60.0 

02.1 

120 

119.9 

04.2 

180 

179.9 

06.3 

240 

239.9 

08.4 

300 

299.8 

10.5 

Dist 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

Dist 

Dep. 

Lat 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat 

For  88  Degrees.                         5^  62m.  | 

TABLE  11.                      19 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  3  DEGREES.    Oh  12"». 

Dial 

,    Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat  !  Dep. 

1 

01.0 

00.1 

61 

60.9 

03.2 

121 

120.8 

06.3 

181 

1^0.8 

09.5 

241 

240.7 

12.6 

2 

02.0 

00.1 

62 

61.9 

03.2 

122 

121.8 

06.4 

1S2 

181.8 

09.5 

242 

241.7 

12.7 

3 

03.0 

00.2 

63 

62.9 

03.3 

123 

122.8 

06.4 

183 

182.7 

09.6 

243 

242.7 

12.7 

4 

04.0 

00.2 

64 

63.9 

03.3 

124 

123.8 

06.5 

184 

183.7 

09.6, 

244 

243.7 

12.8 

5 

05.0 

00.3 

65 

64.9 

03.4 

125 

124.8 

06.5 

185 

184.7 

09.7 

245 

244.7 

12.8 

6 

06.0 

00.3 

66 

65.9 

03.5 

126 

125.8 

06.6 

186 

185.7 

09.7 

246 

245.7 

12.9 

7 

07.0 

0i».4 

67 

66.9 

03.5 

127 

126.8 

06.6 

187 

186.7 

09.8 

247  '  246.7 

12.9 

8 

08.0 

00.4 

68 

67.9 

03.6 

128 

127.8 

06.7 

188 

187.7 

09.8 

248 

247.7 

13.0 

9 

09.0 

00.5 

69 

68.9 

03.6 

129 

128.8 

06.8 

189 

188.7 

09.9 

249 

248.7 

13.0 

10 
11 

10.0 

00.5 

70 

69.9 

03.7 

130 

129.8 

06.8 

190 

189.7 

09.9 

250 

249.7 

13.1 

11.0 

00.6 

71 

70.9 

03.7 

131 

130.8 

06.9 

191 

190.7 

10.0 

251 

250.7 

13.1 

12 

12.0 

00.6 

72 

71.9 

03.8 

132 

131.8 

06.9 

192 

191.7 

10.0 

252 

251.7 

13.2 

13 

13.0 

00.7 

73 

72.9 

03.8 

133 

132.8 

07.0 

193 

192.7 

10.1 

253 

252.7 

13.2 

14 

14.0 

00.7 

74 

73.9 

03.9 

134 

133.8 

07.0 

194 

193.7 

10.2 

254 

253.7 

13.3 

15 

15.0 

00.8 

75 

74.9 

03.9 

135 

134.8 

07.1 

195 

194.7 

10.2 

255 

254.7 

13.3 

16 

16.0 

00.8 

76 

75.9 

04.0 

136 

135.8 

07.1 

196 

195.7 

10.3 

256 

255.6 

13.4 

17 

17.0 

00.9 

77 

76.9 

04.0 

137 

136.8 

07.2 

197 

196.7 

10.3 

257 

256.6 

13.5 

18 

18.0 

00.9 

78 

77.9 

04.1 

138 

137.8 

07.2 

198 

197.7 

10.4 

258 

257.6 

13.5 

19 

19.0 

01.0 

79 

78.9 

04.1 

139 

138.8 

07.3 

199 

198.7 

10.4 

259 

258.6 

13.6 

20 

20.0 

01.0 

80 

79.9 

04.2 

140 

139.8 

07.3 

200 

199.7 

10.5 

260 

259.6 

13.6 

21 

21.0 

01.1 

81 

80.9 

04.2 

141 

140.8 

07.4 

201 

200.7 

10.5 

261 

260.6 

13.7 

22 

22.0 

01.2 

82 

81.9 

04.3 

142 

141.8 

07.4 

202 

201.7 

10.6 

262 

261,6 

13.7 

23 

23.0 

01.2 

83 

82.9 

04.3 

143 

142.8 

07.5 

203 

202.7 

10.6 

263 

262.6 

13.8 

24 

24.0 

01.3 

84 

83.9 

04.4 

144 

143.8 

07.5 

204 

203.7 

10.7 

264 

263.6 

13.8 

25 

25.0 

01.3 

85 

84.9 

04.4 

145 

144.8 

07.6 

205 

204.7 

10.7 

265  .  264.6 

13.9 

26 

26.0 

01.4 

86 

85.9 

04.5 

146 

145.8 

07.6 

206 

205.7 

10.8 

266 

265.6 

13.9 

27 

27.0 

01.4 

87 

86.9 

04.6 

147 

146.8 

07.7 

207 

206.7 

10.8 

267 

266.6. 14.n| 

28 

28.0 

01.5 

88 

87.9 

04.6 

148 

147.8 

07.7 

208 

207.7 

10.9 

268 

267.6 '14.01 

29 

29.0 

01.5 

89 

88.9 

04.7 

149 

148.8 

07.8 

209 

208.7 

10.9 

269 

268.6 

14.1 

30 

30.0 

01.6 

90 

89.9 

04.7 

04.8 

150 

149.8 

07.9 

210 

209.7 

11.0 

270 

269.6 

14.1 

31 

31.0 

01.6 

91 

90.9 

151 

150.8 

07.9 

211 

210.7 

11.0 

271  1  270.6 

14.2 

: 

32 

32.0 

01.7 

92 

91.9 

04.8 

152 

151.8 

08.0 

212 

211.7 

11.1 

272 

271.6 

14.2 

33 

33.0 

01.7 

93 

92.9 

04.9 

153 

152.8 

08.0 

213 

212.7 

11.1 

273  !  272.6 

14.3 

34 

34.0 

01.8 

94 

93.9 

04.9 

154 

153.8 

08.1 

214 

213.7 

11.2 

274 

273.6 

14.3 

35 

35.0 

01.8 

95 

94.9 

05.0 

155 

154.8 

08.1 

215 

214.7 

11.3 

275 

274.6 

14.4 

36 

36.0 

01.9 

96 

95.9 

05.0 

156 

155.8 

08.2 

216 

215.7 

11.3 

276 

275.6 

14.4 

37 

36.9 

01.9 

97 

96.9 

05.1 

157 

156.8 

0«.2 

217 

216.7 

11.4 

277 

276.6 

14.5 

38 

37.9 

02.0 

98 

97.9 

05.1 

158 

157.8 

08.3 

218 

217.7 

11.4 

278 

277.6 

14.5 

39 

38.9 

02.0 

99 

98.9 

05.2 

159 

158.8 

08.3 

219 

218.7 

11.5 

279 

278.6 

14.6 

40 

39.9 

02.1 

100 

99.9 

05.2 

160 

159.8 

08.4 

220 

219.7 

11.5 

280 

279.6 

14.7 

41 

40.9 

02.1 

101 

100.9 

05.3 

161 

160.8 

08.4 

221 

220.7 

11.6 

281 

280.6 

14.7 

42 

41.9 

02.2 

102 

101.9 

05.3 

162 

161.8 

08.5 

222 

221.7 

11.6 

282 

281.6 

14.8 

43 

42.9 

02.3 

103 

102.9 

05.4 

163 

162.8 

08.5 

223 

222.7 

11.7 

283 

282.6 

14.8 

44 

43.9 

02.3 

104 

103.9 

05.4 

164 

163.8 

08.6 

224 

223.7  1  11.7  1 

284 

283.6  14.9 

45 

44.9 

02.4 

105 

104.9 

05.5 

165 

164.8 

08.6 

225 

224.7 

11.8 

285 

284.6  14.9 

46 

45.9 

02.4 

106 

105.9 

05.5 

166 

165.8 

08.7 

226 

225.7 

11.8 

286 

285.6  15.0 

47 

46.9 

02.5 

107 

106.9 

05.6 

167 

166.8 

08.7 

227 

226.7 

11.9 

287 

286.6  15.0 

48 

47.9 

02.5 

108 

107.9 

05.7 

168 

167.8 

08.8 

2-28 

227.7 

11.9 

288 

287.6  15.1 

49 

48.9 

02.6 

109 

108.9 

05.7 

169 

168.8 

08.8 

22!) 

228.7 

12.0 

289 

288.6 

15.1 

50 
51 

49.9 

02.6 

110 

109.8 

05.8 

170 

169.8 

08.9 

230 

229.7 

12.0 

290 

289.6 

15.2 

50.9 

02.7 

111 

110.8 

05.8 

171 

170.8 

08.9 

231 

230.7 

12.1 

291 

290.6 

15.2 

52 

51.9 

02.7 

112 

111.8 

05.9 

172 

171.8 

09.0 

232  231.7 

12.1 

292 

291.6 

15.3 

53 

52.9 

02.8 

113 

112.8 

05.9 

173 

172.8 

09.1 

233 

232.7 

12.2 

293 

292.6  15.3  1 

54 

53.9 

02.8 

114 

113.8 

06.0  174 

173.8 

09.1 

234 

233.7 

12.2  294 

293.6 

15.4 

55 

54.9 

02.9 

115 

114.8 

06.0  175 

174.8 

09.2 

235 

234.7 

12.3  295 

294.6 

15.4 

56 

55.9 

02.9 

116 

115.8 

06.1  176 

175.8 

09.2 

236 

235.7 

12.4  296 

295.6 

15.5 

57 

56.9 

03.0 

117 

116.8 

06.1  177 

176.8 

Ov^.3 

237 

236.7 

12.4  297 

296.6 

15.5 

58 

57.9 

03.0 

118 

117.8 

06.2 

178 

177.8 

09.3 

238 

237.7 

12.5  298 

297.6 

15.6 

59 

58.9 

03.1 

119 

118.8 

06.2 

179 

178.8 

09.4 

239 

238.7 

12.5  299 

298.6 

15.6 

60 

59.9 

03.1 

120 

119.8 

06.3 

180 

179.8 

09.4 

240 

239.7 

12.6 

300  1 

299.6 

15.7 

] 

3i8t 

Dep.   Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist  Dep.  1  Lat  1 

^^^ 

Fiif  87  Detrrt'es.                              ^^>   J-Sm    1 

20 

TABLE  11. 

1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  4  DEGREES.   Oh  16"  t 

Diat.  Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

LaU 

Dep. 

Dist. 

LaL 

Dep. 

Dist. 

Lat 

Dep 
16.8 

1  01.0 

00.1 

61 

60.9 

04.3 

121 

120.7 

08.4 

181 

180.6 

12.6 

241 

240.4 

2 

02.0 

00.1 

62 

61.8 

04.3 

122 

121.7 

08.5 

182 

181.6 

12.7 

242 

241.4 

16.9 

3 

03.0 

00.2 

63 

62.8 

04.4 

123 

122.7 

08.6 

183 

182.6 

12.8 

243 

242.4 

17.0 

4 

04.0 

00.3 

64 

63.8 

04.5 

124 

123.7 

08.6 

184 

183.6 

12.8 

244 

243.4 

17.0 

5 

05.0 

00.3 

65 

64.8 

04.5 

125 

124.7 

08.7 

185 

184.5 

12.9 

245 

244.4 

17.1 

6 

06.0 

00.4 

66 

65.8 

04.6 

126 

125.7 

08.8 

186 

185.5 

13.0 

246 

245.4 

17.2 

7 

07.0 

00.5 

67 

66.8 

04.7 

127 

126.7 

08.9 

187 

186.5 

13.0 

247 

246.4 

17.2 

8 

08.0 

00.6 

68 

67.8 

04.7 

128 

127.7 

08.9 

188 

187.5 

13.1 

248 

247.4 

17.3 

9 

09.0 

00.6 

69 

68.8 

04.8 

129 

128.7 

09.0 

189 

188.5 

13.2 

249 

248.4 

17.4 

10 

10.0 

00.7 

70 

69.8 

04.9 

130 

129.7 

09.1 

190 
191 

189.5 

13.3 

250 

249.4 

17.4 
17.5 

11 

11.0 

00.8 

71 

70.8 

05.0 

131 

130.7 

09.1 

190.5 

13.3 

251 

250.4 

12 

12.0 

00.8 

72 

71.8 

05.0 

132 

131.7 

09.2 

192 

191.5 

13.4 

252 

251.4 

17.6 

13 

13.0 

00.9 

73 

72.8 

05.1 

133 

132.7 

09.3 

193 

192.5 

13.5 

253 

252.4 

17.6 

14 

14.0 

01.0 

74 

73.8 

05.2 

134 

133.7 

09.3 

194 

193.5 

13.5 

254 

253.4 

17.7 

15 

15.0 

01.0 

75 

74.8 

05.2 

135 

134.7 

09.4 

195 

194.5 

13.6 

255 

254.4 

17.8 

16 

16.0 

01.1 

76 

75.8 

05.3 

136 

135.7 

09.5 

196 

195.5 

13.7 

256 

255.4 

17.9 

17 

17.0 

01.2 

77 

76.8 

05.4 

137 

136.7 

09.6 

197 

196.5 

13.7 

257 

256.4 

17.9 

18 

18.0 

01.3 

78 

77.8 

05.4 

138 

137.7 

09.6 

198 

197.5 

13.8 

258 

257.4 

18.0 

19 

19.0 

01.3 

79 

78.8 

05.5 

139 

138.7 

09.7 

199 

198.5 

13.9 

259 

258.4 

18.1 

20 
21 

20.0 

01.4 

80 

79.8 

05.6 

140 

139.7 

09.8 

200 

199.5 

14.0 

260 

259.4 

18.1 
18.2 

20.9 

01.5 

81 

80.8 

05.7 

141 

140.7 

09.8 

201 

200.5 

14.0 

261 

260.4 

22 

21.9 

01.5 

82 

81.8 

05.7 

142 

141.7 

09.9 

202 

201.5 

14.1 

262 

261.4 

18.3 

23 

22.9 

01.6 

83 

82.8 

05.8 

143 

142.7 

10.0 

203 

202.5 

14.2 

263 

262.4 

18.3 

24 

23.9 

01.7 

84 

83.8 

05.9 

144 

143.6 

10.0 

204 

203.5 

14.2 

264 

263.4 

18.4 

25 

24.9 

01.7 

85 

84.8 

05.9 

145 

144.6 

10.1 

205 

204.5 

14.3 

265 

264.4 

18.5 

26 

25.9 

01.8 

86 

85.8 

06.0 

146 

145.6 

10.2 

206 

205.5 

14.4 

266 

265.4  18.6 

27 

26.9 

01.9 

87 

86.8 

06.1 

147 

146.6 

10.3 

207 

206.5 

14.4 

267 

266.3  18.6 

28 

27.9 

02.0 

88 

87.8 

06.1 

148 

147.6 

10.3 

208 

207.5 

14.5 

268 

267.3  18.7 

29 

28.9 

02.0 

89 

88.8 

06.2 

149 

148.6 

10.4 

209 

208.5 

14.6 

269 

268.3  18.8 

30 
31 

29.9 

02.1 

90 

89.8 

06.3 

150 
151 

149.6 

10.5 

210 

209.5 

14.6 

270 

269.3  18.8 

30.9 

02.2 

91 

90.8 

06.3 

150.6 

10.5 

211 

210.5 

14.7 

271 

270.3 

18.9 

32 

31.9 

02.2 

92 

91.8 

06.4 

152 

151.6 

10.6 

212 

211.5 

14.8 

272 

271.3 

19.0 

33 

32.9 

02.3 

93 

92.8 

06.5 

153 

152.6 

10.7 

213 

212.5 

14.9 

273 

272.3 

19.0 

34 

33.9 

02.4 

94 

93.8 

06.6 

154 

153.6 

10.7 

214 

213.5 

14.9 

274 

273.3 

19.1 

35 

34.9 

02.4 

95 

94.8 

06.6 

155 

154.6 

10.8 

215 

214.5 

15.0 

275 

274.3 

19.2 

36 

35.9 

02.5 

96 

95.8 

06.7 

156 

155.6 

10.9 

216 

215.5 

15.1 

276 

275.3 

19.3 

37 

36.9 

02.6 

97 

96.8 

06.8 

157 

156.6 

11.0 

217 

216.5 

15.1 

277 

276.3 

19.3 

38 

37.9 

02.7 

98 

97.8 

06.8 

158 

157.6 

11.0 

218 

217.5 

15.2 

278 

277.3 

19.4 

39 

38.9 

02.7 

99 

98.8 

06.9 

159 

158.6 

11.1 

219 

218.5 

15.3 

279 

278.3 

19.5 

40 

39.9 

02.8 

100 

99.8 

07.0 

160 

159.6 

11.2 

220 

219.5 

15.3 

280 

279.3 

19.5 

41 

40.9 

02.9 

101 

100.8 

07.0 

161 

160.6 

11.2 

221 

220.5 

15.4 

281 

280.3 

19.6 

42 

41.9 

02.9 

102 

101.8 

07.1  162 

161.6 

11.3 

222 

221.5 

15.5 

282 

281.3 

19.7 

43 

42.9 

03.0 

103 

102.7 

07.2 

163 

162.6 

11.4 

223 

222.5 

15.6 

283 

282.3 

19.7 

44 

43.9 

03.1 

104 

103.7 

07.3 

164 

163.6 

11.4 

224 

223.5 

15.6 

284 

283.3 

19.8 

45 

449 

03.1 

105 

104.7 

07.3 

165 

164.6 

11.5 

225 

224.5 

15.7 

285 

284.3 

19.9 

46 

45.9 

03.2 

106 

105.7 

07.4 

166 

165.6 

11.6 

226 

225.4 

15.8 

286 

285.3 

20.0 

47 

46.9 

03.3 

107 

106.7 

07.5 

167 

166.6 

11.6 

227 

226.4 

15.8 

287 

286.3 

20.0 

48 

47.9 

03.3 

108 

107.7 

07.5 

168 

167.6 

11.7 

226 

227.4 

15.9 

288 

287.3 

20.1 

49 

48.9 

03.4 

109 

108.7 

07.6 

169 

168.6 

11.8 

229 

228.4 

16.0 

289 

288.3 

20.2 

50 

49.9 

03.5 

110 

109.7 

07.7 

170 

169.6 

11.9 

230 

229.4 

16.0 

290 

289.3 

20.2 

51 

50.9 

03.6 

111 

110.7 

07.7 

171 

170.6 

11.9 

231 

230.4 

16.1 

291 

290.3 

20.3 

52 

51.9 

03.6 

112 

111.7 

07.8 

172 

171.6 

12.0 

232 

231.4 

16.2 

292 

291.3 

20.4 

53 

52.9 

03.7 

113 

112.7 

07.9 

173 

172.6 

12.1 

233 

232.4 

16.3 

293 

292.3 

20.4 

54 

53.9 

03.8 

114 

113.7 

08.0 

174 

173.6 

12.1 

234 

233.4 

16.3 

294 

293.3 

20.5 

55 

54.9 

03.8 

115 

114.7 

08.0 

175 

174.6 

12.2 

235 

234.4 

16.4 

295 

294.3 

20.6 

56 

55.9 

03.9 

116 

115.7 

08.1 

176 

175.6 

12.3 

236 

235.4 

16.5 

296 

295.3 

20.6 

57 

56.9 

04.0 

117 

116.7 

08.2 

177 

176.6 

12.3 

237 

236.4 

16.5 

297 

296.3 

20.7 

58 

57.9 

04.0 

118 

117.7;  08.2 

178 

177.6 

12.4 

238 

237.4 

16.6 

298 

297.3 

20.8 

59 

58.9 

04.1 

119 

118.7 

08.3 

179 

178.6 

12.5 

239 

238.4 

16.7 

299 

298.3 

20.9 

60 

59.9 

04.2 

120 

119.7 

08.4 

180 

179.6 

12.6 

240 

239.4 

16.7 

300 

299.3 

20.9 

Hint 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

LaL 

Dist. 

Dep. 

Lat. 

For  86  Decrees. 

6h  44m.   1 

TABLE  U. 

..   1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  5  DE(}REES.   Oh  20ni. 

Diet. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

01.0 

00.1 

61 

60.8 

05.3 

121 

120.5 

10.5 

181 

INO.3 

15.8 

241 

240.1  '21.0 

2 

02.0 

00.2 

62 

61.8 

05.4 

122 

121.5 

10.6 

182 

181.3 

15.9 

242 

241.1  21.1 

3 

03.0 

00.3 

()3 

62.8 

05.5 

123 

122.5 

10.7 

183  182.3 

15.9 

243 

242.1  |21.2 

4 

04.0 

00.3 

64 

63.8 

05.6 

124 

123.5 

10.8 

184  183.3 

16.0 

244 

243.1  21.3 

5 

05.0 

00.4 

()5 

64.8 

05.7 

125 

124.5 

10.9 

185 

184.3 

16.1 

245 

244.1 

21.4 

6 

06.0 

00.5 

66 

65.7 

05.8 

126 

125.5 

11.0 

186 

185.3 

16.2 

246 

245.1 

21.4 

7 

07.0 

00.6 

67 

66.7 

05.8 

127 

126.5 

11,1 

1S7 

186.3 

16.3 

247 

246. 1 

21.5 

8 

08.0 

00.7 

68 

67.7 

05.9 

128 

127.5 

1L2 

188 

187.3 

16.4 

248 

247.1 

21.6 

9 

09.0 

00.8 

69 

68.7 

06.0 

120 

128.5 

11.2 

189 

188.3 

16.5 

249 

248.1 

21.7 

10 
11 

10.0 

00.9 

70 

69.7 

06.1 
06.2 

1  :{0 

129.5 

11.3 

190 

189.3 

16.6 

250 

249.0 

21.8 

11.0 

01.0 

71 

70.7 

131 

130.5 

11.4 

191 

190.3 

16.6 

251  ]  250.01  21.91 

12 

1  ; 
li 

i2.C^^l..0 

72 

71.7 

06.3 

132 

131.5 

11.5 

192 

1913 

16.7 

252 

251.0 

22.0 

13.0 

01.1 

73 

72.7 

06.4 

133 

132.5 

11.6 

193 

192.3 

16.8 

253 

252.0 

22.1 

139 

01.2 

74 

73.7 

06.4 

134 

133.5 

11.7 

194 

193.3 

16.9 

254 

253.0 

22.1 

15 

14.9 

01.3 

75 

74.7 

06.5 

135 

134.5 

11.8 

195 

194.3 

17.0 

255 

254.0 

22.2 

16 

15.9 

01.4 

76 

75.7 

06.6 

136 

135.5 

11.9 

196 

195.3 

17.1 

256 

255.0 

22.3 

17 

16.9 

01.5 

77 

76.7 

06.7 

137 

136.5 

11.9 

197 

1963 

17.2 

257 

256.0 

22.4 

18 

17.9 

01.6 

78 

77.7 

06.8 

138 

137.5 

12.0 

198 

197.2 

17.3 

258 

257.0 

22.5 

19 

18.9 

01.7 

79 

78.7 

06.9 

139 

138.5 

12.1 

199 

198.2 

n.3 

259 

258.0 

22.6 

20 

19.9 

01.7 

80 

79.7 

07.0 
07.1 

140 

139.5 

12.2 

200 

199.2 

XY.4 

260 

259.0 

22.7 

21 

20.9 

01.8 

81 

80.7 

141 

140.5 

12.3 

201 

200.2 

17.5 

261 

260.0 

22.7 

22 

21.9 

01.9 

82 

81.7 

07.1 

142 

141.5 

12.4 

202 

201.2 

17.6 

262 

261.0 

22.8 

23 

22.9 

02.0 

83 

82.7 

07.2 

143 

142.5 

12.5 

203 

202.2 

17.7 

263 

262.0 

22.9 

24 

23.9 

02.1 

84 

83.7 

07.3 

144 

143.5 

12.6 

204 

203.2 

17.8 

264 

263.0 

23.0 

25 

24.9 

02.2 

85 

84.7 

07.4 

145 

144.4 

12.6 

205 

204.2 

17.9 

265 

264.0 

231 

26 

25.9 

02.3 

86 

85.7 

07.5 

146 

145.4 

12.7 

206 

205.2 

18.0 

266 

265.0 

23.2 

27 

26.9 

02.4 

87 

86.7 

07.6 

147 

146.4 

12.8 

207 

206.2 

18.0 

267 

266.0 

23.3 

28 

27.9 

02.4 

88 

87.7 

07.7 

148 

147.4 

12.9 

208 

207.2 

18.1 

268 

267.0 

23.4 

29 

28.9 

02.5 

89 

88.7 

07.8 

149 

148.4=  13  0 

209 

208.2 

18.2 

269 

268.0  ,  23.4  1 

30 

29.9 

02.6 

90 

89.7 

07.8 
07.9 

150 
151 

149.4 

13.1 

210 

209.2 

18.3 

270  ■  269.0  ,  23.5  \ 

31 

30.9 

02.7 

91 

90.7 

150.4 

13.2 

211 

210.2 

18.4 

271 

270.0  '  23.6 

32 

31.9 

02.8 

92 

91.6 

08.0 

152 

151.4 

13.2 

212 

211.2 

18.5 

272 

271.0  23.7 

33 

32.9 

02.9 

93 

92.6 

08.1 

153 

152.4 

13.3 

213 

212.2 

18.6 

273 

272.0  23.8 

34 

33.9 

03.0 

94 

93.6 

08.2 

154 

1.53.4 

13.4 

214 

213.2 

18.7 

274 

273.0 

23.9 

35 

34.9 

03.1 

95 

94.6 

08.3 

155 

154.4 

13.5 

215 

214.2 

18.7 

275 

274.0 

24.0 

36 

35.9 

03.1 

96 

95.6 

08.4 

156 

155.4 

13.6 

216 

215.2 

18.8 

276 

274.9 

24.1 

37 

36.9 

03.2 

97 

96.6 

08.5 

157 

156.4 

13.7 

217 

216.2 

18.9 

277 

275.9 

24.1 

38 

37.9 

03.3 

98 

97.6 

08.5 

158 

157.4 

13.8 

218 

217.2 

19.0 

278 

278.9 

24.2 

39 

38.9 

03.4 

99 

98.6 

08.6 

159 

158.4 

13.9 

219 

218.2 

19.1 

279 

277.9 

24.3 

40 

39.8 

03.5 

100 

99.6 

08.7 

160 

159.4 

13.9 

220 

219.2 

19.2 

280 

278.9 

24.4 

41 

40.8 

03.6 

101 

100.6 

08.8 

161 

160.4 

14.0 

221 

220.2 

19.3 

281 

279.9 

24.5 

42 

41.8 

03.7 

102 

101.6 

08.9 

162 

161.4 

14.1 

222 

221.2 

19.3 

282 

280.9 

24.6 

43 

42.8 

03.7 

103 

102.6 

09.0 

163 

162.4 

14.2 

223 

222.2 

19.4 

283 

281.9 

24.7 

44 

43.8 

03.8 

104 

103.6 

09.1 

164 

163.4 

14.3 

224 

223.1 

19.5 

284 

282.9 

24.8 

45 

44.8 

03.9 

105 

104.6 

09.2 

165 

164.4 

14.4 

225 

224.1 

19.6 

285 

283.9 

24.8 

46 

45.8 

04.0 

106 

105.6 

09.2 

166 

1654 

14.5 

226 

225.1 

19.7 

286 

284.9 

24.9 

47 

46.8 

04.1 

107 

106.6 

09.3 

167 

166.4 

14.6 

227 

220.1 

19.8 

287 

285.9 

25.0 

48 

47.8 

04,2 

108 

107.6 

09.4 

168 

167.4 

14.6 

228 

227.1 

19.9 

288 

286.9 

25.1 

49 

48.8 

04.3 

109 

108.6 

09.5 

169 

168.4 

14.7 

229 

228.1 

20.0 

289 

287.9 

25.2 

50 

49.8 

04.4 

110 

109.6 

09.6 

170 

169.4 

14.8 

230 

229.1 

20.0 

290 

288.9 

25.3 

51 

50.8 

044 

111 

110.6 

09.7 

171 

170.3 

14.9 

231 

230.1 

20.1 

291 

289.9 

25.4 

52 

51.8 

04  5 

112 

111.6 

09.8 

172 

171.3 

15.0 

232 

231.1 

20.2 

292 

290.9  25.4  1 

53 

52.  S 

04.6 

113 

112.6 

09.8 

173 

172.3 

15.1 

233 

232.1 

20.3 

293 

291.9  25.5  1 

54 

53.8 

04.7 

114 

113.6 

09.9 

174 

173.3 

15.2 

234 

23.3.1 

20.4 

294 

292.9 

25.6 

55 

54.8 

04.8 

115 

114.6 

10.0 

175 

174.3 

15.3 

235 

234.1 

20.5 

295 

293.9 

25.7 

5t) 

55  8 

04.9 

116 

115.6 

10.1 

176 

175.3 

15.3 

236 

235.1 

20.6 

296 

294.9 

25.8 

57 

56.8 

05.0 

117 

116.6 

10.2 

177 

176.3 

15.4 

237 

236.1 

20.7 

297 

295.9 

25.9 

58 

57.8 

05.1 

118 

117.6 

10.3 

178 

177.3 

15.5 

238 

237.1 

20.7 

298 

296.9 

26.0 

59 

58.  s 

05.1 

119 

118.5 

10.4 

179 

178.3 

15.6 

239 

238.1 

20.8 

29^ 

297.9 

26.1 

60 

Dist. 

59.8 

05.2 

120 

119.5 

10.5 

180 

179.3 

15.7 

240 

239.1 

20.9 

300 

298.9 

26.1 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.   Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

For  85  Deijrees. 

6fi  40".   1 

22         '          TABLE  II. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  6  DEGREES.   Oh  24m. 

DiBt 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Diet 

Lat 

Dep.» 

1 

01.0 

00.1 

61 

60.7 

06.4 

121 

120.3 

12.6 

181 

180.0 

18.9 

241 

239.7 

25.2 

2 

02.0 

00.2 

62 

61.7 

06.5 

122 

121.3 

12.8 

182 

181.0 

19.0 

242 

240.7 

25.3 

3 

03.0 

00.3 

63 

62.7 

06.6 

123 

122.3 

12.9 

183 

182.0 

19.1 

243 

241.7 

25.4 

4 

04.0 

00.4 

64 

63.6 

06.7 

124 

123.3 

13.0 

184 

183.0 

19.2 

244 

242.7 

25.5 

5 

05.0 

00.5 

65 

64.6 

06.8 

125 

124.3 

13.1 

185 

184.0 

19.3 

245 

243.7 

25.6 

6 

06.0 

00.6 

66 

65.6 

06.9 

126 

125.3 

13.2 

186 

185.0 

19.4 

246 

244.7 

25.7 

7 

07.0 

00.7 

67 

66.6 

07.0 

127 

126.3 

13.3 

187 

186.0 

19.5 

247 

245.6 

25.8 

8 

08.0 

00.8 

68 

67.6 

07.1 

128 

127.3 

13.4 

188 

187.0 

19.7 

248 

246.6 

25.9 

9 

09.0 

00.9 

69 

68.6 

07.2 

129 

128.3 

13.5 

189 

188.0 

19.8 

249 

247.6 

26.0 

10 

09.9 

01.0 

70 

69.6 

07.3 

130 

129.3 

13.6 
13.7 

190 
191 

189.0 

19.9 

250 
251 

248.6 
249.6 

26.1 
26.2 

11 

10.9 

01.1 

71 

70.6 

07.4 

131 

130.3 

190.0 

20.0 

12 

11.9 

01.3 

72 

71.6 

07.5 

132 

131.3 

13.8 

192 

190.9 

20.1 

252 

250.6 

26.3 

13 

12.9 

01.4 

73 

72.6 

07.6 

133 

132.3 

13.9 

193 

191.9 

20.2 

253 

251.6 

26.4 

14 

13.9 

01.5 

74 

73.6 

07.7 

134 

133.3 

14.0 

194 

192.9 

20.3 

254 

252.6 

26.6 

15 

14.9 

01.6 

75 

74.6 

07.8 

135 

134.3 

14.1 

195 

193.9 

20.4 

255 

253.6 

26.7 

16 

15.9 

01.7 

76 

75.6 

07.9 

136 

135.3 

14.2 

196 

194.9 

20.5 

256 

254.6 

26.8 

17 

16.9 

01.8 

77 

76.6 

08.0 

137 

136.2 

14.3 

197 

195.9 

20.6 

257 

255.6 

26.9 

18 

17.9 

01.9 

78 

77.6 

08.2 

138 

137.2 

14.4 

198 

196.9 

20.7 

258 

256.6 

27.0 

19 

18.9 

02.0 

79 

78.6 

08.3 

139 

138.2 

14.5 

199 

197.9 

20.8 

259 

257.6 

27.1 

20 

19.9 

02.1 

80 

79.6 

08.4 

140 

139.2 

14.6 

200 

198.9 

20.9 

260 

258.6 

27.2 
27.3 

21 

20.9 

02.2 

81 

80.6 

08.5 

141 

140.2 

14.7 

201 

199.9 

21.0 

261 

259.6 

22 

21.9 

02.3 

82 

81.6 

08.6 

142 

141.2 

14.8 

202 

200.9 

21.1 

262 

260.6 

27.4 

23 

22.9 

02.4 

83 

82.5 

08.7  143 

142.2 

14.9 

203 

201.9 

21.2 

263 

261.6 

27.5 

24 

23.9 

02.5 

84 

83.5 

08.8  144 

143.2 

15.1 

204 

202.9 

21.3 

264 

262.6 

27.6 

25 

24.9 

02.6 

85 

84.5 

08.9 

145 

144.2 

15.2 

205 

203.9 

21.4 

265 

263.5 

27.7 

26 

25.9 

02.7 

86 

85.5 

09.0 

146 

145.2 

15.3 

206 

204.9 

21.5 

266 

264.5 

27.8 

27 

26.9 

02.8 

87 

86.5 

09.1 

147 

146.2 

15.4 

207 

205.9 

21.6 

267 

265.5 

27.9 

28 

27.8 

02.9 

88 

87.5 

09.2 

148 

147.2 

15.5 

208 

206.9 

21.7 

268 

266.5 

28.0 

29 

28.8 

03.0 

89 

88.5 

09.3 

149 

148.2 

15.6 

209 

207.9 

21.8 

269 

267.5 

28.1 

30 
31 

29.8 

03.1 

90 

89.5 

09.4 

150 

149.2 

15.7 

210 

208.8 

22.0 

270 

268.5 

28.2 

30.8 

03.2 

91 

90.5 

09.5 

151 

150.2 

15.8 

211 

209.8 

22.1 

271 

269.5 

28.3 

32 

31.8 

03.3 

92 

91.5 

09.6 

152 

151.2 

15.9 

212 

210.8 

22.2 

272 

270.5 

28.4 

33 

32.8 

03.4 

93 

92.5 

09.7 

153 

152.2 

16.0 

213 

211.8 

22.3 

273 

271.5 

•28.5 

34 

33.8 

03.6 

94 

93.5 

09.8 

154 

153.2 

16.1 

214 

212.8 

22.4 

274 

272.5 

28.6 

35 

34.8 

03.7 

95 

94.5 

09.9 

155 

154.2 

16.2 

215 

213.8 

22.5 

275 

273.5 

28.7 

36 

35.8 

03.8 

96 

95.5 

10.0 

156 

155.1 

16.3 

216 

214.8 

22.6 

276 

274.5 

28.8 

37 

36.8 

03.9 

97 

96.5 

10.1 

157 

156.1 

16.4 

217 

215.8 

22.7 

277 

275.5 

29.0 

38 

37.8 

04.0 

98 

97.5 

10.2 

158 

157.1 

16.5 

218 

216.8 

22.8 

278 

276.5 

29.1 

39 

38.8 

04.1 

99 

98.5 

10.3 

159 

158.1 

16.6 

219 

217.8 

22.9 

279 

277.5 

29.2 

40 

39.8 

04.2 

100 

99.5 

10.5 

160 

159.1 

16.7 

220 

218.8 

23.0 

280 

278.5 

29.3 

41 

40.8 

04.3 

101 

100.4 

10.6 

161 

160.1 

16.8 

221 

219.8 

23.1 

281 

279.5 

29.4 

42 

41.8 

04.4 

102 

101.4 

10.7 

162 

161.1 

16.9 

222 

220.8 

23.2 

282 

280.5 

29.5 

43 

42.8 

04.5 

103 

102.4 

10.8 

163 

162.1 

17.0 

223 

221.8 

23.3 

283 

281.4 

29.6 

14 

43.8 

04.6 

104 

103.4 

10.9 

164 

163.1 

17.1 

224 

222.8 

23.4 

284 

282.4 

29.7 

45 

44.8 

04.7 

105 

104.4 

11.0 

165 

164.1 

17.2 

225 

223.8 

23.5 

285 

283.4 

29.8 

4t3 

45.7 

04.8 

106 

105.4 

11.1 

166 

165.1 

17.4 

226 

224.8 

23.6 

286 

284.4 

29.9 

47 

46.7 

04.9 

107 

106.4 

11.2 

167 

166.1 

17.5 

227 

225.8 

23.7 

287 

285.4 

30.0 

46 

47.7 

05.0 

108 

107.4 

11.3 

168 

167.1 

17.t; 

228 

226.8 

23.8 

288 

286.4 

30.1 

49 

48.7 

05.1 

109 

108.4 

11.4 

169 

168.1 

17.7 

229 

227.8 

23.9 

289 

287.4 

30.2 

50 

49.7 

05.2 

110 

109.4 

11.5 

170 

169.1 

17.8 

230 

228.7 

24.0 

290 

288.4 

30.3 

51 

50.7 

05.3 

111 

110.4 

11.6 

171 

170.1 

17.9 

231 

229.7 

24.1 

291 

289,4 

30.4 

52 

51.7 

05.4 

112 

111.4 

11.7 

172 

171.1 

18.0 

232 

230.7 

24.3 

292 

290.4 

30.5 

53 

52.7 

05.5 

113 

112.4 

11.8 

173 

172.1 

18.1 

233 

231.7 

24.4 

293 

291.4 

30.6 

54 

53.7 

05.6 

114 

113.4 

11.9 

174 

173.0 

18.2 

234 

232.7 

24.5 

294 

292.4 

30.7 

55 

54.7 

05.7 

115 

114.4 

12.0 

175 

174.0 

18.3 

2.S5 

233.7 

24.6 

295 

293.4 

30.8 

56 

55.7 

05.9 

116 

115.4 

12.1 

176 

175.0 

18.4 

236 

234.7 

24.7 

296 

294.4 

30.9 

57 

56.7 

06.0 

117 

110.4 

12.2 

177 

176.0 

18.5 

237 

235.7 

24.8 

297 

295.4 

31.0 

58 

57.7 

06.1 

118 

117.4 

12.3 

178 

177.0 

18.6 

238 

236.7 

24.9 

298 

296.4 

31.1 

59 

58.7 

06.2 

119 

118.3 

12.4 

179 

178.0 

18.7 

239 

237.7 

2.').0 

299 

297.4 

31.3 

60 

59,7 

06.3 

120 

119.3 

12.5 

180 

179.0 

18.8 

240 

238.7 

25.1 

300 

298.4 

31.4 

Lat 

Dist 

.  Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

Dist 

Dep. 

•  Lat. 

Dist 

Dep. 

For  84  Df-moes,                            5^^  S6m.  | 

TABLE  n. 

.3 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  7  DEGREES.   Oh  28m.  1 

Dist 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist.   Lat 

Dep. 

Dist   Lat 

Dep. 

1 

01.0 

00.1 

61 

60.5 

07.4 

121 

120.1 

14.7 

181  ;  179.7 

22.1 

241 

239,2 

29.4 

2 

02.0 

00.2 

62 

61.5 

07.6 

122 

121.1 

14.9 

182;  180.6 

22.2 

242 

240.2 

29.5 

3 

03.0 

00.4 

63 

62.5 

07.7 

123 

122.1 

15.0 

183 

181.6 

22.3 

243 

241.2 

29.6 

4 

04.0 

00.5 

64 

63.5 

07.8 

124 

123.1 

15.1 

184 

182.6 

22.4 

244 

242.2 

29.7 

5 

05.0 

00.6 

65 

64.5 

07.9 

125 

124.1 

15.2 

185 

183.6 

22.5 

245 

243.2 

29.9 

6 

06.0 

00.7 

66 

65.5 

08.0 

126 

125.1 

15.4 

186 

184.6 

22.7 

246 

244.2  30.0 1 

7 

06.9 

00.9 

67 

66.5 

08.2 

127 

126.1 

15.5 

187 

185.6 

22.8 

247 

245.2 

30.1 

8 

07.9 

01.0 

68 

67.5 

08.3 

128 

127.0 

15.6 

188 

186.6 

22.9 

248 

246.2 

30.2 

9 

08.9 

01.1 

69 

68.5 

08.4 

129 

128.0 

15.7 

189 

187.6 

23.0 

249 

247.1 

30.3 

10 
11 

09.9 

01.2 

70 

69.5 

08.5 

130 

129.0 

15.8 

190 

188.6 

23.2 

250 

248.1 

30.5 

10.9 

01.3 

71 

70.5 

08.7 

131 

130.0 

16.0 

191 

189.6 

23.3 

251 

249.1 

30.6 

12 

11.9 

01.5 

72 

71.5 

08.8 

132 

131.0 

16.1 

192 

190.6 

23.4 

252 

250.1 

30.7 

13 

12.9 

01.6 

73 

72.5 

08.9 

133 

132.0 

16.2 

193 

191.6 

23.5 

253 

251.1 

30.8 

14 

13.9 

01.7 

74 

73.4 

09.0 

134 

133.0 

16.3 

194 

192.6 

23.6 

254 

252.1 

31.0 

15 

14.9 

01.8 

75 

74.4 

09.1 

135 

134.0 

16.5 

195 

193.5 

23.8 

255 

253.1 

31.1 

16 

15.9 

01.9 

76 

75.4 

09.3 

136 

135.0 

16.6 

196 

194.5 

23.9 

256 

254.1 

31.2 

17 

16.9 

02.1 

77 

76.4 

09.4 

137 

136.0 

16.7 

197 

195.5 

24.0 

257 

255.1 

31.3 

18 

17.9 

02.2 

78 

77.4 

09.5 

138 

137.0 

16.8 

198 

196.5 

24.1 

258 

256.1 

31.4 

19 

18.9 

02.3 

79 

78.4 

09.6 

139 

138.0 

16.9 

199 

197.5 

24.3 

259 

257.1 

31.6 

20 

19.9 

02.4 

80 

79.4 

09.7 

140 

139.0 

17.1 

200 

198.5 

24.4 

260 

258.1 

31.7 

21 

20.8 

02.6 

81 

80.4 

09.9 

141 

139.9 

17.2 

201 

199.5 

24.5 

261 

259.] 

31.8 

22 

21.8 

02.7 

82 

81.4 

10.0 

142 

140.9 

17.3 

202 

200.5 

24.6 

262 

260.0  31.9 1 

23 

22.8 

02.8 

83 

82.4 

10.1 

143 

141.9 

17.4 

203 

201.5 

24.7 

263 

261.0 

32.1 

24 

23.8 

02.9 

84 

83.4 

10.2 

144 

142.9 

17.5 

204 

202.5 

24.9 

264 

262.0 

32.2 

25 

24.8 

03.0 

85 

84.4 

10.4 

145 

143.9 

17.7 

205 

203.5 

25.0 

265 

263.0 

32.3 

26 

25.8 

03.2 

86 

85.4 

10.5 

146 

144.9 

17.8 

206 

204.5 

25.1 

266 

264.0 

32.4 

27 

26.8 

03.3 

87 

86.4 

10.6 

147 

145.9 

17.9 

207 

205.5 

25.2 

267 

265.0 

32.5 

28 

27.8 

03.4 

88 

87.3 

10.7 

148 

146.9 

18.0 

208 

206.4 

25.3 

268 

266.0 

32.7 

29 

28.8 

03.5 

89 

88.3 

10.8 

149 

147.9 

18.2 

209 

207.4 

25.5 

269 

267.0 

32.8 

30 

29.8 

03.7 

90 

89.3 

11.0 
11.1 

150 

148.9 

18.3 

210 

208.4 

25.6 

270 

268.0 

32.9 

31 

30.8 

03.8 

91 

90.3 

151 

149.9 

18.4 

211 

209.4 

25.7 

271 

269.0 

33.0 

32 

31.8 

03.9 

92 

91.3 

11.2 

152 

150.9 

18.5 

212 

210.4 

25.8 

272 

270.0 

33.1 

33 

32.8 

04.0 

93 

92.3 

11.3 

153 

151.9 

18.6 

213 

211.4 

26.0 

273 

271.0 

33.3 

34 

33.7 

04.1 

94 

93.3 

11.5 

154 

152.9 

18.8 

214 

212.4 

26.1 

274 

272.0 

33.4 

35 

34.7 

04.3 

95 

94.3 

11.6 

155 

153.8 

18.9 

215 

213.4 

26.2 

275 

273.0 

33.5 

36 

35.7 

04.4 

96 

95.3 

11.7 

156 

154.8 

19.0 

216 

214.4 

26.3 

276 

273.9 

33.6 

37 

36.7 

04.5 

97 

96.3 

11.8 

157 

155.8 

19.1 

217 

215.4 

26.4 

277 

274.9 

33.8 

38 

37.7 

04.6 

98 

97.3 

11.9 

158 

156.8 

19.3 

218 

216.4 

26.6 

278 

275.9 

33.9 

39 

38.7 

04.8 

99 

98.3 

12.1 

159 

157.8 

19.4 

219 

217.4 

26.7 

279 

276.9 

34.0 

40 

39.7 

04.9 

100 

99.3 

12.2 

160 

158.8 

19.5 

220 

218.4 

26.8 

280  !  277.9 

34.1 

41 

40.7 

05.0 

101 

100.2 

12.3 

161 

159.8 

19.6 

221 

219.4 

26.9 

281 

278.9 

34.2 

42 

41.7 

05.1 

102 

101.2 

12.4 

162 

160.8 

19.7 

222 

220.3 

27.1 

282 

279.9 

34.4 

43 

42.7 

05.2 

103 

102.2 

12.6 

163 

161.8 

19.9 

223 

221.3 

27.2 

283 

280.9 

34.5 

44 

43.7 

05.4 

104 

103.2 

12.7 

164 

162.8 

20.0 

224 

222.3 

27.3 

284 

281.9 

34.6 

45 

44.7 

05.5 

105 

104.2 

12.8 

165 

163.8 

20.1 

225 

223.3 

27.4 

285 

282.9 

34.7 

46 

45.7 

05.6 

10() 

105.2 

12.9 

166 

164.8 

20.2 

226 

224.3 

27.5 

286 

283.9 

34.9 

47 

46.6 

05.7 

107 

106.2 

13.0 

167 

165.8 

20.4 

227 

225.3 

27.7 

287 

284.9 

35.0 

48 

47.6 

05.8 

108 

107.2 

13.2 

168 

166.7 

20.5 

228 

226.3 

27.8 

288 

285.9 

35.1 

49 

48.6 

06.0 

109 

108.2 

13.3 

169 

167.7 

20.6 

229 

227.3 

27.9 

289 

286.8 

35.2 

50 

49.6 

06.1 

110 

109.2 

13.4 

170 

168.7 

20.7 

230 

228.3 

28.0 

290 

287.8 

35.3 

51 

50.6 

06.2 

111 

110.2 

13.5 

171 

159.7 

20.8 

231 

229.3 

28.2 

291 

288.8 

35.5 

52 

51.6 

06.3 

112 

111.2 

13.6 

172 

170.7 

21.0 

232 

230.3 

28.3 

292 

289.8  ,  85.6 1 

53 

52.6 

06.5 

113 

112.9 

13.8 

173 

171.7 

21.1 

233 

231.3 

28.4 

293 

290.8 

35.7 

54 

53.6 

06.6 

114 

113.2 

13.9 

174 

172.7 

21.2 

234 

232.3 

28.5 

294 

291.8 

35,8 

55 

54.6 

06.7 

115 

114.1 

14.0 

175 

173.7 

21.3 

235 

233.2 

28.6 

295 

292.8 

36.0 

5() 

55.6 

06.8 

116 

115.1 

14.1 

176 

174.7 

21.4 

236 

234.2 

28.8 

296 

293.8 

36.1 

57 

56.6 

06.9 

117 

116.1 

14.3 

177 

175.7 

21.6 

237 

235.2 

28.9 

297 

294.8 

36.2 

58 

57.6 

07.1 

118 

117.1 

14.4 

178 

176.7 

21.7 

238 

236.2 

29.0 

298 

295.8 

36.3 

59 

58.6 

07.2 

119 

118.1 

14.5 

179 

177.7 

21.8 

239 

237.2 

29.1 

299 

296.8 

36.4 

60 

Dist 

59.6 

Dep. 

07.3 

120 

119.1 

14.6 

180 

178.7 

21.9 

240 

238.2 

29.2 

300 

297.8 

36.6 

Lat. 

Dist. 

Dop. 

Lat. 

Dist 

Dep. 

Lnt. 

Dist 

Dep. 

Lat 

Dist 

Dep. 

Lat 

F(ir  S3  De".>-ii<-es. 

5''  32'".   1 

24                    TABLE  11. 

DIFFERENCE  OF  T-ATITUDE  AND  DEPARTURE  FOR  8  DEGREES.  '  Ob  32">. 

Diat  Lat  Pep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 
33.5 

1  01.0 

00.1 

61 

60.4 

08.5 

121 

119.8 

16.8 

181 

179.2 

25.2 

241 

23S.7 

2  02.0 

00.3 

62 

61.4 

08.6 

122 

120.8 

17.0 

182 

180.2 

25.3 

242 

239.6 

33.7 

3  03.0 

00.4 

63 

62.4 

08.8 

123 

121.8 

17.1 

183 

181.2 

25.5 

243 

240.6 

33.8 

4 

04.01 

00.6 

64 

63.4 

08.9 

124 

122.8 

17.3 

184 

182.2 

25.6 

244 

241.6 

34  0 

5 

05.0  00.7  1 

65 

64.4 

09.0 

125 

123.8 

17.4 

185 

183.2 

25.7 

245 

242.6 

34  1 

6 

05.9 

00.81 

66 

65.4 

09.2 

126 

124.8 

17.5 

186 

184.2 

25.9 

246 

243.6 

34.2 

7 

06.9 

01.0  67 

66.3 

09.3 

127 

125.8 

17.7 

187 

185.2 

26.0 

247 

244.6 

34.4 

8 

07.9 

01.1   68 

67.3 

09.5 

128 

126.8 

17.8 

188 

186.2 

26.2 

248 

245.6 

34.5 

9 

08.9 

01.3 

69 

68.3 

09.6 

129 

127.7 

18.0 

189 

187.2 

26.3 

249 

246.6 

34  7 

10 
11 

09.9 

01.4 

70 

69.3 

09.7 

130 

128.7 

18.1 

190 

188.2 

26.4 

250 

247.6 

34.8 
34.9 

10.9 

01.5 

71 

70.3 

09.9 

131 

129.7 

18.2 

191 

189.1 

26.6 

251 

248.6 

12 

11.9 

01.7 

72 

71.3 

10.0 

132 

130.7 

18.4 

192 

190.1 

26.7 

252 

249.5 

35.1 

13 

12.9 

01.8 

73 

72.3 

10.2 

133 

131.7 

18.5 

193 

191.1 

26.9 

253 

250.5 

35.2 

W 

13.9 

01.9 

74 

73.3 

10.3 

134 

132.7 

18.6 

194 

192.1 

27.0 

254 

251.5 

35.3 

15 

14.9 

02.1 

75 

74.3 

10.4 

135 

133.7 

18.8 

195 

193.1 

27.1 

255 

252.5  35.5 

16 

15.8 

02.2 

76 

75.3 

10.6 

136 

134.7 

18.9 

196 

194.1 

27.3 

256 

253.5  35.6 

17 

16.8 

02.4 

77 

76.3 

10.7 

137 

135.7 

19.1 

197 

195.1 

27.4 

257 

254.5  35.8 

IS 

17.8 

02.5 

78 

77.2 

10.9 

138 

136.7 

19.2 

198 

196.1 

27.6 

258 

255.5  35.9 

19 

18.8 

02.6 

79 

78.2 

11.0 

139 

137.7 

19.3 

199 

197.1 

27.7 

259 

256.5  36.0 

20 

19.8 

02.8 

80 

79.2 

11.1 

140 

138.6 

19.5 

200 

198.1 

27.8 

260 

257.5 

36.2 

21 

20.8 

02.9 

81 

80.2 

11.3 

141 

139.6 

19.6 

201 

199.0 

28.0 

261 

258.5 

36.3 

22 

21.8 

03.1 

82 

81.2 

11.4 

i42 

140.6 

19.8 

202 

200.0 

28.1 

262 

259.5 

36.5 

23 

22.8 

03.2 

83 

82.2 

11.6 

143 

141.6 

19.9 

203 

201.0 

28.3 

263 

260.4 

36.6 

24 

23.8 

03.3 

84 

83.2 

11.7 

144 

142.6 

20.0 

204 

202.0 

28.4 

264 

261.4 

36.7 

25 

24.8 

03.5 

85 

84.2 

11.8 

145 

143.6 

20.2 

205 

203.0 

28.5 

265 

262.4 

36.9 

26 

25.7 

03.6 

86 

85.2 

12.0 

146 

144.6 

20.3 

206 

204.0 

28.7 

266 

263.4 

37.0 

27 

26.7 

03.8 

87 

86.2 

12.1 

147 

145.6 

20.5 

207 

205.0 

28.8 

267 

264.4 

37.2 

28 

27.7 

03.9 

88 

87.1 

12.2 

148 

146.6 

20.6 

208 

206.0 

28.9 

268 

265.4 

37.3 

29 

28.7 

04.0 

89 

88.1 

12.4 

149 

147.5 

20.7 

209 

207.0 

29.1 

269 

266.4 

37.4 

30 
31 

29.7 

04.2 

90 

89.1 

12.5 

150 

148.5 

20.9 

210 

208.0 

29.2 

270 

267.4 

37.6 

30.7 

04.3 

91 

90.1 

12.7 

151 

149.5 

21.0 

211 

208.9 

29.4 

271 

268.4 

37.7 

32 

31.7 

04.5 

92 

91.1 

12.8 

152 

150.5 

21.2 

212 

209.9 

29.5 

272 

269.4 

37.9 

33 

32.7 

04.6 

93 

92.1 

12.9 

153 

151.5 

21.3 

213 

210.9 

29.6 

273 

270.3 

38.0 

34 

33.7 

04.7 

94 

93.1 

13.1 

154 

152.5 

21.4 

214 

211.9 

29.8 

274 

271.3 

38.1 

35 

34.7 

04.9 

95 

94.1 

13.2 

155 

153.5 

21.6 

215 

212.9 

29.9 

275 

272.3  ■  38.3 

36 

35.6. 

05.0 

96 

95.1 

13.4 

156 

154.5 

21.7 

216 

213.9 

30.1 

276 

273.3  38  4 

37 

36.6 

05.1 

97 

96.1 

13.5 

157 

155.5 

21.9 

217 

214.9 

30.2 

277 

274.3  38.6 

:  38 

37.6 

05.3 

98 

97.0 

13.6 

158 

156.5 

22.0 

218 

215.9 

30.3 

278 

275.3  38.7 

39 

38.6 

05.4 

99 

98.0 

13.8 

159 

157.5 

22.1 

219 

216.9 

30.5 

279 

276.3 

3S.8 

40 
41 

39.6 

05.6 

100 

99.0 

13.9 

160 

158.4 

22.3 

220 
221 

217.9 

30.6 

280 

277.3 

39.0 

40.6 

05.7 

101 

100.0 

14.1 

161 

159.4 

22.4 

218.8 

30.8 

281 

278.3 

39.1 

42 

41.6 

05.8 

102 

101.0 

14.2 

162 

160.4 

22.5 

222 

219.8 

30.9 

282 

279.3 

39.2 

43 

42.6 

06.0 

103 

102.0 

14.3 

163 

161.4 

22.7 

223 

220.8 

31.0 

283 

280.2 

39.4 

44 

43.6 

06.1 

104 

103.0 

14.5 

164 

162.4 

22.8 

224 

221.8 

31.2 

284 

281.2 

39.5 

45 

44.6 

06.3 

105 

104.0 

14.6 

165 

163.4 

23.0 

225 

222.8 

31.3 

285 

282.2 

39.7 

46 

45.6 

06.4 

106 

105.0 

14.8 

166 

164.4 

23.1 

226 

223.8 

31.5 

286 

283.2 

39.8 

47 

46.5 

06.5 

107 

106.0 

14.9 

167 

165.4 

23.2 

227 

224.8 

31.6 

287 

284.2 

39.9 

48 

47.5 

06.7 

108 

106.9 

15.0 

168 

166.4 

23.4 

228 

225.8 

31.7 

288 

285.2 

40.1 

49 

48.5 

06.8 

109 

107.9 

15.2 

169 

167.4 

23.5 

229 

226.8 

31.9 

289 

286.2 

40.2 

50 
51 

49.5 

07.0 

110 

108.9 

15.3 

170 

168.3 

23.7 

230 

227.8 

32.0 

290 

287.2 

40.4 
40.5 

50.5 

07.  ^ 

111 

109.9 

15.4 

171 

169.3 

23.8 

231 

228.8 

32.1 

291 

288.2 

52 

51.5 

07.2 

112 

110.9 

15.6 

172 

170.3 

23.9 

232 

229.7 

32.3 

292 

289.2 

40.6 

53 

52.5 

07.4 

113 

111.9 

15.7 

173 

171.3 

24.1 

233 

230.7 

32.4 

293 

290.1 

40.8 

54 

53.5 

07.5 

114 

112.9 

15.9 

174 

172.3 

24.2 

234 

231.7 

32.6 

294 

291.1 

40.9 

55 

54.5 

07.7 

115 

113.9 

16.0 

175 

173.3 

24.4 

235 

232.7 

32.7 

295 

292.1 

41.1 

56 

55.5 

07,8 

116 

114.9 

16.1 

176 

174.3 

24.5 

236 

233.7 

32.8 

296 

293.1 

41.2 

57 

56.4 

07.9 

117 

115.9 

16.3 

177 

175.3 

24.6 

237 

234.7 

33.0 

297 

294.1 

41.3 

58 

57.4 

08.1 

118  116.9 

16.4 

178 

176.3 

24.8 

238 

235.7 

33.1 

298 

295.1 

41.5 

59 

58.4 

08.2 

119 

117.8 

16.6 

179 

177.3 

24.9 

239 

236.7 

33.3 

299 

296.1 

41.6 

60 
Disi 

59.4 

08.4 

120 

118.8 

16.7 
Lat. 

180 
Dist. 

178.3 

25.1 

240 

237.7 

33.4 

300 

297.1 

41.8 

Lat, 

.  Dep. 

Lat. 

Dist. 

Dep. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

For  82  Degrees.                           5h  28™.  | 

TABLE  11.                     26 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  9  DEGREES.   Oh  SBm. 

Dist 

1 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

Dist 

Lat 

Dep. 

01.0 

00.2 

61 

60.2 

09.5 

121 

119.5 

18.9 

181 

178.8 

28.3 

241 

238.0 

37.7 

•) 

02.0 

00.3 

62 

61.2 

09.7 

122 

120.5 

19.1 

182 

179.8 

28.5 

242 

239.0 

37.9 

o 

03.0 

00.5 

63 

62.2 

09.9 

123 

121.5 

19.2 

183 

180.7 

28.6 

243 

240.0 

38.0 

4 

04.0 

00.6  64 

63.2 

10.0 

124 

122.5 

19.4 

184 

181.7 

28.8 

244 

241.0 

38.2 

5 

04.9 

00.8  65 

64.2 

10.2 

125 

123.5 

19.6 

185 

182.7 

28.9 

245 

242.0 

38.3 

6 

05.9 

00.9  66 

65.2 

10.3 

126 

124.4 

19.7 

186 

183.7 

39.1 

246 

243.0 

38.5 

/ 

06.9 

01.1 

67 

66.2 

10.5 

127 

125.4 

19.9 

187 

184.7 

29.3 

247 

244.0 

38.6 

8 

07.9 

01.3 

68 

67.2 

10.6 

128 

126.4 

20.0 

188 

185.7 

29.4 

248 

244.9 

38.8 

9 

08.9 

01.4 

69 

68.2 

10.8 

129 

127.4 

20.2 

189 

186.7 

29.6 

249 

245.9 

39.0 

10 

09.9 

01.6 

70 
71 

69.1 

11.0 

130 

128.4 

20.3 

190 

187.7 

29.7 

250 

246.9 
247.9 

39.1 
39.3 

11 

10.9 

01.7 

70.1 

11.1 

131 

129.4 

20.5 

191 

188.6 

29.9 

251 

12 

11.9 

01.9 

72 

71.1 

11.3 

132 

130.4 

20.6 

192 

189.6 

30.0 

252 

248.9 

39.4 

13 

12.8 

02.0 

73 

72.1 

11.4 

133 

131.4 

20.8 

193 

190.6 

30.2 

253 

249.9 

39.6 

14 

13.8 

02.2 

74 

73.1 

11.6 

134 

132.4 

21.0 

194 

191.6 

30.3 

254 

250.9 

39.7 

15 

14.8 

02.3 

75 

74.1 

11.7 

135 

133.3 

21.1 

195 

192.6 

30.5 

255 

251.9 

39.9 

U) 

15.8 

02.5 

76 

75.1 

11.9 

136 

134.3 

21.3 

196 

193.6 

30.7 

256 

252.8 

40.0 

17 

16.8 

02.7 

77 

76.1 

12.0 

137 

135.3 

21.4 

197 

194.6 

30.8 

257 

253.8 

40.2 

18 

17.8 

0-2.8 

78 

77.0 

12.2 

138 

136.3 

21.6 

198 

195.6 

31.0 

258 

254.8 

40.4 

19 

1S.8 

03.0 

79 

78.0 

12.4 

139 

137.3 

21.7 

199 

196.5 

31.1 

259 

255.8 

40.5 

20 
2i 

19.8 

03.1 

80 

79.0 

12.5 

140 

138.3 

21.9 

200 

197.5 

31.3 

260 

256.8 

257.8 

40.7 
40.8 

20.7 

03.3 

81 

80.0 

12.7 

141 

139.3 

22.1 

201 

198.5 

31.4 

261 

22 

21.7 

03.4 

82 

81.0 

12.8 

142 

140.3 

22.2 

202 

199.5 

31.6 

262 

2.58.8 

41.0 

23 

22.7 

03.6 

83 

82.0 

13.0 

143 

141.2 

22.4 

203 

200.5 

31.8 

263 

259.8 

41.1 

24 

23.7 

03.S 

84 

83.0 

13.1 

144 

142.2 

22.5 

204 

201.5 

319 

264 

260.7 

41.3 

25 

24.7 

03.9 

85 

84.0 

13.3 

145 

143.2 

22.7 

205 

202.5 

32.1 

265 

261.7 

41.5 

26 

25.7 

04.1   86 

84.9 

13.5 

146 

144.2 

22.8 

206 

203.5 

32.2 

266 

262.7 

41.6 

27 

26.7 

04.2  87 

85.9 

13.6 

147 

145.2 

23.0 

207 

204.5 

32.4 

267 

263.7 

41.8 

28 

27.7 

04.4  88 

86.9 

13.8 

.148 

146.2 

23.2 

208 

205.4 

32.5 

268 

264.7 

41.9 

29 

28.6 

04.5  89 

87.9 

13.9 

149 

147.2 

23.3 

209 

206.4 

32.7 

269 

265.7 

42.1 

30 
31 

29.6 

04.7 

90 

88.9 

14.1 

150 

148.2 

23.5 

210 
211 

207.4 

32.9 

270 
271 

266.7 

42.2 

30.6 

04.8 

91 

89.9 

14.2 

151 

149.1 

23.6 

208.4 

33.0 

267.7 

42.4 

32 

31.6 

05.0 

92 

90.9 

14.4 

152 

150.1 

23.8 

212 

209.4 

33.2 

272 

268.7 

42.6 

33 

32.6 

05.2 

93 

91.9 

14.5 

153 

151.1 

23.9 

213 

210.4 

33.3 

273 

269.6 

42.7 

34 

33.6 

05.3 

94 

92.8 

14.7 

154 

152.1 

24.1 

214 

211.4 

33.5 

274 

270.6 

42.9 

35 

34.6 

05.5 

95 

93.8 

14.9 

155 

153.1 

24.2 

215 

212.4 

33.6 

275 

271.6 

43.0 

3(3 

35.6 

05.6 

96 

94.8 

15.0 

156 

154.1 

24.4 

216 

213.3 

33.8 

276 

272.6 

43.2 

37 

36.5 

05.8 

97 

95.8 

15.2 

157 

155.1 

24.6 

217 

214.3 

33.9 

277 

273.6 

43.3 

38 

37.5 

05.9 

98 

96.8 

15.3 

158 

156.1 

24.7 

218 

215.3 

34.1 

278 

274.6 

43.5 

39 

38.5 

06.1 

99 

97.8 

15.5 

159 

157.0 

24.9 

219 

216.3 

34.3 

279 

275.6 

43.6 

40 

39.5 

06.3 

100 

,  98.8 

15.6 

160 

158.0 

250 

220 

217.3 

34.4 

280 

276.6 

43.8 

41 

40.5 

06.4 

101 

99.8 

15.8 

161 

159.0 

25.2 

221 

218.3 

34.6 

281 

277.5 

44.0 

42 

41.5 

06.6 

102 

100.7 

16.0 

162 

160.0 

25.3 

222 

219.3 

34.7 

282 

278.5 

44.1 

43 

42.5 

06.7 

103 

101.7 

16.1 

163 

161.0 

25.5 

223 

220.3 

34.9 

283 

279.5 

44.3 

44 

43.5 

06.9 

104 

102.7 

1().3 

1()4 

162.0 

25.7 

224 

221.2 

35.0 

284 

280.5 

44.4 

45 

44.4 

07.0 

105 

103.7 

16.4 

165 

163.0 

25.8 

225 

222.2 

35.2 

285 

281.5 

44.6 

46 

45.4 

07.2 

106 

104.7 

16.6 

166 

164.0 

26.0 

226 

223.2 

35.4 

286 

282.5 

44.7 

47 

46.4 

07.4 

107 

105.7 

16.7 

167 

164.9 

26.1 

227 

224.2 

35.5 

287 

283.5 

44.9 

48 

47.4 

07.5 

108 

106.7 

16.9 

168 

165.9 

26.3 

228 

225.2 

35.7 

288 

284.5 

45.1 

49 

48.4 

07.7 

109 

107.7 

17.1 

1()9 

166.9 

26.4 

229 

226.2 

35.8 

289 

285.4 

45.2 

50 

49.4 

07.8 

110 

108.6 

17.2 

170 

167.9 

26.6 

230 

227.2 

36.0 

290 

286.4 

45.4 

51 

50.4 

08.0 

111 

109.6 

17.4 

171 

168.9 

26.8 

231 

228.2 

36.1 

291 

287.4 

45.5 

52 

51.4 

08.1 

112 

110.6 

17.5 

172 

169.9 

26.9 

232 

229.1 

36.3 

292 

288.4 

45.7 

53 

52.3 

08.3 

113 

111.6 

17.7 

173 

170.9 

27.1 

233 

230.1 

36.4 

293 

289.4 '  45.8 

54 

53.3 

08.4 

114 

112.6 

17.8 

174 

171.9 

27.2 

234 

231.1 

36.6 

294 

290.4  46.0 

55 

54.3 

08.6 

115 

113.6 

18.0 

175 

172.8 

27.4 

235 

232.1 

36.8 

295 

291.4  46.1 

56 

55.3 

08.8 

116 

114.6 

18.1 

176 

173.8 

27.5 

236 

233.1 

36.9 

296 

292.4 

46.3 

57 

56.3 

08.9 

117 

115.6 

18.3 

177 

174.8 

27.7 

237 

234.1 

37.1 

297 

293.3 

46.5 

58 

57.3 

09.1 

118 

116.5 

18.5 

178 

175.8 

27.8 

238 

235.1 

37.2 

298 

294.3 

46.6 

59 

58.3 

0'.>.2 

119 

117.5 

18.6 

179 

176.8 

28.0 

239 

236.1 

37.4 

299 

295.3 

46.8 

60 

59.3 

09.4 

120 

118.5 

18.8 

Lat. 

180 

177.8 

28.2 

240 

237.0 

37.5 

300 

296.3 

46.9 

Di8t.  Dep. 

Lat. 

Dist.'  Dep. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist 

Dep. 

Lat 

For  81  Decrees.                          6^  24m.  | 

26 

TABLE  II. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  10  DEGREES.  0^  40m.  J 

DisL 

Lat. 

De£^ 

Dist, 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.  Lat.  1  Dep.  | 

1 

01.0 

00.2 

61 

60.1 

10.6 

121 

119.2 

21.0 

181 

178.3 

31.4 

241  237  3 

41.81 

2 

02.0 

00.3 

62 

61.1 

10.8 

122 

120.1 

21.2 

1^2 

i^9.2 

31.6 

242  238.3 

42.0  1 

3 

03.0 

00.5 

63 

62.0 

10.9 

123 

121.1 

21.4 

183 

180.2 

31.8 

2431239.3  42.2 

4 

03.9 

00.7 

64 

63.0 

11.1 

124 

122.1 

21.5 

184 

181.2 

32.0 

244  240.3  i2.4 

5 

04.9 

00.9 

65 

64.0 

11.3 

125 

123.1 

21.7 

185 

182.2 

32.1 

245  241.3142.5  " 

6 

05.9 

01.0 

66 

65.0 

11.5 

126 

124.1 

21.9 

186 

183.2 

32.3 

246  242.3  42.7 

7 

06.9 

01.2 

67 

66.0 

11.6 

127 

125.1 

22.1 

187 

184.2 

32.5 

247  243.2  142.9  : 

8 

07.9 

01.4 

68 

67.0 

11.8 

128 

126.1 

22.2 

188 

185.1  32.6  1 

248  244.2;  43.1 

9 

08.9 

01.6 

69 

68.0 

12.0 

129 

127.0 

22.4 

189 

186.1 

32.8 

249 

245.2 

43.2 

10 
11 

09.8 

01.7 

70 

68.9 

12.2 

130 

128.0 

22.6 

190 

187.1 

33.0 

250 

246.2 

43.4 

10.8 

01.9 

71 

69.9 

12.3 

131 

129.0 

22.7 

191 

188.1 

33.2 

251 

247.2 

43.0 

12 

11.8 

02.1 

72 

70.9 

12.5 

132 

130.0 

22.9 

192 

189.1 

33.3 

252 

248.2 

43.8 

13 

12.8 

02.3 

73 

71.9 

12.7 

133 

131.0 

23.1 

193 

190.1 

33.5 

253 

249.2 

43.9 

14 

13.8 

02.4 

74 

72.9 

12.8 

134 

132.0 

23.3 

194 

191.1 

33.7 

254 

250.1 

44.1 

15 

14.8 

02.6 

75 

73.9 

13.0 

135 

132.9 

23.4 

195 

192.0 

33.9 

255 

251.1  ■  44.3 

16 

15.8 

02.8 

76 

74.8 

13.2 

136 

133.9 

23.6 

196 

193.0 

34.0 

256 

252.1 '44.5 

17 

16.7 

03.0 

77 

75.8 

13.4 

137 

134.9 

23.8 

197 

194.0 

34.2 

257 

253.1144.6 

18 

17.7 

03.1 

78 

76.8 

13.5 

138 

135.9 

24.0 

198 

195.0 

34.4 

258 

254.1 

44.8 

19 

18.7 

03.3 

79 

77.8 

13.7 

139 

136.9 

24.1 

199 

196.0 

34.6 

259 

255.1 

45.0 

20 

19.7 

03.5 

03.6 

80 

78.8 

13.9 

140 

137.9 

24.3 

200 

197.0 

34.7 

260 

256.1 

45.1 
45.3 

21 

20.7 

81 

79.8 

14.1 

141 

138.9 

24.5 

201 

197.9 

34.9 

261 

257.0 

22 

21.7 

03.8 

82 

80.8 

14.2 

142 

139.8 

24.7 

202 

198.9 

35.1 

262 

258.0 

45.5 

23 

22.7 

04.0 

83 

81.7 

14.4 

143 

140.8 

24.8 

203 

199.9 

35.3 

263 

259.0 

45.7 

24 

23.6 

04.2 

84 

82.7 

14.6 

144 

141.8 

25.0 

204 

200.9 

35.4 

264 

260.0 

45.8 

25 

24.6 

04.3 

85 

83.7 

14.8 

145 

142.8 

25.2 

205 

201.9 

35.6 

265 

261.0 

46.0 

26 

25.6 

04.5 

86 

84.7 

14.9 

146 

143.8 

25.4 

206 

202.9 

35.8 

266 

262.0 

46.2 

27 

26.6 

04.7 

87 

85.7 

15.1 

147 

144.8 

25.5 

207 

203.9 

35.9 

267 

262.9 

46.4 

28 

27.6 

04.9 

88 

86.7 

15.3 

148 

145.8 

25.7 

208 

204.8 

36.1 

268  •  2()3.9 

46.5 

29 

28.6 

05.0 

89 

87.6 

15.5 

149 

146.7 

25.9 

209 

205.8 

36.3 

269  264.9 

46.7 

30 

29.5 

05.2 

90 

88.6 

15.6 

150 

147.7 

26.0 



210 

206.8 

36.5 

270 

265.9  1  46.9 

31 

30.5 

05.4 

91 

89.6 

15.8 

151 

148.7  26.2 

211 

207.8 

36.6 

271 

266.9  1  47.1 

32 

31.5 

05.6 

92 

90.6 

16.0 

152 

149.7  26.4 

212 

208.8 

36.8 

272 

267.9 

47.2 

33 

32.5 

05.7 

93 

91.6 

16.1 

153 

150.7  26.6 

213 

209.8 

37.0 

273 

268.9 

47.4 

34 

33.5 

05.9 

94 

92.6 

16.3 

154 

151.7  26.7 

214 

210.7 

37.2 

274 

269.8 

47.6 

35 

34.5 

06.1 

95 

93.6 

16.5 

155 

152.6  26.9 

215 

211.7 

37.3 

275 

270.8 

47.8 

36 

35.5 

06.3 

96 

94.5 

16.7 

156 

153.6  i  27.1 

216 

212.7 

37.5 

276 

271.8 

47.9 

37 

36.4 

06.4 

97 

95.5 

16.8 

157 

154.6 

27.3 

217 

213.7 

37.7 

277  272.8 

48.1 

38 

37.4 

06.6 

98 

96.5 

17.0 

158 

155.6 

27.4 

218 

214.7 

37.9 

278 

273.8 

48.3 

39 

38.4 

06.8 

99 

97.5 

17.2 

159 

156.6- 

27.6 

219 

215.7 

38.0 

279 

274.8 

48.4 

40 

39.4 

06.9 

100 

98.5 

17.4 

160 

157.6 

27.8 

220 

216.7 

38.2 

280 

275.7 

48.6 

41 

40.4 

07.1 

101 

99.5 

17.5 

161 

158.6 

28.0 

221 

217.6 

38.4 

281 

276.7 

48.8 

42 

41.4 

07.3 

102 

100.5 

17.7 

162 

159.5 

28.1 

222 

218.6 

38.5 

282 

277.7 

49.0 

43 

42.3 

07.5 

103 

101.4 

17.9 

163 

160.5 

28.3 

223 

219.6 

38.7 

283 

278.7 

49.1 

44 

43  3 

07.6 

104 

102.4 

18.1 

164 

161.5 

28.5 

224 

220.6 

38.9 

284 

279.7 

49.3 

45 

44.3 

07.8 

105 

103.4 

18.2 

165 

162.5 

28.7 

225 

221.6 

39.1 

285 

280.7 

49.5 

46 

45.3 

08.0 

106 

104.4 

18.4 

166 

163.5 

28.8 

226 

222.6 

39.2 

286 

281.7 

49.7 

47 

46.3 

08.2 

107 

105.4 

18.6 

167 

164.5 

29.0 

227 

223.6 

39.4 

287 

282.6 

49.8 

48 

47.3 

08.3 

108 

106.4 

18.8 

1()8 

165.4 

29.2 

228 

224.5 

39.6 

288 

283.6 

50.0 

49 

48.3 

08.5 

109 

107.3 

18.9 

169 

166.4 

29.3 

229 

225.5 

39.8 

289 

284.6 

50.2 

50 
5] 

49.2 

08.7 

110 

108.3 

19.1 

170 

167.4 

29.5 

230 

226.5 

39.9 

290 

285.6 

504 

50.2 

08.9 

111 

109.3 

19.3 

171 

168.4 

29.7 

231 

227.5 

40.1 

291 

286.6 

50.5 

52 

51.2 

09.0 

112 

110.3 

19.4 

172 

169.4 

29.9 

232 

228.5 

40.3 

292 

287.6  ,  50.7  1 

53 

52.2 

09.2 

113 

111.3 

19.6 

173 

170.4 

30.0 

233 

229.5 

40.5 

293 

288.5 

50.9 

54 

53.2 

09.4 

114 

112.3 

19.8 

174 

171.4 

30.2 

234 

230.4 

40.6 

294 

289.5 

51  1 

55 

54.2 

09.6 

115 

113.3 

20.0 

175 

172.3 

30.4 

235 

231.4 

40.8 

295 

290.5 

512 

56 

55.1 

09.7 

116 

114.2 

20.1 

176 

173.3 

30.6 

236 

232.4 

41.0 

296 

291.5 

51.4 

57 

56.1 

09.9 

117 

115.2 

20.3 

177 

174.3 

30.7 

237 

233.4 

41.2 

297 

292.5 

51.6 

58 

57.1 

10.1 

118 

116.2 

20.5 

178 

175.3 

30.9 

238 

234.4 

41.3 

298 

293.5 

51.7 

59 

58.1 

10.2 

119 

117.2 

20.7 

179 

176.3 

31.1 

239 

235.4 

41.5 

299 

294.5 

51.9 

60 

59.1 

10.4 

120 

118.2 

20.8 

180 

177.3 

31.3 

240 

236.4 

41.7 

300 

295.4152.11 

Dist 

Dep. 

Lat. 

Dist. 

Dep.   Lat.  Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.  1 

For  RO  Degrees. 

6h  20".  1 

TABLE  11. 

27 
GREES.  Oil  44ra. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  11  DE 

Diet  Lat. 

Dep. 

Dist. 

Lilt. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 
241 

LaL 

236.6 

Dep. 
46.0 

1  01.0 

00.2 

61 

59.9 

11.6 

121 

118.8 

23.1 

181 

177.7 

34.5 

2  02.0 

00.4 

62 

60.9 

11.8 

122 

119.8 

23.3 

182 

178.7 

34.7 

242 

237.6 

46.2 

3  02.9 

00.6 

63 

61.8 

12.0 

123 

120.7 

23.5 

183 

179.6 

34.9 

243 

238.5 

46.4 

4  03.9 

00.8 

64 

62.8 

12.2 

124 

121.7 

23.7 

184 

180.6 

35.1 

244 

239.5 

46.6 

5  04.9 

01.0 

65 

63.8 

12.4 

125 

122.7 

23.9 

185 

181.6 

35.3 

245 

240.5 

46.7 

6 

05.9 

01.1 

66 

64.8 

12.6 

126 

123.7 

24.0 

186 

182.6 

35.5 

246 

241.5 

46.9 

7 

06.9 

01.3 

67 

65.8 

12.8 

127 

124.7 

24.2 

187 

183.6 

35.7 

247 

242.5 

47.1 

8 

07.9 

01.5 

68 

66.8 

13.0 

128 

125.6 

"^4.4 

188 

184.5 

35.9 

248 

243.4 

47.3 

9 

08.8 

01.7 

69 

67.7 

13.2 

129 

126.6 

24.6 

189 

185.5 

36.1 

249 

244.4 

47.5 

10 

09.8 

01.9 

70 

68.7 

13.4 

130 
131 

127.6 

24.8 

190 
191 

186.5 

36.3 

250 

245.4 

47.7 

11 

10.8 

02.1 

71 

69.7 

13.5 

128.6 

25.0 

187.5 

36.4 

251 

246.4 

47.9 

12 

11.8 

02.3 

72 

70.7 

13.7 

132 

129.6 

25.2 

192 

188.5 

36.6 

252 

247.4 

48.1 

13 

12.8 

02.5 

73 

71.7 

13.9 

133 

130.6 

25.4 

193 

189.5 

36.8 

253 

248.4 

48.3 

14 

13.7 

02.7 

74 

72.6 

14.1 

134 

131.5 

25.6 

194 

190.4 

37.0 

254 

249.3 

48.5 

15 

14.7 

02.9 

75 

73.6 

14.3 

135 

132.5 

25.8 

195 

191.4 

37.2 

255 

250.3 

48.7 

U) 

15.7 

03.1 

76 

74.6 

14.5 

136 

133.5 

26.0 

196 

192.4 

37.4 

256 

251.3 

48.8 

17 

16.7 

03.2 

77 

75.6 

14.7 

137 

134.5 

26.1 

197 

193.4 

37.6 

257 

252.3 

49.0 

18 

17.7 

03.4 

78 

76.0 

14.9 

138 

135.5 

26.3 

198 

194.4 

37.8 

258 

253.3 

49.2 

19 

18.7 

03.6 

79 

77.5 

15.1 

139 

136.4 

26.5 

199 

19.5.3 

38.0 

259 

254.2 

49.4 

21 

19.6 
20.6 

03.8 

80 

78.5 

15.3 

140 
141 

137.4 
138.4 

26.7 

200 

196.3 

38.2 

260 

255.2 
256.2 

49.6 

49.8 

04.0 

81 

79.5 

15.5 

26.9 

201 

197.3 

38.4 

261 

22 

21.6 

04.2 

82 

80.5 

15.6 

142 

139.4 

27.1 

202 

198.3 

38.5 

262 

257.2 

50.0 

23 

22.6 

04.4 

83 

81.5 

15.8 

143 

140.4 

27.3 

203 

199.3 

38.7 

263 

258.2 

50.2 

24 

23.6 

04.6 

84 

82.5 

16.0 

144 

141.4 

27.5 

204 

200.3 

38.9 

264 

259.1 

50.4 

25 

24.5 

04.8 

85 

83.4 

16.2 

145 

142.3 

27.7 

205 

201.2 

39.1 

265 

260.1 

50.6 

26 

25.5 

05.0 

86 

84.4 

16.4 

146 

143.3 

27.9 

206 

202.2 

39.3 

266 

261.1 

50.8 

27 

26.5 

05.2 

87 

85.4 

16.6 

147 

144.3 

28.0 

207 

203.2 

39.5 

267 

262.1 

50.9 

28 

27.5 

05.3 

88 

86.4 

16.8 

148 

145.3 

28.2 

208 

204.2 

39.7 

268 

263.1 

51.1 

29 

28.5 

05.5 

89 

87.4 

17.0 

149 

146.3 

28.4 

209 

205.2 

39.9 

269 

264.1 

51.3 

30 
31 

29.4 
30.4 

05.7 

90 

88.3 

17.2 

150 

147.2 

28.6 

210 

206.1 

40.1 

270 

265.0 

51.5 
51.7 

05.9 

91 

89.3 

17.4 

151 

148.2 

28.8 

211 

207.1 

40.3 

271 

266.0 

32 

31.4 

06.1 

92 

90.3 

17.6 

152 

149.2 

29.0 

212 

208.1 

4U.4 

272 

267.0 

51.9 

33 

32.4 

06.3 

93 

91.3 

17.7 

153 

150.2 

29.2 

213 

209.1 

40.5 

273 

268.0 

52.1 

34 

33.4 

06.5 

94 

92.3 

17.9 

154 

151.2 

29.4 

214 

210.1 

40.8 

274 

269.0 

52.3 

35 

34.4 

06.7 

95 

93.3 

18.1 

155 

152.2 

29.6 

215 

211.0 

41.0 

275 

269.9 

52.5 

36 

35.3 

06.9 

96 

94.2 

18.3 

156 

153.1 

29.8 

216 

212.0 

41.2 

276 

270.9 

52.7 

37 

36.3 

07.1 

97 

95.2 

18.5 

157 

154.1 

30.0 

217 

213.0 

41.4 

277 

271.9 

52.9 

38 

37.3 

07.3 

98 

96.2 

18.7 

158 

155.1 

30.1 

218 

214.0 

41.6 

278 

272.9 

53.0 

39 

38.3 

07.4 

99 

97.2 

18.9 

159 

156.1 

30.3 

219 

215.0 

41.8 

279 

273.9 

53.2 

40 

39.3 

07.6 

100 

98.2 

19.1 

160 

157.1 

30.5 

220 

216.0 

42.0 

280 

274.9 

53.4 

41 

40.2 

07.8 

101 

99.1 

19.3 

161 

158.0 

30.7 

221 

2i6.9 

42.2 

281 

275.8 

53.6 

42 

41.2 

08.0 

102 

100.1 

19.5 

162 

159.0 

30.9 

222 

217.9 

42.4 

282 

276.8 

53.8 

43 

42.2 

08.2 

103 

101.1 

19.7 

163 

160.0 

31.1 

223 

218.9 

42.6 

283 

277.8 

54.0 

44 

43.2 

08.4 

104 

102.1 

19.8 

.164 

161.0 

31.3 

224 

219.9 

42.7 

284 

278.8 

54.2 

45 

44.2 

08.6 

105 

103.1 

20.0 

165 

162.0 

31.5 

225 

220.9 

42.9 

285 

279.8 

54.4 

46 

45.2 

08.8 

106 

104.1 

20.2 

166 

163.0 

31.7 

226 

221.8 

43.1 

286 

280.7 

54.6 

47 

46.1 

09.0 

107 

105.0 

20.4 

167 

163.9 

31.9 

227 

222.8 

43.3 

287 

281.7 

54.8 

48 

47.1 

09.2 

108 

106.0 

20.6 

168 

164.9 

32.1 

228 

223.8 

43.5 

288 

282.7 

55.0 

49 

48.1 

09.3  109 

107.0 

20.8 

169 

165.9 

32.2 

229 

224.8 

43.7 

289 

283.7 

55.1 

50 

49.1 

09.5 

110 

108.0 

21.0 

170 

166.9 

32.4 

230 

225.8 

43.9 

290 

284.7 

55.3 

51 

50.1 

09.7 

HI 

109.0 

21.2 

171 

167.9 

32.6 

231 

226.8 

44.1 

291 

285.7 

55.5 

52 

51.0 

0l>.9 

1  12 

109.9 

21.4 

172 

168.8 

32.8 

232 

227.7 

44.3 

292 

286.6 

55.7 

53 

52.0 

10.1 

113 

110.9 

21.6 

173 

169.8 

33.0 

233 

228.7 

44.5 

293 

287.6 

55.9 

54 

.53.0 

10.3 

114 

111.9 

21.8 

174 

170.8 

33.2 

234 

229.7 

44.6 

294 

288.6 

56.1 

55 

54.0 

10.5 

115 

112.9 

21.9 

175 

171.8 

33.4 

235 

230.7 

44.8 

295 

289.6 

56.3 

56 

55.0 

10.7 

116 

113.9 

22.1 

176 

172.8 

33.6 

236 

231.7 

45.0 

296 

290.6 

56.5 

57 

56.0 

10.9 

117 

114.9 

22.3 

177 

173.7 

33.8 

237 

232,« 

45.2 

297 

291.5 

56.7 

58 

56.9 

11.1 

118 

115.8 

22.5 

178 

174.7 

34.0 

238 

233.6 

45.4 

298 

292.5 

56.9 

59 

57.9 

11.3 

119 

lir,.8 

22.7 

179 

175.7 

34.2 

239 

284.6 

45.6 

299 

293.5 

57.1 

60 

58.9 

11.4 

120 

117.8 

22.9 

Lat. 

180 

176.7 

34.3 

240 

235.6 

45.8 

300 

294.5 

57.2 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

For  79  Deajrees. 

5^   16-.  1 

28 

TABLE  II.                        1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  12  DEGREES.  0^  48m,  | 

Dist. 
1 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. '  Lat. 

Dep. 

Dist 

Lat. 

Dep. 

01.0 

00.2 

61 

59.7 

12.7 

121 

118.4 

25.2 

181 

177.0 

37.6 

241 

235.7 

50.1 

2 

02.0 

00.4 

62 

60.6 

12.9 

122 

119.3 

25.4 

182 

178.0 

87.8 

242 

236.7 

50.3 

3 

02.9 

00.6 

63 

61.6 

13.1 

123 

120.3  25.6 

183 

179.0 

38.0 

243 

237.7  50.5 

4 

03.9 

00.8 

64 

62.6 

13.3 

124 

121.3'  25.8 

184 

180.0 

38.3 

244 

238.7  :  50.7 

5 

04.9 

01.0 

65 

63.6 

13.5 

125 

122.3'  26.0 

185 

181.0 

38.5 

245 

239.6  50.9 

6 

05.9 

01.2 

66 

64.6 

13.7 

126 

123.2 

26.2 

186 

181.9 

38.7 

246 

240.6  ■  51.1 

7 

06.8 

01.5 

67 

65.5 

13.9 

127 

124.2 

26.4 

187 

182.9 

38.9 

247 

241.6:51.4 

8 

07.8 

01.7 

68 

66.5 

14.1 

128 

125.2 

•26.6 

188 

183.9 

39.1 

248 

242.6 '51.6 

9 

08.8 

01.9 

69 

67.5 

14.3 

129 

126.2 

26.8 

189 

184.9 

39.3 

249 

243.6:51.8 

10 
11 

09.8 

02.1 

70 

68.5 

14.6 

130 

127.2 

27.0 

190 

185.8 

39.5 

250 

244.5  52.0 

10.8 

02.3 

71 

69.4 

14.8 

131 

128.1 

27.2 

191 

186.8 

39.7 

251 

245.5 

52.2  1 

12 

11.7 

02.5 

72 

70.4 

15.0 

132 

129.1 

27.4 

192 

187.8 

39.9 

252 

246.5  52.4  1 

13 

12.7 

02.7 

73 

71.4 

15.2 

133 

130.1 

27.7 

193 

188.8 

40.1 

253 

247.5  1  52.6  | 

14 

13.7 

02.9 

74 

72.4 

15.4 

134 

131.1 

27.9 

194 

189.8 

40.3 

254 

248.4 

52.8 

15 

14.7 

03.1 

75 

73.4 

15.6 

135 

132.0 

28.1 

195 

190.7 

40.5 

255 

249.4 

53.0 

16 

15.7 

03.3 

76 

74.3 

15.8 

136 

133.0 

28.3 

196 

191.7 

40.8 

256 

250.4 

53.2 

IT 

16.6 

03.5 

77 

75.3 

16.0 

137 

134.0 

28.5 

197 

192.7 

41.0 

257 

251.4 

53.4 

18 

17.6 

03.7 

78 

76.3 

16.2 

138 

135.0 

28.7 

198 

193.7 

41.2 

258 

252.4 

53.6 

19 

18.6 

04.0 

79 

77.3 

16.4 

139 

136.0 

28.9 

199 

194.7 

41.4 

259 

253.3 

53.8 

20 

19.6 

04.2 

80 

78.3 

16.6 

140 

136.9 

29.1 

200 

195.6 

41.6 

260 

254.3 

54.1 

21 

20.5 

04.4 

81 

79.2 

16.8 

141 

137.9 

29.3 

201 

196.6 

41.8 

261  255.3' 54.3 1 

22 

21.5 

04.6 

82 

80.2 

17.0 

142 

138.9 

29.5 

202 

197.6 

42.0 

262 

256.3  '  54.5  1 

23 

22.5 

04.8 

83 

81.2 

17.3 

143 

139.9 

29.7 

203 

198.6 

42.2 

263 

257.3  1  54.7  | 

24 

23.5 

05.0 

84 

82.2 

17.5 

144 

140.9 

29.9 

204 

199.5 

42.4 

264 

258.2 

54.9 

25 

24,5 

05.2 

85 

83.1 

17.7 

145 

141.8 

30.1 

205 

200.5 

42.6 

265 

259.2 

55.1 

26 

25.4 

05.4 

86 

84.1 

17.9 

146 

142.8 

30.4 

206 

201.5 

42.8 

266  260.2 

55.3 

27 

26.4 

05.6 

87 

85.1 

18.1 

147 

143.8 

30.6 

207 

202.5 

43.0 

267  261.2:55.51 

28 

27.4 

05.8 

88 

86.1 

18.3 

148 

144.8 

30.8 

208 

203.5 

43.2 

268  1262.1  155.7/ 

29 

28.4 

06.0 

89 

87.1 

18.5 

149 

145.7 

31.0 

209 

204.4 

43.5 

269 

263.1  i55.9' 

30 

29.3 

06.2 

90 

88.0 

18.7 

150 

146.7 

31.2 

210 

205.4 

43.7 

270 

264.1  '56.1| 

31 

30.3 

06.4 

91 

89.0 

18.9 

151 

147.7 

31.4 

211 

206.4 

43.9 

271 

265.1 

56.3 

32 

31.3 

06.7 

92 

90.0 

19.1 

152 

148.7 

31.6 

212 

207.4 

44.1 

272 

266.1 

56.6 

33 

32.3 

06.9 

93 

91.0 

19.3 '153 

149.7 

31.8 

213 

208.3 

44.3 

273 

267.0 

56.8 

34 

33.3 

07.1 

94 

91.9 

19.5  154 

150.6 

32.0 

214 

209.3 

44.5 

274 

268.0 

57.0 

35 

34.2 

07.3 

95 

92.9 

19.8  155 

151.6 

32.2 

215 

210.3 

44.7 

275 

269.0 

57.2 

36 

35.2 

07.5 

96 

93.9 

20.0  156 

152.6 

32.4 

216 

211.3 

44.9 

276 

270.0 

57.4 

37 

36.2 

07.7 

97 

94.9 

20.2 

157 

153.6 

32.6 

217 

212.3 

45.1 

277 

270.9 

57.6 

38 

37.2 

07.9 

98 

95.9 

20.4 

158 

154.5 

32.9 

218 

213.2 

45.3 

278 

271.9 

57.8 

39 

38.1 

08.1 

99 

96.8 

20.6 

159 

155.5 

33.1 

219 

2142 

45.5 

279 

272.9 

58.0 

40 

39.1 

08.3 

100 

97.8 

20.8 

160 

156.5 

33.3 

220 

215.2 

45.7 

280 

273.9 

58.2 

41 

40.1 

08.5 

101 

98.8 

21.0 

161 

157.5 

33.5 

221 

216.2 

45.9 

281 

274.9 

58.4 

42 

41.1 

08.7 

102 

99.8 

21.2 

162 

158.5 

33.7 

222 

217.1 

46.2 

282 

275.8 

58.6 

43 

42.1 

08.9 

103 

100.7 

21.4 

163 

159.4 

33.9 

223 

218.1 

46.4 

283 

276.8 

58.8 

44 

43.0 

09.1 

104 

101.7 

21.6 

164 

160.4 

34.1 

224 

219.1 

46.6 

284 

277.8 

59.0 

45 

44.0 

09.4 

105 

102.7 

21.8 

165 

161.4 

34.3 

225 

220.1 

46.8 

285 

278.8 

59.3 

46 

45.0 

09.6 

106 

103.7 

22.0 

166 

162.4 

34.5 

226 

221.1 

47.0 

286 

279.8 

59.5 

47 

46.0 

09.8 

107 

104.7 

22.2 

167 

163.4 

34.7 

227 

222.0 

47.2 

287 

280.7 

59.7 

48 

47.0 

10.0 

108 

105.7 

22.5 

168 

164.3 

34.9 

228 

223.0 

47.4 

288 

281.7 

59.9 

49 

47.9 

10.2 

109 

106.6 

22.7 

169 

165.3 

35.1 

229 

224.0 

47.6 

289 

282.7 

60.1 

50 

48.9 

10.4 

110 

107.6 

22.9 

170 

166.3 

35.3 

230 

225.0 

47.8 

290 

283.7 

60.3 

51 

49.9 

10.6 

111 

108.6 

23.1 

171 

167.3 

35.6 

231 

226.0 

48.0 

291 

284.6 

60.5 

52 

50  9 

10.8 

112 

109.6 

23.3 

172 

168.2 

35.8 

232 

226.9 

48.2 

292 

285.6 

60.7 

53 

51,8 

11.0 

113 

110.5 

23.5 

173 

169.2 

36.0 

233 

227.9 

48.4 

293 

286.6  1  60.9  1 

54 

52,8 

11.2 

114 

111.5 

23.7 

174 

170.2 

36.2 

234 

228.9 

48.7 

294 

287.6 

61.1 

55 

53,8 

11.4 

115 

112.5 

23.9 

175 

171.2 

36.4 

235 

229.9 

48.9 

295 

288.6 

61.3 

56 

54.8 

11.6 

116 

113.5 

24.1 

176 

172.2 

36.6 

236 

230.8 

49.1 

296 

289.5 

61.5 

57 

55.8 

11.9 

117 

114.4 

24.3 

177 

173.1 

36.8 

237 

231.8 

49.3 

297 

290.5 '61.7 

58 

56.7 

12.1 

118 

115.4 

24.5 

17S 

174.1 

37.0 

238 

232.8 

49.5 

298 

291.5  1  62.0 

59 

57.7 

12.3 

119 

116.4 

24.7 

179 

175.1 

37.2 

239 

233.8 

49.7 

299 

292.5 '  62.2 

60 
Dist 

58.7 

12.5 

120 

117.4 

24.9 

180 

176.1 

37.4 

240 

234.8 

49.9 

300 

293.4  1  62.4 

^  Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist!  Dep  ;  Lat  1 

For  78  Degrees.                        0"  i'-J"-  1 

TABLE  11. 

29   1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  13  DEGREES.   Oh  52>n  | 

Dist 
1 

Lat. 
01.0 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 
234.8 

Dep. 
54.2 

00.2 

61 

59.4 

13.7 

121 

117.9 

27.2 

181 

176.4 

40.7 

241 

•  > 

01.9 

00.4 

62 

60.4 

13.9 

122 

118.9 

27.4 

182 

177.3 

40.9 

242 

235.8 

54.4 

02.9 

00.7 

63 

61.4 

14.2 

123 

119.8 

27.7 

183 

178.3 

41.2 

243 

236.8 

54.7 

4 

03.9 

00.9 

64 

62.4 

14.4 

124 

120.8 

27.9 

184 

179.3 

41.4 

244 

237.7 

54.9 

5 

04.9 

01.1 

65 

63.3 

14.6 

125 

121.8 

28.1 

185 

180.3 

41.6 

245 

2;;8.7  55.1 

6 

05.8 

01.3 

66 

64.3 

14.8 

126 

122.8 

28.3 

186 

181.2 

41.8 

246 

239.7  55.3 

i 

06.8 

01.6 

67 

65.3 

15.1 

127 

123.7 

^8.6 

187 

182.2 

42.1 

247 

240.7  55.6 

8 

07.S 

01.8 

68 

66.3 

15.3 

128 

124.7 

28.8 

188 

183.2 

42.3 

248 

241.6 

55.8 

9 

08.8 

02.0 

69 

67.2 

15.5 

129 

125.7 

29.0 

189 

184.2 

42.5 

249 

242.6 

56.0 

10 

09.7 

02.2 

70 

68.2 

15.7 

130 

126.7 

29.2 

190 

185.1 

42.7 

250 

243.6 

56.2 

11 

10.7 

02.5 

71 

69.2 

16.0 

131 

127.6 

29.5 

191 

186.1 

43.0 

251 

244.6 

56.5 

12 

11.7 

02.7 

72 

70.2 

16.2 

132 

128.6 

29.7 

192 

187.1 

43.2 

252 

245.5 

56.7 

13 

12.7 

02.9 

73 

71.1 

16.4 

133 

129.6 

29.9 

193 

188.1 

43.4 

253 

246.5 

56.9 

14 

13.6 

03.1 

74 

72.1 

16.6 

134 

130.6 

30.1 

194 

189.0 

43.6 

254 

247.5 

57.1 

15 

14.6 

03.4 

75 

73.1 

16.9 

135 

131.5 

30.4 

195 

190.0 

43.9 

255 

248.5 

57.4 

IG 

15.6 

03.6 

76 

74.1 

17.1 

136 

132.5 

30.6 

196 

191.0 

44.1 

256 

249.4 

57.6 

17 

16.6 

03.8 

77 

75.0 

17.3 

137 

133.5 

30.8 

197 

192.0 

44.3 

257 

250.4 

57.8 

18 

17.5 

04.0 

78 

76.0 

17.5 

138 

134.5 

31.0 

198 

192.9 

44.5 

258 

251.4 

58.0 

19 

18.5 

04.3 

79 

77.0 

17.8 

139 

135.4 

31.3 

199 

193.9 

44.8 

259 

252.4 

58.3 

20 
21 

19.5 

04.5 

80 

77.9 

18.0 

140 
141 

136.4 

31.5 

200 
201 

194.9 
195.8 

45.0 

260 

253.3 

58.5 

20.5 

04.7 

81 

78.9 

18.2 

137.4 

31.7 

45.2 

261 

254.3 

58.7 

22 

21.4 

04.9 

82 

79.9 

18.4 

142 

138.4 

31.9 

202 

196.8 

45.4 

262 

255.3 

58.9 

23 

22.4 

05.2 

83 

80.9 

18.7 

143 

139.3 

32.2 

203 

197.8 

45.7 

263 

256.3 

59.2 

24 

23.4 

05.4 

84 

81.8 

18.9 

144 

140.3 

32.4 

204 

198.8 

45.9 

264 

257.2 

59.4 

25 

24.4 

05.6 

85 

82.8 

19.1 

145 

141.3 

32.6 

205 

199.7 

46.1 

265 

258.2 

59.6' 

26 

25.3 

05.8 

86 

83.8 

19.3 

146 

142.3 

32.8 

206 

200.7 

46.3 

266 

259.2 

59.8 

27 

26.3 

06.1 

87 

84.8 

19.6 

147 

143.2 

33.1 

207 

201.7 

46.6 

267 

260.2 

60.1 

28 

27.3 

06.3 

88 

85.7 

19.8 

148 

144.2 

33.3 

208 

202.7 

46.8 

268 

261.1 

60.3 

29 

28.3 

06.5 

89 

86.7 

20.0 

149 

145.2 

33.5 

209 

203.6 

47.0 

269 

262.1  60.5 

30 

29.2 

06.7 

90 

87.7 

20.2 

150 

146.2 

33.7 

210 

204.6 

47.2 

270 

263.1 

60.7 

31 

30.2 

07.0 

91 

88.7 

20.5 

151 

147.1 

34.0 

211 

205.6 

47.5 

271 

264.1 

61.0 

32 

31.2 

07.2 

92 

89.6 

20.7 

152 

148.1 

34.2 

212 

206.6  47.7 

272 

265.0 

01.2 

33 

32.2 

07.4 

93 

90.6 

20.9 

153 

149.1 

34.4, 

213 

207.5 ,  47.9 

273 

266.0 

61.4 

34 

33.1 

07.6  94 

91.6 

21.1 

154 

150.1 

34.6 

214 

208.5 

48.1 

274 

267.0 

61.6 

35 

34.1 

07.9  95 

92.6 

21.4 

155 

151.0 

34.9 

215 

209.5 

•48.4 

275 

268.0 

61.9 

36 

35.1 

08.1   96 

93.5 

21.6 

156 

152.0 

35.1 

216 

210.5 

48.6 

276 

268.9 

62.1 

37 

36.1 

08.3  97 

94.5 

21.8 

157 

153.0 

35.3 

217 

211.4 

48.8 

277 

269.9 

62.3 

38 

37.0 

08.5  98 

95.5 

22.0 

158 

154.0 

35.5 

218 

212.4 

49.0 

278 

270.9 

62.5 

39 

38.0 

08.8 

99 

96.5 

22.3 

159 

154.9 

35.8 

219 

213.4 

49.3 

279 

271.8 

62.8 

40 
41 

39.0 

09.0 

100 

97.4 

22.5 

160 

155.9 

36.0 

220 

214.4 

49.5 

280 

272.8 

63.0 
63.2 

39.9 

09.2 

101 

98.4 

22.7 

161 

156.9 

36.2 

221 

215.3 

49.7 

281 

273.8 

42 

40.9 

09.4 

102 

99.4 

22.9 

162 

157.8 

36.4 

222 

216.3 

49.9 

282 

274.8 

63.4 

43 

41.9 

09.7 

103 

100.4 

23.2 

163 

158.8 

36.7 

223 

217.3 

50.2 

283 

275.7 

63.7 

44 

42.9 

09.9 

104 

101.3 

23.4 

164 

159.8 

36.9 

224 

218.3 

50.4 

284 

276.7 

63.9 

45 

43.8 

10.1 

105 

102.3 

23.6 

165 

160.8 

37.1 

225 

219.2 

50.6 

285 

277.7 

64.1 

46 

44.8 

10.3 

106 

103.3 

23.8 

166 

161.7 

37.3 

226 

220.2 

50.8 

286 

278.7 

64.3 

47 

45.8 

10.6 

107 

104.3 

24.1 

167 

162.7 

37.6 

227 

221.2 

51.1 

287 

279.6 

64.6 

48 

46.8 

10.8 

108 

105.2 

24.3 

168 

163.7 

37.8 

228 

222.2 

51.3 

288 

280.6 

64.8 

49 

47.7 

11.0 

109 

106.2 

24.5 

169 

164.7 

38.0 

229 

223.1 

51.5 

289 

281.6 

65.0 

50 
51 

48.7 

11.2 

110 

107.2 

24.7 

170 

165.6 

38.2 

230 

224.1 

51.7 

290 

282.6 

65.2 

49.7 

11.5 

111 

108.2 

25.0 

171 

166.6 

38.5 

231 

225.1 

52.0 

291 

283.5 

65.5 

52 

50.7 

11.7 

112 

109.1 

25.2 

172 

167.6 

38.7 

232 

226.1 

52.2 

292 

284.5  65.7 

53 

51.6 

11.9 

113 

110.1 

25.4 

173 

168.6 

38.9 

233 

227.0 

52.4 

293 

285.5  65.91 

54 

52.6 

12.1 

114 

111.1 

25.6 

174 

169.5 

39.1 

234 

228.0 

52.6 

294 

286.5  66.1  1 

55 

53.6 

12.4 

115 

112.1 

25.9 

175 

170.5 

39.4 

235 

229.0 

52.9 

295 

287.4 

66.4 

56 

54.6 

12.6 

116 

113.0 

26.1 

176 

171.5 

39.6 

236 

230.0 

53.1 

296 

288.4 

66.6 

57 

55.5 

12.8 

117 

114.0 

26.3 

177 

172.5 

39.8 

237 

230.9 

53.3 

297 

289.4 

66.8 

58 

56.5 

13.0 

118 

115.0 

26.5 

178 

173.4 

40.0 

238 

231.9 

53.5 

298 

290.4 

67.0 

59 

57.5 

13.3 

119 

ii<;.o 

26.8 

179 

174.4 

40.3 

239 

232.9 

53.8 

299 

291.3 

67.3 

60 

58.5 

13.5 

120 

116.9 

27.0 

Lat. 

180 

175.4 

40.5 

240 

233.8 

54.0 

300 

292.3 

67.5 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

I 

"or  77  Decrees. 

5h  8n>.  1 

30                   TABLE  II. 

DIFFERENCE  OF  LATITUDE  AND  DFt^ARTURE  FOR  14  DEGREES.  0^  SBm. 

Diff. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

DistI 

Lat  1 

Dep. 

1 

01.0 

00.2 

61 

59.2 

14.8 

121 

117.4 

29.3 

181 

175.6 

43.8 

241 

233.8 

58.3 

2 

01.9 

00.5 

62 

60.2 

15.0 

122 

118.4 

29.5 

182 

176.6 

44.0 

242 

234.8 

58.5 

3 

02.9 

00.7 

63 

61.1 

15.2 

123 

119.3 

29.8 

183 

177.6 

44.3 

243 

235.8  •  58.8 1 

4 

03.9 

01.0 

64 

62.1 

15.5 

124 

120.3  30.0 

184  178.5 

44.5 

244 

236.8 

59.0 

5 

04.9 

01.2 

65 

63.1 

15.7 

125 

121.3  30.2 

185  179.5 

44.8 

245 

237.7 

59.3 

6 

05.8 

01.5 

66 

64.0 

16.0 

126 

122.3  30.5 

186  180.5 

45.0 

246 

238.7 

59.5 

7 

06.8 

01.7 

67 

65.0 

16.2 

127 

123.2  30.7 

187 

181.4 

45.2 

247 

239.7 

59.8 

8 

07.8 

01.9 

68 

66.0 

16.5 

128 

124.2  31.0 

188 

182.4 

45.5 

248 

240.6 

60.0 

9 

08.7 

02.2 

69 

67.0 

16.7 

129 

125.2 

31.2 

189 

183.4  45.7 

249 

241.6 

60.2 

10 
11 

09.7 

02.4 

70 

67.9 

16.9 

130 

126.1 

31.4 

190 

184.4'  46.0 

250 

242.6 

60.5 

10.7 

02.7 

71 

68.9 

17.2 

131 

127.1 

31.7 

191 

185.3 

46.2 

251 

243.5 

60.7 

12 

11.6 

02.9 

72 

69.9 

17.4 

132 

128.1 

31.9 

192 

186.3 

46.4 

252 

244.5 

61.0 

13 

12.6 

03.1 

73 

70.8 

17.7 

1:^3 

129.0 

32.2 

193 

187.3 

46.7 

253 

245.5 

61.2 

14 

13.6 

03.4 

74 

71.8 

17.9 

134 

130.0 

32.4 

194 

188.2 

46.9 

254 

246.5 

61.4 

15 

14.6 

03.6 

75 

72.8 

18.1 

135 

131.0 

32.7 

195 

189.2 

47.2 

255 

247.4 

61.7 

16 

15.5 

03.9 

76 

73.7 

18.4 

136 

132.0 

32.9 

196 

190.2 

47.4 

256 

248.4 

61.9 

17 

16.5 

04.1   77 

74.7 

18.6 

137 

132.9 

33.1 

197 

191.1 

47.7 

257 

249.4 

62.2 

18 

17.5 

04.4  78 

75.7 

18.9 

138 

133.9 

33.4 

198 

192.1 

47.9 

258 

250.3 

H2.4 

19 

18.4 

04.6  79 

76.7 

19.1 

139 

134.9 

33.6 

199 

193.1 

48.1 

259 

251.3 

«>2.7 

20 

19.4 

04.8 

80 

77.6 

19.4 

140 

135.8 

33.9 

200 

194.1 

48.4 

260 

252.3 

♦•,2.9 
63.1 

21 

20.4 

05.1 

81 

78.6 

19.6 

141 

136.8 

34.1 

201 

195.0 

48.6 

261 

253.2 

22 

21.3 

05.3 

82 

79.6 

19.8 

142 

137.8 

34.4 

202 

196.0 

48.9 

262 

254.2 

63.4 

23 

22.3 

05.6 

83 

80.5 

20.1 

143 

138.8 

34.6 

203 

197.0 

49.1 

263 

255.2 

63.6 

24 

23.3 

05.8 

84 

81.5 

20.3 

144 

139.7 

34.8 

204 

197.9 

49.4 

264 

256.2 

63.9 

25 

24.3 

06.0 

85 

82.5 

20.6 

145 

140.7 

35.1 

205 

198.9 

49.6 

265 

257.1  !»4. 11 

26 

25.2 

06.3 

86 

83.4 

20.8 

146 

141.7 

35.3 

206 

199.9 

49.8 

266 

258.1  1  64.4 1 

27 

26.2 

06.5 

87 

84.4 

21.0 

147 

142.6  35.6 

207 

200.9 

50.1 

267 

259.1 

64.6 

28 

27.2 

06.8 

88 

85.4 

21.3 

148 

143.6 

35.8 

208 

201.8 

50.3 

268 

260.0 

64.8 

29 

28.1 

07.0 

89 

86.4 

21.5 

149 

144.6 

36.0 

209 

202.8 

50.6 

269 

261.0 

o5.] 

30 

29.1 

07.3 

90 

87.3 

21.8 

150 

145.5 

36.3 

210 

203.8 

50.8 

270 

262.0 

v,5.8 
65.6 

31 

30.1 

07.5 

91 

88.3 

22.0 

151 

146.5 

36.5 

211 

204.7 

51.0 

271;  263.0 

32 

31.0 

07.7 

92 

89.3 

22.3 

152 

147.5 

36.8 

212 

205.7 

51.3 

272  ;  263.9  ■  ^5.8  \ 

33 

32.0 

08.0 

93 

90.2 

22.5 

153 

148.5 

37.0 

213 

206.7 

51.5 

273  ;  264.9 

66.0 

34 

33.0 

08.2 

94 

91.2 

22.7 

154 

149.4 

37.3 

214 

207.6:  51.8 

274 

265.9 

66.3 

35 

34.0 

08.5 

95 

9*2.2 

23.0 

155 

150.4 

37.5 

215 

208.6 

52.0 

275 

266.8 

66.5 

36 

34.9 

08.7 

96 

93.1 

23.2 

156 

151.4 

37.7 

216 

209.6 

52.3 

276 

267.8 

66.8 

37 

35.9 

09.0 

97 

94.1 

23.5 

157 

152.3 

38.0 

217 

210.6 

52.5 

277 

268.8 

67.0 

38 

36.9 

09.2 

98 

95.1 

23.7 

158 

153.3 

38.2 

218 

211.5 

52.7 

278 

269.7 

67.3 

39 

37.8 

09.4 

99 

96.1 

24.0 

159 

154.3 

38.5 

219 

212.5 

53.0 

279 

270.7 

67.5 

40 
41 

38.8 

09.7 

100 

97.0 

24.2 

160 

155.2 

38.7 

220 

213.5 

53.2 

280 

271.7 

67.7 

39.8 

09.9 

101 

98.0 

24.4 

161 

156.2 

38.9 

221 

214.4 

53.5 

281 

272.7 

68.0 

42 

40.8 

10.2 

102 

99.0 

24.7 

162 

157.2 

39.2 

222 

215.4 

53.7 

282 

273.6 

68.2 

43 

41.7 

10.4 

103 

99.9 

24.9 

163 

158.2 

39.4 

223 

216.4 

53.9 

283 

274.6 

68.5 

44 

42.7 

10.6 

104 

100.9 

25.2 

164 

159.1 

39.7 

224 

217.3 

54.2 

284 

275.6 

68.7 

45 

43.7 

10.9 

105 

101.9 

25.4 

165 

160.1 

39.9 

225 

218.3 

54.4 

285 

276.5  ;  68.9 

46 

44.6 

11.1 

106 

102.9 

25.6 

166 

161.1 

40.2 

226 

219.3 

,  5i.7 

286 

277.5  1  69.2 

47 

45.6  11.4 

107 

103.8 

25.9 

167 

162.0 

40.4 

227 

220.3 

54.9 

287 

278.5  '  69.4 

48 

46.6  11.6 

108 

104.8 

26.1 

168 

163.0 

40.6 

228 

221.2 

55.2 

288 

279.4 '  69.7 

49 

47.5 

11.9 

109 

105.8 

26.4 

169 

164.0 

40.9 

229 

222.2 

55.4 

289  1  280.4 

69.9 

50 

48.5 

12.1 

110 

106.7 

26.6 

170 

165.0 

41.1 

230 

223.2 

55.6 

290  1281.4 

70.2 

51 

49.5 

12.3 

111 

107.7 

26.9 

171 

165.9 

41.4 

231 

224.1 

55.9 

291  '282.4 

70.4 

52 

50.5 

12.6 

112 

108.7 

27.1 

172 

166.9 

41.6 

232 

225.1 

56.1 

292  '  283.3 

70.6 

53 

51.4 

12.8 

113 

109.6 

27.3 

173 

167.9 

41.9 

233 

226.1 

56.4 

293  284.3 

70.9 

54 

52.4 

13.1 

114 

110.6 

27.6 

174 

168.8 

42.1 

234 

227.01  56.6 

294  285.3 

71.1 

55 

53.4 

13.3 

115 

111.6 

27.8 

175 

169.8 

42.3 

235 

228.01  56.9 

295 

1  286.2 

71.4 

56 

54.3 

13.5 

116 

112.6 

28.1 

176 

170.8 

42.6 

236 

229.0  57.1 

296 

1 287.2 

71.6 

57 

55.3 

13.8 

117 

113.5 

28.3 

177 

171.7 

42.8 

237 

230.0  57.3 

297  :  288.2 

71.9 

58 

56.3 

14.0 

118 

114.5 

28.5 

178 

172.7 

43.1 

238 

230.9  57.6 

298  1289.1 

72.1 

59 

57.2 

14.3 

119 

115.5 

28.8 

179 

173.7 

43.3 

239 

231.9 

57.8 

299  290.1 

72.3 

60 
uist 

58.2 

14.5 

120 

116.4 

29.0 

180 

174.7 

43.5 

240 

232.9 

58.1 

300 

291.1 

72.6 

.  Den. 

I,at. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

For  7(i  Dei^rees.                          5h  4'".     | 

TABLE  11.                       31  1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  15  DEGREES.    Ih  Qm.  1 

Dist 
1 

Lat 
01.0 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat.    Dep.  | 

Dist 

Lat 
232.8 

Dep. 
62.4 

00.3 

61 

58.9 

15.8 

121 

116.9 

31.3 

181 

174.8 

46.8 

241 

2 

01.9 

00.5 

62 

59.9 

16.0 

122 

117.8 

31.6 

182 

175.8 

47.1 

242 

233.8 

62.6 

3 

02.9 

00.8 

63 

60.9 

16.3 

123 

118.8 

31.8 

183 

176.8 

47.4 

243 

234.7 

62.9 

4 

03.9 

01.0 

64 

61.8 

16.6 

124 

119.8 

32.1 

184 

177.7 

47.6 

244 

235.7 

63.2 

5 

04.8 

01.3 

65 

62.8 

16.8 

125 

120.7 

32.4 

185 

178.7 

47.9 

245 

236.7 

63.4 

6 

05.8 

01.6 

66 

63.8 

17.1 

126 

121.7 

32.6 

186 

179.7 

48.1 

246 

237.6  63.71 

7 

06.8 

01.8 

67 

64.7 

17.3 

127 

122.7 

32.9 

187 

180.6 

48.4 

247 

238.6  63.91 

8 

07.7 

02.1 

68 

65.7 

17.6 

128 

123.6 

3S.1 

188 

181.6 

48.7 

248 

239.5 

64.2 

9 

08.7 

02.3 

69 

66.6 

17.9 

129 

124.6 

33.4 

189 

182.6 

48.9 

249 

240.5 

64.4 

10 

09.7 

02.6 

70 

67.6 

18.1 

130 
131 

125.6 

33.6 

190 

183.5 

49.2 

250 

241.5 

64.7 

11 

10.6 

02.8 

71 

68.6 

18.4 

126.5 

33.9 

191 

184.5 

49.4 

251 

242.4 

65.0 

12 

11.6 

03.1 

72 

69.5 

18.6 

132 

127.5 

34.2 

192 

185.5 

49.7 

252 

243.4 

65.2 

13 

12.6 

03.4 

73 

70.5 

18.9 

133 

128.5 

34.4 

193 

186.4 

50.0 

253 

244.4 

65.5 

14 

13.5 

03.6 

74 

71.5 

19.2 

134 

129.4 

34.7 

194 

187.4 

50.2 

254 

245.3 

65.7 

15 

14.5 

03.9 

75 

72.4 

19.4 

135 

130.4 

34.9 

195 

188.4 

50.5 

255 

246.3 

66.0 

16 

15.5 

04.1 

76 

73.4 

19.7 

136 

131.4 

35.2 

196 

189.3 

50.7 

256 

247.3 

66.3 

17 

16.4 

04.4 

77 

74.4 

19.9 

137 

132.3 

35.5 

197 

190.3 

51.0 

257 

248.2 

66.5 

18 

17.4 

04.7 

78 

75.3 

20.2 

138 

133.3 

35.7 

198 

191.3 

51.2 

258 

249.2 

66.8 

19 

18.4 

04.9 

79 

76.3 

20.4 

139 

134.3 

36.0 

199 

192.2 

51.5 

259 

250.2 

67.0 

20 
21 

19.3 
20.3 

05.2 

80 

77.3 

20.7 

140 

135.2 
136.2 

36.2 

200 
201 

193.2 

51.8 

260 

251.1 

67.3 

05.4 

81 

78.2 

21.0 

141 

36.5 

194.2 

52.0 

261 

252.1 

67.6 

22 

21.3 

05.7 

82 

79.2 

21.2 

142 

137.2 

36.8 

202 

195.1 

52.3 

262 

253.1 

67.8 

23 

22.2 

06.0 

83 

80.2 

21.5 

143 

138.1 

37.0 

203 

196.1 

52.5 

263 

254.0 

68.1 

24 

23.2 

06.2 

84 

81.1 

21.7 

144 

139.1 

37.3 

204 

197.0 

52.8 

264 

255.0 

68.3 

25 

24.1 

06.5 

85 

82.1 

22.0 

145 

140.1 

37.5 

205 

198.0 

53.1 

265 

256.0 

68.6 

26 

25.1 

06.7 

86 

83.1 

22.3 

146 

141.0 

37.8 

206 

199.0 

53.3 

266 

256.9 

68.8 

27 

26.1 

07.0 

87 

84.0 

22.5 

147 

142.0 

38.0 

207 

199.9 

53.6 

267 

257.9 

69.1 

28 

27.0 

07.2 

88 

85.0 

22.8 

148 

143.0 

38.3 

208 

200.9 

53.8 

268 

258.9 

69.4 

29 

28.0 

07.5 

89 

86.0 

23.0 

149 

143.9 

38.6 

209 

201.9 

54.1 

269 

259.8 

69.6 

30 

29.0 

07.8 

90 

86.9 

23.3 

150 

144.9 

38.8 

210 
211 

202.8 

54.4 

270 

260.8 

69.9 

31  29.9 

(>80 

91 

87.9 

23.6 

151 

145.9 

39.1 

203.8 

54.6 

271 

261.8 

70.1 

32  30.9 

08.3 

92 

88.9 

23.8 

152 

146.8 

39.3 

212 

204.8 

54.9 

272 

262.7 

70.4 

33 

31.9 

08.5 

93 

89.8 

24.1 

153 

147.8 

39.6 

213 

205.7 

55.1 

273 

263.7 

70.7 

34 

32.8 

08.8 

94 

90.8 

24.3 

154 

148.8 

39.9 

214 

206.7 

55.4 

274 1 

264.7 

70.9 

35 

33.8 

09.1 

95 

91.8 

24.6 

155 

149.7 

40.1 

215 

207.7 

55.6 

275 

265.6 

71.2 

36 

34.8 

09.3 

96 

92.7 

24.8 

156 

150.7 

40.4 

216 

208.6 

55.9 

276 

266.6 

71.4 

37 

35.7 

09.6 

97 

93.7 

25.1 

157 

151.7 

40.6 

217 

209.6 

56.2 

277 

267.6 

71.7 

38 

36.7 

09.8 

98 

94.7 

25.4 

158 

152.6 

40.9 

218 

210.6 

56.4 

278 

268.5 

72.0 

39 

37.7 

10.1 

99 

95.6 

25.6 

159 

153.6 

41.2 

219 

211.5 

56.7 

279 

269.5 

72.2 

40 

38.6 

10.4 

100 

96.6 

25.9 

160 

154.5 

41.4 

220 

212.5 

56.9 

280 

270.5 

72.5 

72.7 

41 

39.6 

10.6 

101 

97.6 

26.1 

161 

155.5 

41.7 

221 

213.5  57.2 

281 

271.4 

42 

40.6 

10.9 

102 

98.5 

26.4 

162 

156.5 

41.9 

222 

214.4 

57.5 

282 

272.4 

73.0 

43 

41.5 

11.1 

103 

99.5 

26.7 

163 

157.4 

42.2 

223 

215.4 

57.7 

283 

273.4 

73.2 

44 

42.5 

11.4 

104 

100.5 

26.9 

164 

158.4 

42.4 

224 

216.4 

58.0 

284 

274.3 

73.5 

45 

43.5 

11.6 

105 

101.4 

27.2 

165 

159.4 

42.7 

225 

217.3 

58.2 

285 

275.3 

73.8 

46 

444 

11.9 

106 

102.4 

27.4 

166 

160.3 

43.0 

226 

218.3 

58.5 

286 

276.3 

74.0 

47 

45.4 

12.2 

107 

103.4 

27.7 

167 

161.3 

43.2 

227 

219.3 

58.8 

287 

277.2 

74.3 

48 

46.4 

12.4 

108 

104.3 

28.0 

168 

162.3 

43.5 

228 

220.2 

59.0 

288 

278.2 

74.5 

49 

47.3 

12.7 

109 

105.3 

28.2 

169 

163.2 

43.7 

229 

221.2 

59.3 

289 

279.2 

74.8 

50 

48.3 

12.9 

110 

106.3 

28.5 

170 

164.2 

44.0 

230 

222.2 

59.5 

290 

280.1 

75.1 

51  i  49.3 

13.2 

111 

107.2 

28.7 

171 

165.2 

44.3 

231 

223.1 

59.8 

291 

281.1 

75.3 

52  50.2 

13.5 

112 

108.2 

29.0 

172 

166.1 

44.5 

232 

224.1 

60.0 

292 

282.1 

75.6 

53  51.2 

13.7 

113 

109.1 

29.2 

173 

167.1 

44.8 

233 

225.1 

60.3 

293 

283.0 

75.8 

54  52.2 

14.0 

114 

110.1 

29.5 

174 

168.1 

45.0 

234 

226.0 

60.6 

294 

284.0 

76.1 

55  53.1 

14.2 

115 

111.1 

29.8 

175 

169.0 

45.3 

235 

227.0 

60.8 

295 

284.9 

76.4 

56  54.1 

14.5 

116 

112.0 

30.0 

176 

170.0 

45.6 

236 

228.0 

61.1 

296 

285.9 

76.6 

57  1  55.1 

14.8 

117 

113.0 

30.3 

177 

171.0 

45.8 

237 

228.9 

61.3 

297  286.9 

76.9 

58 

56.0 

15.0 

118 

114.0 

30.5 

178 

171.9 

46.1 

238 

229.9 

61.6 

298 ,  287.8 

77.1 

59 

57.0 

15.3 

119 

114.9 

30.8 

179 

172.9 

46.3 

239 

230.9 

61.9 

299 

288.8  77.4 

60 

58.0 

15.5 

120 

115.9 

31.1 

Lat. 

180 
Dist 

173.9 

46.6 

240 

231.8 

62.1 

300 

289.8 

77.6 

Dist 

.  Dep. 

Lat. 

Dist. 

Dep. 

Dep. 

Lat 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

For  75  Des-'-ees.                            5*^  Om.  | 

32 

TABLE  II. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  16  DEGREES.   l^  4ni.  1 

Dist 

Lat 

Dep. 

Dibt 

Lat. 

Dep. 

Dl8t 

Lat. 

Dep. 
33.4 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

1 

01.0 

00.3 

61 

58.6 

16.8 

121 

116.3 

181 

174.0 

49.9 

241 

231.7 

66.4 

2 

01.9 

00.6 

62 

59.6 

17.1 

122 

117.3 

33.6 

182 

174.9 

50.2 

242 

232.6 

66.7 

3 

02.9 

00.8 

63 

60.6 

17.4 

123 

118.2 

33.9 

183 

175.9 

50.4 

243 

233.6 

67.0 

4 

03.8 

01.1 

64 

61.5 

17.6 

124 

119.2 

34.2 

184 

176.9 

50.7 

244 

234.5 

67.3 

5 

04.8 

01.4 

65 

62.5 

17.9 

125 

120.2 

34.5 

185 

177.8 

51.0 

245 

235.5 

((7.5 

6 

05.8 

01.7 

66 

63.4 

18.2 

126 

121.1 

34.7 

186 

178.8 

51.3 

246,236  5 

67.8 

7 

06.7 

01.9 

67 

64.4 

18.5 

127 

122.1 

35.0 

187 

179.8 

51.5 

247  237.4 

68.1 

8 

07.7 

02.2  68 

65.4 

18.7 

128 

123.0 

35.3 

188 

l.sO.7 

51.8 

248 

238.4 

68.4 

9 

08.7 

02.5 

69 

66.3 

19.0 

129 

124.0 

35.6 

189 

181.7 

52.1 

249 

239.4 

68.6 

10 
11 

09.6 

02.8 

70 

67.3 

19.3 

130 

125.0 

35.8 

190 

182.6 

52.4 

250 

240.3 

68.9 

10.6 

03.0 

71 

68.2 

19.6 

131 

125.9 

36.1 

191 

183.6 

52.6 

251 

241.3 

69.2 

12 

11.5 

03.3 

72 

69.2 

19.8 

132 

126.9 

36.4 

192 

184.6 

52.9 

252 

242.2 

69.5 

13 

12.5 

03.6 

73 

70.2 

20.1 

133 

127.8 

36.7 

193 

185.5 

53.2 

253 

243.2 

69.7 

14 

13.5 

03.9 

74 

71.1 

20.4 

134 

128.8 

36.9 

194 

186.5 

53.5 

254 

244.2 

70.0 

15 

14.4 

04.1 

75 

72.1 

20.7 

135 

129.8 

37.2 

195 

187.4 

53.7 

255 

245.1 

70.3 

16 

15.4 

04.4 

76 

73.1 

20.9 

136 

130.7 

37.5 

196,188.4 

54.0 

256 

246.1 

70.6 

17 

16.3 

04.7 

77 

74.0 

21.2 

137 

131.7 

37.8 

197 

189.4 

54.3 

257 

247.0 

70.8 

18 

17.3 

05.0 

78 

75.0 

21.5 

138 

132.7 

38.0 

198 

190.3 

54.6 

258 

248.0 

71.1 

19 

18.3 

05.2 

79 

75.9 

21.8 

139 

133.6 

38.3 

199 

191.3 

54.9 

259 

249.0 

71.4 

20 

19.2 

05.5 

80 

76.9 

22.1 

140 

134.6 

38.6 

200 

192.3 

55.1 

260 

249.9 

71.7 

21 

20.2 

05.8 

81 

77.9 

22.3 

141 

13.5.5 

38.9 

201 

193.2 

55.4 

261 

250.9 

71.9 

22 

21.1 

06.1 

82 

78.8 

22.6 

142 

136.5 

39.1 

202 

194.2 

55.7 

262 

251.9 

72.2 

23 

22.1 

06.3 

83 

79.8 

22.9 

143 

137.5 

39.4 

203 

195.1 

56.0 

263 

252.8 

72.5 

24 

23.1 

06.6 

84 

80.7 

23.2 

144 

138.4 

39.7 

204 

196.1 

56.2 

264 

253.8 

72.8 

25 

24.0 

06.9 

85 

81.7 

23.4 

145 

139.4 

40.0 

205 

197.1 

56.5 

265 

254.7 

73.0 

26 

25.0 

07.2 

86 

82.7 

23.7 

146 

140.3 

40.2 

206 

198.0 

56.8 

266 

255.7 

73.3 

27 

26.0 

07.4 

87 

83.6 

24.0 

147 

141.3.  40.5 

207 

199.0 

57.1 

267 

256.7 

73.6 

28 

26.9 

07.7 

.  88 

84.6 

24.3 

148 

142.3  i  40.8 

208 

199.9 

57.3 

268 

257.6  '  73.9 

29 

27.9 

08.0 

89 

85.6 

24.5 

149 

143.2 

41.1 

209 

200.9 

57.6 

269 

258.6 

74.1 

30 

28.8 

08.3 

90 

86.5 

24.8 

150 

144.2 

41.3 

210 

201.9 

57.9 

270 

259.5 

74.4 

31 

29.8 

08.5 

91 

87.5 

25.1 

151 

145.2 

41.6 

211 

202.8 

58.2 

271 

260.5 

74.7 

;^2 

30.8 

08.8 

92 

88.4 

25.4 

152 

146.1 

41.9 

212 

203.8 

58.4 

272 

261.5 

75.0 

33 

31.7 

09.1 

93 

89.4 

25.6 

153 

147.1 

42.2 

213 

204.7 

58.7 

273 

262.4 

75.2 

34 

32.7 

09'.4 

94 

90.4 

25.9 

154 

148.0 

42.4 

214 

205.7 

59.0 

274 

263.4 

75.5 

35 

33.6 

09.6 

95 

91.3 

26.2 

155 

149.0 

42.7 

215 

206.7 

59.3  ^275 

264.3 

75.8 

36 

34.6 

09.9 

96 

92.3 

26.5 

156 

150.0 

43.0 

216 

207.6 

59.5  276 

265.3 

76.1 

37 

35.6 

10.2 

97 

93.2 

26.7 

157 

150.9 

43.3 

217 

208.6 

59.8  277 

266.3 

76.4 

38 

36.5 

10.5 

98 

94.2 

27.0 

158 

151.9'  43.6 

218 

209.6 

60.1  ,278 

267.2 

76.6 

39 

37.5 

10.7 

99 

95.2 

27.3 

159 

152.8 

43.8 

219 

210.5 

60.4 

279 

268.2 

76.9 

40 

38.5 

11.0 

100 

96.1 

27.6 

160 

153.8 

44.1 

220 

211.5 

60.6 

280 

269.2 

77.2 

41 

39.4 

11.3 

101 

97.1 

27.8 

161 

154.8 

44.4 

221 

212.4 

60.9 

281 

270.1 

77.5 

42 

40.4 

11.6 

102 

98.0 

28.1 

162 

15.5.7 

44.7 

222 

213.4 

61.2 

282 

271.1  '  77.7 

43 

41.3 

1].9 

103 

99.0 

28.4 

163 

156.7 

44.9 

223 

214.4 

61.5 

283 

272.0  78.0 

44 

42.3 

12.1 

104 

100.0 

28.7 

164 

157.6 

45.2 

224 

215.3 

61.7 

284 

273.0  78.3 

45 

43.3 

12.4 

105 

100.9 

28.9 

165 

158.6 

45.5 

225 

216.3 

62.0 

285 

274.0 

78.6 

46 

44.2 

12.7 

106 

101.9 

29.2 

166 

159.6 

45.8 

226 

217.2 

62.3 

286 

274.9 

78.8 

47 

45.2 

13.0 

107 

102.9 

29.5 

167 

160.5 

46.0 

227 

218.2 

62.6 

287 

275.9 

79.1 

48 

46.1 

13.2 

108 

103.8 

29.8 

1(58 

161.5 

46.3 

228 

219.2 

62.8 

288 

276.8 

r9.4 

49 

47.1 

13.5 

109 

104.8 

30.0 

169 

162.5 

46.6 

229 

220.1 

63.1 

289 

277.8 

^9.7 

50 

48.1 

13.8 

110 

105.7 

30.3 

170 

163.4 

46.9 

230 

221.1 

63.4 

290 

278.ts 

/9.9 

60.2 

j 

51 

49.0 

14.1 

11  1 

106.7 

30.6 

171 

164.4 

47.1 

231 

222.1 

63.7 

291 

279.7 

52 

50.0 

14.3 

112 

107.7 

30.9 

172 

165  3 

47.4 

232 

223.0 

63.9 

292 

280.7 

-80.5 

53 

50.9 

14.6 

113 

108.6 

31.1 

173 

166.3 

47.7 

233 

224.0 

64.2 

293 

281.6 

80.8 

54 

51.9 

14.9 

114 

109.6 

31.4 

174 

167.3 

48.0 

234 

224.9 

64.5 

294 

282.6 

8..0 

55 

52.9 

15.2 

115 

110.5 

31.7 

175 

168.2 

48.2 

235 

225.9 

64.8 

295 

283.6 

81.3 

5(5 

53.8 

15.4 

IK) 

111.5 

32.0 

176 

169.2 

48.5 

236 

226.9 

65.1 

296 

284.5 

81.6 

57 

54.8 

15.7 

117 

112.5 

32.2 

177 

170.1 

48.8 

237 

227.8 

65.3 

297 

285.5 

81.9 

58 

55  8 

16.0 

118 

113.4 

32.5 

17S 

171.1 

49.1 

238 

228.8 

65.6 

298 

286.5 

82.1 

59 

56.7 

16  3 

119 

114.4 

32.8 

179 

172.1 

49.3 

239 

229.7 

65.9 

299 

287.  t 

82.4 

60 

Dist. 

57.7 

16.5 

Lnt 

120 

115.4 

33.1 

180 

173.0 

49.6 

240 

230.7 

66.2 

300 

288.4 

82.7 

Den. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lnt. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

] 

■for  74  Deii:roe.s. 

4  56™.  1 

TABLE  11.                       3S  1 

DIFFERENCE  OF  LATITUDE  AND 

DEPARTURE  FOR  17  DEGREES.    Ih8n>.  1 

Diet 

1 

Lat. 
01.0 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

Dist 
241 

Lat  j 

Dep. 

00.3 

61 

58.3 

17.8 

121 

115.7 

35.4 

181 

173.1 

52.9 

230.5 

70.5 

2 

01.9 

00.6 

62 

59.3 

18.1 

122 

116.7 

35.7 

182 

174.0 

53.2 

242 

231.4  70.8 

3 

02.9 

00.9 

63 

60.2 

18.4 

123 

117.6 

36.0 

183 

175.0 

53.5 

243 

232.4  71.0 

4 

03.8 

01.2 

64 

61.2 

18.7 

124 

118.6 

36.3 

184 

176.0 

53.8 

244 

233.3  71.3 

5 

04.8 

01.5 

65 

62.2 

19.0 

125 

119.5 

36.5 

185 

176.9 

54.1 

245 

234.3  71.6 

6 

05.7 

01.8 

6Q 

63.1 

19.3 

126 

120.5 

36.8 

186 

177.9 

54.4 

246 

235.3  71.9 

7 

06.7 

02.0 

67 

64.1 

19.6 

127 

121.5 

37.1 

187 

178.8 

54.7 

247 

236.2  72.2 

8 

07.7 

02.3 

68 

65.0 

19.9 

128 

122.4 

37.4 

188 

179.8 

55.0 

248 

237.2  72.5 

9 

08.6 

02.6 

69 

66.0 

20.2 

129 

123.4 

37.7 

189 

180.7 

55.3 

249 

238.1 

72.8 

10 

09.6 

02.9 

70 

66.9 

20.5 

130 

124.3 

38.0 

190 

181.7 

55.6 

250 

239.1 

73.] 

11 

10.5 

03.2 

71 

67.9 

20.8 

131 

125.3 

38.3 

191 

182.7 

55.8 

251 

240.0 

73.4 

12 

11.5 

03.5 

72 

68.9 

21.1 

132 

126.2 

38.6 

192 

183.6 

56.1 

252 

241.0 

73.7 

13 

12.4 

03.8 

73 

69.8 

21.3 

133 

127.2 

38.9 

193 

184.6 

56.4 

253 

241.9 

74.0 

14 

13.4 

04.1 

74 

70.8 

21.6 

134 

128.1 

39.2 

194 

185.5 

56.7 

254 

242.9 

74.3 

15 

14.3 

04.4 

75 

71.7 

21.9 

135 

129.1 

39.5 

195 

186.5 

57.0 

255 

243.9 

74.6 

U) 

15.3 

04.7 

76 

72.7 

22.2 

136 

130.1 

39.8 

196 

187.4 

57.3 

256 

244.8 

74.8 

17 

16.3 

05.0 

77 

73.6 

22.5 

137 

131.0 

40.1 

197 

188.4 

57.6 

257 

245.8 

75.1 

18 

17.2 

05.3 

78 

74.6 

22.8 

138 

132.0 

40.3 

198 

189.3 

57.9 

258 

246.7 

75.4 

19 

18.2 

05.6 

79 

75.5 

23.1 

139 

132.9 

40.6 

199 

190.3 

58.2 

259 

247.7 

75.7 

20 

19.1 

05.8 

80 

76.5 

23.4 

140 

133.9 

40.9 

200 

191.3 

58.5 

260 

248.6 

76.0 

21 

20.1 

06.1 

81 

77.5 

23.7 

141 

134.8 

41.2 

201 

192.2 

58.8 

261 

249.6 

76.3 

22 

21.0 

06.4 

82 

78.4 

24  0 

142 

135.8 

41.5 

202 

193.2 

59.1 

262 

250.6 

76.6 

23 

22.0 

06.7 

83 

79.4 

24.3 

143 

136.8 

41.8 

203 

194.1 

59.4 

263 

251.5 

76.9 

24 

23.0 

07.0 

84 

80.3 

24.6 

144 

137.7 

42.1 

204 

195.1 

59.6 

264 

252.5 

77.2 

25 

23.9 

07.3 

85 

81.3 

24.9 

145 

138.7 

42.4 

205 

196.0 

59.9 

265 

253.4 

77.5 

26 

24.9 

07.6 

86 

82.2 

25.1 

146 

139.6 

42.7 

206 

197.0 

60.2 

266 

254.4 

77.8« 

27 

25.8 

07.9 

87 

83.2 

25.4 

147 

140.6 

43.0 

207 

198.0 

60.5 

267 

255.3 

78.1 

28 

26.8 

08.2 

88 

84.2 

25.7 

148 

141.5 

43.3 

208 

198.9 

60.8 

268 

256.3 

78.4 

29 

27.7 

08.5 

89 

85.1 

26.0 

149 

142.5 

43.6 

209 

199.9 

61.1 

269 

257.2 

78.6 

30 

28.7 

08.8 

90 

86.1 

26.3 

150 

143.4 

43.9 

210 

200.8 

61.4 

270 

258.2 

78.9 

31 

29.6 

09.1 

91 

87.0 

26.6 

151 

144.4 

44.1 

211 

201.8 

61.7 

271 

-.259.2 

79.2 

32 

30.6 

09.4 

92 

88.0 

26.9 

152 

145.4 

44.4 

212 

202.7 

62.0 

272 

260.1 

79.5 

33 

31.6 

09.6 

93 

88.9 

27.2 

153 

146.3 

44.7 

213 

203.7 

62.3 

273 

261.1 

79.8 

34 

32.5 

09.9 

94 

89.9 

27.5 

154 

147.3 

45.0 

214 

204.6 

62.6 

274 

262.0 

80.1 

35 

33.5 

10.2 

95 

90.8 

27.8 

155 

148.2 

45.3 

215 

205.6 

62.9 

275 

263.0 

80.4 

36 

34.4 

10.5 

96 

91.8 

28.1 

156 

149.2 

45.6 

216 

206.6 

63.2 

276 

263.9 

80.7 

37 

35.4 

10.8 

97 

92.8 

28.4 

157 

150.1 

45.9 

217 

207.5 

63.4 

277 

264.9 

81.0 

38 

36.3 

11.1 

98 

93.7 

28.7 

158 

151.1 

46.2 

218 

208.5 

63.7 

278 

265.9 

81.3 

39 

37.3 

11.4 

99 

94.7 

28.9 

159 

152.1 

46.5 

219 

209.4 

64.0 

279 

266.8 

81.6 

40 

38.3 

11.7 

100 

95.6 

29.2 

160 

153.0 

46.8 

220 

210.4 

64.3 

280 

267.8 

81.9 

82.2 

41 

39.2 

12.0 

101 

96.6 

29.5 

161 

154.0 

47.1 

221 

211.3 

64.6 

281 

268.7 

42 

40.2 

12.3 

102 

97.5 

29.8 

162 

154.9 

47.4 

222 

212.3 

64.9 

282 

269.7 

82.4 

43 

41.1 

12.6 

103 

98.5 

30.1 

163 

155.9 

47.7 

223 

213.3 

65.2 

283 

270.6 

82.7 

44 

42.1 

12.9 

104 

99.5 

30.4 

164 

156.8 

47.9 

224 

214.2 

65.5 

284 

271.6 

83.0 

45 

43.0 

13.2 

105 

100.4 

30.7 

165 

157.8 

48.2 

225 

215.2 

65.8 

285 

272.5 

83.3 

46 

44.0 

13.4 

106 

101.4 

31.0 

166 

158.7 

48.5 

226 

216.1 

66.1 

286 

273.5 

83.6 

47 

44.9 

13.7 

107 

102.3 

31.3 

167 

159.7 

48.8 

227 

217.1 

66.4 

287 

274.5 

83.9 

48 

45.9 

14.0 

108 

103.3 

31.6 

168 

160.7 

49.1 

228 

218.0 

66.7 

288 

275.4 

84.2 

49 

46.9 

14.3 

109 

104.2 

31.9 

169 

161.6 

49.4 

229 

219.0 

67.0 

289 

276.4 

84.5 

50  47.8 

14.6 

110 

105.2 

32.2 

170 

162.6 

49.7 

230 

220.0 

67.2 

290 

277.3 

84.8 

51  148.8 

14.9 

111 

106.1 

32.5 

171 

163.5 

50.0 

231 

220.9 

67.5 

291 

278.3 

85.1 

52  49.7 

15.2 

112 

107.1 

32.7 

172 

164.5 

50.3 

232 

221.9 

67.8 

292 

279.2 

85.4 

53  50.7 

15.5 

113 

108.1 

33.0 

173 

165.4 

50.6 

233 

222.8 

68.1 

293 

280.2 

85.7 

54  51.6 

1.5.8 

114 

109.0 

33.3 

174 

166.4 

50.9 

234 

223.8 

68.4  '294 

281.2 

86.0 

55 

52.6 

16.1 

115 

110.0 

33.6 

175 

167.4 

51.2 

235 

224.7 

68.7  295 

282.1 

86.2 

56 

53.6 

16.4 

116 

110.9 

33.9 

176 

168.3 

51.5 

236 

225.7 

69.0  296 

283.1 

86.5 

57 

54.5 

16.7 

117 

111.9 

34.2 

177 

169.3 

51.7 

237 

226.6 

ef  3  297 

284.0 

86.8 

58 

55.5 

17.0 

118 

112.8 

34.5 

178 

170.2 

52.0 

238 

227.6 

69.0  ^98 

285.0 

87.1 

59 

56.4 

17.2 

119 

113.8 

34.8 

179 

171.2 

52.3 

239 

228.6 

69.9  299 

285.9 

87.4 

60 
Dist 

57.4 

17.5 

120 

114.8 

35.1 

Lat. 

180 
Dist. 

172.1 

52.6 

240 

229.5 

70.2  300 

286.9 

87.7 

Dep.  1  Lat. 

Dist. 

Dep. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat   Dist. 

Dep. 

Lat 

For  73  U 

ee:rees.                          4^'  52™.  | 

34 

TABLE  11.                         1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  18  DEGREES.  Ih  12.t«.  1 

DisL 

Lat. 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist. !  Lat. 

Dep. 

1 

01.0 

00.3 

61 

58.0 

18.9 

121 

115.1 

37.4 

181 

172.1 

55.9 

241 

229.2 

74.5 

2 

01.9 

00.6 

62 

59.0 

19.2 

122 

116.0 

37.7 

182 

173.1 

56.2 

242 

230.2  74.8  1 

3 

02.9 

00.9 

63 

59.9 

19.5 

123 

117.0  38.0 

183 

174.0  56.6 

243 

231.1 

75.1 

4 

03.8 

01.2 

64 

60.9 

19.8 

124 

117.9 

38.3 

184 

175.0 

56.9 

244 

232.1 

75.4 

5 

04.8 

01.5 

65 

61.8 

20.1 

125 

118.9 

38.6 

185 

175.9 

57.2 

245 

233.0 

75.7 

6 

05.7 

01.9 

66 

62.8 

20.4 

126 

119.8 

38.9 

186 

176.9 

57.5 

246 

234.0 

76.0 

7 

06.7 

02.2 

67 

63.7 

20.7 

127 

120.8 

39.2 

187 

177.8 

57.8 

247 

234.9 !  76.3 1 

8 

07.6 

02.5 

68 

64.7 

21.0 

128 

121.7 

39.6 

188 

178.8 

58.1 

248 

235.9 ;  76.6 1 

9 

08.6 

02.8 

69 

65.6 

21.3 

129 

122.7 

39.9 

189 

179.7 

58.4 

249 

236.8 

76.9 

10 
11 

09.5 

03.1 

70 

66.6 

21.6 

130 

123.6 

40.2 

190 

180.7 

58.7 

250 

237.8 

77.3 

10.5 

03.4 

71 

67.5 

21.9 

131 

124.6 

40.5 

191 

181.7 

59.0 

251 

238.7 

77.6 

12 

11.4 

03.7 

72 

68.5 

22.2 

132 

125.5 

40.8 

192 

182.6 

59.3 

252 

239.7 

77.9 

13 

12.4 

04.0 

73 

69.4 

22.6 

133 

126.5 

41.1 

193 

183.6 

59.6 

253 

240.6 

78.2 

14 

13.3 

04.3 

74 

70.4 

22.9 

134 

127.4 

41.4 

194 

184.5 

59.9 

254 

241.6 

78.5 

15 

14.3 

04.6 

75 

71.3 

23.2 

135 

128.4 

41.7 

195 

185.5 

60.3 

255 

242.5 

78.8 

16 

15.2 

04.9 

76 

72.3 

23.5 

136 

129.3 

42.0 

196 

186.4 

60.6 

256 

243.5 

79.1 

17 

16.2 

05.8 

77 

73.2 

23.8 

137 

130.3 

42.3 

197 

187.4 

60.9 

257 

244.4 

79.4 

18 

17.1 

05.6 

78 

74.2 

24.1 

138  \131.2 

42.6 

198 

188.3 

61.2 

258 

245.4 

79.7 

19 

18.1 

05.9 

79 

75.1 

24.4 

139  ,  132.2 

43.0 

199 

189.3 

61.5 

259 

246.3 

80.0 

20 

19.0 

06.2 

80 

76.1 

24.7 

140 

133.1 

43.3 

200 

190.2 

61.8 

260 

247.3 

80.3 

21 

20.0 

06.5 

81 

77.0 

25.0 

141 

134.1 

43.6 

201 

191.2 

62.1 

261 

248.2 

80.7 

22 

20.9 

06.8 

82 

78.0 

25.3 

142 

135.1 

43.9 

202 

192.1 

62.4 

262 

249.2 

81.0 

23 

21.9 

07.1 

83 

78.9 

25.6 

143 

136.0 

44.2 

203 

19.3.1 

62.7 

263 

250.1 

81.3 

24 

22.8 

07.4 

84 

79.9 

26.0 

144 

137.0 

44.5 

204 

194.0 

63.0 

264 

251.1 

81.6 

25 

23.8 

07.7 

85 

80.8 

26.3 

145 

137.9 

44.8 

205 

195.0 

63.3 

265 

252.0 

81.9 

26 

24.7 

08.0 

86 

81.8 

26.6 

146 

138.9 

45.1 

206 

195.9 

63.7 

266 

253.0 

82.2 

27 

25.7 

08.3 

87 

82.7 

26.9 

147 

139.8 

45.4 

207 

196.9 

64.0 

267 

253.9 

82.5 

28 

26.6 

08.7 

88 

83.7 

27.2 

148 

140.8 

45.7 

208 

197.8 

64.3 

268 

254.9 

82.8 

29 

27.6 

09.0 

89 

84.6 

27.5 

149 

141.7 

46.0 

209 

198.8 

64.6 

269 

255.8 

83.1 

30 

28.5 

09.3 

90 

85.6 

27.8 

150 

142.7 

46.4 

210 

199.7 

64.9 

270 

256.8 

83.4 

31 

29.5 

09.6 

91 

86.5 

28.1 

151 

143.6 

46.7 

211 

200.7 

65.2 

271 

257.7 

83.7 

32 

30.4 

09.9 

,92 

87.5 

28.4 

152 

144.6 

47.0 

212 

201.6 

65.5 

272 

258.7 

84.1 

33 

31.4 

10.2 

93 

88.4 

28.7 

153 

145.5 

47.3 

213 

202.6 

65.8 

273 

259.6 

84.4 

34 

32.3 

10.5 

94 

89.4 

29.0 

154 

146.5 

47.6 

214 

203.5 

66.1 

274 

260.6 

84.7 

35 

33.3 

10.8 

95 

90.4 

29.4 

155 

147.4 

47.9 

215 

204.5 

66.4 

275 

261.5 

85.0 

36 

34.2 

11.1 

96 

91.3 

29.7 

156 

148.4 

48.2 

216 

205.4 

66.7 

276 

262.5 

85.3 

37 

35.2 

11.4 

97 

92.3 

30.0 

157 

149.3 

48.5 

217 

206.4 

67.1 

277 

263.4 

85.6 

38 

36.1 

11.7 

98 

93.2 

30.3 

158 

150.3  48.8 

218 

207.3 

67.4 

278 

264.4 

85.9 

39 

37.1 

12.1 

99 

94.2 

30.6 

159 

151.2 

49.1 

219 

208.3 

67.7 

279 

265.3 

86.2 

40 

38.0 

12.4 

100 

95.1 

30.9 

160 

152.2 

49.4 

220 

209.2 

68.0 

280 

266.3 

86.5 

41 

39.0 

12.7 

101 

96.1 

31.2 

161 

153.1 

49.8 

221 

210.2 

68.3 

281 

267.2 

86.8 

42 

39.9 

13.0 

102 

97.0 

31.5 

162 

154.1 

50.1 

222 

211.1 

68.6 

282  ;  268.2 

87.1 

43 

40.9 

13.3 

103 

98.0 

31.8 

163 

155.0 

50.4 

223 

212.1 

68.9 

283 

269.1 

87.5 

44 

41.8 

13.6 

104 

98.9 

32.1 

164 

156.0 

50.7 

224 

213.0 

69.2 

284 

270.1  87.8 1 

45 

42.8 

13.9 

105 

99.9 

32.4 

165 

156.9 

51.0 

225 

214.0 

69.5 

285 

271.1 

88.1 

46 

43.7 

14.2 

106 

100.8 

32.8 

166 

157.9 

51.3 

226 

214.9 

69.8 

286 

272.0 

88.4 

47 

44.7 

14.5 

107 

101.8 

33.1 

167 

158.8 

51.6 

227 

215.9 

70.1 

287 

273.0 

88.7 

48 

45.7 

14.8 

108 

102.7 

33.4 

168 

159.8 

51.9 

228 

216.8 

70.5 

288 

273.9 

89.0 

49 

46.6 

15.1 

109 

103.7 

33.7 

169 

160.7 

52.2 

229 

217.8 

70.8 

289 

274.9 

89.3 

50 

47.6 

15.5 

110 

104.6 

34.0 

170 

161.7 

52.5 

230 

218.7 

71.1 

290 

275.8 

89.6 

51 

48.5 

15.8 

111 

105.6 

34.3 

171 

162.6 

52.8 

231 

219.7 

71.4 

291 

276.8  89.9 

52 

49.5 

16.1 

112 

106.5 

34.6 

172 

163.6  53.2 

232 

220.6 

71.7 

292 

277.7  90.2 

53 

50.4 

16.4 

113 

107.5 

34.9 

173 

164.5:  53.5 

233 

221.6 

72.0 

293 

278.7 

90.5 

54 

51.4 

16.7 

114 

108.4 

35.2 

174 

165,5:  53.8 

234 

222.5  1  72.3  | 

294 

279.6 

90.9 

55 

52.3 

17.0 

115 

109.4 

.35.5 

175 

166.4;  54.1 

235 

223.5 

72.6 

295 

280.6 

91.2 

56 

53.3 

17.3 

116 

110.3 

35.8 

176 

167.4 

54.4 

236 

224.4 

72.9 

296 

281.5' 91.5  1 

57 

54.2 

17.6 

117 

111.3 

36.2 

177 

168.3 

54.7 

237 

225.4 

73.2 

297 

282.5 

91.8 

58 

552 

17.9 

118 

112.2 

36.5 

178 

169.3 

55.0 

238 

226.4 

73.5 

298 

283.4 

92.1 

59 

56.1 

18.2 

119 

113.2 

36.8 

179 

170.2 

55.3 

239 

227.3 

73.9 

299 

284.4 

92.4 

60 
Diat 

57.1 
Dep. 

18.5 

120 

114.1 

37.1 

180 

171.2 

55.6 

240 

228.3 

74.2 

300  285.3 

92.7 

Lat. 

Dist.  1 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.   Dist. 

Dep. 

Lat. 

Dist.,  Dep.  1  Lat  | 

For  72  Detrrees.                          4h  48'".  | 

TABLE  11.                      86  1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  19  DEGREES.   Ibi6«  1 

Dist 

1 

Lat. 
00.9 

Dep. 

Dist. 

Lilt. 

Dep. 

Dist. 

Lilt. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 
227.9 

Dep. 

78.5 

00.3 

61 

57.7 

19.9 

12h 

114.4 

39.4 

181 

171.1 

58.9 

241 

2 

01.9 

00.7 

62 

58.6 

20.2 

122 

115.4  39.7 

182 

172.1 

59.3 

242 

228.8 

78.8 

3 

02.8 

01.0 

63 

59.6 

20.5 

123 

116.3  40.0 

183 

173.0 

59.6 

243 

229.8 

79.1 

4 

03.8 

01.3 

64 

60.5 

20.8 

124 

117.2  40.4 

184 

174.0 

59.9 

244 

230.7 

79.4 

5  04.7 

01.6 

65 

61.5 

21.2 

125 

118.2  40.7 

185 

174.9 

60.2 

245 

231.7 

79.8 

;1  05.7 

02.0 

66 

62.4 

21.5 

126 

119.1  41.0 

186 

175.9 

60.6 

246 

232.6 

80.1 

7 

06.6 

02.3 

67 

63.3 

21.8 

127 

120.1  41,3 

187 

176.8 

60.9 

247 

233.5 

80.4 

8 

07.6 

02.6 

68 

64.3 

22.1 

128 

121.0  41.7 

188 

177.8 

61.2 

248 

234.5 

80.7 

9 

08.5 

02.9 

69 

65.2 

22.5 

129 

122.0 

42.0 

189 

178.7 

61.5 

249 

235.4 

81.1 

10 

09.5 

03.3 

70 

66.2 

22.8 

130 

122.9 

42.3 

190 

179.6 

61.9 

250 

236.4 

81.4 

11 

10.4 

03.6 

71 

67.1 

23.1 

131 

123.9 

42.6 

191 

180.6 

62.2 

251 

237.3 

81.7 

12 

11.3 

03.9 

72 

68.1 

23.4 

132 

124.8 

43.0 

192 

181.5 

62.5 

252 

238.3 

82.0 

13 

12.3 

04.2 

73 

69.0 

23.8 

133 

125.8 

43.3 

193 

182.5 

62.8 

253 

239.2 

82.4 

14 

13.2 

04.6 

74 

70.0 

24.1 

134 

126.7 

43.6 

194 

183.4 

63.2 

254 

240.2 

82.7 

15 

14.2 

04.9 

75 

70.9 

24.4 

135 

127.6 

44.0 

195 

184.4 

63.5 

255 

241.1 

83.0 

16 

15.1 

05.2 

76 

71.9 

24.7 

136 

128.6 

44.3 

196 

185.3 

63.8 

256 

242.1 

83.3 

17 

16.1 

05.5 

77 

7^.8 

25.1 

137 

129.5 

44.6 

197 

186.3 

64.1 

257 

243.0 

83.7 

18 

17.0 

05.9 

78 

73.8 

25.4 

138 

130.5 

44.9 

198 

187.2 

64.5 

258 

243.9 

84.0 

19 

18.0 

06.2 

79 

74.7 

25.7 

139 

131.4 

45.3 

199 

188.2 

64.8 

259 

244.9 

84.3 

20 
21 

18.9 

06.5 

80 

75.6 

26.0 

140 

132.4 

45.6 

200 

189.1 

65.1 

260 

245.8 

84.6 
85.0 

19.9 

06.8 

81 

76.6 

26.4 

141 

133.3 

45.9 

201 

190.0 

65.4 

261 

246.8 

22 

20.  S 

07.2 

82 

77.5 

26.7 

142 

134.3 

46.2 

202 

191.0 

65.8 

262 

247.7 

85.3 

23 

21.7 

07.5 

83 

78.5 

27.0 

143 

135.2 

46.6 

203 

191.9 

66.1 

263 

248.7 

85.6 

24 

22.7 

07.8 

84 

79.4 

27.3 

144 

136.2 

46.9 

204 

192.9 

66.4 

264 

249.6 

86.0 

25 

23.6 

08.1 

85 

80.4 

27.7 

145 

137.1 

47.2 

205 

193.8 

66.7 

265 

250.6 

86.3 

26 

24.6 

08.5 

86 

81.3 

28.0 

146 

138.0 

47.5 

206 

194.8 

67.1 

266 

251.5 

86.6 

27 

25.5 

08.8 

87 

82.3 

28.3 

147 

139.0 

47.9 

207 

195.7 

67.4 

267 

252.5 

86.9 

28 

26.5 

09.1 

88 

83.2 

28.7 

148 

139.9 

48.2 

208 

196.7 

67.7 

268 

253.4 

87.3 

29 

27.4 

09.4 

89 

84.2 

29.0 

149 

140.9 

48.5 

209 

197.6 

68.0 

269 

254.3 

87.6 

30 

28.4 

09.8 

90 

85.1 

29.3 

150 

141.8 

48.8 

210 

198.6 

68.4 

270 

255.3 

87.9 

31 

29.3 

10.1 

91 

86.0 

29.6 

151 

142.8 

49.2 

211 

199.5 

68.7 

271 

256.2 

88.2 

32 

30.3 

10.4 

92 

87.0 

30.0 

152 

143.7 

49.5 

212 

200.4 

69.0 

272 

257.2 

88.6 

33 

31.2 

10.7 

93 

87.9 

30.3 

153 

144.7 

49.8 

213 

201.4 

69.3 

273 

258.1 

88.9 

34 

32.1 

11.1 

94 

88.9 

30.6 

154 

145.6 

50.1 

214 

202.3 

69.7 

274 

259.1 

80.2 

35 

33.1 

11.4 

95 

89.8 

30.9 

155 

146.6 

50.5 

215 

203.3 

70.0 

275 

260.0 

89.5 

36 

34.0 

11.7 

96 

90.8 

31.3 

156 

147.5 

50.8 

216 

204.2  70.3 

276 

261.0 

89.9 

37 

35.0 

12.0 

97 

91.7 

31.6 

157 

148.4 

51.1 

217 

205.2 

70.6 

277 

261.9 

90.2 

38 

35.9 

12.4 

98 

92.7 

31.9 

158 

149.4 

51.4 

218 

206.1 

71.0 

278 

262.9 

90.5 

39 

36.9 

12.7 

99 

93.6 

32.2 

159 

150.3 

51.8 

219 

207.1 

71.3 

279 

263.8 

90.8 

40 

37.8 

13.0 

100 

94.6 

32.6 

160 

151.3 

52.1 

220 

208.0 

71.6 

280 

264.7 

91.2 

41 

38.8 

13.3 

101 

95.5 

32.9 

161 

152.2 

52.4 

221 

209.0 

72.0 

281 

265.7 

91.5 

42 

39.7 

13.7 

102 

96.4 

33.2 

162 

153.2 

52.7 

222 

209.9 

72.3 

282 

266.6 

91.8 

43 

40.7 

14.0 

103 

97.4 

33.5 

163 

154.1 

53.1 

223 

210.9 

72.6 

283 

267.6 

92.1 

44 

41.6 

14.3 

104 

98.3 

33.9 

164 

155.1 

53.4 

224 

211.8 

72.9 

284 

268.5 

92.5 

45 

42.5 

14.7 

105 

99.3 

34.2 

165 

156.0 

53.7 

225 

212.7 

73.3 

285 

269.5 

92.8 

46 

43.5 

15.0 

106 

100.2 

34.5 

166 

157.0 

54.0 

226 

213.7 

73.6 

286 

270.4 

93.1 

47 

44.4 

1.5.3 

107 

101.2 

34.8 

167 

157.9 

54.4 

227 

214.6 

73.9 

287 

271.4 

93.4 

48 

45.4 

15.6 

108 

102.1 

35.2 

168 

158.8 

54.7 

228 

215.6 

74.2 

288 

272.3 

93.8 

49 

46.3 

16.0 

lOi) 

103.1 

35.5 

169 

159.8 

55.0 

229 

216.5 

74.6 

289 

273.3 

94.1 

50 

47.3 

16.3 

110 

104.0 

35.8 

170 

160.7 

55.3 

230 

217.5 

74.9 

290 

274.2 

94.4 

51 

48.2 

16.6 

111 

105.0 

36.1 

171 

161.7 

55.7 

231 

218.4 

75.2 

291 

275.1 

94.7 

52 

49.2 

16.9 

112 

105.9 

36.5 

172 

162.6 

56.0 

232 

219.4 

75.5 

292 

276.1 

95.1 

53 

50.1 

17.3 

113 

106.8 

36.8 

173 

163.6 

56.3 

233 

220.3 

75.9 

293 

277.0 

95  4 

54 

51.1 

17.6 

114 

107.8 

37.1 

174 

164.5 

56.6 

234 

221.3 

76.2 

294 

278.0 

95,7 

55 

52.0 

17.9 

115 

108.7 

37.4 

175 

165.5 

57.0 

235 

222.2 

76.5 

295 

278.9 

96.0 

56 

.-2.9 

18.2 

116 

109.7 

37.S 

176 

166.4 

57.3 

236 

223.1 

76.8 

296 

279.9 

96.4 

57 

5/9 

18.6 

117 

110.6 

38.1 

\17 

167.4 

57.6 

237 

224.1 

77.2 

297 

280.8 

96.7 

58 

54.3 

18.9 

118 

111.6 

38.4 

178 

168.3 

58.0 

238 

225.0 

77.5 

298 

281.8 

97.0 

59 

55.8 

19.2 

119 

112.5 

38.7 

179 

169.2 

58.3 

239 

226.0 

77.8 

299 

282.7 

97.3 

60 
Dist 

5tV7 
Dep. 

19.5 

120 

113.5 

39.1 

Lat. 

180 

Dist. 

170.2 

58.6 

240 

226.9 

78.1 

300 

283.7 

97.7  1 

Lat. 

Dist. 

Dep. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.   Dist. 

Dep. 

Lat  1 

^ 

i 

"c.r  71  DeiTiees.                           4'»  44«>.  | 

86 

TABLE  11. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  20  DEGREES.  Ih 

20n». 

Dist 

Lat. 

Dep. 

Dist, 

Lat 

Dep. 

Dist 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist 

Lat 

Dep. 

1 

00.9 

00.3 

61 

57.3 

20.9 

121 

113.7 

41.4 

181 

170.1 

61.9 

241 

226.5 

82.4 

2 

01.9 

00.7 

62 

58.3 

21.2 

122 

114.6 

41.7 

182 

171.0 

62.2 

242 

227.4 

82.8 

3 

02.8 

01.0 

63 

59.2 

21.5 

123 

115.6 

42.1 

183 

172.0 

62.6 

243 

228.3 

83.1 

4 

-03.8 

01.4 

64 

60.1 

21.9 

124 

116.5 

42.4 

184 

172.9 

62.9 

244 

229.3 

83.5 

5 

04.7 

01.7 

65 

61.1 

22.2 

125 

117.5 

42.8 

185 

173.8 

63.3 

245 

230.2 

83.8 

6 

05.6 

02.1 

66 

62.0 

22.6 

126 

118.4 

43.1 

186 

174.8 

63.6 

246 

231.2 

84.1 

7 

06.6 

02.4 

67 

63.0 

22.9 

127 

119.3 

43.4 

187 

175.7 

64.0 

247 

232  1 

84.5 

8 

07.5 

02.7 

68 

63.9 

23.3 

128 

120.3 

43.8 

188 

176.7 

64.3 

248 

233.0 

84.8 

9 

08.5 

03.1 

69 

64.8 

23.6 

129 

121.2 

44.1 

189 

177.6 

64.6 

249 

234.0 

85.2 

10 
11 

09.4 

03.4 

70 

65.8 

23.9 

130 

122.2 

44.5 

190 

178.5 

65.0 

250 

234.9 

85.5 

10.3 

03.8 

71 

66.7 

24.3 

131 

123.1 

44.8 

191 

179.5 

65.3  251 

235.9 

85.8 

12 

11.3 

04.1 

72 

67.7 

24.6 

132 

124.0 

45.1 

192 

180.4 

65.7  2.52 

236.8 

86.2 

13 

12.2 

04.4 

73 

68.6 

25.0 

133 

125.0 

45.5 

193 

181.4 

66.0  253 

237.7 

86.5 

14 

13.2 

04.8 

74 

69.5 

25.3 

134 

125.9 

45.8 

194 

182.3 

66.4 

254 

238.7 

86.9 

15 

14.1 

05.1 

75 

70.5 

25.7 

135 

126.9 

46.2 

195 

183.2 

66.7 

255 

239.6 

87.2 

16 

15.0 

05.5 

76 

71.4 

26.0 

136 

127.8 

46.5 

196 

184.2 

67.0 

256 

240.6 

87.6 

17 

16.0 

05.8 

77 

72.4 

26.3 

137 

128.7 

46.9 

197 

185.1 

.67.4 

257 

241.5 

87.9 

18 

16.9 

06.2 

78 

73.3 

26.7 

138 

129.7 

47.2 

198 

186.1 

67.7 

258 

242.4 

88.2 

19 

17.9 

06.5 

79 

74.2 

27.0 

139 

130.6 

47.5 

199 

187.0 

68.1 

259 

243.4 

88.6 

20 

18.8 

06.8 

80 

75.2 

27.4 

140 

131.6 

47.9 

200 

187.9 

68.4 

260 

244.3 

88.9 

21 

19.7 

07.2 

81 

76.1 

27.7 

141 

132.5 

48.2 

201 

188.9 

68.7 

261 

245.3 

89.3 

22 

20.7 

07.5 

82 

77.1 

28.0 

142 

133.4 

48.6 

202 

189.8 

69.1 

262 

246.2 

89.6 

23 

21.6 

07.9 

83 

78.0 

28.4 

143 

134.4 

48.9 

203 

190.8 

69.4 

263 

247.1 

90.0 

24 

22.6 

08.2 

84 

78.9 

28.7 

144 

135.3 

49.3 

204 

191.7 

69.8 

264 

248.1 

90.3 

25 

23.5 

08.6 

85 

79.9 

29.1 

145 

136.3 

49.6 

205 

192.6 

70.1 

265 

249.0 

90.6 

26 

24.4 

08.9 

86 

80.8 

29.4 

146 

137.2 

49.9 

206 

19.3.6 

70.5 

266 

250.0 

91.0 

27 

25.4 

09.2 

87 

81.8 

29.8 

147 

138.1 

50.3 

207 

194.5 

70.8 

267 

250.9 

91.3 

28 

26.3 

09.6 

88 

82.7 

30.1 

148 

139.1 

50.6 

208 

19.5.5 

71.1 

268 

251.8 

91.7 

29 

27.3 

09.9 

89 

83.6 

30.4 

149 

140.0 

51.0 

209 

196.4 

71.5 

269 

252.8 

92.0 

30 

28.2 

10.3 

90 

84.6 

30.8 

150 

141.0 

51.3 

210 

197.3 

71.8 

270 

253.7 

92.3 

31 

29.1 

10.6 

91 

85.5 

31.1 

151 

141.9 

51.6 

211 

198.3 

72.2 

271 

254.7 

92.7 

32 

30.1 

10.9 

92 

86.5 

31.5 

152 

142.8 

52.0 

212 

199.2 

72.5 

272 

255.6 

93.0 

33 

31.0 

11.3 

93 

87.4 

31.8 

153 

143.8 

52.3 

213 

200.2 

72.9 

273 

256.5 

93.4 

34 

31.9 

11.6 

94 

88.3 

32.1 

154 

144.7 

52.7 

214 

201.1 

73.2 

274 

257.5 

93.7 

35 

32.9 

12.0 

95 

89.3 

32.5 

155 

145.7 

53.0 

215 

202.0 

73.5 

275 

258.4 

94.1 

36 

33.8 

12.3 

96 

90.2 

32.8 

156 

146.6 

53.4 

216 

203.0 

73.9 

276 

259.4 

94.4 

37 

34.8 

12.7 

97 

91.2 

33.2 

157 

147.5 

53.7 

217 

203.9 

74.2 

277 

260.3 

94.7 

38 

S5.7 

13.0 

98 

92.1 

33.5 

158 

148.5 

54.0 

218 

204.9 

74.6 

278 

261.2 

95.1 

39 

36.6 

13.3 

99 

93.0 

33.9 

159 

149.4 

54.4 

219 

205.8 

74.9 

279 

262.2 

95.4 

40 

37.6 

13.7 

100 

94.0 

34.2 

160 

150.4 

54.7 

220 

206.7 

75.2 

280 

263.1 

95.8 

41 

38.5 

14.0 

101 

94.9 

34.5 

161 

151.3 

,55.1 

221 

207.7 

75.6 

281 

264.1 

96.1 

42 

39.5 

14.4 

102 

95.8 

34.9 

162 

152.2 

55.4 

222 

208.6 

75.9 

282 

265.0 

96.4 

43 

40.4 

14.7 

103 

96.8 

35.2 

163 

153.2 

55.7 

223 

209.6 

76.3 

283 

265.9 

96.8 

44 

41.3 

15.0 

104 

97.7 

35.6 

164 

154.1 

56.1 

224 

210.5 

76.6 

284 

266.9 

97.1 

45 

42.3 

15.4 

105 

98.7 

35.9 

165 

155.0 

56.4 

225 

211.4 

77.0 

285 

267.8 

97.5 

46 

43.2 

15.7 

106 

99.6 

36.3 

166 

156.0 

56.8 

226 

212.4 

77.3 

286 

268.8 

97.8 

47 

44.2 

16.1 

107 

100.5 

36.6 

167 

156.9 

57.1 

227 

213.3 

77.6 

287 

269.7 

98.2 

48 

45.1 

16.4 

108 

101.5 

36.9 

lf.8 

157.9 

57.5 

228 

214.2 

78.0 

288 

270.6 

98.5 

49 

46.0 

16.8 

109 

102.4 

37.3 

169 

158.8 

57.8 

229 

215.2 

78.3 

289 

271.6 

98.8 

50 

47.0 

17.1 

110 

103.4 

37.6 

170 

159.7 

58.1 

230 

216.1 

78.7 

290 

272.5 

99.2 

51 

47.9 

17.4 

111 

104.3 

38.0 

171 

160.7 

58.5 

231 

217.1 

79.0 

291 

273.5 

99.5 

52 

48.9  17.8 

112 

105.2 

38.3 

172 

161.6 

58.8 

232 

218.0 

79.3 

292 

274.4 

99.9 

53 

49.8 

18.1 

113 

106.2 

38.6 

173 

162.6 

59.2 

233 

218.9 

79.7 

293 

275.3 

100.2 

54 

50.7 

18.5 

114 

107.1 

39.0 

174 

163.5 

59.5 

234 

219.9 

80.0 

294 

276.3 

100.6 

55 

51.7 

18.8 

115 

108.1 

39.3 

175 

164.4 

59.9 

235 

220.8 

80.4 

295 

277.2 

100.9 

56 

52.6 

19.2 

116 

109.0 

39.7 

176 

165.4 

60.2 

236 

221.8 

80.7 

296 

278.1 

101.2 

57 

53.6 

19.5 

117 

109.9 

40.0 

177 

166.3 

60.5 

237 

222.7 

81.1 

297 

279.1 

101.6 

58 

54.5 

19.8 

118 

110.9 

40.4 

17S 

167.3 

60.9 

238 

223.6 

81.4 

298 

280.0 

101.9 

59 

554 

20.2 

119 

111.8 

40.7 

179 

168.2 

61.2 

239 

224.6 

81.7 

299 

281.0 

102.3 

60 

Dist 

56.4 

20.5 

120 

112.8 

41.0 

180 

169.1 

61.6 

240 

225..'. 

82.1 



300 

281.9 

102.6 

Dep. 

Lat. 

Dist 

Dep.   Lat 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat  1 

For  70  Degrees. 

4h 

40'V  1 

TABLE  11. 

37  1 

DIFFEKENCE  OF  LATITUDE  AND  DEPARTURE  FOR  21  DEGREES.   Ih  24m.  1 

Dist 
1 

Lat. 
00.9 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

00.4 

61 

56.9 

21.9 

121 

113.0 

43.4 

181 

169.0 

64.9 

241 

225.0 

86.4 

2  01.9 

00.7 

62 

57.9 

22.2 

122 

113.9 

43.7 

182 

169.9 

65.2 

242 

225.9 

86.7 

3  02.8 

01. 1 

63 

58.8 

22.6 

123 

114.8 

44,1 

183 

170.8 

65.6 

243 

226.9 

87.1 

4  03.7 

01.4 

64 

59.7 

22.9 

124 

115.8 

44.4 

184 

171.8 

65.9 

244 

227.8 

87.4 

5 ,  04.7 

01.8 

65 

60.7 

23.3 

125 

116.7 

44.8 

185 

172.7 

66.3 

245 

228.7 

87.8 

6 

05.6 

022 

66 

61.6 

23.7 

126 

117.6 

45.2 

186 

173.6 

66.7 

246 

229.7 

88.2 

7  '  0(5.5 

02.5 

67 

62.5 

24.0 

127 

118.6 

45.5 

187 

174.6 

67.0 

247 

230.6 

88.5 

8  07.5 

02.9 

68 

63.5 

24.4 

128 

119.5 

45.& 

188 

175.5 

67.4 

248 

231.5 

88.9 

9  ,  08.4 

03.2 

69 

64.4 

24.7 

129 

120.4 

46.2 

189 

176.4 

67.7 

249 

232.5 

89.2 

10 

09.3 

03.6 

70 

65.4 

25.1 

130 
131 

121.4 

46.6 

190 

1-77.4 

68.1 

250 

233.4 

89.6 

11 

10.3 

03.9 

71 

66.3 

25.4 

122.3 

46.9 

191 

178.3 

68.4 

251 

234.3 

90.0 

1^ 

11.2 

04.3 

72 

67.2 

25.8 

132 

123.2 

47.3 

192 

179.2 

68.8 

252 

235.3 

90.3 

13 

12.1 

04.7 

73 

68.2 

26.2 

133 

124.2 

47.7 

193 

180.2 

69.2 

253 

236.2 

90.7 

14 

13.1 

05.0 

74 

69.1 

26.5 

134 

125.1 

48.0 

194 

181.1 

69.5 

254 

237.1 

91.0 

15 

14.0 

05.4 

75 

70.0 

26.9 

135 

126.0 

48.4 

195 

182.0 

69.9 

255 

238.1 

91.4 

16 

14.9 

05.7 

76 

71.0 

27.2 

136 

127.0 

48.7 

196 

183.0 

70.2 

256 

239.0 

91.7 

17 

15.9 

06.1 

77 

71.9 

27.6 

137 

127.9 

49.1 

197 

183.9 

70.6 

257 

239.9 

92.1 

18 

16.8 

06.5 

78 

72.8 

28.0 

138 

128.8 

49.5 

198 

184.8 

71.0 

258 

240.9 

92.5 

19 

17.7 

06.8 

79 

73.8 

28.3 

139 

129.8 

49.8 

199 

185.8 

71.3 

259 

241.8 

92.8 

20 
21 

18.7 

07.2 

80 

74.7 

28.7 

140 
141 

130.7 
131.6 

50.2 

200 

186.7 

71.7 

260 

242.7 

93.2 

19.6 

07.5 

81 

75.6 

29.0 

50.5 

201 

187.6 

72.0 

261 

243.7 

93.5 

22 

20.5 

07.9 

82 

76.6 

29.4 

142 

132.6 

50.9 

202 

188.6 

72.4 

262 

244.6 

93.9 

23 

21.5 

08.2 

83 

77.5 

29.7 

143 

133.5 

51.2 

203 

189.5 

72.7 

263 

245.5 

94.3 

24 

22.4 

08.6 

84 

78.4 

30.1 

144 

134.4 

51.6 

204 

190.5 

73.1 

264 

246.5 

94.6 

25 

23.3 

09.0 

85 

79.4 

30.5 

145 

135.4 

52.0 

205 

191.4 

73.5 

265 

247.4 

95.0 

26 

24.3 

09.3 

86 

80.3 

30.8 

146 

136.3 

52.3 

206 

192.3 

73.8 

266 

248.3 

95.3 

27 

25.2 

09.7 

87 

81.2 

31.2 

147 

137.2 

52.7 

207 

193.3 

74.2 

267 

249.3 

95.7 

28 

26.1 

10.0 

88 

82.2 

31.5 

148 

138.2 

53.0 

208 

194.2 

74.5 

268 

250.2 

96.0 

29 

27.1 

10.4 

89 

83.1 

31.9 

149 

139.1 

53.4 

209 

195.1 

74.9 

269 

251.1 

96.4 

30 

28.0 

lO.s 

90 

84.0 

32.3 

150 

140.0 

53.8 

210 

196.1 

75.3 

270 

252.1 

96.8 

31 

2S.9 

11.1 

91 

85.0 

32.6 

151 

141.0 

54.1 

211 

197.0 

75.6 

271 

253.0 

97.1 

32 

29.9 

11.5 

92 

85.9 

33.0 

152 

141.9 

54.5 

212 

197.9 

76.0 

272 

253.9 

97.5 

33 

30.8 

11.8 

93 

86.8 

33.3 

153 

142.8 

54.8 

213 

198.9 

76.3 

273 

254.9 

97.8 

34 

31.7 

12.2 

94 

87.8 

33.7 

154 

143.8 

55.2 

214 

199.8 

76.7 

274 

255.8 

98.2 

35 

32.7 

12.5 

95 

88.7 

34.0 

155 

144.7 

55.5 

215 

200.7 

77.0 

275 

256.7 

98.6 

36 

33.6 

12.9 

96 

89.6 

34.4 

156 

145.6 

55.9 

216 

201.7 

77.4 

276 

257.7 

98.9 

37 

34.5 

13.3 

97 

90.6 

34.8 

157 

146.6 

56.3 

217 

202.6 

77.8 

277 

258.6 

99.3 

38 

35.5 

13.6 

98 

91.5 

35.1 

158 

147.5 

56.6 

218 

203.5 

78.1 

278 

259.5 

99.6 

39 

36.4 

14.0 

99 

92.4 

35.5 

159 

148.4 

57.0 

219 

204.5 

78.5 

279 

260.5 

lOO.O 

40 

37.3 

14.3 

100 

93.4 

35.8 

160 

149.4 

57.3 

220 

205.4 

78.8 

280 

261.4 
262.3 

100.3 

41 

38.3 

14.7 

101 

94.3 

36.2 

161 

150.3 

57.7 

221 

206.3 

79.2 

281 

100.7 

42 

39.2 

15.1 

102 

95.2 

36.6 

162 

151.2 

58.1 

222 

207.3 

79.6 

282 

263.3 

101.1 

43 

40.1 

15.4 

103 

96.2 

36.9 

163 

152.2 

58.4 

223 

208.2 

79.9 

283 

264.2 

101.4 

44 

41.1 

15.8 

104 

97.1 

37.3 

164 

153.1 

58.8 

224 

209.1 

80.3 

284 

265.1 

101.8 

45 

42.0 

16.1 

105 

98.0 

37.6 

165 

154.0 

59.1 

225 

210.1 

80.6 

285 

266.1 

102.1 

46 

42.9 

16.5 

106 

99.0 

38.0 

166 

155.0 

59.5 

226 

211.0 

81.0 

286 

267.0 

102.5 

47 

43.9 

16.8 

107 

99.9 

38.3 

167 

155.9 

59.8 

227 

211.9 

81.3 

287 

267.9 

102.9 

48 

448 

17.2 

108 

100.8 

38.7 

168 

156.8 

i»/^  '->  ^'^O^ 

212.9 

81.7 

288 

268.9 

103.2 

49 

45.7 

17.6 

lOi) 

101.8 

39.1 

169 

157.8 

60.6 

229 

^i«.3 

^•>l     289 

269.8 

103.6 

50 
51 

46.7 

17.9 

110 

102.7 

39.4 

170 

158.7 

60.9 

230 

214.7 

82.4 

290 

270.7 

103.9 

47.6 

18.3 

HI 

103.6 

39.8 

171 

159.6 

61.3 

231 

215.7 

82.8 

291 

271.7 

104.3 

52 

48.5 

18.6 

112 

104.6 

40.1 

172 

160.6 

61.6 

232 

216.6 

83.1 

292 

272.6 

104.6 

53 

49.5 

19.0 

113 

105.5 

40.5 

173 

161.5 

62.0 

233 

217.5 

83.5 

293 

273.5 

105.0 

54 

50.4 

19.4 

114 

106.4 

40.9 

174 

162.4 

62.4 

234 

218.5 

83.9 

294 

274.5 

105.4 

55 

51.3 

19.7 

115 

107.4 

41.2 

175 

163.4 

62.7 

235 

219.4 

84.2 

295 

275.4 

105.7 

56 

52.3 

20.1 

116 

108.3 

41.6 

176 

164.3 

63.1 

236 

220.3 

84.6 

296 

276.3 

106.1 

i)  / 

53.2 

20.4 

117 

109.2 

41.9 

177 

165.2 

()3.4 

237 

221.3 

84.9 

297 

277.3 

106.4 

58 

54.1 

20.8 

118 

110.2 

42.3 

178 

166.2 

63.8 

238 

222.2 

85.3 

298 

278.2 

106.8 

59 

55.1 

21.1 

119 

111.1 

42.6 

179 

167.1 

64.1 

239 

223.1 

85.6 

299 

279.1 

107.2 

60 
Dist. 

56.0 
Dep. 

21.5 

120 

112.0 

43.0 

Lat. 

180 

168.0 

64.5 

240 

224.1 

86.0 

300 

280.1 

107.5 

Lat. 

Dist. 

Dep. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

I 

'or  69  Desjrees. 

4h 

86m. 

38                    TABLE  11.                         1 
DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  22  DEGREES.   In  28™. 

Dist 

Lat. 

Dep. 

Dist 

Lat   Dep.  | 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

1 

00.9 

00.4 

61 

56.6 

22.9 

121 

112.2 

45.3 

181 

167.8 

67.8 

241 

223.5 

90.3 

2  01.9 

00.7 

62 

57.5 

23.2 

122 

113.1 

45.7 

182 

168.7 

68.2 

242 

224.4 

90.7 

3  02.8 

01.1 

63 

58.4 

23.6 

123 

114.0 

46.1 

183 

169.7 

68.6 

243 

225.3 

91.0 

4  03.7 

01.5 

64 

59.3 

24.0 

124 

115.0 

46.5 

184 

170.6 

68.9 

244 

226.2 

91.4 

5  04.6  01.91 

65 

60.3 

24.3 

125 

115.9 

46.8 

185 

171.5 

69.3 

245 

227.2 

91.8 

6 

05.6  02.2 

66 

61.2 

24.7 

126 

116.8 

47.2 

186 

172.5 

69.7 

246 

228.1 

92.2 

7 

06.5  02.6 

67 

62.1 

25.1 

127 

117.8 

47.6 

187 

173.4 

70.1 

247 

229.0 

92.5 

8 

07.4  03.0 

68 

63.0 

25.5 

128 

118.7 

47.9 

188 

174.3 

70.4 

248 

229.9 

92.9 

9 

08.3 

03.4 

69 

64.0 

25.8 

129 

119.6 

48.3 

189 

175.2 

70.8 

249 

230.9 

93.3 

10 

09.3 

03.7 

70 

64.9 

26.2 

130 
131 

120.5 

48.7 

190 

176.2 

71.2 

250 

231.8 

93.7 

11 

10.2 

04.1 

71 

65.8 

26.6 

121.5 

49.1 

191 

177.1 

71.5 

251 

232.7 

94.0 

12 

11.1 

04.5 

72 

66.8 

27.0 

132 

122.4 

49.4 

192 

178.0 

71.9 

252 

233.7 

94.4 

13 

12.1 

04.9 

73 

67.7 

27.3 

133 

123.3 

49.8 

193 

178.9 

72.3 

253 

234.6 

94.8 

14 

13.0 

05.2 

74 

6S.Q 

27.7 

134 

124.2 

50.2 

194 

179.9 

72.7 

254 

235.5 

95.2 

15 

13.9 

05.6 

75 

69.5 

28.1 

135 

125.2 

50.6 

195 

180.8 

73.0 

255 

236.4 

95.5 

16 

14.8 

06.0 

76 

70.5 

28.5 

136 

126.1 

50.9 

196 

181.7 

73.4 

256 

237.4 

95.9 

17 

15.8 

06.4 

77 

71.4 

28.8 

137 

127.0 

51.3 

197 

182.7 

73.8 

257 

238.3 

96.3 

18 

16.7 

06.7 

78 

72.3 

29.2 

138 

128.0 

51.7 

198 

183.6 

74.2 

258 

239.2 

96.6 

19 

17.6 

07.1 

79 

73.2 

29.6 

139 

128.9 

52.1 

199 

184.5 

74.5 

259 

240.1 

97.0 

20 

21 

18.5 

07.5 

80 

74.2 

30.0 
30.3 

140 
141 

129.8 

52.4 

200 

185.4 

74.9 

260 

241.1 

97.4 

19.5 

07.9 

81 

75.1 

130.7 

52.8 

201 

186.4 

75.3 

261 

242.0 

97.8 

22 

20.4 

08.2 

82 

76.0 

30.7 

142 

131.7 

53.2 

202 

187.3 

75.7 

262 

242.9 

98.1 

23 

21.3 

08.6 

83 

77.0 

31.1 

143 

132.6 

53.6 

203 

188.2 

76.0 

263 

243.8 

98.5 

24 

22.3 

09.0 

84 

77.9 

31.5 

144 

133.5 

53.9 

204 

189.1 

76.4 

264 

244.8  98.9 

25 

23.2 

09.4 

85 

78.8 

31.8 

145 

134.4 

54.3 

205 

190.1 

76.8 

265 

245.7  99.3 

26 

24.1 

09.7 

86 

79.7 

32.2 

146 

135.4 

54.7 

206 

191.0 

77.2 

266 

246.6  99.6 

27 

25.0 

10.1 

87 

80.7 

32.6 

147 

136.3 

55.1 

207 

191.9 

77.5 

267 

247.6 

100.0 

28 

26.0 

10.5 

88 

81.6 

33.0 

148 

137.2 

55.4 

208 

192.9 

77.9 

268 

248.5 

100.4 

29 

26.9 

10.9 

89 

82.5 

33.3 

149 

138.2 

55.8 

209 

193.8 

78.3 

269 

249.4 

100.8 

30 

27.8 

11.2 

90 

83.4 

33.7 

150 

139.1 

56.2 
56.6 

210 

194.7 

78.7 

270 

250.3 

101.1 

31 

28.7 

11.6 

91 

84.4 

34.1 

151 

140.0 

211 

195.6 

79.0 

271 

251.3 

101.5 

32 

29.7 

12.0 

92 

85.3 

34.5 

152 

140.9 

;">6.9 

212 

196.6 

79.4 

272 

252.2 

101.9 

33 

30.6 

12.4 

93 

86.2 

34.8 

153 

141.9 

57.3 

213 

197.5 

79.8 

273 

253.1 

102.3 

34 

31.5 

12.7 

94 

87.2 

35.2 

154 

142.8 

57.7 

214 

198.4 

80.2 

274 

254.0 

102  6 

35 

32.5 

13.1 

95 

88.1 

35.6 

155 

143.7 

58.1 

215 

199.3 

80.5 

275 

255.0 

103.0 

36 

33.4 

13.5 

96 

89.0 

36.0 

156 

144.6 

58.4 

216 

200.3 

80.9 

276 

255.9 

103.4 

37 

34.3 

13.9 

97 

89.9 

36.3 

157 

145.6 

58.8 

217 

201.2 

81.3 

277 

256.8 

103.8 

38 

35.2 

14.2 

98 

90.9 

36.7 

158 

146.5 

59.2 

218 

202.1 

81.7 

278 

257.8 

104.1 

39 

36.2 

14.6 

99 

91.8 

37.1 

159 

147.4 

59.6 

219 

203.1 

82.0 

279 

258.7 

104.5 

40 

37.1 

15.0 

100 

92.7 

37.5 

160 

148.3 

59.9 

220 

204.0 

82.4 

280 

259.6 

104.9 

41 

38.0 

15.4 

101 

93.6 

37.8 

161 

149.3 

60.3 

221 

204.9 

82.8 

281 

260.5 

105.3 

42 

38.9 

15.7 

102 

94.6 

38.2 

162 

150.2 

60.7 

222 

205.8 

83.2 

282 

261.5 

105.6 

43 

39.9 

16.1 

103 

95.5 

38.6 

163 

151.1 

61.1 

223 

206.8 

83.5 

283 

262.4 

106.0 

44 

40.8 

16.5 

104 

96.4 

39.0 

164 

152.1 

61.4 

224 

207.7 

83.9 

284 

263.3 

106.4 

45 

41.7 

16.9 

105 

97.4 

39.3 

165 

153.0 

61.8 

225 

208.6 

84.3 

285 

264.2 

106.8 

46 

42.7 

17.2 

106 

98.3 

39.7 

166 

153.9 

62.2 

226 

209.5 

84.7 

286 

365.2 

107.1 

47 

43.6 

17.6 

107 

99.2 

40.1 

167 

154.8 

62.6 

227 

210.5 

85.0 

287 

266.1 

107.5 

48 

44.5 

18.0 

108 

100.1 

40.5 

168 

155.8 

62.9 

228 

211.4 

85.4 

288 

267.0 

107.9 

49 

45.4 

18.4 

109 

101.1 

40.8 

169 

156.7 

63.3 

229 

212.3 

85.8 

289 

268.0 

108.3 

50 
51 

46.4 

18.7 

110 

102.0 

41.2 

170 

157.6 

63.7 

230 

213.3 

86.2 

290 

268.9 

108.6 

47.3 

19.1 

111 

102.9 

41.6 

171 

158.5 

64.1 

231 

214.2 

86.5 

291 

269.8 

109.0 

52 

48.2 

19.5 

112 

103.8 

42.0 

172 

159.5 

64.4 

232 

215.1 

86.9 

292 

270.7 

109.4 

53 

49.1 

19.9 

113 

104.8 

42.3 

173 

160.4 

64.8 

233 

216.0 

87.3 

293 

271.7 

109.8 

54 

50.1 

20.2 

114 

105.7 

42.7 

174 

161.3 

65.2 

234 

217.0 

87.7 

294 

272.6 

110.1 

55 

51.0 

20.6 

115 

106.6 

43.1 

175 

162.3 

65.6 

235 

217.9 

88.0 

295 

273.5 

110.5 

56 

51.9 

21.0 

116 

107.6 

43.5 

176 

163.2 

65.9 

236 

218,8 

88.4 

296 

274.4 

110.9 

57 

52.8 

21.4 

117 

108.5 

43.8 

177 

164.1 

66.3 

237 

219.7 

88.8 

297 

275.4 

111.3 

58 

53.8 

21.7 

118 

109.4 

44.2 

178 

165.0 

66.7 

238 

220.7 

89.2 

298 

276.3 

111.6 

59 

54.7 

22.1 

119 

110.3 

44.6 

179 

166.0 

67.1 

239 

221.6 

89.5 

299 

277.2 

112.0 

60 

55.6 

22.5 

120 

111.3 

45  0 

180 

166.9 

67.4 

240 

222.5 

89.9 

300 

278.2 

112.4 

Di8< 

*  Dep. 

Lat 

Dist.  Dep.   Lat. 

Dist 

Dep. 

Lat 

Dist 

Dop. 

Lat  I  Dist 

Dep. 

Lat 

For  68  Dei^rees                           4h  32™. 

TABLE  11. 

89   i 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  23  DEGREES,  l^  32«.  1 

Diet 
1 

Lat 

Dep. 

Dist 

Lat. 

Dep. 

Dist 

Lilt. 

Dep. 

Dist. 

Lat. 

Dep. 

70.7 

Dist 

Lat. 

Dep. 

00.9 

00.4 

61 

56.2 

23.8 

121 

111.4 

47.3 

181 

166.6 

241 

221.8 

94.2 

2 

01.8 

00.8 

62 

57.1 

24.2 

122 

112.3 

47.7 

1«2 

167.5 

71.1 

242 

222.8 

94.6 

3 

02.8 

01.2 

63 

58.0 

24.6 

123 

113.2 

48.1 

183 

168.5 

71.5 

243 

223.7 

94.9 

4 

03.7 

01.6 

64 

58.9 

25.0 

124 

114.1  48.5 

184 

169.4 

71.9 

244  1  224.6 

95.3 

5 

04.6 

02.0 

65 

59.8 

25.4 

125 

115.1  ;48.8 

185 

170.3 

72.3 

245  1  225.5 

95.7 

6 

05.5 

02.3 

66 

60.8 

25.8 

126 

116.0 

49.2 

186 

171.2 

72.7 

246  226  4 

96.1 

7 

06.4 

02.7 

67 

61.7 

26.2 

127 

116.9 

49.6 

187 

172.1 

73.1 

247  1 227.4  96.5  | 

8 

07.4 

03.1 

68 

62.6 

26.6 

128 

117.8 

50.0 

188 

173.1 

73.5 

248 

228.3,  96.9 1 

9 

0S.3 

03.5 

69 

63.5 

27.0 

129 

118.7 

50.4 

189 

174.0 

73.8 

249 

229.2 

97.3 

10 
11 

09.2 

03.9 

70 

64.4 

27.4 

130 

119.7 

50.8 

190 

174.9 

74.2 

250 

230.1 

97.7 

10.1 

04.3 

71 

65.4 

27.7 

131 

120.6 

51.2 

191 

175.8 

74.6 

251 

231.0 

98.1 

12 

11.0 

04.7 

72 

66.3 

28.1 

132 

121.5 

51.6 

192 

176.7 

75.0 

252 

232.0 

98.5 

13 

12.0 

05.1 

73 

67.2 

28.5 

133 

122.4 

52.0 

193 

177.7 

75.4 

253 

232.9 

98.9 

14 

12.9 

05.5 

74 

68.1 

28.9 

134 

123.3 

524 

194 

178.6 

75.8 

254 

233.8 

99.2 

15 

13.8 

05.9 

75 

69.0 

29.3 

135 

124.3 

52.7 

195 

179.5 

76.2 

255 

234.7 

99.6 

16 

14.7 

06.3 

76 

70.0 

29.7 

136 

125.2 

53.1 

196 

180.4 

76.6 

256 

235.6 

100.0 

17 

15.6 

06.6 

77 

70.9 

30.1 

137 

126.1 

53.5 

197 

181.3 

77.0 

257 

236.6 

100.4 

18 

16.6 

07.0 

78 

71.8 

30.5 

138 

127.0 

53.9 

198 

182.3 

77.4 

258 

237.5 

100.8 

19 

17.5 

07.4 

79 

72.7 

30.9 

139 

128.0 

54.3 

199 

183.2 

77.8 

259 

238.4 

101.2 

20 

18.4 

07.8 

80 

73.6 

31.3 

140 

128.9 

54.7 

200 

184.1 

78.1 

260 

239.3 

101.6 

21 

19.3 

08.2 

81 

74.6 

31.6 

141 

129.8,55.1 

201 

185.0 

78.5 

261 

240.3 

102.0 

22 

20.3 

08.6 

82 

75.5 

32.0 

142 

130.7 

55.5 

202 

185.9 

78.9 

262 

241.2 

102.4 

23 

21.2 

09.0 

83 

76.4 

32.4 

143 

131.6 

55.9 

203 

186.9 

79.3 

263 

242.1 

102.8 

24 

22.1 

09.4 

84 

77.3 

32.8 

144 

132.6 

56.3 

204 

187.8 

79.7 

264 

243.0 

103.2 

25 

23.0 

09.8 

85 

78.2 

332 

145 

133.5 

56.7 

205 

188.7 

80.1 

265 

243.9 

103.5 

26 

23.9 

10.2 

86 

79.2 

33.6 

146 

134.4 

57.0 

206 

189.6 

80.5 

266 

244.9 

103.9 

27 

24.9 

10.5 

87 

80.1 

34.0 

147 

135.3 

57.4 

207 

190.5 

80.9 

267 

245.8 

104.3 

28 

25.8 

10.9 

88 

81.0 

34.4 

148 

136.2 

57.8 

208 '191.5 

81.3 

268 

246.7 

104.7 

29 

26.7 

11.3 

89 

81.9 

34.8 

149 

137.2 

58.2 

209  1  192.4 

81.7 

269 

247.6 

105.1 

30 

27.6 

11.7 

90 

82.8 

35.2 

150 

138.1 

58.6 

210 

193.3 

82.1 

270 

248.5 

105.5 

31 

28.5 

12.1 

91 

83.8 

35.6 

151 

139.0 

59.0 

211 

194.2 

82.4 

271 

249.5 

105.9 

32 

29.5 

12.5 

92 

84.7 

35.9 

152 

139.9 

59.4 

212 

195.1 

82.8 

272 

2.50.4 

106.3 

33 

30.4 

12.9 

93 

85.6 

36.3 

153 

140.8 

59.8 

213 

196.1 

83.2 

273 

251.3 

106.7 

34 

31.3 

13.3 

94 

86.5 

36.7 

154 

141.8 

60.2 

214 

197.0 

83.6 

274 

252.2 

107  1 

35 

32.2 

13.7 

95 

87.4 

37,1 

155 

142.7 

60.6 

215 

197.9 

84.0 

275 

253.1 

107.5 

36 

33.1 

14.1 

96 

88.4 

37.5 

156 

143.6 

61.0 

216 

198.8 

84.4 

276 

254.1 

107.8 

37 

34.1 

14.5 

97 

89.3 

37.9 

157 

144.5 

61.3 

217 

199.7 

84.8 

277 

255.0 

108.2 

38 

35.0 

14.8 

98 

90.2 

38.3 

158 

145.4 

61.7 

218 

200.7 

85.2 

278 

255.9 

108.6 

39 

35.9 

15.2 

99 

91.1 

38.7 

159 

146.4^62.1 

219 

201.6 

85.6 

279 

256.8 

109.0 

40 

36.8 

15.6 

100 

92.1 

39.1 

160 

147.3 

62.5 

220 

202.5 

86.0 

280 

257.7 

109.4 

41 

37.7 

16.0 

101 

93.0 

39.5 

161 

148.2 

62.9 

221 

203.4 

86.4 

281 

258.7 

109.8 

42 

38.7 

16.4 

102 

93.9 

39.9 

162 

149.1 

63.3 

222 

204.4 

86.7 

282 

259.6 

110.2 

43 

39.6 

16.8 

103 

94.8 

40.2 

163 

150.0 

63.7 

223 

205.3 

87.1 

283 

260.5 

110.6 

44 

40.5 

17.2 

104 

95.7 

40.6 

164 

151.0 

64.1 

224 

206.2 

87.5 

284 

261.4 

111.0 

45 

41.4 

17.6 

105 

96.7 

41.0 

165 

151.9 

64.5 

225 

207.1 

87.9 

285 

262.3 

111.4 

46 

42.3 

18.0 

106 

97.6 

41.4 

166 

152.8 

64.9 

226 

208.0 

88.3 

286 

263.3 

111.7 

47 

43.3 

18.4 

107 

98.5 

41.8 

167 

153.7 

65.3 

227 

209.0 

88.7 

287 

264.2 

112.1 

48 

44.2 

18.8 

108 

99.4 

42.2 

l«i8 

154.6 

65.6 

228 

209.9 

89.1 

288 

265.1 

112.5 

49 

45.1 

19.1 

109 

100.3 

42.6 

169 

155.6 

66.0 

229 

210.8 

89.5 

289 

266.0 

112.9 

50 

46.0 

19.5 

110 

101.3 

43.0 

170 

156.5 

66.4 

230 

211.7 

89.9 

290 

266.9 

113.3 

51 

46.9 

19.9 

111 

102.2 

43.4 

171 

157.4 

66.8 

231  212.6 

90.3 

291 

267.9 

113.7 

52 

47.9 

20.3 

112 

103.1 

43.8 

172 

158.3 

67.2 

232 

213.6 

90.6 

292 

268.8 

114.1 

53 

48.8 

20.7 

113 

104.0 

44.2 

173 

159.2 

67.6 

233 

214.5 

91.0 

293 

269.7 

114.5 

54 

49.7 

21.1 

114 

104.9 

44.5 

174 

160.2 

68.0 

234 

215.4 

91.4 

294 

270.6 

114.9 

55 

50.6 

21.5 

115 

105.9 

44.9 

175 

161.1 

68.4 

235 

216.3 

91.8 

295 

271.5 

115.3 

56 

51.5 

21.9 

116 

106.8 

45.3 

176 

162.0 

68.8 

236 

217.2 

92.2 

296 

272.5 

115.7 

57 

52.5 

22.3 

117 

107.7 

45.7 

177 

162.9 

69.2 

237 

218.2 

92.6 

297 

273.4 

116.0 

58 

53.4 

22.7 

118 

IOS.6 

46.1 

17S 

163.8 

69.6 

238 

219.1 

93.0 

298 

274.3 

116.4 

59 

54.3 

23.1 

119 

109.5 

46.5 

179 

164.8 

69.9 

239 

220.0 

93.-^ 

299 

275.2 

116.8 

60 

Dist 

55.2 
Dep. 

23.4 

120 

110.5 

46.9 

180 

165.7 

70.3 

240 

220.9 

93.8 

300 

276.2 

117.2 

Lat. 

Dist. 

Dep. 

Lat 

Dist 

Dep. 

Lat.  Dist 

Dep. 

Lat 

Dist 

Dep. 

Lat 

For  67  Detrrees. 

4t»  28m.  1 

40                   TABLE  11. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  24  DEGREES.   Ih  36m. 

Dist 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

LaL 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 
220.2 

Dep. 

1 

00.9 

00.4 

61 

55.7 

24.8 

121 

110.5 

49.2 

181 

165.4 

73.6 

241 

98.0 

2 

01.8 

00.8 

62 

56.6 

25.2 

122 

111.5 

49.6 

182 

166.3 

74.0 

242 

221.1 

98.4 

3 

02.7 

01.2 

63 

57.6 

25.6 

123 

112.4 

50.0 

183 

167.2 

74.4 

243 

222.0 

98.8 

4 

03.7 

01.6 

64 

58.5 

26.0 

124 

113.3 

50.4 

184 

168.1 

74.8 

244 

222.9 

99.2 

5  04.6 

02.0 

65 

59.4 

26.4 

125 

114.2 

50.8 

185 

169.0 

75.2 

245 

223.8 

99.7 

6  05.5 

02.4 

66 

60.3 

2().8 

126 

115.1 

51.2 

186 

169.9 

75.7 

246 

224.7 

100.1 

7  06.4 

02.8 

67 

61.2 

27.3 

127 

116.0 

51.7 

187 

170.8 

76.1 

247 

225.6 

100.5 

8 

07.3 

03.3 

68 

62.1 

27.7 

128 

116.9 

52.1 

188 

171.7 

76.5 

248 

226.6 

100.9 

9 

08.2 

03.7 

69 

63.0 

28.1 

129 

117.8 

52.5 

189 

172.7 

76.9 

249 

227.5 

101.3 

10 

09.1 

04.1 

70 

63.9 

28.5 

130 
131 

118.8 

52.9 

190 
191 

173.6 

77.3 

250 

228.4 

101.7 

11 

10.0 

04.5 

71 

64.9 

28.9 

119.7 

53.3 

174.5 

77.7 

251 

229.3 

102.1 

12 

11.0 

04.9 

72 

65.8 

29.3 

132 

120.6 

53.7 

192 

175.4 

78.1 

252 

230.2 

102.5 

13 

11.9 

05.3 

73 

66.7 

29.7 

133 

121.5 

54.1 

193 

176.3 

78.5 

253 

231.1 

102.9 

14 

12.8 

05.7 

74 

67.6 

30.1 

134 

122.4 

54.5 

194 

177.2 

78.9 

254 

232.0 

103.3 

15 

13.7 

06.1 

75 

68.5 

30.5 

135 

123.3 

54.9 

195 

178.1 

79.3 

255 

233.0 

103.7 

16 

14.6 

06.5 

76 

69.4 

30.9 

136 

124.2 

55.3 

196 

179.1 

79.7 

256 

233.9 

104.1 

17 

15.5 

06.9 

77 

70.3 

31.3 

137 

125.2 

55.7 

197 

180.0 

80.1 

257 

234.8 

104.5 

18 

16.4 

07.3 

78 

71.3 

31.7 

188 

126.1 

56.1 

198 

180.9 

80.5 

258 

235.7 

104.9 

19 

17.4 

07.7 

79 

72.2 

32.1 

139 

127.0 

56.5 

199 

181.8 

80.9 

259 

236.6 

105.3 

20 
21 

18.3 
19.2 

08.1 

80 

73.1 

32.5 
32.9 

140 

127.9 

56.9 

200 
201 

182.7 
183.6 

81.3 

260 

237.5 

105.8 
106.2 

08.5 

81 

74.0 

141 

128.8 

57.3 

81.8 

261 

238.4 

22 

20.1 

08.9 

82 

74.9 

33.4 

142 

129.7 

57.8 

202 

184.5 

82.2 

262 

239.3 

106.6 

23 

21.0 

09.4 

83 

75.8 

33.8 

143 

130.6 

58.2 

203 

185.4 

82.6 

263 

240.3 

107.0 

24 

21.9 

09.8 

84 

76.7 

34.2 

144 

131.6 

58.6 

204 

186.4 

83.0 

264 

241.2 

107.4 

25 

22.8 

10.2 

85 

77.7 

34.6 

145 

132.5 

59.0 

205 

187.3 

83.4 

265 

242.1 

107.8 

26 

23.8 

10.6 

86 

78.6 

3').0 

146 

133.4 

59.4 

206 

188.2 

83.8 

266 

243.0 

108.2 

27 

24.7 

11.0 

87 

79.5 

35.4 

147 

134.3 

59.8 

207 

189.1 

84.2 

267 

243.9 

108.6 

28 

25.6 

11.4 

88 

80.4 

35.8 

148 

135.2 

60.2 

208 

190.0 

84.6 

268 

244.8 

109.0 

29 

26.5 

11.8 

89 

81.3 

36.2 

149 

136.1 

60.6 

209 

190.9 

85.0 

269 

245.7 

109.4 

30 

27.4 

12.2 

90 

.82.2 

36.6 

150 

137.0 

61.0 
61.4 

210 

191.8 

85.4 

270 

246.7 

109.8 

31 

28.3 

12.6 

91 

83.1 

37.0 

151 

137.9 

211  192.8 

85.8 

271 

247.6 

110.2 

32 

29.2 

13.0 

92 

84.0 

37.4 

152 

138.9 

61.8 

212  193.7 

86.2 

272 

248.5 

110.6 

33 

30.1 

13.4 

93 

85.0 

37.8 

153 

139.8 

62.2 

213 

194.6 

86.6 

273 

249.4 

111.0 

34 

31.1 

13.8 

94 

85.9 

38.2 

154 

140.7 

62.6 

214 

195.5 

87.0 

274 

250.3 

111.4 

35 

32.0 

14.2 

95 

86.8 

38.6 

155 

141.6 

63.0 

215 

196.4 

87.4 

275 

251.2 

111.9 

36 

32.9 

14.6 

96 

87.7 

39.0 

156 

142.5 

63.5 

216 

197.3 

87.9 

276 

252.1 

112.3 

37 

33.8 

15.0 

97 

88.6 

39.5 

157 

143.4 

63.9 

217 

198.2 

88.3 

277 

253.1 

112.7 

38 

34.7 

15.5 

98 

89.5 

39.9 

158 

144.3 

64.3 

218 

199.2 

88.7 

278 

254.0 

113.1 

39 

35.6 

15.9 

99 

90.4 

40.3 

159 

145.3 

64.7 

219 

200.1 

89.1 

279 

254.9 

113.5 

40 

36.5 

16.3 

100 

91.4 

40.7 

160 

146.2 

65.1 

220 

201.0 

89.5 

280 

255.8 

113.9 

41 

37.5 

16.7 

101 

92.3 

41.1 

161 

147.1 

65.5 

221 

201.9 

89.9 

281 

256.7 

114.3 

42 

38.4 

17.1 

102 

93.2 

41.5 

162 

148.0 

65.9 

222 

202.8 

90.3 

282 

257.6 

114.7 

43 

39.3 

17.5 

103 

94.1 

41.9 

163 

148.9 

66.3 

223 

203.7 

90.7 

283 

258.5 

115.1 

44 

40.2 

17.9 

104 

95.0 

42.3 

164 

149.8 

66.7 

224 

204.6 

91.1 

284 

259.4 

115.5 

45 

41.1 

18.3 

105 

95.9 

42.7 

165 

150.7 

67.1 

225 

205.5 

91.5 

285 

260.4 

115.9 

46 

42.0 

18.7 

106 

96.8 

43.1 

166 

151.6 

67.5 

226 

206.5 

91.9 

286 

261.3 

116.3 

47 

42.9 

19.1 

107 

97.7 

43.5 

167 

152.6 

67.9 

227 

207.4 

92.3 

287 

262.2 

116.7 

48 

43.9 

19.5 

108 

98.7 

43.9 

168 

153.5 

68.3 

228 

208.3 

92.7 

288 

263.1 

117.1 

49 

44.8 

19.9 

109 

99.6 

44.3 

169 

154.4 

68.7 

229 

209.2 

93.1 

289 

264.0 

117.5 

50 
51 

45.7 

20.3 

110 

100.5 

44.7 

170 

155.3 

69.1 

230 

210.1 

93.5 

290 

264.9 

118.0 

46.6 

20.7 

111 

101.4 

45.1 

171 

156.2 

69.6 

231 

211.0 

94.0 

291 

265.8 

118.4 

52 

47.5 

21.2 

112 

102.3 

45.6 

172 

157.1 

70.0 

232 

211.9 

94.4 

292 

266.8 

118.8 

53 

48.4 

21.6 

113 

103.2 

46.0 

173 

158.0 

70.4 

233 

212.9 

94.8 

293 

267.7 

119.2 

54 

49.3 

22.0 

114 

104.1 

46.4 

174 

159.0 

70.8 

234 

213.8 

95.2 

294 

268.6 

119.6 

55 

50.2 

22.4 

115 

105.1 

46.8 

175 

159.9 

71.2 

235 

214.7 

95.6 

295 

269.5 

120.0 

56 

51.2 

22.8 

116 

106.0 

47.2 

176 

160.8 

71.6 

236 

215.6 

96.0 

296 

270.4 

120.4 

57 

52.1 

23.2 

117 

106.9 

47.6 

177 

161.7 

72.0 

237 

216.5 

96.4 

297 

271.3 

120.8 

58 

53.0 

23.6 

118 

107.8 

48.0 

178 

162.6 

72.4 

238 

217.4 

96.8 

298 

272.2 

121.2 

59 

53.9 

24.0 

119 

108.7 

48.4 

179 

163.5 

72.8 

239 

218.3 

97.2 

299 

273.2 

121.6 

60 

54.8 

24.4 

120 

109.6 

48.8 
Lat. 

180 

164.4 

73.2 

240 

219.3 

97.6 

300 

274.1 

122.0 

Diat 

.  Dep. 

Lat.  I  Dist. 

Dep. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

For  66  De2:rees.                         4h  24m.  | 

TABLE  11. 

<>   1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  25  DEGREES.  Ih  40i».  1 

Dist 
1 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist. 

181 

Lat 

Dep. 

Dist 

Lat 

Dep, 

00.9 

00.4 

31 

55.3 

25.8 

121 

109.7 

51.1 

164.0 

76.5 

241 

218.4 

101.9 

2 

01.8 

00.8 

62 

56.2 

26.2 

122 

110.6151.6 

1^2 

164.9 

76.9 

242 

219.3 

102.3 

3 

02.7 

01.3 

63 

57.1 

26.6 

123 

111.5 

52.0 

183 

165.9 

77.3 

243 

220.2 

102  7 

4 

03.6 

01.7 

64 

58.0 

27.0 

124 

112.4 

52.4 

184  166.8 

77.8 

244 

221.1 

103.1 

5 

04.5 

02.1 

65 

58.9 

27.5 

125 

113.3 

52.8 

185  167.7 

78.2 

245 

222.0 

103.5 

6 

05.4 

02.5 

66 

59.8 

27.9 

126 

114.2 

53.2 

186 

168.6 

78.6 

246 

223.0 

104.0 

7 

06.3 

03.0 

67 

60.7 

28.3 

127 

115.1 

53.7 

187 

169.5 

79.0 

247 

223.9 

104.4 

8 

07.3 

03.4 

68 

61.6 

28.7 

128 

116.0 

54.1 

188 

170.4 

79.5 

248 

224.8 

104  8 

9 

08.2 

03.8 

69 

62.5 

29.2 

129 

116.9 

54.5 

189 

171.3 

79.9 

249 

225.7 

105.2 

10 
11 

09.1 

04.2 

70 

63.4 

29.6 

130 

117.8 

54.9 

190 

172.2 

80.3 

250 

226.6 

105.7 

10.0 

04.6 

71 

64.3 

30.0 

131 

118.7 

55.4 

191 

173.1 

80.7 

251 

227.5 

106.1 

12 

10.9 

05.1 

72 

65.3 

30.4 

132 

119.6 

55.8 

192 

174.0 

81.1 

252 

228.4 

106.5 

13 

11.8 

05.5 

73 

66.2 

30.9 

133 

120.5 

56.2 

193 

174.9 

81.6 

253 

229.3 

106.9 

14 

12.7 

05.9 

74 

67.1 

31.3 

134 

121.4 

56.6 

194 

175.8 

82.0 

254 

230.2 

107.3 

15 

13.6 

06.3 

75 

68.0 

31.7 

135 

122.4 

57.1 

195 

176.7 

82.4 

255 

231.1 

107.8 

16 

14.5 

06.8 

76 

68.9 

32.1 

136 

123.3 

57.5 

196 

177.6 

82.8 

256 

232.0 

108.2 

17 

15.4 

07.2 

77 

69.8 

32.5 

137 

124.2 

57.9 

197 

178.5 

83.3 

257 

232.9 

108.6 

18 

16.3 

07.6 

78 

70.7 

33.0 

138 

125.1 

58.3 

198 

179.4 

83.7 

258 

233.8 

109.0 

19 

17.2 

08.0 

79 

71.6 

33.4 

139 

126.0 

58.7 

199 

180.4 

84.1 

259 

234.7 

109.5 

20 

18.1 

08.5 

80 

72.5 

33.8 

140 

126.9 

59.2 

200 

181.3 

84.5 

260 

235.6 

109.9 

21 

19.0 

08.9 

81 

73.4 

34.2 

141 

127.8 

59.6 

201 

182.2 

84.9 

261 

236.5 

110.3 

22 

19.9 

09.3 

82 

74.3 

34.7 

142 

128.7 

60.0 

202 

183.1 

85.4 

262 

237.5 

110.7 

23 

20.8 

09.7 

83 

75.2 

35.1 

143 

129.6 

60.4 

203 

184.0 

85.8 

263 

238.4 

111.1 

24 

21.8 

10.1 

84 

76.1 

35.5 

144 

130.5 

60.9 

204 

184.9 

86.2 

264 

239.3 

111.6 

25 

22.7 

10.6 

85 

77.0 

35.9 

145 

131.4 

61.3 

205 

185.8 

86.6 

265 

240.2 

112.0 

26 

23.6 

11.0 

86 

77.9 

36.3 

146 

132.3 

61.7 

206 

186.7 

87.1 

266 

241.1 

112.4 

27 

24.5 

11.4 

87 

78.8 

36.8 

147 

133.2 

62.1 

207 

187.6 

^7.5 

267 

242.0 

112.8 

28 

25.4 

11.8 

88 

79.8 

37.2 

148 

134.1 

62.5 

208 

188.5 

87.9 

268 

242.9 

113.3 

29 

•26.3 

12.3 

89 

80.7 

37.6 

149 

135.0 

63.0 

209 

189.4 

88.3 

269 

243.8 

113.7 

30 

27.2 

12.7 

90 

81.6 

38.0 

150 

135.9 

63.4 

210 

190.3 

88.7 

270 

244.711 14.1  1 

31 

28.1 

13.1 

91 

82.5 

38.5 

151 

136.9 

63.8 

211 

191.2 

89.2 

271 

245.6 

114.5 

32 

29.0 

13.5 

92 

83.4 

38.9 

152 

137.8 

64.2 

212 

192.1 

89.6 

272 

246.5 

115.0 

33 

29.9 

13.9 

93 

84.3 

39.3 

153 

138.7 

64.7 

213 

193.0 

90.0 

273 

247.4 

115.4 

34 

30.8 

14.4 

94 

85.2 

39.7 

154 

139.6 

65.1 

214 

193.9 

90.4 

274 

248.3 

115.8 

35 

31.7 

14.8 

95 

86.1 

40.1 

155 

140.5 

65.5 

215 

194.9 

90.9 

275 

249.2 

116.2 

36 

32.6 

15.2 

96 

87.0 

40.6 

156 

141.4 

65.9 

216 

195.8 

91.3 

276 

250.1 

116.6 

37 

33.5 

15.6 

97 

87.9 

41.0 

157 

142.3 

66.4 

217 

196.7 

91.7 

277 

251.0 

117.1 

38 

34.4 

16.1 

98 

88.8 

41.4 

158 

143.2 

66.8 

218 

197.6 

92.1 

278 

252.0 

117.5 

39 

35.3 

16.5 

99 

89.7 

41.8 

159 

144.1 

67.2 

219 

198.5 

92.6 

279 

252.9 

117.9 

40 

36.3 

16.9 

100 

90.6 

42.3 

160 

145.0 

67.6 

220 

199.4 

93.0 

280 

253.8 

118.3 

41 

37.2 

17.3 

101 

91.5 

42.7 

161 

145.9 

68.0 

221 

200.3 

93.4 

281 

254.7 

118.8 

42 

38.1 

17.7 

102 

92.4 

43.1 

162 

146.8 

68.5 

222 

201.2 

93.8 

282 

255.6 

119.2 

43 

39.0 

18.2 

103 

93.3 

43.5 

163 

147.7 

68.9 

223 

202.1 

94.2 

283 

256.5 

119.6 

44 

39.9 

18.6 

104 

94.3 

44.0 

164 

148.6 

69.3 

224 

203.0 

94.7 

284 

257.4 

120.0 

45 

40.8 

19.0 

105 

95.2 

44.4 

165 

149.5 

69.7 

225 

203.9 

95.1 

285 

258.3 

120.4 

46 

41.7 

19.4 

106 

96.1 

44.8 

166 

150.4 

70.2 

226 

204.8 

95.5 

286 

259.2 

120.9 

47 

42.6 

19.9 

107 

97.0 

45.2 

167 

151.4 

70.6 

227 

205.7 

95.9 

287 

260.1  121.3  1 

48 

43.5 

20.3 

108 

97.9 

45.6 

168 

152.3 

71.0 

228 

206.6 

96.4 

288 

261.0 

121.7 

49 

44.4 

20.7 

109 

98.8 

46.1 

169 

153.2 

71.4 

229 

207.5 

96.8 

289 

261.9 

122.1 

50 
51 

45.3 
46.2 

21.1 

110 

99.7 

46.5 

170 

154.1 

71.8 

230 

208.5 

97.2 

290  262.8 

122.6 

21.6 

111 

100.6 

46.9 

171 

155.0 

72.3 

231 

209.4 

97.6 

291 

263.7  123.0 1 

52 

47.1 

22.0 

112 

101.5 

47.3 

172 

155.9 

72.7 

232 

210.3 

98.0 

292 

264.6 

123.4 

53 

48.0 

22.4 

113 

102.4 

47.8 

173 

156.8 

73.1 

233 

211.2 

98.5 

293  1  265.5  1 

123.8 

54 

48.9 

22.8 

114 

103.3 

48.2 

174 

157.7 

73.5 

234 

212.1 

98.9 

294  ,  266.5  ( 

124.2 

55 

49.8 

2:!.2 

11.^. 

104.2 

48.6 

175 

158.6 

74.0 

235 

213.0 

99.3 

295 

267.4 

124.7 

56 

50.8 

23.7 

116 

105.1 

49.0 

176 

1.59.5 

74.4 

236 

213.9 

99.7 

296 

268.3 

125.1 

57 

51.7 

24.1 

117 

106.0 

49.4 

177 

160.4 

74.8 

237 

214.8 

100.2 

297 

269.2 

125.5 

58 

52.6 

24.5 

lis 

106.9 

49.9 

17s 

161.3 

75.2 

238 

215.7 

100.6 

298 

270.1 

125.9 

59 

53.5 

24.9 

119 

107.9 

50.3 

179 

162.2 

75.6 

239 

216.6 

101.0 

299 

271.0 

126.4 

60 

54.4 

25.4 

120 

108.8 

50.7 

180 

163.1 

76.1 

240 

217.5 

101.4 

300 

271.9 

126.8 

Dist 

Dep. 

Lat. 

Dl8t 

Dep. 

Lat 

Dist 

Dep. 

Lat.  Dist 

Dep. 

Lat   Dist 

Dep. 

Lat 

P 

'or  65  Decrees. 

4h  2011.  1 

42 

TABLE  11. 

• 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  26  DEGREES.  Ih  44». 

Dist 

Lat. 

Dep. 

Dist. 

Lat, 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

00.4 

61 

54.8 

26.7 

121 

108.8 

53.0 

181 

162.7 

79.8 

241 

216.6 

105.6 

2 

01.8 

00.9 

62 

55.7 

27.2 

122 

109.7 

53.5 

182 

163.6 

79.8 

242 

217.5 

106.1 

3 

02.7 

01.3 

63 

56.6 

27.6 

123 

110.6 

53.9 

183 

164.5 

80.2 

243 

218.4 

106.5 

4 

03.6 

01.8 

64 

57.5 

28.1 

124 

111.5 

54.4 

184 

165.4 

80.7 

244 

219.3 

107.0 

5 

04.5 

02.2 

65 

58.4 

28.5 

125 

112.3 

54.8 

185 

166.3 

81.1 

245 

220.2 

107.4 

6 

05.4 

02.6 

66 

59.3 

28.9 

126 

113.2 

55.2 

186 

167.2 

81.5 

246 

221.1 

107.8 

7 

06.3 

03.1 

67 

60.2 

29.4 

127 

114.1 

55.7 

187 

168.1 

82.0 

247 

222.0 

108.3 

8 

07.2 

03.5 

68 

61.1 

29.8 

12S 

115.0 

56.1 

188 

169.0 

82.4 

248 

222.9 

108.7 

9 

08.1 

03.9 

69 

62.0 

30.2 

129 

115.9 

56.5 

189 

169.9 

82.9 

249 

223.8 

109.2 

10 
11 

09.0 

04.4 

70 

62.9 

30.7 

130 

116.8 

57.0 

190 

170.8 

83.3 

250 

224.7 

109.6 

09.9 

04.8 

71 

63.8 

31.1 

131 

117.7 

57.4 

191 

171.7 

83.7 

251 

225.6 

110.0 

12 

10.8 

05.3 

72 

64.7 

31.6 

132 

118.6 

57.9 

192 

172.6 

84.2 

252 

226.5 

110.5 

13 

11.7 

05.7 

73 

65.6 

32.0 

133 

119.5 

58.3 

193 

173.5 

84.6 

253 

227.4!  110.9 

14 

12.6 

06.1 

74 

66.5 

32.4 

134 

120.4 

58.7 

194 

174.4 

85.0 

254 

228.3 

111.3 

15 

13.5 

06.6 

75 

67.4 

32.9 

135 

121.3 

59.2 

195 

175.3 

85.5 

255 

229.2 

111.8 

16 

14.4 

07.0 

76 

68.3 

33.3 

1-36 

122.2 

59.6 

196 

176.2 

85.9 

256 

230.1 

112.2 

17 

15.3 

07.5 

77 

69.2 

33.8 

137 

1 23. 1 

60.1 

197 

177.1 

86.4 

257 

231.0 

112.7 

18 

16.2 

07.9 

78 

70.1 

34.2 

138 

124.0 

60.5 

198 

178.0 

86.8 

258 

231.9 

113.1 

19 

17.1 

08.3 

79 

71.0 

34.6 

139 

124.9 

60.9 

199 

178.9 

87.2 

259 

232.8 

113.5 

20 

18.0 

08.8 

80 

71.9 

35.1 

140 

125.8 

61.4 

200 

179.8 

87.7 

260 

233.7 

114.0 

21 

18.9 

09.2 

81 

72.8 

35.5 

141 

126.7 

61.8 

201 

180.7 

88.1 

261 

234.6 

114.4 

22 

19.8 

09.6 

82 

73.7 

35.9 

142 

127.6 

62.2 

202 

181.6 

88.6 

262 

235.5 

114.9 

23 

20.7 

10.1 

83 

74.6 

36.4 

143 

128.5 

62.7 

203 

182.5 

89.0 

263 

236.4 

115.3 

24 

21.6 

10.5 

84 

75.5 

36.8 

144 

129.4 

63.1 

204 

183.4 

89.4 

264 

237.3 

115.7 

25 

22.5 

11.0 

85 

76.4 

37.3 

145 

130.3 

63.6 

205 

184.3 

89.9 

265 

238.2 

116.2 

26 

23.4 

11.4 

86 

77.3 

37.7 

146 

131.2 

64.0 

206 

185.2 

90.3 

266 

239.1 

116.6 

27 

24.3 

11.8 

87 

78.2 

38.1 

147 

132.1 

64.4 

207 

186.1 

90.7 

267 

240.0 

117.0 

28 

25.2 

12.3 

88 

79.1 

38.6 

148 

133.0 

64.9 

208 

186.9 

91.2 

268 

240.9' 

117.5 

29 

26.1 

12.7 

89 

80.0 

39.0 

149 

133.9 

65.3 

209 

187.8 

91.6 

269 

241.8 

117.9 

30 

27.0 

13.2 

90 

80.9 

39.5 

1.50 

134.8 

65.8 

210 

18C.7 

92.1 

270 

242.7 

118.4 

31 

27.9 

13.6 

91 

81.8 

39.9 

151 

135.7 

66.2 

211 

189.6 

92.5 

271 

243.6 

118.8 

:J2 

28.8 

14.0 

92 

82.7 

40.3 

152 

136.6^ 

66.6 

212 

190.5 

92.9 

272 

244.5 

119.2 

33 

29.7 

14.5 

93 

83.6 

40.8 

1.53 

137.5 

67.1 

213 

191.4 

93.4 

273 

245.4 

119.7 

34 

30.6 

14.9 

94 

84.5 

41.2 

154 

138.4 

67.5 

214 

192.3 

93.8 

274 

246.3 

120.1 

35 

31.5 

15.3 

95 

85.4 

41.6 

155 

139.3 

67.9 

215 

193.2 

94.2 

275 

247.2 

120.6 

36 

32.4 

15.8 

96 

86.3 

42.1 

156 

140.2 

68.4 

216 

194.1 

94.7 

276 

248.1 

121.0 

37 

33.3 

16.2 

97 

87.2 

42.5 

157 

141.1 

68.8 

217 

195.0 

95.1 

277 

249.0 

121.4 

38 

34.2 

16.7 

98 

88.1 

43.0 

158 

142.0 

69.3 

218 

195.9 

95.6 

278 

249.9' 

121.9 

39 

35.1 

17.1 

99 

89.0 

43.4 

159 

142.9 

69.7 

219 

196.8 

96.0 

279 

250.8 

122.3 

40 

36.0 

17.5 

100 

89.9 

43.8 

160 

143.8 

70.1 

220 

197.7 

96.4 

280 

251.7 

122.7 

41 

36.9 

18.0 

101 

90.8 

44.3 

161 

144.7 

70.6 

221 

198.6 

96.9 

281 

252.6 

123.2 

42 

37.7 

18.4 

102 

91.7 

44.7 

162 

145.6 

71.0 

222 

199.5 

97.3 

282 

253.5 

123.6 

43 

38.6 

18.8 

103 

92.6 

45.2 

163 

146.5 

71.5 

223 

200.4 

97.8 

283 

254.4 

124.1 

44 

39.5 

19.3 

104 

93.5 

45.6 

164 

147.4 

71.9 

224 

201.3 

98.2 

284 

255.3 

124.5 

45 

40.4 

19.7 

105 

94.4 

46.0 

165 

148.3 

72.3 

225 

202.2 

98.6 

285 

256.2 

124.9 

46 

41.3 

20.2 

106 

95.3 

46.5 

166 

149.2 

72.8 

226 

203.1 

99.1 

286 

257.1 

125.4 

47 

42.2 

20.6 

107 

96.2 

46.9 

167 

150.1 

73.2 

227 

204.0 

99.5 

287  258.0 

125.8 

48 

43.1 

21.0 

108 

97.1 

47.3 

1(58 

151.0 

73.6 

228 

204.9 

99.9 

288 

258.9 

126.3 

49 

44.0 

21.5 

109 

98.0 

47.8 

169 

151.9 

74.1 

229 

205.8 

100.4 

289 

259.8 

126.7 

50 

44.9 

21.9 

110 

98.9 

48.2 

170 

152.8 

74.5 

230 

206.7 

100.8 

290 

260.7 

127.1 

51 

45.8 

22.4 

111 

99.8 

48.7 

171 

153.7 

75.0 

231 

207.6 

101.3 

291 

261.5 

127.6 

52 

46.7 

22.8 

112 

100.7 

49.1 

172 

154.6 

75.4 

232 

208.5 

101.7 

292 

262.4 

128.0 

53 

47.6 

23.2 

113 

101.6 

49.5 

173 

155.5 

75.8 

233 

209.4 

102.1 

293 

263.3 

128.4 

54 

48.5 

23.7 

114 

102.5 

50.0 

174 

1.56.4 

76.3 

234 

210.3 

102.6  2941 

264.2 

128.9 

55 

49.4 

24.1 

115 

103.4 

50.4 

175 

157.3 

76.7 

235 

211.2 

103.0 

295 

265.1 

129,3 

5t) 

50.3 

24.5 

116 

104.3 

50.9 

176 

158.2 

77.2 

236 

212.1 

103.5 

296 

266.0 

129.8 

57 

51.2 

25.0 

117 

105.2 

51.3 

177 

159.1 

77.6 

237 

213.0 

103.9 

297 

266.9 

1.30.2 

58 

52.1 

25.4 

118 

106.1 

51.7 

17S 

160.0 

78.0 

238 

213.9 

104.3 

298 

267.8 

130.6 

59 

53.0 

25.9 

K9 

107.0 

.52.2 

179 

160.9 

78.5 

239 

214.8 

104.8 

299 

268.7 

131.1 

60 

W8t 

53.9 

26.3 

120 

107.9 

,52.6 

180 

161.8 

78.9  240 

215.7 

105.2 

300 

269.6 

131.5 

Dep. 

Lat. 

Dist. 

Dep, 

Lat. 

Dist. 

Dep. 

Lat.  Dist. 

Dep. 

Lat. 

Dist. 

Dep.  1  Lat.  | 

i 

"or  64  Dei,'rfe.s. 

4h  16ra.  1 

TABLE  11.              i                    48 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  27  DEGREES.   la  48m. 

Dist 

1 
«2 

3 
4 
5 
6 

7 

8 

9 

10 

Lat 

00.9 
01.8 
02.7 
03.6 
04.5 
05.3 
06.2 
07.1 
08.0 
08.9 

Dep. 

00.5 
00.9 
01.4 
01.8 
02.3 
02.7 
03.2 
03.6 
04.1 
04.5 

Dist. 

Lat 

Dep. 

Dist. 

Lilt. 

Dep. 

54.9 
55.4 
55.8 
56.3 
56.7 
57.2 
57.7 
58.1 
58.6 
59.0 

Dist. 

Lat. 

Dep. 

Diat. 

241 
242 
243 
244 
245 
246 
247 
248 
249 
250 

Lat 

Dep. 

61 
62 
63 
64 
65 
66 
67 
68 
69 
70 

54.4 
55.2 
56.1 
57.0 
57.9 
58.8 
^  59.7 
60.6 
61.5 
62.4 

27.7 
28.1 
28.6 
29.1 
29.5 
30.0 
30.4 
30.9 
31.3 
31.8 

121 
122 
123 
124 
125 
126 
127 
128 
129 
130 

131 
132 
133 
134 
135 
136 
137 
138 
139 
140 

107.8 
108.7 
109.6 
110.5 
111.4 
112.3 
113.2 
114.0 
114.9 
115.8 

181 
182 
183 

184 
185 
186 
187 
188 
189 
190 

191 
192 
193 
194 
195 
196 
197 
198 
199 
200 

201 
202 

203 
204 
205 

206 
207 
208 
209 
210 

161.3 
162.2 
163.1 
163.9 
164.8 
165.7 
166.6 
167.5 
168.4 
169.3 

82.2 
82.6 
83.1 
83.5 
84.0 
84.4 
84.9 
85.4 
85.8 
86.3 

214.7 
215.6 
216.5 
217.4 
218.3 
219.2 
220.1 
221.0 
221.9 
222.8 

109.4 
109.9 
110.3 
110.8 
111.2 
111.7 
112.1 
112.6 
113.0 
113.5 

11 

12 
13 
14 
15 
16 
17 
18 
19 
20 

21 
22 
23 
24 
25 
26 
27 
28 
29 
30 

09.8 
10.7 
11.6 
12.5 
13.4 
14.3 
15.1 
16.0 
16.9 
17.8 

05.0 
05.4 
05.9 
06.4 

06.8 
07.3 
07.7 
08.2 
08.6 
09.1 

71 

72 
73 
74 
75 

76 
77 
78 
79 
80 

63.3 
64.2 
65.0 
65.9 
66.8 
67.7 
68.6 
69.5 
70.4 
71.3 

32.2 
32.7 
33.1 
33.6 
34.0 
34.5 
35.0 
35.4 
35.9 
36.3 

36.8 
37.2 
37.7 
38.1 
38.6 
39.0 
39.5 
40.0 
40.4 
40.9 

116.7 
117.6 
118.5 
119.4 
120.3 
121.2 
122.1 
123.0 
123.^ 
124.7 

59.5 
59.9 
60.4 
60.8 
61.3 
61.7 
62.2 
62.7 
63.1 
63.6 

64.0 
64.5 
64.9 
65.4 
65.8 
66.3 
66.7 
67.2 
67.6 
6s.  1 

170.2 
171.1 
172.0 
172.9 
173.7 
174.6 
175.5 
176.4 
177.3 
178.2 

86.7 
87.2 
87.6 
88.1 
88.5 
89.0 
89.4 
89.9 
90.3 
90.8 

251 
252 
253 

254 
255 
256 
257 

258 
259 
260 

223.6 
224.5 
225.4 
226.3 
227.2 
228.1 
229.0 
229.9 
230.8 
231.7 

114.0 
114.4 
114.9 
115,3 
115.8 
116.2 
116.7 
117.1 
117.6 
118.0 

18.7 
19.6 
20.5 
21.4 
22.3 
23.2 
24.1 
24.9 
25.8 
26.7 

09.5 
10.0 
10.4 
10.9 
11.3 
11.8 
12.3 
12.7 
13.2 
13.6 

81 

82 
83 
84 
85 
86 
87 
88 
89 
90 

72.2 
73.1 
74.0 

74.8 
75.7 
76.6 
77.5 
78.4 
79.3 
80.2 

141 
142 
143 
144 
145 
146 
147 
148 
149 
150 

125.6 
126.5 
127.4 
128.3 
129.2 
130.1 
131.0 
131.9 
132.8 
133.7 

134  5 
135.4 
136.3 
137.2 
138.1 
139.0 
139.9 
140.8 
141.7 
142.6 

179.1 
180.0 
180.9 
181.8 
182.7 
183.5 
184.4 
185.3 
186.2 
187.1 

91.3 
91.7 
92.2 
92.6 
93.1 
93.5 
94.0 
94.4 
94.9 
95.3 

261 
262 
263 
264 
265 
266 
267 
268 
269 
270 

232.6 
233.4 
234.3 
235.2 
236.1 
237.0 
237.9 
238.8 
239.7 
240.6 

118.5 
118.9 
119.4 
119.9 
120.3 
120.8 
121.2 
121.7 
122.1 
122.6 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

27.6 
28.5 
29.4 
30.3 
31.2 
32.1 
33.0 
33.9 
34.7 
35.6 

14.1 
14.5 
15.0 
15.4 
15.9 
16.3 
16.8 
17.3 
17.7 
18.2 

91 
92 
93 
94 
95 
96 
97 
98 
99 
100 

81.1 

82.0 
82.9 
83.8 
84.6 
85.5 
86.4 
87.3 
88.2 
89.1 

41.3 
41.8 
42.2 
42.7 
43.1 
43.6 
44.0 
44.5 
44.9 
45.4 

151 
152 
153 
154 
155 
156 
157 
158 
159 
160 

68.6 
69.0 
69.5 
69.9 
70.4 
70.8 
71.3 
71.7 
72.2 
72.6 

211 
212 
213 
214 
215 
216 
217 
218 
219 
220 

221 
222 
223 
224 
225 
226 
227 
228 
229 
230 

188.0 
188.9 
189.8 
190.7 
191.6 
192.5 
193.3 
194.2 
195.1 
196.0 

95.8 
96.2 
96.7 
97.2 
97.6 
98.1 
98.5 
99.0 
99.4 
99.9 

271 
272 
273 
274 
275 
276 
277 
278 
279 
280 

241.5 
242.4 
243.2 
244.1 
245.0 
245.9 
246.8 
247.7 
248.6 
249.5 

123.0 
123.5 
123.9 
124.4 
124.8 
125.3 
125.8 
126.2 
126.7 
127.1 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

51 
52 
53 
54 
55 
56 
57 
58 
59 
60 

36.5 
37.4 
38.3 
39.2 
40.1 
41.0 
41.9 
42.8 
43.7 
44.6 

45.4 
46.3 
47.2 
48,1 
49.0 
49.9 
50.8 
51.7 
52.6 
53.5 

18.6 
19.1 
19.5 
20.0 
20.4 
20.9 
21.3 
21.8 
22.2 
22.7 

101 
102 
103 
104 
105 
106 
107 
108 
109 
110 

90.0 
90.9 
91.8 
92.7 
93.6 
94.4 
95.3 
96.2 
97.1 
98.0 

45.9 
46.3 

46.8 
47.2 
47.7 
48.1 
48.6 
49.0 
49.5 
49.9 

161 

162 
163 
164 

165 
166 
167 
168 
169 
170 

143.5 
144.3 
145.2 
146.1 
147.0 
147.9 
148.8 
149.7 
150.6 
151.5 

73.1 
73.5 

74.0 
74.5 
74.9 
75.4 

75.8 
76.3 

76.7 

77.2 

196.9 
197.8 
198.7 
199.6 
200.5 
201.4 
202.3 
203.1 
204.0 
204.9 

100.3 
100.8 
101.2 
101.7 
102.1 
102.6 
103.1 
103.5 
104.0 
104.4 

281 
282 
283 
284 
285 
286 
287 
288 
289 
290 

250.4 
251.3 
2.  2.2 
253.0 
253.9 
254.8 
255.7 
256.6 
257.5 
258.4 

127.6 
128.0 
128.5 
128.9 
129.4 
129.8 
130.3 
130.7 
131.2 
131.7 

23.2 
23.6 
24.1 
24.5 
25.0 
25.4 
25.9 
26.3 
26.8 
27.2 

111 

112 
113 
114 
115 
116 
117 
118 
119 
120 

98.9 
99.8 
100.7 
101.6 
102.5 
103.4 
104.2 
105.1 
106.0 
106.9 

50.4 
50.8 
51.3 
51.8 
52.2 
52.7 
53.1 
53.6 
54.0 
54.5 

L.at. 

171 
172 
173 
174 
175 
176 
177 
178 
179 
180 

152.4 
153.3 
154.1 
15.5.0 
155.9 
156.8 
157.7 
158.6 
159.5 
160.4 

77.6 
78.1 
78.5 
79.0 
79.4 
79.9 
80.4 
80.8 
81.3 
81.7 

231 
232 
233 
234 
235 
236 
237 
238 
239 
240 

205.8 
206,7 
207.6 
208.5 
209.4 
210.3 
211.2 
212.1 
213.0 
213.8 

104.9 
105.3 
105.8 
106.2 
106.7 
107.1 
107.6 
108.0 
108.5 
109.0 

291 
292 
293 
294 
295 
296 
297 
298 
299 
300 

Dist. 

259.3 
260.2 
261.1 
262.0 
262.8 
263.7 
264.6 
2<)5.5 
2<)6.4 
267.3 

132.1 
132.6 
133.0 
133.5 
133.9 
134.4 
134.8 
135.3 
135.7 
136.2 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dep. 

Lat 

For  nS  Detrree*                             4h  12'n.   | 

44 

TABLE  II.                         1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  28  DEGREES,  l^*  52n>. 

Dist 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

1 

00.9 

00.5 

61 

53.9 

28.6 

121 

106.8 

56.8 

181 

159.8 

85.0 

241 

212.8 

113.1 

2 

01.8 

00.9 

62 

54.7 

29.1 

122 

107.7 

57.3 

1S2 

160.7 

85.4 

242 

213.7 

113.6 

3 

02.6 

01.4 

63 

55.6 

29.6 

123 

108.6 

57.7 

183 

161.6 

85.9 

243 

214.6 

114.1 

4 

03.5 

01.9 

64 

56.5 

30.0 

124 

109.5 

58.2 

184 

162.5 

86.4 

244 

215.4 

114.6 

5 

04.4 

02.3 

65 

57.4 

30.5 

125 

110.4 

58.7 

185 

163.3 

86.9 

245 

216.3 

115.0 

6 

05.3 

02.8 

66 

58.3 

31.0 

126 

111.3 

59.2 

186 

164.2 

87.3 

246 

217.2 

115.5 

7 

06.2 

03.3 

67 

59.2 

31.5 

127 

112.1 

59.6 

187 

165.1 

87.8 

247 

218.1 

116.0 

8 

07.1 

03.8 

68 

60.0 

31.9 

128 

113.0 

60.1 

188 

166.0 

88.3 

248 

219.0 

116.4 

9 

07.9 

04.2 

69 

60.9 

32.4 

129 

113.9 

60.6 

189 

166.9 

88.7 

249 

219.9 

116.9 

10 
11 

08.8 

04.7 

70 

61.8 

32.9 

i:!0 

114.8 

61.0 

190 

167.8 

89.2 

250 

220.7 

117.4 
117.8 

09.7 

05.2 

71 

62.7 

33.3 

131 

115.7 

61.5 

191 

108.6 

89.7 

251 

221.6 

12 

10.6 

05.6 

72 

63.6 

33.8 

132 

116.5 

62.0 

192 

169.5 

90.1 

252 

222.5 

118.3 

13 

11.5 

06.1 

73 

64.5 

34.3 

133 

117.4 

62.4 

193 

170.4 

90.6 

253 

223.4 

118.8 

14 

12.4 

06.6 

74 

65.3 

34.7 

134 

118.3 

62.9 

194 

171.3 

91.1 

254 

224.3 

119.2 

15 

13.2 

07.0 

75 

66.2 

35.2 

135 

119.2 

63.4 

195 

172.2 

91.5 

255 

225.2 

119.7 

16 

14.1 

07.5 

76 

67.1 

35.7 

136 

120.1 

63.8 

196 

173.1 

92.0 

256 

226.0 

120.2 

17 

15.0 

08.0 

77 

68.0 

36.1 

137 

(21.0 

64.3 

197 

173.9  92.5 

257 

226.9 

120.7 

18 

15.9 

08.5 

78 

68.9 

36.6 

138 

121.8 

64.8 

198 

174.8 

93.0 

258 

227.8 

121.1 

19 

16.8 

08.9 

79 

69.8 

37.1 

139 

122.7  65.3 

199 

175.7 

93.4 

259 

228.7 

121.6 

20 

17.7 

09.4 

80 

70.6 

37.6 

140 

123.6 

65.7 

200 

176.6 

93.9 

260 

229.6 

122.1 

21 

18.5 

09.9 

81 

71.5 

38.0 

141 

124.5 

66.2 

201 

177.5 

94.4 

261 

230.4 

122.5 

22 

19.4 

10.3 

82 

72.4 

38.5 

142 

125.4 

66.7 

202 

178.4 

94.8 

262 

231.3 

123.0 

23 

20.3 

10.8 

83 

73.3 

39.0 

143 

126.3 

67.1 

203 

179.2 

95.3 

263 

232.2 

123.5 

24 

21.2 

11.3 

84 

74.2 

39.4 

144 

127.1 

67.6 

204 

180.1 

95.8 

264 

233.1 

123.9 

25 

22.1 

11.7 

85 

75.1 

39.9 

145 

128.0 

68.1 

205 

181.0 

96.2 

265 

234.0 

124.4 

2(^ 

23.0 

12.2 

86 

75.9 

40.4 

146 

128.9 

68.5 

206 

181.9 

96.7 

266 

234.9 

124.9 

27 

23.8 

12.7  87 

76.8 

40.8 

147 

129.8 

69.0 

207 

182.8 

97.2 

267 

235.7 

125.3 

28 

24.7 

13.1   88 

77.7 

41.3 

148 

130.7 

69.5 

208 

183.7 

97.7 

268 

236.6 

125.8 
126.3 

29 

25.6 

13.6  89 

78.ft 

41.8 

149 

131.6 

70.0 

209 

184.5 

98.1 

269 

237.5 

30 
31 

26.5 

14.1 

90 
91 

79.5 

42.3 

150 

132.4 

70.4 

210 

185.4 

98.6 

270 

238.4 

126.8 

27.4 

14.6 

80.3 

42.7 

151 

133.3 

70.9 

211 

186.3 

99.1 

271 

239.3 

127.2 

32 

28.3 

15.0 

92 

81.2 

43.2 

152 

134.2 

71.4 

212 

187.2 

99.5 

272 

240.2 

127.7 

33 

29.1 

15.5 

93 

82.1 

43.7 

153 

135.1 

71.8 

213 

188.1 

100.0 

273 

241.0 

128.2 

34 

30.0 

16.0 

94 

83.0 

44.1 

154 

136.0 

72.3 

214 

189.0 

100.5 

274 

241.9 

128.6 

35 

30.9 

16.4 

95 

83.9 

44.6  155 

136.9 

72.8 

215 

189.8 

100.9 

275 

242.8 

129.1 

36 

31.8 

16.9 

96 

84.8 

45.1  156 

137.7 

73.2 

216 

190.7 

101.4 

276 

243.7 

129.6 

37 

327 

17.4 

97 

85.6 

45.5  157 

138.6 

73.7 

217 

191.6 

101.9 

277 

244.6 

130.0 

38 

33.6 

17.8 

98 

86.5 

46.0  158 

139.5 

74.2 

218 

192.5 

102.3 

278 

245.5 

130.5 

39 

34.4 

18.3 

99 

87.4 

46.5  159 

140.4 

74.6 

219 

193.4 

102.8 

279 

246.3 

131.0 

40 
41 

35.3 

36.2 

18.8 

100 

88.3 

46.9  160 

141.3 

75.1 

220 

194.2 

103.3 

280 

247.2 

131.5 

19.2 

101 

89.2 

47.4 

161 

142.2 

75.6 

221 

195.1 

103.8 

281 

248.1 

131.9 

42 

.S7.1 

19.7 

102 

90.1 

47.9 

162 

143.0 

76.1 

222 

196.0 

104.2 

282 

249.0 

132.4 

43 

38.0 

20.2 

103 

90.9 

48.4 

163 

143.9 

76.5 

223 

196.9 

104.7 

283 

249.9 

132.9 

44 

38.8 

20.7 

104 

91.8 

48.8 

164 

144.8 

77.0 

224 

197.8 

105.2 

284  '  250.8 

133.3 

45 

39.7 

21.1 

105 

92.7 

49.3 

165 

145.7 

77.5 

225 

198.7 

105.6 

285 

251.6 

133.8 

46 

40.6 

21.6 

106 

93.6 

49.8 

166 

146.6 

77.9 

226 

19:».5 

106.1 

286 

252.5 

134.3 

47 

41.5 

22.1 

107 

94.5 

50.2 

167 

147.5 

78.4 

227 

200.4 

106.6 

287 

253.4 

134.7 

48 

42.4 

22.5 

108 

95.4 

50.7 

i(;8 

148.3 

78.9 

228 

201.3 

107.0 

288 

254.3 

135.2 

49 

43,3 

23.0 

109 

96.2 

51.2 

169 

149.2 

79.3 

221> 

202.2 

107.5 

289 

255.2 

135.7 

50 

44.1  23.5 

110 

97.1 

51.6 

170 

150.1 

79.8 

230 

203.1 

108.0 

290 

256.1  j  136.1 1 

51 

45.0 

23.9 

HI 

98.0 

52.1 

171 

151.0 

80.3 

231 

204.0 

108.4 

291 

256.9 

136.6 

52 

45.9 

24.4 

112 

98.9 

52.6 

172 

151.9 

80.7 

232 

204.8 

108.9 

292 

257.8 

137.1 

53 

46  8 

24.9 

113 

99.8 

53.1 

173 

152.7 

81.2 

233 

205.7 

109.4 

293 

258.7 

137.6 

54 

47.7 

25.4 

114 

100.7 

53.5  174 

153.6 

81.7 

234 

206.6 

109.9 

294 

259.6 

138.0 

55 

48.6 

25.8 

ll.i 

101.5 

54.0  175 

154.5 

82.2 

235 

207.5 

110.3 

295 

260.5 

138.5 

5(') 

49.4 

26.3 

116 

102.4 

54.5 

176 

155.4 

82.6 

236 

208.4 

110.8 

296 

261.4 

139.0 

57 

50.3 

2(5.8 

117 

10:].3 

54.9 

177 

156  3 

83.1 

237 

209.3 

111.3 

297 

262.2 

139.4 

58 

51.2 

27.2 

118 

104.2 

55.4 

17S 

157.2 

83.6 

238 

210.1 

111.7 

298 

263.1 

139.9 

59 

52.1 

27.7 

119 

105.1 

55.9 

179 

158.0 

84.0 

239 

211.0 

112.2 

299 

264.0 

140.4 

60 
Dist. 

53.0 

28.2 
Lilt. 

120 

106.0 

56.3 

180 

158.9 

84.5 

240 

211.9 

112.7 

300 

264.9  1  140.8  1 

Dep. 

Dist. 

Dep. 

Lut. 

Dist, 

D<'p. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.  1 

] 

For  62  Decrees.                          4h  8"'.  | 

TABLE  11. 

46 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  29  DEGREES.   Ih  66m. 

• 

Dist 
1 

Lat. 
00.9 

Dep. 

Di3t. 

Lat. 
53.4 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 

Lat 

Dep. 

Dist. 
241 

Lat 

Dep. 

00.5 

61 

29.6 

121 

105.8 

58.7 

181 

158.3 

87.8 

210.8 

116.8 

o 

01.7 

01.0 

62 

54.2 

30.1 

122 

10t}.7 

59.1 

182 

159.2 

88.2 

242 

211.7 

117.3 

n 

02.6 

01.5 

63 

55  1 

30.5 

123 

1U7.6 

59.6 

183 

160.1 

8S.7 

243 

212.5 

117.8 

4 

03.5 

01.9 

64 

56.0 

31.0 

124 

108.5 

60.1 

184 

160.9 

89.2 

244 

213.4 

118.3 

5 

04.4 

02.4 

65 

56.9 

31.;. 

125 

109.3 

60.6 

185 

161.8 

89.7 

24.-. 

214.3 

118.8 

6 

05.2 

02.9 

66 

57.7 

32.0 

126 

110.2 

61.1 

186 

1 62.7 

90.2 

246 

215.2 

119.3 

7 

06.1 

03.4 

67 

58.6 

32.5 

127 

111.1 

6k6 

187 

163.6 

90.7 

247 

216.0 

119.7 

8 

07.0 

03.9 

68 

5i>.5 

33.0 

128 

112.0 

62.1 

188 

1 1)4.4 

91.1 

248 

216.9 

120.2 

9 

07.9 

04.4 

69 

60.3 

33.5 

129 

112.8 

<)2.5 

189 

16.5.3 

91.6 

249 

217.8 

120.7 

10 
11 

08.7 

04.^ 

70 

61.2 

33.9 

130 
131 

113.7 

63  0 

190 
191 

166.2 

92.1 

250 

218.7 

121.2 
121.7 

09.6 

05.3 

71 

62.1 

34.4 

114.6 

63.5 

167.1 

92.6 

251 

219.5 

12 

10.5  0.-).8 

72 

63.0 

34.9 

132 

115.4 

64.0 

192 

167.9 

93.1 

252 

220.4 

122.2 

13 

11.4  06.3 

73 

63.8 

35.4 

133 

116.3 

64.5 

193 

168.8 

93.6 

253 

221.3 

122.7 

14 

12.2 

06.8 

74 

64.7 

35.9 

134 

117.2 

65.0 

194 

169.7 

94.1 

254 

222.2 

123.1 

15 

13.1 

07.3 

75 

65.6 

36.4 

135 

118.1 

65.4 

195 

170.6 

94.5 

255 

223.0 

123.6 

l() 

14.0 

07.8 

76 

66.5 

36.8 

136 

118.9 

65.9 

196 

171.4 

95.0 

256 

223.9 

124.1 

17 

14.9 

OS  2 

67.3 

37.3 

137 

119.8 

66.4 

197 

172.3 

95.5 

257 

224.8 

124.6 

18 

15.7 

08.7 

78 

68.2 

37.8 

138 

120.7 

66.9 

198 

173.2 

96.0 

258 

225.7 

125.1 

19 

16.6 

09.2 

79 

69.1 

38.3 

139 

121.6 

67.4 

199 

174.0 

96.5 

259 

226.5 

125.6 

■10 
21 

17.5 
18.4 

09.7 

80 

70.0 

38.8 

140 

122.4 

67.9 

200 

174.9 
175.8 

97.0 

260 

227.4 

126.1 

10.2 

81 

70.8 

39.3 

141 

123.3 

()S.4 

201 

97.4 

261 

228.3 

126.5 

22 

19.2 

10.7 

82 

71.7 

39.8 

142 

124.2 

68.8 

202 

176.7 

97.9 

262 

229.2 

127.0 

23 

20.1 

11.2 

83 

72.6 

40.2 

143 

125.1 

69.3 

203 

177.5 

98.4 

263 

230.0 

127.5 

24 

21.0 

11.6 

84 

73.5 

40.7 

144 

125.9 

69.8 

204 

178.4 

98.9 

264 

230.9 

128.0 

25 

21.9 

12.1 

85 

74.3 

41.2 

145 

126.8 

70.3 

205 

179.3 

91>.4 

265 

231.8 

128.5 

26 

22.7 

12.6 

86 

75.2 

41.7 

146 

127.7 

70.8 

206 

180.2 

99.9 

266 

232.6 

129.0 

27 

23.6 

13.1 

87 

76.1 

42.2 

147 

128.6 

71.3 

207 

181.0 

100.4 

267 

233.5 

129.4 

28 

24.5 

13.6 

88 

77.0 

42.7 

148 

129.4 

71.8 

208 

181.9 

100.8 

268 

234.4 

129.9 

29 

25.4 

14.1 

89 

77.8 

43.1 

149 

130.3 

72.2 

209 

182.8 

101.3 

269 

235.3 

130.4 

30 

26.2 

14.5 

90 

78.7 

43.6 

150 

131.2 

72.7 
73.2 

210 

183.7 

101.8 

270 

236.1 

130.9 

31 

27.1 

15.0 

91 

79.6 

44.1 

151 

132.1 

211 

184.5 

102.3 

271 

237.0 

131.4 

32  28.0 

15.5 

92 

80.5 

44.6 

152 

132.9 

73.7 

212 

185.4 

102.8 

272 

237.9 

131.9 

33  28.9 

l.i.O 

93 

81.3 

45.1 

153 

133.8 

74.2 

213 

186.3 

103.3 

273 

238.8 

132.4 

34 

29.7 

16.5 

94 

82.2 

45.6 

154 

134.7 

74.7 

214 

187.2 

1 03.7 

274 

239.6 

132.8 

35 

30.6 

17.0 

95 

83.1 

46.1 

155 

135.6 

75.1 

215 

188.0 

104.2 

275 

240.5 

133.3 

36 

31.5 

17.5 

96 

84.0 

46.5 

156 

136.4 

75.6 

216 

188.9 

104.7 

276 

241.4 

133.8 

->  / 

32.4 

17.9 

97 

84.8 

47.0 

157 

137.3 

76.1 

217 

189.8 

105.2 

277 

242.3 

134.3 

38 

33.2 

18.4 

98 

85.7 

47.5 

158 

138.2 

76.6 

218 

190.7 

105.7 

278 

243.1 

134.8 

39 

34.1 

IS.9 

99 

86.6 

48.0 

159 

139.1 

77.1 

219 

191.5 

106.2 

279 

244.0 

135.3 

40 

35.0 

19.4 

100 

87.5 

48.5 

160 

1 3!>.9 

77.6 

220 

192.4 

106.7 

280 

244.9 

135.7 

41 

35.9 

19.9 

101 

88.3 

49.0 

161 

140.8 

78.1 

221 

193.3 

107.1 

281 

245.8 

136.2 

42 

36.7 

20.4 

102 

89.2 

49.5 

162 

141.7 

78.5 

222 

194.2 

107.6 

282 

246.6 

136.7 

43 

37.6 

20.8 

103 

90.1 

49.9 

163 

142.6 

79.0 

223 

195.0 

108.1 

283 

247.5 

137.2 

44 

38.5 

21.3 

104 

91.0 

50.4 

164 

143.4 

79.5 

224 

195.9 

108.6 

284 

248.4 

137.7 

45 

39.4 

21.8 

105 

91.8 

50.9 

165 

144.3 

80.0 

225 

196.8 

109.1 

285 

249.3 

138.2 

46 

40.2 

22.3 

106 

92.7 

51.4 

166 

145.2 

80.5 

226 

197.7 

109.6 

286 

250.1 

138.7 

47 

41.1 

22.8 

107 

93.6 

51.9 

167 

146.1 

81.0 

227 

198.5 

110.1 

287 

251.0 

139.1 

48 

42.0 

23.3 

108 

94.5 

52.4 

168 

146.9 

81.4 

228 

199.4 

110.5 

288 

251.9  139.61 

49 

42.9  '  23.8 

10i> 

95.3 

52.8 

169 

147.8 

81.9 

229 

200.3 

111.0 

289 

252.8  140.11 

50 
51 

43.7  24.2 

1  10 

96.2 

53.3 

170 

148.7 

82.4 

230 

201.2 

111.5 

290 

253.6 

140.6 

44.6 

24.7 

111 

97.1 

53.8 

171 

149.6 

82.9 

231 

202.0 

112.0 

291 

254.5 

141.1 

52 

45.5 

25.2 

1  12 

98.0 

54.3 

172 

150.4 

83.4 

232 

202.9 

112.5 

292 

255.4 

141.6 

53 

46.4 

25.7 

113 

98.8 

54.8 

173 

151.3 

83.9 

233 

203.8 

113.0 

293 

2r.6.3 

142.0 

54 

47.2 

26.2 

114 

99.7 

55.3 

174 

152.2 

84.4 

234 

204.7 

113.4 

294 

257.1 

142.5 

55  4fS.l 

26.7 

115 

100.6 

55.8 

175 

153.1 

84.8 

235 

205.5 

113.9 

295 

258.0 

143.0 

50  49.0 

27.1 

116 

101.5 

56.2 

176 

1.53.9 

85.3 

236 

206.4 

114.4 

296 

2.58.9 

143.5 

57 

49.9 

27.6 

117 

102.3 

56.7 

177 

-154.8 

85.8 

237 

207.3 

114.9 

297 

259.8 

144.0 

58 

50.7 

28.1 

118 

io;;.2 

57.2 

178 

155.7 

86.3 

238 

208.2 

115.4 

298 

260.6 

144.5 

59 

51.6 

2.S.6 

119 

104.1 

57.7 

179 

156.6 

86.8 

239 

209.0 

115.9 

299 

261.5 

145.0 

60 
Dist 

52.5 

Dep. 

29.1 

120 

105.0 

58.2 
Lat. 

180 

157.4 

87.3 

240 

209.9 

116.4 

300 

262.4 

145.4 

Lat. 

Dist. 

Dep. 

Dist. 

Dep 

Lnt. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

For  61  Dpp^i'Ges. 

4h  4m.   1 

46 

TABLE  II. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  30  DEGREES.   2 

Q  0». 

DisL 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dl8t. 

Lat. 

Dep. 

Dist. 

Lat. 

'  Dep. 
90.5 

Dist.'  Lat. 

Dep. 
120.5 

1 

00.9 

00.5 

61 

52.8 

30.5 

121 

104.8 

60.5 

181 

156.8 

241  1  208.7 

2 

01.7 

01.0 

62 

53.7 

31.0 

122 

105.7 

61.0 

182 

157.6 

91.0 

242 

209.6 

121.0 

3 

02.6 

01.5 

63 

54.6 

31.5 

123 

106.5 

61.5 

183 

158.5 

91.5 

243 

210.4 

121.5 

4 

03.5 

02.0 

64 

55.4 

32.0 

124 

107.4 

62.0 

184 

159.3 

92.0 

244  211.3" 

122.0 

5 

04.3 

02.5 

65 

56.3 

32.5 

125 

108.3 

62.5 

185 

160.2 

92.5 

245  212.2 

122.5 

6 

05.2 

03.0 

66 

57.2 

33.0 

126 

109.1 

63.0 

186 

161.1 

93.0 

246 

213.0 

123.0 

7 

06.1 

03.5 

67 

58.0 

33.5 

127 

110.0 

63.5 

187 

161.9 

93.5 

217 

213.9 

123  5 

8 

06.9 

04.0 

68 

58.9 

34.0 

128 

1 10.9  1  64.0 

188 

162.8 

94.0 

248 

214.8 

124.0 

9 

07.8 

04.5 

69 

59.8 

34.5 

129 

111.7  64.5 

189 

163.7 

94.5 

249 

215.6 

124.5 

10 

08.7 

05.0 

70 

60.6 

35.0 

130 

112.6 

65.0 

190 

164.5 

95.0 

250 

.216.5 

125.0 

11 

09.5 

05.5" 

71 

61.5 

35.5 

131 

113.4 

65.5 

191 

165.4 

95.5 

251 

217.4 

125.5 

12 

10.4 

06.0 

72 

62.4 

36.0 

132 

114.3 

66.0 

192 

166.3 

96.0 

252 

218.2 

126.0 

13 

ll.o 

06.5 

73 

63.2 

36.5 

133 

115.2 

66.5 

193 

167.1 

96.5 

253 

219.1 

126.5 

14 

12.1 

07.0 

74 

64.1 

37.0 

134 

116.0 

67.0 

194 

168.0 

97.0 

254 

220.0 

127.0 

15 

13.0 

07.5 

75 

65.0 

37.5 

135 

116.9 

67.5 

195 

168.9 

97.5 

255 

220.8 

127.5 

16 

13.9 

08.0 

76 

65.8 

38.0 

136 

117.8 

68.0 

196 

169.7 

98.0 

256 

221.7 

128.0 

17 

14.7 

08.5 

77 

66.7 

^38.5 

137 

118.6 

68.5 

197 

170.6 

98.5 

257 

222.6 

128.5 

18 

15.6 

09.0 

78 

67.5 

39.0 

138 

119.5 

69.0 

198 

171.5 

99.0 

258 

223.4 

129.0 

19 

16.5 

09.5 

79 

68.4 

39.5 

139 

120.4 

69.5 

199 

172.3 

99.5 

259 

224.3 

129.5 

20 

17.3 

10.0 

80 

69.3 

40.0 

140 

121.2 

70.0 

200 

173.2 

100.0 

260 

225.2 

130.0 

21 

18.2 

10.5 

81 

70.1 

40.5 

141 

122.1 

70.5 

201 

174.1 

100.5 

261 

226.0 

130  5 

22 

19.1 

11.0 

82 

71.0 

41.0 

142 

123.0 

71.0 

202 

174.9 

101.0 

262 

226.9 

131.0 

23 

19.9 

11.5 

83 

71.9 

41.5 

143 

123.8 

71.5 

203 

175.8 

101.5 

263 

227.8 

131.5 

24 

20.8 

12.0 

84 

72.7 

42.0 

144 

124.7 

72.0 

204 

176.7 

102.0 

2(54 

228.6 

132.0 

25 

21.7 

12.5 

85 

73.6 

42.5 

145 

125.6 

72.5 

205 

177.5 

102.5 

265 

229.5 

132.5 

26 

22.5 

13.0 

86 

74.5 

43.0 

146 

126.4 

73.0 

206 

178.4 

103.0 

266 

230.4 

133.0 

27 

23.4 

13.5 

87 

75.3 

43.5 

147 

127.3 

73.5 

207 

179.3 

103.5 

267 

231.2 

133.5 

28 

24.2 

14.0 

88 

76.2 

44.0 

148 

128.2 

74.0 

208 

180.1 

104.0 

268 

232.1 

134.0 

29 

25.1 

14.5 

89 

77.1 

44.5 

149 

129.0 

74.5 

209 

181.0 

104.5 

269 

233.0 

134.5 

30 

26.0 

15.0 

90 

77.9 

45.0 

150 

129.9 

75.0 

210 
211 

181.9 

105.0 

270 

233.8 

135.0 

31 

26.8 

15.5 

91 

78.8 

45.5 

151 

130.8 

75.5 

182.7 

105.5 

271 

234.7 

135.5 

32 

27.7 

16.0 

92 

79.7 

46.0 

152 

131.6 

76.0 

212 

183.6 

106.0 

272 

235.6 

136.0 

33 

28.6 

16.5 

93 

80.5 

46.5 

153 

132.5 

76.5 

213 

184.5 

106.5 

273 

236.4 

136.5 

34 

29.4 

17.0 

94 

81.4 

47.0 

154 

133.4 

77.0 

214 

185.3 

107.0 

274 

237.3 

137.0 

35 

30.3 

17.5 

95 

82.3 

47.5 

155 

134.2 

77.5 

215 

186.2 

107.5 

275 

238.2 

137.5 

36 

31.2 

18.0 

96 

83.1 

48.0 

156 

135.1 

78.0 

216 

187.1 

108.0 

276 

239.0 

138.0 

37 

32.0 

18.5 

97 

84.0 

48.5 

157 

136.0 

78.5 

217 

187.9 

108.5 

277 

239.9 

138.5 

38 

32.9 

19.0 

98 

84.9 

49.0 

158 

136.8 

79.0 

218 

188.8 

109.0 

278 

240.8 

139.0 

39 

33.8 

19.5 

99 

85.7 

49.5 

159 

137.7 

79.5 

219 

189.7 

109.5 

279 

241.6 

139.5 

40 

34.6 

20.0 

100 

86.6 

50.0 

160 

138.6 

80.0 

220 

190.5 

110.0 

280 

242.5 

140.0 

41 

35.5 

20.5 

101 

87.5 

50.5 

161 

139.4 

80.5 

221 

191.4 

110.5 

281 

243.4 

140.5 

42 

36.4 

21.0 

102 

88.3 

51.0 

162 

140.3 

81.0 

222 

192.3 

111.0 

282 

244.2 

141.0 

43 

37.2 

21.5 

103 

89.2 

51.5 

163 

141.2 

81.5 

223 

193.1 

111.5 

283 

245.1 

141.5 

44 

38.1 

22.0 

104 

90.1 

52.0 

164 

142.0 

82.0 

224 

194.0 

112.0 

284 

246.0 

142.0 

45 

39.0 

22.5 

105 

90.9 

52.5 

165 

142.9 

82.5 

225 

194.9 

112.5 

285 

246.8 

142.5 

46 

39.8 

23.0 

106 

91.8 

53.0 

16« 

143.8 

83.0 

226 

195.7 

113.0 

286 

247.7 

143.0 

47 

40.7 

23.5 

107 

92.7 

53.5 

167 

144.6 

83.5 

227 

196.6 

113.5 

287 

248.5 

143.5 

48 

41.6 

24.0 

108 

93.5 

54.0 

168 

145.5 

84.0 

228 

197.5 

114.0 

288 

249.4 

144.0 

49 

42.4 

24.5 

109 

94.4 

54.5 

169 

146.4 

84.5 

229 

198.3 

114.5 

289 

250.3 

144.5 

50 

43.3  25.0 

110 

95.3 

55.0 

170 

147.2 

85.0 

230 

19i».2 

115.0 

290 

251.1 

145.0 

51 

44.2 

25.5 

111 

96.1 

55.5 

171 

148.1 

85.5 

231 

200.1 

115.5 

291 

252.0 

145.5 

52 

45.0 

26.0 

112 

97.0 

56.0 

172 

149.0 

86.0 

232 

200.9 

116.0 

292 

252.9 

146.0 

53 

45  9 

26.5 

113 

97.9 

56.5 

173 

149.8 

8(5.5 

233 

201.8 

116.5 

293 

253.7 

146.5 

54 

46.8 

27.0 

114 

98.7 

57.0 

174 

150.7 

87.0 

234 

202.6 

117.0 

294 

254.6 

147.0 

55 

47.6 

27.5 

115 

99.6 

57.5 

175 

151.6 

87.5 

235 

203.5 

117.5 

295 

255.5 

147.5 

56 

48.5 

28.0 

116 

100.5 

58.0 

176 

152.4 

88.0 

236 

204.4 

118.0 

296 

256.3 

148.0 

57 

49.4 

28.5 

117 

101.3 

58.5 

177 

153.3 

88.5 

237 

205.2 

118.5 

297 

257.2 

148.5 

58 

50.2 

29.0 

118 

102.2 

59.0 

17S 

154.2 

89.0 

238 

206.1 

119.0 

•298  258.1 

149.0 

59 

51.1 

29.5 

119 

103.1 

59.5 

179 

155.0 

89.5 

239 

207.0 

119.5 

299  258.9 

149.5 

60 

Di3t 

52.0 

30.0 

120 

103.9 

60.0 

180 

1 55.9 

90.0 

240 

207.8 

120.0 

300  1  259.8 

150.0 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Di8t. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist.  1  Dep. 

Lat.  1 

1 

''or  60  Desjrees. 

4 

ii  0™.  1 

TABLE  11.                         47  1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  31  DEGREES.   2h  4in  1 

Diet  Lat 

1  00.9 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lut 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

00.5 

61 

52.3 

31.4 

121 

103.7 

62.3 

181 

155.1 

93.2 

241 

206.6 

124.1 

2  Ol.T 

01.0 

62 

53.1 

31.9 

122 

104.6 

62.8 

182 

156.0 

93.7 

242 

207.4 

124.6 

3 

02.6 

01.5 

63 

54.0 

32.4 

123 

105.4 

63.3 

183 

156.9 

94.3 

243 

208.3 

125.2 

4 

03.4 

02.1 

64 

54.9 

:;3.0 

124 

106.3 

63.9 

184 

157.7 

94.8 

244 

209.1 

125.7 

5 

04.3 

02.6 

65 

55.7 

33.5 

125 

107.1 

64.4 

185 

158.6 

95.3 

245 

210.0 

126.2 

6 

05.1 

03.1 

m 

56.6 

34.0 

126 

108.0 

64.9 

186 

159.4 

95  8 

246 

210.9 

126.7 

7 

06.0 

03.6 

67 

57.4 

34.5 

127 

108.9 

65.4 

187 

160.3 

96  3 

247 

211.7 

127.2 

8 

06.9 

04.1 

68 

58.3 

35.0 

128 

109.7 

65'.9 

188 

161.1 

96  8 

248 

212.6 

127.7 

9 

07.7 

04.6 

69 

59.1 

35.5 

129 

110.6 

66.4 

189 

162.0 

97.8 

249 

213.4 

128  2 

10 

08.6 

05.2 

70 

60.0 

36.1 

130 
131 

111.4 

67.0 

190 

162.9 

97.9 

250 

214.3 

128.8 

11 

09.4 

05.7 

71 

60.9 

36.6 

112.3 

67.5 

191 

163.7 

98.4 

251 

215.1 

129.3 

12 

10.3 

06.2 

72 

61.7 

37.1 

132 

113.1 

68.0 

192 

164.6 

98.9 

252 

216.0 

129  8 

13 

11.1 

06.7 

73 

62.6 

37.6 

133 

114.0 

68.5 

193 

165.4 

99.4 

253 

216.9 

130.3 

14 

12.0 

07.2 

74 

63.4 

38.1 

134 

114.9 

69.0 

194 

166.3 

99.9 

254 

217.7 

130.8 

15 

12.9 

07.7 

75 

64.3 

38.6 

135 

115.7 

69.5 

195 

167.1 

100.4 

255 

218.6 

131.3 

16 

13.7 

08.2 

76 

65.1 

39.1 

136 

116.6 

70.0 

196 

168.0 

100.9 

256 

219.4 

131.8 

17 

14.6 

08.8 

77 

66.0 

39.7 

137 

117.4 

70.6 

197 

168.9 

101.5 

257 

220.3 

132.4 

18 

15.4 

09.3 

78 

66.9 

40.2 

138 

118.3 

71.1 

198 

169.7 

102.0 

258 

221.1 

132.9 

19 

16.3 

09.8 

79 

67.7 

40.7 

139 

119.1 

71.6 

199 

170.6 

102.5 

259 

222.0 

133.4 

20 
21 

17.1 

10.3 

80 

68.6 

41.2 

41.7 

140 

120.0 

72.1 

200 
201 

171.4 
172.3 

103.0 

260 

222.9 

133.9 

:3.o 

10.8 

81 

69.4 

141 

120.9 

72.6 

103.5 

261 

223.7 

134.4, 

22 

18.9 

11.3 

82 

70.3 

42.2 

142 

121.7 

73.1 

202 

173.1 

104.0 

262 

224.6 

134.9 

23 

19.7 

11.8 

83 

71.1 

42.7 

143 

122.6 

73.7 

203 

174.0 

104.6 

263 

225.4 

135.5 

24 

•20.6 

12.4 

84 

72.0 

43.3 

144 

123.4 

74.2 

204 

174.9 

105.1 

264 

226.3 

136.0 

25 

21.4 

12.9 

t85 

72.9 

43.8 

145 

124.3 

74.7 

205 

175.7 

105.6 

265 

227.1 

136.5 

26 

22.3 

13.4 

86 

73.7 

44.3 

146 

125.1 

75.2 

206 

176.6 

106.1 

266 

228.0 

137.0 

27 

23.1 

13.9 

87 

74.6 

44.8 

147 

126.0 

75.7 

207 

1^7.4 

106.6 

267 

228.9 

137.5 

28 

24.0 

14.4 

88 

75.4 

45.3 

148 

126.9 

76.2 

208 

178.3 

107.1 

268 

229.7 

138.0 

2y 

24.9 

14.9 

89 

76.3 

45.8 

149 

127.7 

76.7 

209 

179.1 

107.6 

269 

230.6 

138.5 

30 

25.7 

15.5 

90 
91 

77.1 

46.4 

150 

128.6 

77.3 

77.8 

210 

180.0 

108.2 

270 

231.4 

139.1 

31 

26.6 

16.0 

78.0 

46.9 

151 

129.4 

211 

180.9 

108.7 

271 

232.3 

139.6 

32 

27.4 

16.5 

92 

78.9 

47.4 

152 

130.3 

78.3 

212 

181.7 

109.2 

272 

233.1 

140.1 

33 

28.3 

17.0 

93 

79.7 

47.9 

153 

131.1 

78.8 

213 

182.6 

109.7 

273 

234.0 

140.6 

34 

29.1 

17.5 

94 

80.6 

48.4 

154 

132.0 

79.3 

214 

183.4 

110.2 

274 

234.9 

141.1 

35 

30.0 

18.0 

95 

81.4 

48.9 

155 

132.9 

79.8 

215 

184.3 

110.7 

275 

235.7 

141.6 

36 

30.9 

18.5 

96 

82.3 

49.4 

156 

133.7 

80.3 

216 

185.1 

111.2 

276 

236.6 

142.2 

37 

31.7 

19.1 

97 

83.1 

50.0 

157 

134.6 

80.9 

217 

186.0 

111.8 

277 

237.4 

142.7 

38 

32.6 

19.6 

98 

84.0 

50.5 

158 

135.4 

81.4 

218 

186.9 

112.3 

278 

238.3 

143.2 

39 

33.4 

20.1 

99 

84.9 

51.0 

159 

136.3 

81.9 

219 

187.7 

112.8 

279 

239.1 

143.7 

40 

34.3 

20.6 

100 

85.7 

51.5 

160 

137.1 

82.4 

220 

188.6 

113.3 

280 

240.0 

144.2 

41 

35.1 

21.1 

101 

86.6 

52.0 

161 

138.0 

82.9 

221 

189.4 

113.8 

281 

240.9 

144.7 

42 

36.0 

21.6 

102 

87.4 

52.5 

162 

138.9 

83.4 

222 

190.3 

114.3 

282 

241.7 

145.2 

43 

36.9 

22.1 

103 

88.3 

53.0 

163 

139.7 

84.0 

223 

191.1 

114.9 

283 

242.6 

145.8 

44 

37.7 

22.7 

104 

89.1 

53.6 

164 

140.6 

84.5 

224 

192.0 

115.4 

284 

243.4 

146.3 

45 

38.6 

23.2 

105 

90.0 

54.1 

165 

141.4 

85.0 

225 

192.9 

1 15.9 

285 

244.3 

146.8 

46 

39.4 

23.7 

106 

90.9 

54.6 

166 

142.3 

85.5 

226 

193.7 

116.4 

286 

245.1 

147.3 

47 

40.3 

24.2 

107 

91.7 

55.1 

167 

143.1 

86.0 

227 

194.6 

116.9 

287 

246.0 

147.8 

48 

41.1 

24.7 

108 

92.6 

55.6 

168 

144.0 

86.5 

228 

195.4 

117.4 

288 

246.9 

148.3 

49 

42.0 

25.2 

109 

93.4 

56.1 

169 

144.9 

87.0 

229 

196.3 

117.9 

289 

247.7 

148.8 

50 

42.9 

25.8 

110 

94.3 

56.7 

170 

145.7 

87.6 

230 

197.1 

118.5 

290 

248.6 

149.4 

51 

43.7 

26.3 

111 

95.1 

57.2 

171 

146.6 

88.1 

231 

198.0 

119.0 

291 

249.4  149.9 1 

52 

44.6 

26.8 

112 

96.0 

57.7 

172 

147.4 

88.6 

232 

198.9 

119.5 

292 

250.3 

150.4 

53 

45.4 

27.3 

113 

96.9 

58.2 

173 

148.3 

89.1 

233 

199.7 

120.0 

293 

251.2 

150.9 

54 

46.3 

27.8 

114 

97.7 

58.7 

174 

149.1 

89.6 

234 

200.6 

120.5 

294 

252.0 

151.4 

55 

47.1 

28.3 

115 

98.6 

59.2 

175 

150.0 

90.1 

235 

201.4 

121.0 

295 

252.9 

151.9 

56 

48.0 

28.8 

116 

99.4 

59.7 

176 

150.9 

90.6 

236 

202.3 

121.5 

296 

253.7 

152.5 

57 

48.9 

29.4 

117 

100.3 

60.3 

177 

151.7 

91.2 

237 

203.1 

122.1 

297 

254.6 

153.0 

58 

49.7 

29.9 

118 

101.1 

60.8 

178 

152.6 

91.7 

238 

204.0 

122.6 

298 

255.4 

153.5 

50 

50.6 

30.4 

119 

102.0 

61.3 

179 

153.4 

92.2 

239 

204.9 

123.1 

299 

256.3 

154.0 

(•>0 
Dist 

5 1 .4 
.  D.?p. 

30.9 

120 

102.9 

61.8 
Lat. 

180 

154.3 

92.7 

240 

205.7 

123.6 

300 
Dist 

257.1 

154.5 

Lat. 

Dist. 

Dep. 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dep. 

Lat. 

; 

Fit  59  Deyrrees.                           S^   56iii   | 

48 

• 

TABLE  11. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  32  DEGREES.   2b  Sm.  1 

Dist. 
1 

Lat. 

Dep. 

Dibt 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 
181 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

00.8 

00.5 

61 

51.7 

32.3 

121 

102.6 

64.1 

153.5 

95.9 

241 

204.4 

127.7 

2 

01.7 

01.1 

62 

52.6 

32.9 

122 

103.5 

64.7 

KS2 

154.3 

96.4 

242 

205.2 

128.2 

3 

02.5 

01.6 

63 

53.4 

33.4 

123 

104.3 

65.2 

183 

155.2 

97.0 

243  206.1 

128.8 

4 

03.4 

02.1 

64 

54.3 

33.9 

124 

105.2  65.7 

184 

156.0 

97.5 

244 

206.9 

129.3 

5 

04.2 

02.6 

65 

55.1 

34.4 

125 

106.0  66.2  185 

15t).9 

98.0 

245 

207.8 

129.8 

6 

05.1 

03.2 

66 

56.0 

35.0 

126 

106.9 

66.8  186 

157.7 

98.6 

246 

208.6 

130.4 

7 

05.9 

03.7 

67 

56.8 

35.5 

127 

107.7 

67.3,187 

158.6 

99.1 

247 

209.5 

130.9 

8 

06.8 

04.2 

68 

57.7 

36.0 

128 

108.6 

67.8 

188 

159.4 

99.6 

248 

210.3 

131.4 

9 

07.6 

04.8 

69 

58.5 

36.6 

129 

109.4 

68.4 

189 

160.3 

100.2 

249 

211.2 

131.9 

10 
11 

08.5 
09.3 

05.3 

70 

59.4 

37.1 

130 

110.2 

68.9 

190 

161.1 

100.7 

250 

212.0 

132.5 

05.8 

71 

60.2 

37.6 

131 

1 11.1 

69.4 

191 

162.0 

101.2 

251 

212.9 

13.3.0 

12 

10.2 

06.4 

72 

61.1 

38.2 

132 

111.9 

69.9 

192 

162.8 

101.7 

252 

213.7 

133.5 

13 

11.0 

06.9 

73 

61.9 

38.7 

133 

112.8 

70.5 

193 

163.7 

102.3 

253 

214.6 

134.1 

14 

11.9 

07.4 

74 

62.8 

39.2 

134 

113.6 

71.0 

194 

164.5 

102.8 

254 

215.4 

134.6 

15 

12.7 

07.9 

75 

63.6 

39.7 

135 

114.5 

71.5 

195 

16.5.4 

103.3 

255 

216.3 

135.1 

16 

13.6 

08.5 

76 

64.5 

40.3 

136 

115.3 

72.1 

196 

166.2 

103.9 

256 

217.1 

135.7 

17 

14.4 

09.0 

77 

65.3 

40.8 

137 

116.2 

72.6 

197 

167.1 

104.4 

257 

217.9 

136.2 

18 

15.3 

09.5 

78 

66.1 

41.3 

138 

117.0 

73.1 

198 

167.9 

104.9 

258 

218.8 

136.7 

19 

16.1 

10.1 

79 

67.0 

41.9 

139 

117.9 

73.7 

199 

168.8 

105.5 

259 

219.6 

137.2 

20 

17.0 

10.6 

80 

67.8 

42.4 

140 

118.7 

74.2 

200 

169.6 

106.0 

260 

220.5 

137.8 

21 

17.8 

11.1 

81 

68.7 

42.9 

141 

119.6 

74.7 

201 

170.5 

106.5 

261 

221.3 

138.3 

22 

18.7 

11.7 

82 

69.5 

43.5 

142 

120.4 

75.2 

202 

171.3 

107.0 

262 

222.2 

138.8 

23 

19.5 

12.2 

83 

70.4 

44.0 

143 

121.3 

75.8 

203 

172.2 

107.6 

263 

223.0 

139.4 

24 

20.4 

12.7 

84 

71.2 

44.5 

144 

122.1 

76.3 

204 

173.0 

108.1 

264 

223.9 

139.9 

25 

21.2 

13.2 

85 

72.1 

45.0 

145 

123.0 

76.8 

205 

173.8 

10S.6 

265 

224.7 

140.4 

26 

22.0 

13.8 

86 

72.9 

45.6 

146 

123.8 

77.4 

206 

174.7 

109.2 

266 

225.6 

141.0 

27 

22.9 

14.3 

87 

73.8 

46.1 

147 

124.7 

77.9 

207 

175.5 

109.7 

267 

226.4 

141.5 

28 

23.7 

14.8 

88 

74.6 

46.6 

148 

125.5 

78.4 

208 

176.4 

110.2 

268 

227.3 

142.0 

29 

24.6 

15.4 

89 

75.5 

47.2 

149 

126.4 

79.0 

209 

177.2 

110.8 

269 

228.1 

142.5 

30 
31 

•J  5.4 

15.9 
16.4 

90 

76.3 

47.7 

1.50 

127.2 

79.5 

210 

178.1 

111.3 

270 

229.0 

143.1 

26.3 

91 

77.2 

48.2 

151 

128.1 

80.0 

211 

178.9 

111.8 

271 

229.8 

14.3.6 

32 

27.1 

17.0 

92 

78.0 

48.8 

152 

12^.9 

80.5 

212 

179.8 

112.3 

272 

230.7 

144.1 

33 

28.0 

17.5 

93 

78.9 

49.3 

153 

129.8 

81.1 

213 

180.6 

112.9 

273 

231.5 

144.7 

34 

28.8 

18.0 

94 

79.7 

49.8 

154 

130.6 

81.6 

214 

181.5 

113.4 

274 

232.4 

145.2 

35 

29.7 

18.5 

95 

80.6 

50.3 

155 

131.4 

82.1 

215 

182.3 

113.9 

275 

233.2 

145.7 

36 

30.5 

19.1 

96 

81.4 

50.9 

156 

132.3 

82.7 

216 

183.2 

114.5 

276 

234.1 

146.3 

37 

31.4 

19.6 

97 

82.3 

51.4 

157 

133.1 

83.2 

217 

184.0 

115.0 

277 

2,34.9 

146.8 

38 

32.2 

20.1 

98 

83.1 

51.9 

158 

134.0 

83.7 

218 

184.9 

115.5 

278 

235.8 

147.3 

39 

33.1 

20.7 

99 

84.0 

52.5 

159 

134.8 

84.3 

219 

185.7 

116.1 

279 

236.6 

147.8 

40 

33.9 

21.2 

100 

84.8 

53.0 

160 

135.7 

84.8 

220 

186.6 

116.6 

280 

237.5 

148.4 

41 

34.8 

21.7 

101 

85.7 

53.5  161 

136.5 

85.3 

221 

187.4 

117.1 

281 

238.3 

148.9 

42 

35.6 

22.3 

102 

86.5 

54.1  162 

137.4 

85.8 

222 

188.3 

117.6 

282 

239.1 

149.4 

43 

36.5 

22.8 

103 

87.3 

.54.6 

163 

138.2 

86.4 

223 

18!>.l 

118.2 

283 

240.0 

150.0 

44 

37.3 

23.3 

104 

88.2 

55.1 

164 

139.1 

86.9 

224 

190.0 

118.7 

284 

240.8 

150.5 

45 

38.2 

23.8 

105 

89.0 

55.6 

165 

139.9 

87.4 

225 

190.8 

119.2 

285 

241.7 

151.0 

46 

39.0 

24.4 

106 

89.9 

56.2 

166 

140.8 

88.0 

226 

191.7 

119.8 

286 

242.5 

151.6 

47 

39.9 

24.9 

107 

90.7 

56.7 

167 

141.6 

88.5 

227 

192.5 

120.3 

287 

243.4 

152.1 

48 

40.7 

25.4 

108 

91.6 

57.2 

168 

142.5 

89.0 

228 

193.4 

120.8 

288 

244.2 

152.6 

49 

41.6 

26.0 

109 

92.4 

57.8 

169 

143.3 

89.6 

229 

194.2 

121.4 

289 

245.1 

153.1 

50 

42.4 

26.5 

110 

93.3 

58.3 

170 

144.2 

90.1 

230 

195.1 

121.9 

290 

245.9 

153.7 

51 

43.3 

27.0 

111 

94.1 

58.8 

171 

145.0 

90.6 

231 

195.9 

122.4 

291 

246.8 

154.2 

52 

44.1 

27.6 

112 

95.0 

59.4 

172 

145.9 

91.1 

232 

196.7 

122.9 

292 

247.6 

154.7 

53 

44  9 

28.1 

113 

95.8 

59.9 

173 

146.7 

91.7 

233 

197.6 

123.5 

293 

248.5 

155.3 

54 

45.8 

28.6 

114 

96.7 

60.4 

174 

147.6 

92.2 

234 

198.4 

124.0 

294f 

249.3 

155.8 

55 

46.6 

29.1 

115 

97.5 

60.9 

175 

148.4 

92.7 

235  199.3 

124.5 

295 

250.2 

156.3 

56 

47.5 

29.7 

116 

98.4 

61.5 

176 

149.3 

93.3 

236 

200.1 

125.1 

296 

251.0 

156.9 

57 

48.3 

30.2 

117 

99.2 

62.0 

177 

150.1 

93.8 

237 

201.0 

125.6 

297 

251.9 

157.4 

5^ 

49.2 

30.7 

118 

100.1 

62.5 

178 

151.0 

94  3 

238 

201.8 

126.1 

298 

252.7 

157.9 

59 

50.0 

31.3 

119 

100.9 

63.1 

179 

151.8 

94.9 

239 

202.7 

126.7 

299 

253.6 

158.4 

60 
Dist 

50.9 

31.8 

120 

101.8 

63.6 

180 

152.6 

95.4 

240 

203.5 

127.2 

300 

254.4 

159.0 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat   Dist  1  Dep. 

Lat 

For  58  Degrees. 

3h 

62".  1 

TABLE  11.                          [I'age49.  1 

DIFFERENCE  OF  LATITUDE  AND  DKl'ARTURE  FOR  33  DEGREES.   2h  12m.  1 

Dist. 

1 

Lat. 
00.8 

Dep. 

Dist. 

Lat. 
51.2 

Dep. 

Dist 

LaL 

Dep. 
65.9 

Dist. 

Lat. 

Dep. 

Dist. 

Lat 
202.1 

Dep. 

00.5 

61 

33.2 

121 

101.5 

181 

151.8 

98.6 

241 

131.3 

01.7 

01.1 

62 

52.0 

33.8 

122 

102.3 

66.4 

182 

152.6 

99.1 

242 

203.0 

131.S 

3 

02.5 

01.6 

63 

52.8 

34.3 

123 

103.2 

67.0 

183 

153.5 

99.7 

243 

203.8 

132.3 

4 

03.4 

02.2 

64 

,53.7 

34.9 

124 

104.0 

67.5 

184 

154.3 

100.2 

244 

204.6 

132.9 

5 

04.2 

02.7 

65 

54.5 

35.4 

125 

104.8 

68.1 

185 

155.2 

100.8 

245 

205.5 

133.4 

6 

05.0 

03.3 

m 

55.4 

35.9 

126 

105.7 

68.6 

186 

156.0 

101.3 

246 

206.3 

134.0 

7 

05.9 

03.8 

67 

56.2 

36.5 

127 

106.5 

69.2 

187 

156.8 

101.8 

247 

207.2 

134.5 

8 

06.7 

04.4 

68 

57.0 

37.0 

128 

107.3 

69.V 

188 

157.7 

102.4 

248 

208.0 

135.1 

9 

07.5 

04.9 

69 

57.9 

37.6 

129 

108.2 

70.3 

189 

158.5 

102.9 

249 

208.8 

135.6 

10 

08.4 

05.4 

70 

58.7 

38.1 

130 
131 

109.0 

70.8 

190 

159.3 

103.5 

250 

209.7 

136.2 
136.7 

11 

09.2 

06.0 

71 

59.5 

38.7 

109.9 

71.3 

191 

160.2 

104.0 

2^1 

210.5 

12 

10.1 

06.5 

72 

60.4 

39.2 

132 

110.7 

71.9 

192 

161.0 

104.6 

252 

211.3 

1 37.2 

13 

10.9 

07.1 

73 

61.2 

39.8 

133 

111.5 

72.4 

193 

161.9 

105.1 

253 

212.2 

137.8 

14 

11.7 

07.6 

74 

62.1 

40.3 

134 

112.4 

73.0 

194 

162.7 

105.7 

254 

213.0 

138.3 

15 

12.6 

08.2 

75 

62.9 

40.8 

135 

113.2 

73.5 

195 

163.5 

106.2 

255 

213.9 

138.9 

16 

13.4 

08.7 

76 

63.7 

41.4 

136 

114.1 

74.1 

196 

164.4 

106.7 

256 

214.7 

139.4 

17 

14.3 

09.3 

77 

64.6 

41.9 

]37 

114.9 

74.6 

197 

165.2 

107.3 

257 

215.5 

140.0 

18 

15.1 

09.8 

78 

65.4 

42.5 

138 

115.7 

75.2 

198 

166.1 

107.8 

258 

216.4 

140.5 

19 

15.9 

10.3 

79 

66.3 

43.0 

139 

116.6 

75.7 

199 

166.9 

108.4 

259 

217.2 

141.1 

20 
21 

16.8 
17.6 

10.9 

80 

81 

67.1 

43.6 

140 
141 

117.4 

76.2 

76.8 

200 
201 

167.7 

168.6 

108.9 

260 

218.1 

141.6 

11.4 

67.9 

44.1 

118.3 

109.5 

261 

218.9 

142.2 

22 

18.5 

12.0 

82 

68.8 

44.7 

142 

119.1 

77.3 

202 

169.4 

110.0 

262 

219.7 

142.7 

23 

19.3 

12.5 

83 

69.6 

45.2 

143 

119.9 

77.9 

203 

170.3 

110.6 

263 

220.6 

143.2 

24 

20.1 

13.1 

84 

70.4 

45.7 

144 

120.8 

78.4 

204 

171.1 

111.1 

264 

221.4 

143.8 

25 

21.0 

13.6 

85 

71.3 

46.3 

145 

121.6 

79.0 

205 

171.9 

111.7 

265 

222.2 

144.3 

26 

21.8 

14.2 

86 

72.1 

46.8 

146 

122.4 

79.5 

206 

172.8 

112.2 

266 

223. 1 

144.9 

27 

22.6 

14.7 

87 

73.0 

47.4 

147 

123.3 

80.1 

207 

173.6 

112.7 

267 

.223.9 

145.4 

28 

23.5 

15.2 

88 

73.8 

47.9 

148 

124.1 

80.6 

208 

174.4 

113.3 

268 

224.8 

146.0 

29 

24.3 

15.8 

89 

74.6 

48.5 

149 

125.0 

81.2 

209 

175.3 

113.8 

269 

22.5.6 

146.5 

30 

25.2 

16.3 

90 

75.5 

49.0 

150 

125.8 

81.7 

210 

176.1 

114.4 

270 

226.4 

147.) 

31 

26.0 

16.9 

91 

76.3 

49.6 

151 

126.6 

82.2 

211 

177.0 

114.9 

271 

227.3 

147  6 

32 

26.8 

17.4 

92 

77.2 

50.1 

152 

127.5 

82.8 

212 

177.8 

115.5 

272 

228.1 

148.1 

33 

27.7 

18.0 

93 

78.0 

50.7 

1.53 

128.3 

83.3 

213 

178.6 

116.0 

273 

229.0 

148.7 

34 

28.5 

18.5 

94 

78.8 

51.2 

154 

129.2 

83.9 

214 

179.5 

116.6 

274 

229.8 

149.2 

35 

29.4 

19.1 

95 

79.7 

51.7 

155 

130.0 

84.4 

215 

180.3 

117.1 

275 

230.6 

149.8 

36 

30.2 

19.6 

96 

80.5 

52.3 

156 

130.8 

85.0 

216 

181.2 

117.6 

276 

231.5 

150.3 

37 

31.0 

20.2 

97 

81.4 

52.8 

157 

131.7 

85.5 

217 

182.0 

118.2 

277 

232.3 

150.9 

38 

31.9 

20.7 

98 

82.2 

53.4 

158 

132.5 

86.1 

218 

182.8 

118.7 

278 

233.2 

151.4 

39 

32.7 

21.2 

99 

83.0 

53.9 

159 

133.3 

86.6 

219 

183.7 

119.3 

279 

234.0 

152.0 

40 

33.5 

21.8 

100 

83.9 

54.5 

160 

134.2 

87.1 

220 
221 

184.5 

119.8 

280 

234.8 
235.7 

152.5 

41 

34.4 

22.3 

101 

84.7 

55.0 

161 

135.0 

87.7 

185.3 

120.4 

281 

153.0 

42 

35.2 

22.9 

102 

85.5 

55.6 

162 

135.9 

88.2 

222 

186.2 

120.9 

282 

236.5 

153.6 

43 

36.1 

23.4 

103 

86.4 

56.1 

163 

136.7 

88.8 

223 

187.0 

121.5 

283 

237.3 

154.1 

44 

36.9 

24.0 

104 

87.2 

56.6 

164 

137.5 

89.3 

224 

187.9 

122.0 

284 

238.2 

154.7 

45 

37.7 

24.5 

105 

88.1 

57.2 

165 

138.4 

89.9 

225 

188.7 

122.5 

285 

239.0 

155.2 

46 

38.6 

25.1 

106 

88.9 

57.7 

166 

139.2 

90.4 

226 

189.5 

123.1 

286 

239.9 

155.8 

47 

39.4 

25.6 

107 

89.7 

58.3 

167 

140.1 

91.0 

227 

190.4 

123.6 

287 

240.7 

156.3 

48 

40.3 

26.1 

108 

90.6 

58.8 

168 

140.9 

91.5 

228 

191.2 

124.2 

288 

241.5 

156.9 

49 

41.1 

26.7 

109 

9t.4 

59.4 

169 

141.7 

92.0 

229 

192.1 

124.7 

289 

242.4 

157.4 

50 
51 

41.9 

42.8 

27.2 

110 

92.3 

59.9 

170 

142.6 

92.6 

230 

192.9 

125.3 

290 

243.2 

157.9 

27.8 

111 

93.1 

60.5 

171 

143.4 

93.1 

231 

193.7 

125.8 

291 

244.1 

158.5 

52  43.6 

28.3 

112 

93.9 

61.0 

172 

144.3 

93.7 

232 

194.6 

126.4 

292 

244.9 

159.0 

53  44.4 

28.9 

113 

94.8 

61.5 

173 

145.1 

94.2 

233 

195.4 

126.9 

293 

245.7 

159.6 

54  45.3 

29.4 

114 

95.6 

62.1 

174 

14.5.9 

94.8 

234 

196.2 

127.4 

294 

246.6 

160.1 

55  46.1 

30.0 

115 

96.4 

62.6 

175 

146.8 

95.3 

235 

197.1 

128.0 

295 

247.4 

160.7 

56 

47.0 

30.5 

116 

97.3 

63.2 

176 

147.6 

95.9 

236 

197.9 

128.5 

296 

248.2 

161.2 

57 

47.8 

31.0 

117 

98.1 

63.7 

177 

148.4 

96.4 

237 

198.8 

129.1 

297 

249.1 

161.8 

58 

48.6 

31.6 

118 

99.0 

64.3 

178 

149.3 

96.9 

238 

199.6 

129.6 

298 

249.9 

162.3 

59 

49.5 

32.1 

119 

99.8 

64.8 

179 

150.1 

97.5 

239 

200.4 

130.2 

299 

250.8 

162.8 

60 
Dist 

50.3 
Dep. 

32.7 

120 

100.6 

65.4 

Lat. 

180 
Dist. 

151.0 

98.0 

240 

201.3 

130.7 

300 

251.6 

163.4 

Lat. 

Di8t. 

Dep. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

For  57  Deerrees.                          3^  48m.   | 

60 

TABLE  11. 

1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  34  DEGREES.  2^  16™.  | 

Dist 

Lat. 

Dep. 

DistI  Lat 

Dep. 

Dist. 

L.at. 

Dep. 

Dist 

Lat. 

Dep. 

Dist 

Lat  1  Dep.  1 

1 

00.8 

00.6 

61 

50.6 

34.1 

121 

100.3 

67.7 

181 

150.1 

101.2 

241  .199.8  134.8  1 

2 

01.7 

01.1 

62 

51.4 

34.7 

122 

101.1 

68.2 

182 

150.9 

101.8 

242  200.6 

135.31 

3 

02.5 

01.7 

63 

52.2 

35.2 

123 

102.0 

68.8 

183 

151.7 

102.3 

243  201.5 

135.91 

4 

03.3 

02.2 

64  53.1 

35.8 

124 

102.8 

69.3 

184 

152.5 

102.9 

244 

202.3  ' 

136.4 

5 

04.1 

02.8 

65  53.9 

36.3 

125 

103.6  69.9 

185 

153.4 

103.5 

245 

203.1 

137.0 

6 

05.0 

03.4 

66 

54.7 

36.9 

126 

104.5  70.5 

186 

154.2 

104.0 

246 

203.9 

137.6 

7 

05.8 

03.9 

67 

55.5 

37.5 

127 

105.3  1  71.0 

187 

155.0 

104.6 

247  204.8 '138.11 

8 

06.6 

04.5 

68 

56.4 

38.0 

128 

106.1 

71.6 

188 

155.9 

105.1 

248 

205.61  138.7 1 

9 

07.5 

05.0 

69 

57.2 

38.6 

129 

106.9 

72.1 

189 

156.7 

105.7 

249 

206.4 

139.2 

10 
11 

08.3 

05.6 

70 

58.0 

39.1 

130 

107.8 

72.7 

190 

157.5 

106.2 

250 

207.3 

139.8 

09.1 

06.2 

71 

58.9 

39.7 

131 

108.6 

73.3 

191 

158.3 

106.8 

251 

208.1 

140.4 

12 

09.9 

06.7 

72 

59.7 

40.3 

132 

109.4 

73.8 

192 

159.2 

107.4 

252 

208.9 

140.9 

13 

10.8 

07.3 

73 

60.5 

40.8 

133 

a  10.3 

74.4 

193 

160.0 

107.9 

253 

209.7 

141.5 

14 

11.6 

07.8 

74 

61.3 

41.4 

134 

111.1 

74.9 

194 

160.8 

108.5 

254 

210.6 

142.0 

15 

12.4 

08.4 

75 

62.2 

41.9 

135 

111.9 

75.5 

195 

161.7 

109.0 

255 

211.4 

142.6 

16 

13.3 

08.9 

76 

63.0 

42.5 

136 

112.7 

76.1 

196 

162.5 

109.6 

256 

212.2 

143.2 

17 

14.1 

09.5 

77 

63.8 

43.1 

137 

113.6 

76.6 

197 

163.3 

110.2 

257 

21.3.1 

H-3  7 

18 

14.9 

10.1 

78 

64.7 

43.6 

138 

114.4 

77.2 

198 

164.1 

110.7 

258 

213.9 

144.3 

19 

15.8 

10.6 

79 

65.5 

44.2 

139 

115.2 

77.7 

199 

165.0 

111.3 

259 

214.7 

144.8 

20 

16.6 

11.2 

80 

66.3 

44.7 

140 

116.1 

78.3 

200 

165.8 

111.8 

260 

215.5 

145.4 

21 

17.4 

11.7 

81 

67.2 

45.3 

141 

116.9 

78.8 

201 

166.6 

112.4 

261 

216.4 

145.9 

22 

18.2 

12.3 

82 

68.0 

45.9 

142 

117.7 

79.4 

202 

167.5 

113.0 

262 

217.2 

146.5 

23 

19.1 

12.9 

83 

68.8 

46.4 

143 

118.6 

80.0 

203 

168.3 

113.5 

263 

218.0 

147.1 

24 

19.9 

13.4 

84 

69.6 

47.0 

144 

119.4 

80.5 

204 

169.1 

114.1 

264 

218.9 

147.6 

25 

20.7 

14.0 

85 

70.5 

47.5 

145 

120.2 

.  81.1 

205 

170.0 

114.6 

265 

219.7 

148.2 

26 

21.6 

14.5 

86 

71.3 

48.1 

146 

121.0 

81.6 

206 

170.8 

115.2 

266 

220.5 

148.7 

27 

22.4 

15.1 

87 

72.1 

48.6 

147 

121.9 

82.2 

207 

171.6 

115.8 

267 

221.4 

149.3 

28 

23.2 

15.7 

88 

73.0 

49.2 

148 

122.7 

82.8 

208 

172.4 

116.3 

268 

222.2 

149.9 

29 

24.0 

16.2 

89 

73.8 

49.8 

149 

123.5 

8.3.3 

209 

173.3 

116.9 

269 

223.0 

150.4 

30 

24.9 

16.8 

90 

74.6 

50.3 

150 

124.4 

83.9 

210 

174.1 

117.4 

270 

223.8 

151.0 

31 

25.7 

17.3 

91 

75.4 

50.9 

151 

125.2 

84.4 

211 

174.9 

118.0 

271 

224.7 

151.5 

32 

26.5 

17.9 

92 

76.3 

51.4 

152 

126.0 

85.0 

212 

175.8 

118.5 

272 

225.5 

152.1 

33 

27.4 

18.5 

93 

77.1 

52.0 

153 

126.8 

8.5.6 

213 

176.6 

119.1 

273 

226.3 

152.7 

34 

28.2 

19.0 

94 

77.9 

52.6 

154 

127.7 

86.1 

214 

177.4 

119.7 

274 

227.2 

153.2 

35 

29.0 

19.6 

95 

78.8 

53.1 

155 

128.5 

86.7 

215 

178.2 

120.2 

275 

228.0 

153.8 

36 

29.8 

20.1 

96 

79.6 

53.7 

156 

129.3 

87.2 

216 

179.1 

120.8 

276 

228.8 

154.3 

37 

30.7 

20.7 

97 

80.4 

54.2 

157 

130.2 

87.8 

217 

179.9 

121.3 

277 

229.6.  154.9| 

38 

31.5 

21.2 

98 

81.2 

54.8 

158 

131.0 

88.4 

218 

180.7 

121.9 

278 

230.5 

155.5 

39 

32.3 

21.8 

99 

82.1 

.")5.4 

159 

131.8 

88.9 

219 

181.6 

122.5 

279 

231.3 

156.0 

40 

33.2 

22.4 

100 

82.9 

55.9 

160 

132.6 

89.5 

220 

182.4 

123.0 

280 

232.1 

156.6 

41 

34.0 

22.9 

101 

83.7 

56.5 

161 

133.5 

90.0 

221 

183.2 

123.6 

281 

233.0 

157.1 

42 

34.8 

23.5 

102 

84.6 

57.0 

162 

134.3 

90.6 

222 

184.0 

124.1 

282 

233.8 

157.7 

43 

35.6 

24.0 

103 

85.4 

57.6 

163 

135.1  1  91.1 

223 

184.9 

124.7 

283 

234.6 

158.3 

44 

36.5 

24.6 

104 

86.2 

58.2 

164 

136.01  91.7 

224 

185.7 

125.3 

284 

235.4 

158.8 

45 

37.3 

25.2 

105 

87.0 

58.7 

165 

136.8 

92.3 

225 

186.5 

125.8 

285 

236.3 

159.4 

46 

38.1 

25.7 

106 

87.9 

59.3 

166 

137.6 

92.8 

226 

187.4 

126.4 

286 

237.1 

159.9 

47 

39.0 

26.3 

107 

88.7 

59.8 

167 

138.4 

93.4 

227 

188.2 

126.9 

287 

237.9 

160.5 

48 

39.8 

26.8 

108 

89.5 

60.4 

168 

139.3 

93.9 

228 

189.0 

127.5 

288 

238.8 

161.0 

49 

40.6 

27.4 

109 

90.4 

61.0 

169 

140.1 

94.5 

229 

189.8 

128.1 

289 

239.6 

161.6 

50 

41.5 

28.0 

110 

91.2 

61.5 

170 

140.9 

95.1 

230 

190.7 

128.6 

290 

240.4 

162.2 

51 

42.3 

28.5 

HI 

92.0 

62.1 

171 

141.8 

95.6 

231 

191.5 

129.2 

291 

241.2 

162.7 

52 

43.1 

29.1 

112 

92.9 

62.6 

172 

142.6 

96.2 

232 

192.3 

129.7 

292 

242.1 

163.3 

53 

43.9 

29.6 

113 

93.7 

63.2 

173 

143.4 

96.7 

233 

193.2 

130.3 

293 

242.9 

163.8 

54 

44.8 

30.2 

114 

94.5 

63.7 

174 

144.3 

97.3 

234 

194.0 

130.9 

294 

243.7 

164.4 

55 

45.6 

30.8 

115 

95.3 

64.3 

175 

145.1 

97.9 

235 

194.8 

131.4 

295  ;  244.6 

165.0 1 

56 

46.4 

31.3 

116 

96.2 

64.9 

176 

145.9 

98.4 

236 

195.7 

132.0 

2961245.4  165.5 1 

57 

47.3 

31.9 

117 

97.0 

65.4 

177 

146.7 

99.0 

237 

196.5 

132.5 

297  1 246.2 

166.1 

58 

48.1 

32.4 

118 

97.8 

66.0 

178 

147.6 

99.5 

238 

197.3 

133.1 

298  1247.1 

166.6 

59 

48.9 

33.0 

119 

98.7 

66.5 

179 

148.4 

100.1 

239 

198.1 

133.6 

299 

247.9 

167.2 

60 
DiaL 

49.7 

33.6 

120 

99.5 

67.1 

180 

149.2 

100.7 

240 

199.0 

134.2 

300 

248.7 

167.8 

Bep. 

Lat 

Dist 

Dep. 

Lat 

Dist 

Dep.   Lat. 

Dist 

Dep. 

Lat 

Dist  Dep. 

Lat 

For  56  Degrees. 

3h 

_44"«._ 

i 

TABLE  II. 

tl 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  35  DEGREES.   2h  02m. 

Dl8t 

1 

Lat. 

Dep. 

Dist. 

Lilt. 
50>0 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 
241 

Lat. 

Dep. 

00.8 

00.6 

61 

35.0 

121 

99.1 

69.4 

181 

148.3 

103.8 

197.4 

138.2 

o 

01.6 

01.1 

62 

50.8 

35.6 

122 

99.9 

70.0 

182 

149.1 

104.4 

242 

198.2 

1M8.8 

3 

0-2.5 

01.7 

63 

51.6 

36.1 

123 

100.8 

70.5 

183 

149.9 

105.0 

243 

199.1 

139.4 

4 

03.3 

02.3 

64 

52.4 

36.7 

124 

101.6 

71.1 

184 

150.7 

105.5 

244 

199.9  140.0 

5  04.1 

02.9 

65 

53.2 

37.3 

125 

102.4 

71.7 

185 

151.5 

106.1 

245 

200.7  140.5 

6  04.9 

03.4 

66 

54.1 

37.9 

126 

103.2 

72.3 

186 

152.4 

106.7 

246 

201.5  141.1 

7  05.7 

04.0 

67 

54.9 

38.4 

127 

104.0 

72.8 

187 

153.2 

107.3 

247 

202.3  141.7 

8  06.6 

04.6 

68 

55.7 

39.0 

128 

104.9 

73.4 

188 

154.0 

107.8 

248 

203.1 

142.2 

9 

07.4 

05.2 

69 

56.5 

39.6 

129 

105.7 

74.0 

189 

154.8 

108.4 

249 

204.0 

142.8 

10 
11 

08.2 
09.0 

05.7 

70 

57.3 

40.2 

130 

106.5 

74.6 

190 
191 

155.6 

109.0 

250 

204.8 

143.4 

06.3 

71 

58.2 

40.7 

131 

107.3 

75.1 

156.5 

109.6 

251 

205.6 

144.0 

12 

09.8 

06.9 

72 

59.0 

41.3 

132 

108.1 

75.7 

192 

157.3 

110.1 

252 

206.4 

144.5 

13 

10.6 

07.5 

73 

59.8 

41.9 

133 

108.9 

76.3 

193 

158.1 

110.7 

253 

207.2 

145.1 

14 

11.5 

08  0 

74 

60.6 

42.4 

134 

109.8 

76.9 

194 

158.9 

111.3 

254 

208.1 

145.7 

15 

12.3 

08.6 

75 

61.4 

43.0 

135 

110.6 

77.4 

195 

159.7 

111.8 

255 

208.9 

146.3 

16 

13.1 

09.2 

76 

62.3 

43.6 

136 

111.4 

78.0 

196 

160.6 

112.4 

256 

209.7 

146.8 

17 

13.9 

09.8 

77 

63.1 

44.2 

137 

112.2 

78.6 

197 

161.4 

113.0 

257 

210.5 

147.4 

18 

14.7 

10.3 

78 

63.9 

44.7 

138 

113.0 

79.2 

198 

162.2 

113.6 

258 

211.3 

148.0 

19 

15.6 

10.9 

79 

64.7 

45.3 

139 

113.9 

79.7 

199 

163.0 

114.1 

259 

212.2 

148.6 

20 
21 

16.4 

17.2 

11.5 

12.0 

80 

65.5 

45.9 
46.5 

140 

114.7 

80.3 

200 
201 

163.8 
164.6 

114.7 

260 

213.0 

149.1 

81 

66.4 

141 

115.5 

80.9 

115.3 

261 

213.8 

149.7 

22 

18.0 

12.6 

82 

67.2 

47.0 

142 

116.3 

81.4 

202 

165.5 

115.9 

262 

214.6 

150.3 

23 

18.8 

13.2 

83 

68.0 

47.6 

143 

117.1 

82.0 

203 

166.3 

116.4 

263 

215.4 

150.9 

24 

19.7 

13.« 

84 

68.8 

48.2 

144 

118.0 

82.6 

204 

167.1 

117.0 

264 

216.3 

151.4 

25 

20.5 

14.3 

85 

69.6 

48.8 

145 

118.8 

83.2 

205 

167.9 

117.6 

265 

217.1 

152.0 

26 

21.3 

14.9 

86 

70.4 

49.3 

146 

119.6 

83.7 

206 

168.7 

118.2 

266 

217.9 

152.6 

27 

22.1 

15.5 

87 

71.3 

49.9 

147 

120.4 

84.3 

207 

169.6 

118.7 

267 

218.7 

153.1 

28 

22.9 

16.1 

88 

72.1 

50.5 

148 

121.2 

84.9 

208 

170.4 

119.3 

268 

219.5 

153.7 

29 

23.8 

16.6 

89 

72.9 

51.0 

149 

122.1 

85.5 

209 

171.2 

119.9 

269 

220.4 

154.3 

30 

24.6 

17.2 

90 
91 

73.7 
74.5 

51.6 

150 

122.9 

86.0 

210 

172.0 

120.5 

270 

221.2 

154.9 

31 

25.4 

17.8 

52.2 

151 

123.7 

86.6 

211 

172.8 

121.0 

271 

222.0 

155.4 

32 

26.2 

18.4 

92 

75.4 

52.8 

152 

124.5 

87.2 

212 

173.7 

121.6 

272 

222.8 

156.0 

33 

27.0 

18.9 

93 

76.2 

53.3 

153 

125.3 

87.8 

213 

174.5 

122.2 

273 

223.6 

156.6 

34 

27.9 

19.5 

94 

77.0 

53.9 

154 

126.1 

88.3 

214 

175.3 

122.7 

274 

224.4 

157.2 

35 

28.7 

20.1 

95 

77.8 

54.5 

155 

127.0 

88.9 

215 

176.1 

123.3 

275 

225.3 

157.7 

36 

29.5 

20.6 

96 

78.6 

55.1 

156 

127.8 

89.5 

216 

176.9 

123.9 

276 

226.1 

158.3 

37 

30.3 

21.2 

97 

79.5 

55.6 

157 

128.6 

90.1 

217 

177.8 

124.5 

277 

226.9 

158.9 

38 

31.1 

21.8 

98 

80.3 

56.2 

158 

129.4 

90.6 

218 

178.6 

125.0 

278 

227.7 

159.5 

39 

31.9 

22.4 

99 

81.1 

56.8 

159 

130.2 

91.2 

219 

179.4 

125.6 

279 

228.5 

160.0 

40 

32.8 

22.9 

100 

81.9 

57.4 

160 

131.1 

91.8 

220 

180.2 

126.2 

280 

229.4 
230.2 

160.6 

41 

33.6 

23.5 

101 

82.7 

57.9 

161 

131.9 

92.3 

221 

181.0 

126.8 

281 

161.2 

42 

34.4 

24.1 

102 

83.6 

58.5 

162 

132.7 

92.9 

222 

181.9 

127.3 

282 

231.0 

161.7 

43 

35.2 

24.7 

103 

84.4 

59.1 

163 

133.5 

93.5 

223 

182.7 

127.9 

283 

231.8 

162.3 

44 

36.0 

25.2 

104 

85.2 

59.7 

164 

134.3 

94.1 

224 

183.5 

128.5 

284 

232.6 

162.9 

45 

36.9 

25.8 

105 

86.0 

60.2 

165 

135.2 

94.6 

225 

184.3 

129.1 

285 

233.5 

163.5 

46 

37.7 

26.4 

106 

86.8 

60.8 

166 

136.0 

95.2 

226 

185.1 

129.6 

286 

234.3 

164.0 

47 

38.5 

27.0 

107 

87.6 

61.4 

167 

136.8 

95.8 

227 

185.9 

130.2 

287 

235.1 

164.6 

48 

39.3 

27.5 

108 

88.5 

61.9 

168 

137.6 

96.4 

228 

186.8 

130.8 

288 

235.9 

165.2 

49 

40.1 

28.1 

109 

89.3 

62.5 

1()9 

138.4 

96.9 

229 

187.6 

131.3 

289 

236.7 

165.8 

50 
51 

41.0 

28.7 

110 

90.1 

63.1 

170 

139.3 

97.5 

230 

188.4 

131.9 

290 

237.6 

166.3 

41.8 

29.3 

111 

90.9 

63.7 

171 

140.1 

98.1 

231 

189.2 

132.5 

291 

238.4 

166.9 

52 

42.6 

29.8 

112 

91.7 

64.2 

172 

140.9 

98.7 

232 

190.0 

133.1 

292 

239.2 

167.5 

53 

43.4 

30.4 

113 

92.6 

64.8 

173 

141.7 

99.2 

233 

190.9 

133.6 

293 

240.0  168.1  1 

54 

44.2 

31.0 

114 

93.4 

65.4 

174 

142.5 

99.8 

234 

191.7 

134.2 

294 

240.8  168.61 

55 

45.1 

31.5 

115 

94.2 

66.0 

175 

143.4 

100.4 

235 

192.5 

134.8 

295 

241.6 

169.2 

56 

45.9 

32.1 

116 

95.0 

66.5 

176 

144.2 

100.9 

236 

193.3 

135.4 

296 

242.5 

169.8 

57 

46.7 

32.7 

117 

95.8 

67.1 

177 

145.0 

101.5 

237 

194.1 

135.9 

297 

243.3 

170.4 

58 

47.5 

33.3 

118 

96.7 

67.7 

178 

145.8 

102.1 

238 

195.0 

136.5 

298 

244.1 

170.9 

59 

48.3 

33.8 

119 

97.5 

68.3 

179 

146.6 

102.7 

239 

195.8 

137.1 

299 

244.9 

171.5 

60 

49.1 

34.4 

Lat. 

120 

98.3 

68.8  180 

147.4 

103.2 

240 

196.6 

137.7 

300 

245.7 

172.1 

DiBt 

Dep. 

Dist. 

Dep. 

Lat.  Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

For  66  Dee:i'ee8. 

8^  40D1.  1 

52 

TABLE  II. 

» 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  36  DEGREES.  2h  24ra.  1 

Diat 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

1 

00.8 

00.6 

61 

49.4 

35.9 

121 

97.9 

71.1 

181 

146.4 

106.4 

241 

195.0 

141.7 

2 

01.6 

01.2 

62 

50.2 

36.4 

122 

98.7 

71.7 

182 

147.2 

107.0 

242 

195.8 

142.2 

3 

02.4 

01.8 

63 

51.0 

37.0 

123 

99.5 

72.3 

183 

148.1 

107.6 

243 

196.6 

142.8 

4 

03.2 

02.4 

64 

51.8 

37.6 

124 

100.3 

72.9 

184 

148.9 

108.2 

244 ''  197.4 

143.4 

5 

04.0 

02.9 

65 

52.6 

38.2 

125 

101.1 

73.5 

185 

149.7 

108.7 

245  198.2 

144.0 

6 

04.9 

03.5 

66 

53.4 

38.8 

126 

101.9 

74.1 

186 

150.5 

109.3 

246 

199.0 

144.6 

7 

05.7 

04.1 

67 

54.2 

39.4 

127 

102.7 

74.-6 

187 

151.3 

109.9 

247 

199.8 

145.2 

8 

06.5 

04.7 

68 

55.0 

40.0 

128 

103.6 

75.2 

188 

152.1 

110.5 

248 

200.6 

145.8 

9 

07.3 

05.3 

69 

.55.8 

40.6 

129 

104.4 

75.8 

189 

152.9 

111.1 

249 

201.4 

146.4 

10 

n 

08.1 

05.9 

70 

56.6 

41.1 

130 

105.2 

76.4 

190 

153.7 

111.7 

250 

202.3 

146.9 

08.9 

06.5 

71 

57.4 

41.7 

131 

106.0 

77.0 

191 

154.5 

112.3 

251 

203.1 

147.5 

12 

09.7 

07.1 

72 

58.2 

42.3 

132 

106.8 

77.6 

192 

155.3 

112.9 

252 

203.9 

148.1 

13 

10.5 

07.6 

73 

59.1 

42.9 

133 

107.6 

78.2 

193 

156.1 

113.4 

253 

204.7 

148.7 

14 

11.3 

08.2 

74 

59.9 

43.5 

134 

108.4 

78.8 

194 

156.9 

114.0 

254 

205.5 

149.3 

15 

12.1 

08.8 

75 

60.7 

44.1 

135 

109.2 

79.4 

195 

157.8 

114.6 

255 

206.3 

149.9 

16 

12.9 

09.4 

76 

61.5 

44.7 

136 

110.0 

79.9 

196 

158.6 

115.2 

256 

207.1 

150.5 

17 

13.8 

10.0 

77 

62.3 

45.3 

137 

110.8 

80.5 

197 

159.4 

115.8 

257 

207.9 

151.1 

18 

14.6 

10.6 

78 

63.1 

45.8 

138 

111.6 

81.1 

198 

160.2 

116.4 

258 

208.7 

151.6 

19 

15.4 

11.2 

79 

63.9 

46.4 

139 

112.5 

81.7 

199 

161.0 

117.0 

259 

209.5 

152.2 

20 

16.2 

11.8 
12.3 

80 

64.7 

47.0 

140 

113.3 

82.3 

200 

161.8 

117.6 

260 

210.3 

152.8 

21 

17.0 

81 

65.5 

47.6 

141 

114.1 

82.9 

201 

162.6 

118.1 

261 

211.2 

153.4 

22 

17.8 

12.9 

82 

66.3 

48.2 

142 

114.9 

83.5 

202 

163.4 

118.7 

262 

212.0 

154.0 

23 

18.6 

13.5 

83 

67.1 

48.8 

143 

115.7 

84.1 

203 

164.2 

119.3 

263 

212.8 

154.6 

24 

19.4 

14.1 

84 

68.0 

49.4 

144 

116.5 

84.6 

204 

165.0 

119.9 

264 

213.6 

155.2 

25 

20.2 

14.7 

85 

68.8 

50.0 

145 

117.3 

85.2 

205 

165.8 

120.5 

265 

214.4 

155.8 

26 

21.0 

15.3 

86 

69.6 

50.5 

146 

118.1 

85.8 

206 

166.7 

121.1 

2661215.2 

156.4 

27 

21.8 

15.9 

87 

70.4 

51.1 

147 

118.9 

86.4 

207 

167.5 

121.7 

267 

216.0 

156.9 

28 

22.7 

16.5 

88 

71.2 

51.7 

148 

119.7 

87.0 

208 

168.3 

122.3 

268 

216.8,157.51 

29 

23.5 

17.0 

89 

72.0 

52.3 

149 

120.5 

87.6 

209 

169.1 

122.8 

269 '217.6' 158.1 1 

30 

.>4.3 

17.6 

90 

72.8 

52.9 

150 

121.4 

88.2 

210 

169.9 

123.4 

270  ,  218.4 

158.7 

31 

25.1 

18.2 

91 

73.6 

53.5 

151 

122.2 

88.8 

211 

170.7 

124.0 

271 

219.2 

159.3 

:^2 

25.9 

18.8 

92 

74.4 

54.1 

152 

123.0 

89.3 

212 

171.5 

124.6 

272 

220.1 

159.9 

33 

26.7 

19.4 

93 

75.2 

54.7 

153 

123.8 

89.9 

213 

172.3 

125.2 

273 

220.9 

160.5 

34 

27.5 

20.0 

94 

76.0 

55.3 

154 

124.6 

90.5 

214 

173.1 

125.8 

274 

221.7  ;  161.1 1 

35 

28.3 

20.6 

95 

70.9 

55.8 

155 

125.4 

91.1 

215 

173.9 

126.4 

275 

222.5 

161.6 

36 

29.1 

21.2 

96 

77.7 

56.4 

156 

126.2 

91.7 

216 

174.7 

127.0 

276 

223.3 

162.2 

37 

29.9 

21.7 

97 

78.5 

57.0 

157 

127.0 

92.3 

217 

175.6 

127.5 

277  1  224.1 

162.8 

38 

30.7 

22.3 

98 

79.3 

57.6 

158 

127.8 

92.9 

218 

176.4 

128.1 

278  224.9 

163.4 

39 

31.6 

22.9 

99 

80.1 

58.2 

159 

128.6 

93.5 

21'9 

177.2 

128.7 

279 

225.7 

164.0 

40 

32.4 

23.5 

100 

80.9 

58.8 

160 

129.4 

94.0 

220 

178.0 

129.3 

280 

226.5 

164.6 

41 

33.2 

24.1 

101 

81.7 

59.4 

161 

130.3 

94.6 

221 

178.8 

129.9 

281 

227.3 

165.2 

42 

34.0 

24.7 

102 

82.5 

60.0 

162 

131.1 

95.2 

222 

179.6 

130.5 

282 

228.1 

165.8 

43 

34.8 

25.3 

103 

83.3 

60.5 

163 

131.9 

95.8 

223 

180.4 

131.1 

283  '  229.0 

166.3 

44 

35.6 

25.9 

104 

84.1 

61.1 

164 

132.7 

96.4 

224 

181.2 

131.7 

284 

229.8 

160.9 

45 

36.4 

26.5 

105 

84.9 

61.7 

165 

133.5 

97.0 

225 

182.0 

132.3 

285 

230.6 

167.5 

46 

37.2 

27.0 

106 

85.8 

62.3 

166 

134.3 

97.6 

226 

182.8 

132.8 

286 

231.4 

168.1 

47 

38.0 

27.6 

107 

86.6 

62.9 

167 

135.1 

98.2 

227 

183.6 

133.4 

287  ,  232.2 

168.7 

48 

38.8 

28.2 

108 

87.4 

63.5 

168 

135.9 

98.7 

228 

184.5 

134.0 

288  233.0 

169.3 

49 

39.6 

28.8 

109 

88.2 

64.1 

169 

136.7 

99.3 

229 

185.3 

134.6 

289 

233.8 

169.9 

50 
51 

40.5 

29.4 

110 

89.0 

64.7 

170 

137.5 

99.9 

230 

186.1 

135.2 

290 

234.6 

170.5 

41.3 

30.0 

111 

89.8 

65.2 

171 

138.3 

100.5 

231 

186.9 

135.8 

291 

235.4 

171.0 

52 

42.1 

30.6 

112 

90.6 

6.5.8 

172 

139.2 

101.1 

232 

187.7 

136.4 

292  i  236.2 

171.6 

53 

42  9 

31.2 

113 

91.4 

66.4 

173 

140.0 

101.7 

233 

188.5 

137.0 

293  237.0 

172.2 

54 

43.7 

31.7 

114 

92.2 

67.0 

174 

140.8 

102.3 

234 

189.3 

137.5 

294 

237.9 

172.8 

55 

44.5 

32.3 

115 

93.0 

67.6 

175 

141.6 

102.9 

235 

190.1 

138.1 

295 

238.7 

173.4 

56 

45.3 

32.9 

116 

93.8 

68.2 

176 

142.4 

103.5 

236 

190.9 

138.7 

296 

239.5 

174.0 

57 

46.1 

33.5 

117 

94.7 

68.8 

177 

143.2 

104.0 

237 

191.7 

139.3 

297 

240.3 

174.6 

58 

46.9 

34.1 

118 

95.5 

69.4 

178 

144.0 

104.6 

238 

192.5 

139.9 

298 

241.1 

175.2 

59 

47.7 

34.7 

119 

96.3 

69.9 

179 

144.8 

105.2 

239 

193.4 

140.5 

299 

241.9 

175.7 

60 

48.5 

35.3 

120 

97.1 

70.5 

180 

145.6 

105.8 

240 

194.2 

141.1 

300 

242.7 

176.3 

Diet 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat 

Dist 

Dep. 

Lat 

» 

For  54 

Degrees. 

" 

TABLE  11.                       68  1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  37  DEGREES.   2». 

28n>.  1 
Dep. 

Diet 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lilt. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

LaL 

00.8 

00.0 

01 

48.7 

36.7 

121 

96.0 

72.8 

181 

144.6 

108.9 

241 

192.5  145.0  1 

2 

01.0 

01.2 

02 

49.5 

37.3 

122 

97.4 

73.4 

182 

145.4 

109.5 

242 

19.3.3 

145.6 

3 

0-2A 

01.8 

03 

503 

37.9 

123 

9S.2 

74.0 

183 

146.2 

110.1 

243 

194.1 

146.2 

4 

03.2 

02.4 

04 

51.1 

38.5 

124 

99.0 

74.6 

184 

146.9 

110.7 

244 

194.9 

146.8 

5 

04.0 

03.0 

05 

51.9 

39.1 

125 

99.8 

75.2 

185 

147.7 

111.3  245' 

195.7 

147.4 

6 

04.8 

03.6 

06 

52.7 

39.7 

126 

100.0 

75.8 

186 

148.5 

111.9  246  196.5 

148.0 

t 

05.6 

04.2 

67 

53.5 

40.3 

127 

101.4 

7(^.4 

187 

149.3 

112.5  247,197.3 

148.0 

8 

00.4 

04.8 

68 

54.3 

40.9 

128 

102.2 

77.0 

188 

150.1 

113.1 

248 

li»8.1 

149.3 

1> 

07.2 

05.4 

69 

55.1 

41.5 

129 

103.0 

77.6 

189 

150.9 

113.7 

249 

198.9 

149.9 

10 

08.0 

00.0 

70 

55.9 

42.1 

130 
131 

103.8 

78.2 

190 

151.7 

114.3 

250 

199.7 

150.5 

11 

08.8 

06.6 

71 

56.7 

42.7 

104.0 

78.8 

191 

152.5 

114.9 

251 

200.5 

151.1 

12 

09.0 

07.2 

72 

57.5 

43.3 

132 

105.4 

79.4 

192 

153.3 

115.5 

252 

201.3 

151.7 

13 

10.4 

07.8 

73 

58.3 

43.9 

133 

100.2 

80.0 

193 

154.1 

116.2 

253 

202.1 

152.3 

14 

11.2 

08.4 

74 

59.1 

44.5 

134 

107.0 

80.6 

194 

154.9 

116.8 

254 

202.9  152.9  1 

15 

12.0 

09.0 

75 

59.9 

45.1 

135 

107.8 

81.2 

195 

155.7 

117.4 

255 

203.7 

153.5 

lt> 

12.8 

09.6 

76 

()0.7 

45.7 

136 

108.6 

81.8 

196 

156.5 

118.0 

256 

204.5 

154.1 

17 

13.0 

10.2 

77 

61.5 

46.3 

137 

109.4 

82.4 

197 

157.3 

118.6 

257 

205.2 

154.7 

18 

14.4 

10.8 

78 

02.3 

46.9 

138 

110.2 

83.1 

198 

158.1 

119.2 

258 

206.0 

155.3 

19 

15.2 

11.4 

79 

63.1 

47.5 

139 

111.0 

83.7 

199 

158.9 

119.8 

259 

206.8 

155.9 

20 
21 

16.0 
16.8 

12.0 

80 

63.9 
64.7 

48.1 

48.7 

140 

111.8 

84.3 

200 

159.7 

120.4 

260 

207.6 

156.5 

12.6 

81 

141 

112.6 

84.9 

201 

160.5 

121.0 

261 

208.4 

157.1 

22 

17.6 

13.2 

82 

65.5 

49.3 

142 

113.4 

85.5 

202 

161.3 

121.6 

262 

209.2 

157.7 

23 

18.4 

13.8 

83 

66.3 

50.0 

143 

114.2 

86.1 

203 

162.1 

122.2 

203 

210.0 

158.3 

24 

19.2 

14.4 

84 

67.1 

50.6 

144 

115.0 

86.7 

204 

162.9 

122.8 

204 

210.8 

158.9 

25 

20.0 

15.0 

85 

67.9 

51.2 

145 

115.8 

87.3 

205 

163.7 

123.4 

205 

211.6 

159.5 

20 

20.8 

15.6 

86 

08.7 

51.8 

146 

116.6 

87.9 

206 

164.5 

124.0 

266 

212.4 

160.1 

27 

21.6 

10.2 

87 

09.5 

52.4 

147 

117.4 

88.5 

207 

165.3 

124.6 

267 

213.2 

160.7 

28 

22.4 

16.9 

88 

70.3 

53.0 

148 

118.2 

89.1 

208 

166.1 

125.2 

268 

214.0 

161.3 

29 

23.2 

17.5 

89 

71.1 

53.0 

149 

119.0 

89.7 

209 

166.9 

125.8 

269 

214.8 

161.9 

30 
31 

24.0 

18.1 

90 
91 

71.9 

72.7 

54.2 

150 

119.8 

90.3 

210 

167.7 

126.4 

270 

215.6 

162.5 

24.8 

18.7 

54.8 

151 

120.6 

90.9 

211 

168.5 

127.0 

271 

216.4 

163.1 

32 

25.0 

19.3 

92 

73.5 

55.4 

152 

121.4 

91.5 

212 

169.3 

127.6 

272 

217.2 

163.7 

33 

20.4 

19.9 

93 

74.3 

50.0 

153 

122.2 

92.1 

213 

170.1 

128.2 

273 

218.0 

164.3 

34 

27.2 

20.5 

94 

75.1 

56.0 

154 

123.0 

92.7 

214 

170.9 

128.8 

274 

218.8 

164.9 

35 

28.0 

21.1 

95 

75.9 

57.2 

155 

123.8 

93.3 

215 

171.7 

129.4 

275 

219.6 

165.5 

36 

28.8 

21.7 

96 

70.7 

57.8 

156 

124.6 

93.9 

216 

172.5 

130.0 

276 

220.4 

166.1 

37 

29.5 

22.3 

97 

77.5 

58.4 

157 

125.4 

94.5 

217 

173.3 

130.6 

277 

221.2 

106.7 

38 

30.3 

22.9 

98 

78.3 

59.0 

158 

126.2 

95.1 

218 

174.1 

131.2 

278 

222.0 

167.3 

39 

31.1 

2;:!.5 

99 

79.1 

59.6 

159 

127.0 

95.7 

219 

174.9 

131.8 

279 

222.8 

167.9 

40 
41 

31.9 

24.1 

100 

79.9 

60.2 

100 

127.8 

96.3 

220 

175.7 

132.4 

280 

223.0 

168.5 

32.7 

24.7 

101 

80.7 

60.8 

161 

128.6 

96.9 

221 

176.5 

133.0 

281 

224.4 

109.1 

42 

33.5 

25.3 

102 

81.5 

61.4 

162 

129.4 

97.5 

222 

177.3 

133.6 

282 

225.2 

109.7 

43 

34.3 

25.9 

103 

82.3 

62.0 

163 

130.2 

98.1 

223 

178.1 

134.2 

283 

226.0 

170.3 

44 

35.1 

26.5 

104 

83.1 

62.6 

164 

131.0 

98.7 

224 

178.9 

134.8 

284 

226.8 

170.9 

45 

35.9 

27.1 

105 

83.9 

63.2 

105 

131.8 

99.3 

225 

179.7 

135.4 

285 

227.6 

171.5 

40 

36.7 

27.7 

106 

84.7 

63.8 

166 

132.6 

99.9 

226 

180.5 

130.0 

286 

228.4 

172.1 

47 

37.5 

28.3 

107 

85.5 

64.4 

167 

133.4 

100.5 

227 

181.3 

13«).0 

287 

229.2 

172.7 

48 

38.3 

28.9 

108 

86.3 

65.0 

168 

134.2 

101.1 

228 

182.1 

137.2 

288 

230.0 

173.3 

49 

39.1 

29.5 

109 

87.1 

65.6 

109 

135.0 

101.7 

229 

182.9 

137.8 

289 

230.8 

173.9 

50 

51 

39.9 

30.1 

110 

87.8 

60.2 

170 

135.8 

102.3 

230 

183.7 

138.4 

290 

231.6 

174.5 

40.7 

30.7 

HI 

88.6 

66.8 

171 

136.6 

102.9 

231 

184.5 

139.0 

291 

232.4 

175.1 

52 

41.5 

31.3 

112 

89.4 

67.4 

172 

137.4 

103.5 

232 

185.3 

139.6 

292 

233.2 

175.7 

53 

42.3 

31.9 

113 

90.2 

68.0 

173 

138.2 

104.1 

233 

186.1 

140.2 

293 

234.0 

176.3 

54 

43.1 

32.5 

114 

91.0 

68.6 

174 

139.0 

104.7 

234 

186.9 

140.8 

294 

234.8 

176.9 

55 

43.9 

33.1 

115 

91.8 

69.2 

175 

139.8 

105.3 

235 

187.7 

141.4 

295 

235.6 

177.5 

50 

44.7 

33.7 

116 

92.6 

69.8 

176 

140.0 

105.9 

236 

188.5 

142.0 

296 

236.4 

178.1 

57 

45.5 

34.3 

117 

93.4 

70.4 

177 

141.4 

106.5 

237 

189.3 

142.6 

297 

237.2 

178.7 

58 

46.3 

34.9 

118 

94.2 

71.0 

178 

142.2 

107.1 

238 

190.1 

143.2 

298 

238.0 

179.3 

59 

47.1 

35.5 

119 

95.0 

71.6 

179 

143.0 

107.7 

239 

190.9 

143.8 

299 

238.8 

179.9 

00 
DiBt 

47.9 
.  Dep. 

30.1 

Lat. 

120 

Dist. 

95.8 
Dep. 

72.2 

Lat. 

180 
Dist. 

143.8 

108.3 

240 

Dist. 

191.7 

144.4 

300 

239.6 

180.5 

Dep. 

Lat. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

For  53  De2:fee8.                          3^  82n>.  | 

54 

TABLE  II. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  38  DEGREES.  2^  32m. 

Dist!  Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist. 

181 

Lat 

Dep. 

Dist 

Lat 

Dep. 

-^ 

1 

00.8 

00.6 

61 

48.1 

37.6 

121 

95.3 

74.5 

142.6 

111.4 

241 

189.9 

148.4 

2 

01.6 

01.2 

62 

48.9 

38.2 

122 

96.1 

75.1 

182 

143.4 

112.1 

242 

190.7 

149.0 

3 

02.4 

01.8 

63 

49.6 

38.8 

123 

96.9 

75.7 

183 

144.2 

112.7 

243 

191.5 

149.6 

4 

03.2 

02.5 

64 

50.4 

39.4 

124 

97.7 

76.3 

184 

145.0 

113.3 

244 

192.3 

150.2 

5 

03.9 

03.1 

65 

51.2 

40.0 

125 

98.5 

77.0 

185 

145.S 

113.9 

245 

193.1 

150.8 

6 

04.7 

03.7 

66 

52.0 

40.6 

126 

99.3 

77.6 

180 

146.6 

114.5 

246 

193.9 

151,5 

7 

05.5 

04.3 

67 

52.8 

41.2 

127 

100.1 

78:2 

187 

147.4 

115.1 

247 

194.6 

152.1 

8 

06.3 

04.9 

68 

53.6 

41.9 

128 

100.9 

78.8 

188 

148.1 

115.7 

248 

195.4 

152.7 

9 

07.1 

05.5 

69 

54.4 

42.5 

129 

101.7 

79.4 

189 

148.9 

116.4 

249 

196.2 

153.3 

10 
11 

07.9 

08.7 

06.2 

70 

55.2 

43.1 

130 

102.4 

80.0 

190 

149.7 

117.0 

250 

197.0 

153.9 
1.54.5 

06.8 

71 

55.9 

43.7 

131 

103.2 

80.7 

191 

150.5 

117.6 

251 

197.8 

12 

09.5 

07.4 

72 

56.7 

44.3 

132 

104.0 

81.3 

192 

151.3 

118.2 

252 

198.6 

155.1 

13 

10.2 

08.0 

73 

57.5 

44.9 

133 

104.8 

81.9 

193 

152.1 

118.8 

253 

199.4 

155.8  - 

14 

ll.,0 

08.6 

74 

58.3 

45.6 

134 

105.6 

82.5 

194 

152.9 

119.4 

254 

200.2 

156.4 

15 

11.8 

09.2 

75 

59.1 

46.2 

135 

106.4 

83.1 

195 

153.7 

120.1 

255 

200.9 

157.0 

16 

12.6 

09.9 

76 

59.9 

46.8 

136 

107.2 

83.7 

196 

154.5 

120.7 

256 

201.7 

157.6 

17 

13.4 

10.5 

77 

60.7 

47.4 

137 

108.0 

84.3 

197 

155.2 

121.3 

257 

202.5 

158.2 

18 

14.2 

11.1 

78 

61.5 

48.0 

138 

108.7 

85.0 

198 

156.0 

121.9 

258 

203.3 

1.58.8 

19 

15.0 

11.7 

79 

62.3 

48.6 

139 

109.5 

85.6 

199 

156.8 

122.5 

259 

204.1 

159.5 

20 

15.8 

12.3 

80 

63.0 

49.3 

140 

110.3 

86.2 

200 

157.6 

123.1 

260 

204.9 

160.1 

21 

16.5 

12.9 

81 

63.8 

49.9 

141 

111.1 

86.8 

201 

158.4 

123.7 

261 

205.7 

160.7 

22 

17.3 

13.5 

82 

64.6 

50.5 

142 

111.9 

87.4 

202 

159.2 

124.4 

262 

206.5 

161.3 

23 

18.1 

14.2 

83 

65.4 

51.1 

143 

112.7 

88.0 

203 

160.0 

125.0 

263 

207.2 

161.9 

24 

18.9 

14.8 

84 

66.2 

51.7 

144 

113.5 

88.7 

204 

160.8 

125.6 

264 

208.0 

162.5 

25 

19.7 

15.4 

85 

67.0 

52.3 

145 

114.3 

89.3 

205 

161.5 

126.2 

265 

208.8 

163.2 

26 

20.5 

IG.O 

86 

67.8 

52.9 

146 

115.0 

89.9 

206 

162.3 

126.8 

266 

209.6 

163.8 

27 

21.3 

16.6 

87 

68.6 

53.6 

147 

115.8 

90.5 

207 

163.1 

127.4 

267 

210.4 

164.4 

28 

22.1 

17.2 

88 

69.3 

54.2 

148 

116.6 

91.1 

208 

163.9 

128.1 

268 

211.2 

165.0 

29 

22.9 

17.9 

89 

70.1 

54.8 

149 

117.4 

91.7 

209 

164.7 

128.7 

269 

212.0 

165.6 

30 

23.6 

18.5 

90 

70.9 

55.4 

150 

118.2 

92.3 

210 

165.5 

129.3 

270 

212.8 

166.2 

31 

24.4 

19.1 

91 

71.7 

56.0 

151 

119.0 

93.0 

211 

166.3 

129.9 

271 

213.6 

166.8 

32 

25.2 

19.7 

92 

72.5 

56.6 

152 

119.8 

93.6 

212 

167.1 

130.5 

272 

214.3 

167.5 

33 

26.0 

20.3 

93 

73.3 

.57.3 

153 

120.6 

94.2 

213 

167.8 

131.1 

273 

215.1 

168.1 

34 

26.8 

20.9 

94 

74.1 

57.9 

154 

121.4 

94.8 

214 

168.6 

131.8 

274 

215.9 

168.7 

35 

27.6 

21.5 

95 

74.9 

58.5 

155 

122.1 

95.4 

215 

169.4 

132.4 

275 

216.7 

169.3 

36 

28.4 

22.2 

96 

75.6 

59.1 

156 

122.9 

96.0 

216 

170.2 

133.0 

276 

217.5 

169.9 

37 

29.2 

22.8 

97 

76.4 

59.7 

157 

123.7 

96.7 

217 

171.0 

133.6 

277 

.218.3 

170.5 

38 

29.9 

23.4 

98 

77.2 

60.3 

158 

124.5 

97.3 

218 

171.8 

134.2 

278 

219.1 

171.2 

39 

30.7 

24.0 

99 

78.0 

61.0 

159 

125.3 

97.9 

219 

172.6 

134.8 

279 

219.9 

171.8 

40 

31.5 

24.6 

100 

78.8 

61.6 

160 

126.1 

98.5 

220 

173.4 

135.4 

280 

220.6 

172.4 

41 

32.3 

25.2 

101 

79.6 

62.2 

161 

126.9 

99.1 

221 

174.2 

136.1 

281 

221.4 

173.0 

42 

33.1 

25.9 

102 

80.4 

62.8 

162 

127.7 

99.7 

222 

174.9 

136.7 

282 

222.2 

173.6 

43 

33.9 

26.5 

103 

81.2 

63.4 

163 

128.4 

100.4 

223 

1  175.7 

137.3 

283 

223.0 

174.2 

44 

34.7 

27.1 

104 

82.0 

64.0 

164 

129.2 

101.0 

224 

176.5 

137.9 

284 

223.8 

174.8 

45 

35.5 

27.7 

105 

82.7 

64.6 

165 

130.0 

101.6 

225 

177.3 

138.5 

285 

224.6 

175.5 

46 

36.2 

28.3 

106 

83.5 

65.3 

166 

130.8 

102.2 

226 

178.1 

139.1 

286 

225.4 

176.1 

47 

37.0 

28.9 

107 

84.3 

65.9 

167 

131.6 

102.8 

227 

178.9 

139.8 

287 

226.2 '176.71 

48 

37.8 

29.6 

108 

85.1 

66.5 

168 

1 32.4 

103.4 

228 

17i«.7 

140.4 

288  1226.9;  177.3 

49 

38.6 

30.2 

109 

85.9 

67.1 

169 

133.2 

104.0 

229 

180.5 

141.0 

289  227.7  1177.9 

50 

39.4 

30.8 

110 

86.7 

67.7 

170 

134.0 

104.7 

230 

181.2 

141.6 

290  1  228.5  ,  178.5 

51 

40.2 

31.4 

111 

87.5 

68.3 

171 

134.7 

105.3 

231 

182.0 

142.2 

291 

229.3 

179.2 

52 

41.0 

32.0 

112 

88.3 

69.0 

172 

135.5 

105.9 

232 

182.8 

142.8 

292 

230.1 

179.8 

53 

41.8 

32.6 

113 

89.0 

69.6 

173 

136.3 

106.5 

233 

183.6 

143.4 

293 

230.9 

180.4 

54 

42.6 

33.2 

114 

89.8 

70.2 

174 

137.1 

107.1 

234 

184.4 

144.1 

294 

231.7  181.0 

55 

43.3 

33.9 

115 

90.6 

70.8 

175 

137.9 

107.7 

235 

185.2 

144.7 

295 

232.5  181.6 

5() 

44.1 

34.5 

116 

91.4 

71.4 

176 

138.7 

108.4 

236 

186.0 

14.5.3 

296 

233.3  '■  182.2 

57 

44.9 

35.1 

117 

92.2 

72.0 

177 

139.5 

109.0 

237 

186.8 

14,5.9 

297 

234.0 

182.9 

58 

45.7 

35.7 

118 

93.0 

72.6 

178 

140.3 

109.6 

238 

187.5 

146.5 

298 

234.8 

183.5 

59 

46.5 

36.3 

119 

93.8 

73.3 

179 

141.1 

110.2 

239 

188.3 

147.1 

299 

235.6 

184  1 

60 

DIst 

47.3 

36.9 

120 

94.6 

73.9 

180 

141.8 

110.8 

240 

189.1 

147.8 

300 

236.4 

184.7 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat 

Dist 

Dep. 

Lat 

For  52  Degrees. 

30  28".  ^ 

TABLE  11. 

6i     1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  39  DEGREES.   2b  86«".  | 

Dist 

1 

Lat. 
00.8 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat 

Dep. 

Dist 

Lat. 

Dep. 

Dist 

Lat 
187.3 

Dep. 
151.7 

00.6 

61 

47.4 

38.4 

121 

94.0 

76.1 

181 

140.7 

113.9 

241 

2 

01.6 

01.3 

62 

48.2 

39.0 

122 

94.8 

76.8 

182 

141.4 

114.5 

242 

188.1 

152.3 

3 

02.3 

01.9 

63 

49.0 

39.6 

123 

95.6 

77.4 

183 

142.2 

115.2 

243 

188.8 

152.9 

4 

03.1 

02.5 

64 

49.7 

40.3 

124 

96.4 

78.0 

184 

143.0 

115.8 

244 

189.6 

153.6 

5 

03.9 

03.1 

65 

50.5 

40.9 

125 

97.1 

78.7 

185 

143.8 

116.4 

245 

190.4 

154.2 

6 

04.7 

03.8 

66 

51.3 

41.5 

126 

97.9 

79.3 

186 

144.5 

117.1 

246 

191.2 

154.8 

1 

05.4 

04.4 

(>7 

52.1 

42.2 

127 

98.7 

79.9 

187 

145.3 

117.7 

247 

192.0 

155.4 

8 

06.2 

0.").0 

68 

52.8 

42. » 

128 

99.5 

80.6 

188 

146.1 

118.3 

248 

192.7 

156.1 

9 

07.0 

05.7 

69 

53.6 

43.4 

129 

100.3 

81.2 

189 

146.9 

118.9 

249 

193.5 

1567 

10 

07.8 

06.3 
06.9 

70 

54.4 

44.1 

130 
131 

101.0 

81.8 

190 
191 

147.7 

119.6 

250 

194.3 

157.3 
158.0 

11 

08.5 

71 

5.').  2 

44.7 

101.8 

82.4 

148.4 

120.2 

251 

195.1 

12 

09.3 

07.6 

72 

56.0 

4.3.3 

132 

102.6 

83.1 

192 

149.2 

120.8 

252 

195.8 

158.6 

13 

1(1.1 

08.2 

73 

56.7 

45.9 

133 

103.4 

83.7 

193 

150.0 

121.5 

253 

196.6 

159.2 

14 

10.9 

08.8 

74 

57.5 

46.6 

134 

104.1 

84.3 

194 

150.8 

122.1 

254 

197.4 

159.8 

15 

11.7 

0!».4 

75 

58.3 

47.2 

135 

104.9 

85.0 

195 

151.5 

122.7 

255 

198.2 

160.5 

16 

12.4 

10.1 

7(5 

59.1 

47.S 

136 

105.7 

85.6 

196 

152.3 

123.3 

256 

19S.9 

161.1 

17 

13.2 

10.7 

77 

59.8 

48.5 

137 

106.5 

86.2 

197 

153.1 

124.0 

257 

199.7 

161.7 

18 

14.0 

11.3 

78 

60.6 

49.1 

138 

107.2 

86.8 

198 

153.9 

124.6 

258 

200.5 

1 62.4 

19 

14.8 

12.0 

79 

61.4 

49.7 

139 

108.0 

87.5 

199 

154.7 

125.2 

259 

201.3 

163.0 

20 
21 

15.5 
16.3 

12.6 

80 

62.2 
62.9 

50.3 
51.0 

140 

108.8 

88.1 

200 
201 

155.4 
156.2 

125.9 

260 

202.1 

163.6 

13.2 

81 

141 

109.6 

88.7 

126.5 

261 

202.8 

164.3 

22 

17.1 

13.8 

82 

63.7 

51.6 

142 

110.4 

89.4 

202 

157.0 

127.1 

262 

203.6 

164.9 

23 

17.9 

14.5 

83 

64.5 

52.2 

143 

111.1 

90.0 

203 

157.8 

127.8 

263 

204.4 

165.5 

24 

18.7 

15.1 

84 

65.3 

52.9 

144 

111.9 

90.6 

204 

158.5 

128.4 

264 

205.2 

l<k5.1 

25 

19.4 

15.7 

85 

66.1 

53.5 

145 

112.7 

91.3 

205 

159.3 

129.0 

265 

205.9 

1 66.8 

26 

20.2 

16.4 

86 

66.8 

54.1 

146 

113.5 

91.9 

206 

160.1 

129.6 

266 

206.7 

1 67.4 

27 

21.0 

17.0 

87 

67.6 

54.8 

147 

114.2 

92.5 

207 

160.9 

130.3 

267 

207.5 

168.0 

28 
29 

21.8 

17.6 

88 

68.4 

55.4 

148 

115.0 

93.1 

208 

161.6 

130.9 

268 

208.3 

168.7 

22.5 

18.3 

89 

69.2 

56.0 

149 

115.8 

93.8 

209 

162.4 

131.5 

269 

209.1 

169.3 

30 

23.3 

18.9 

90 

69.9 
70.7 

56.6 

150 

116.6 

94.4 

210 

163.2 

132.2 

270 

209.8 

169.9 

31 

24.1 

19.5 

91 

57.3 

151 

117.3 

95.0 

211 

164.0 

132.8 

271 

210.6 

170.5 

32 

24.9 

20.1 

92 

71.5 

57.'J 

152 

118.1 

95.7 

212 

164.8 

133.4 

272 

211.4 

171.2 

33 

25.6 

20.8 

93 

72.3 

58.5 

153 

118.9 

96.3 

213 

165.5 

134.0 

273 

212.2 

171.8 

34 

26.4 

21.4 

94 

73.1 

59.2 

154 

119.7 

96.9 

214 

166.3 

134.7 

274 

212.9 

172.4 

35 

27.2 

22.0 

95 

73.8 

59.8 

155 

120.5 

97.5 

215 

167.1 

135.3 

275 

213.7 

173.1 

36 

28.0 

22.7 

96 

74.6 

60.4 

156 

121.2 

98.2 

216 

167.9 

135.9 

276 

214.5 

173.7 

37 

28.8 

23.3 

97 

75.4 

61.0 

157 

122.0 

98.8 

217 

168.6 

136.6 

277 

215.3 

174.3 

38 

29.5 

23.9 

98 

76.2 

61.7 

158 

122.8 

99.4 

218 

169.4 

137.2 

278 

216.0 

175.0 

39 

30.3 

24.5 

99 

76.9 

62.3 

159 

123.6 

100.1 

219 

170.2 

137.8 

279 

216.8 

175.6 

40 

31.1 

25.2 

100 

77.7 

62.9 

160 

124.3 

100.7 

220 

171.0 

138.5 

280 

217.6 

176.2 

41 

31.9 

25.8 

101 

78.5 

63.6 

161 

125.1 

101.3 

221 

171.7 

139.1 

281 

218.4 

176.8 

42 

32.6 

26.4 

102 

79.3 

64.2 

1(>2 

125.9 

101.9 

222 

172.5 

1 39.7 

282 

219.2 

177.5 

43 

33.4 

27.1 

103 

80.0 

64.8 

163 

126.7 

102.6 

223 

173.3 

140.3 

283 

219.9 

178.1 

44 

34.2 

27.7 

104 

80.8 

65.4 

1()4 

127.5 

103.2 

224 

174.1 

141.0 

284 

220.7 

178.7 

45 

35.0 

28.3 

105 

81.6 

66.1 

l(*)5 

128.2 

103.8 

225 

174.9 

141.6 

285 

221.5 

179.4 

46 

35.7 

28.9 

106 

82.4 

66.7 

166 

129.0 

104.5 

226 

175.6 

142.2 

286 

222.3 

180.0 

47 

36.5 

29.r, 

107 

83.2 

67.3 

167 

129.8 

105.1 

227 

17(5.4 

142.9 

287 

223.0 

180.6 

48 

37.3 

30.2 

108 

83.9 

68.0 

168 

130.6 

105.7 

228 

177.2 

143.5 

288 

223.8 

181.2 

49 

38.1 

30.8 

109 

84.7 

68.6 

1()9 

131.3 

106.4 

229 

178.0 

144.1 

289 

224.6 

181.9 

50 
51 

38.9 
39.6 

31.5 

110 

85.5 

69.2 

170 

132.1 

107.0 

230 

178.7 

144.7 

290 

225.4 

182.  .3 

32.1 

111 

8().3 

69.9 

171 

132.9 

107.6 

231 

179.5 

145.4 

291 

226.1 

1S3  1 

52 

40.4 

32.7 

1  12 

87.0 

70.5 

172 

133.7 

108.2 

232 

180.3 

146.0 

292 

22(5.9 

ly3.s 

53 

41.2 

33.4 

113 

87.8 

71.1 

173 

134.4 

108.9 

233 

181.1 

14(5.6 

293 

227.7 

184.4 

54 

42.0 

34.0 

114 

88.6 

71.7 

174 

13.5.2 

109.5 

234 

181.9 

1 47.3 

294 

228.5 

185.0 

55 

42.7 

34.6 

115 

89.4 

72.4 

175 

136.0 

110.1 

235 

182.6 

147.9 

295 

229.3 

185.6 

56 

43.5 

35.2  116 

90.1 

73.0 

176 

1  •••.6.8 

110.8 

236 

183.4 

148.5 

296 

230.0 

186.3 

57 

44.3 

3.-).  9 

117 

90.1> 

73.6 

177 

137.6 

111.4 

237 

184.2 

149.1 

297 

230.8 

186.9 

58  45.1 

36.5 

118 

91.7 

74.3 

178 

138.3 

1 12.0 

238 

185.0 

149.8 

298 

231.6 

187.5 

59  45.9 

3r.i 

119 

92.5 

74.9 

179 

139.1 

112.6 

239 

185.7 

150.4 

299 

232.4 

188.2 

60 

46.6 

37.8 

120 

Dist 

93.3 

Dep. 

75.5 

L.it 

180 

139.9 

113.3 

240 

Di.*t 

186.5 

151.0 

300 

233.1 

188.8 

Dist 

Dep. 

Lat. 

Dist 

Dep. 

Lat. 

Dep. 

Lat. 

Diet. 

Dep. 

Lat 

For  51 

3e!^rees. 

3^ 

24m. 

66                \ 

TABLE  11. 

1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  40  DEGREES.  2>>  40m  1 

DisL 

1 

Lilt. 

Dep. 

Dist. 

Lat. 
46.7 

Dep. 

Dist. 

LaU 

Dep. 

Dist. 
181 

Lat. 

Dep. 
116.3 

Dist. 

Lat. 

Dep. 

00.8 

00.6 

61 

39.2 

!21 

92.7 

77.8 

138.7 

241 

1S4.6 

154.9 

2 

01.5 

01.3 

()2 

47.5 

39.9 

122 

93.5 

78.4 

Ls2 

139.4 

117.0 

242 

185.4 

155.6 

3 

02.3 

01.9 

63 

48.3 

40.5 

123 

94.2 

79.1 

183 

140.2 

117.6 

243 

186.1 

156.2 

4 

03.1 

02.6 

64 

49.0 

41.1 

124 

95.0 

79.7 

184 

141.0 

118.3 

244 

186.9 

156.8 

5 

03  8 

03.2 

(')5 

49.8 

41.8 

125 

95.8 

80.3 

185 

141.7 

118.9 

245 

187.7 

157.5 

6  04.0 

03.9 

66 

50.6 

42.4 

126 

9(').5 

81.0 

186 

142.5 

119.6 

246 

188.4 

158.1 

7  1  05.4 

04.5 

67 

51.3 

43.1 

127 

97.3 

81.6 

187 

143.3 

120.2 

247 

189.2 

158,8 

8 

06.1 

05.1 

68 

52.1 

43.7 

128 

98.1 

82.3 

188 

144.0 

120.8 

248 

190.0 

1 59.4 

9 

06.9 

05.8 

69 

52.9 

44.4 

129 

98.8 

82.9 

189 

144.8 

121.5 

249  1  190.7 

160.1 

10 
11 

07.7 
08. -l 

0().4 

70 

53.6 

45.0 

1  :!0 

99.6 

83.6 

190 

145.5 

122.1 

250 

191.5 

160.7 
161.3 

07.1 

71 

54.4 

45.6 

131 

100.4 

84.2 

191 

146.3 

122.8 

251 

192.3 

12 

09.2 

07.7 

72 

55.2 

46.3 

1 32 

101.1 

84.8 

192 

147.1 

123.4 

252 

193.0 

162.0 

13 

10.0 

08.4 

73 

55.9 

46.9 

i;;3 

101.9 

85.5 

193 

147.8 

124.1 

253 

193.8 

162.6 

14 

10.7 

09.0 

74 

56.7 

47.6 

134 

102.6 

86.1 

194 

14'«.6 

124.7 

254 

194.6 

163.3 

15 

11.5 

09.6 

75 

57.5 

48.2 

135 

103.4 

86.8 

195 

149.4 

125.3 

255 

195.3 

163.9 

16 

12.3 

10  3 

76 

58.2 

48.9 

136 

104.2 

87.4 

196 

150.1 

126.0 

256 

196.1 

164.6 

17 

13.0 

10.9 

77 

59.0 

49.5 

137 

!  04.9 

88.1 

197 

150.9 

126.6 

257 

196.9 

165.2 

18 

13.8 

11.6) 

78 

59.8 

50.1 

138 

105.7 

88.7 

198 

151.7 

127.3 

258 

197.6 

165.8 

19 

14.6 

12.2 

79 

60.5 

50.8 

139 

106.5 

89.3 

1 99 

152.4 

127.9 

259 

198.4 

166.5 

20 

15.3 

12.9 

80 

61.3 

51.4 

140 

107.2 

90.0 

200 

153.2 

128.6 

260 

199.2 

167.1 

21 

16.1 

13.5 

81 

()2.0 

52.1 

141 

108.0 

90.6 

201 

J  54.0 

129.2 

261  '  199.9 

167.8 

22 

16.9 

14.1 

82 

62.8 

52.7 

142 

108.8 

91.3 

202 

154.7 

129.8 

262 

200.7 

168.4 

23 

17.6 

14.8 

83 

63.6 

53.4 

143 

109.5 

91.9 

203 

155.5 

130.5 

263 

201.5 

169.1 

24 

18.4 

15.4 

84 

64.3 

54.0 

144 

110.3 

92.6 

204 

156.3 

131.1 

264 

202.2 

169.7 

25 

19.2 

16.1 

85 

65.1 

54.6 

145 

111.1 

93.2 

205 

157.0 

131.8 

265 

203.0 

170.3 

2*) 

19.9 

16.7 

86 

65.9 

55.3 

146 

111.8 

93.8 

206 

1 57.8 

132.4 

266 

203.8 

171.0 

27 

20.7 

17.4 

87 

66.6 

55.9 

147 

112.6 

94.5 

207 

158.6 

133.1 

267 

204.5 

171.6 

28 

21.4 

18.0 

88 

67.4 

56.6 

148 

113.4 

95.1 

208 

159.3 

1337 

268 

205.3  172.3 

29 

22  2 

18.6 

89 

68.2 

57.2 

149 

114.1 

95.8 

209 

160.1 

134.3 

269 

206.1  172.9 

30 

23.0 

19.3 

90 
91 

68.9 
69.7 

57.9 

150 

114.9 

96.4 

210 

160.9 

135.0 

270 

206.8  1  173.6 

31 

23.7 

19.9 

58.5 

151 

115.7 

97.1 

211 

161.6 

135.6 

271 

207.6 

174.2 

32 

24.5 

20.6 

92 

70.5 

59.1 

152 

116.4 

97.7 

212 

162.4 

136.3 

272 

208.4 

174.8 

33 

25.3 

21.2 

93 

71.2 

59.8 

153 

117.2 

98.3 

213 

163.2 

136.9 

273 

209.1 

175.5 

34 

26.0 

21.9 

94 

72.0 

60.4 

154 

118.0 

99.0 

214 

163.9 

137.6 

274 

209.9 

176.1 

35 

2<).8 

22.5 

95 

72.8 

61.1 

155 

118.7 

99.6 

215 

1<)4.7 

138.2 

275 

210.7 

176.8 

3t) 

27.() 

23.1 

!»6 

73.5 

61.7 

156 

119.5 

100.3 

216 

165.i 

138.8 

276 

211.4 

177.4 

37 

2S.3 

23.8 

97 

74.3 

62.4 

157 

120.3 

100.9 

217 

166.2 

139.5 

277 

212.2 

178.1 

38 

29.1 

24.4 

98 

75.1 

63.0 

158 

121.0 

101.6 

218 

167.0 

140.1 

278 

213.0 

178.7 

39 

29.9 

25.1 

99 

75.8 

63.6 

159 

121.8 

102.2 

219 

167.8 

140.8 

279 

213.7 

179.3 

40 

30.6 

25.7 

100 

76.6 

64.3 

160 

122.6 

102.8 

220 

168.5 

141.4 

280 

214.5 

180.0 

41 

31.4 

26.4 

101 

77.4 

64.9 

ir>i 

123.3 

103.5 

221 

16i).3 

142.1 

281 

215.3 

180.6 

42 

32.2 

27.0 

102 

78.1 

65.6 

162 

124.1 

104.1 

222 

170.1 

142.7 

282 

216.0 

181.3 

43 

32.9 

27.6 

103 

78.9 

66.2 

163 

124.9 

104.8 

223 

170.8 

143.3 

283 

216.8 

181.9 

44 

33.7 

28.3 

104 

79.7 

66.8 

164 

125.6 

105.4 

224 

171.6 

144.0 

284 

217.6 

182.6 

45 

34.5 

28.9 

105 

80.4 

67.5 

165 

126.4 

106.1 

225 

172.4 

144.6 

285 

218.3 

183.2 

4() 

35.2 

29.6 

lOr. 

81.2 

68.1 

166 

127.2 

106.7 

226 

173.1 

145.3 

286 

219.1 

183.8 

47 

36.0 

30.2 

107 

82.0 

68.8 

167 

127.9 

107.3 

227 

173.9 

145.9 

287 

219.9 

184.5 

48 

36.8 

30.9 

108 

82.7 

69.4 

1()8 

12S.7 

108.0 

228 

174.7 

146.6 

288 

220.6 

185.1 

49 

37.5 

.•il.5 

109 

83.5 

70.1 

169 

129.5 

108.6 

22i) 

175.4 

147.2 

289 

221.4 

185.8 

50 

38.3 

32.1 

110 

84.3 

70.7 

170 

130.2 

109.3 

230 

1 76.2 

147.8 

290 

222.2  1S6.4| 

51 

39.1 

32.8 

HI 

85.0 

71.3 

171 

131.0 

109.9 

231 

177.0 

148.5 

291  1222.9 '187.1 

52 

39.8 

33.4 

112 

85.8 

72.0 

172 

131.8 

1 10.6 

232 

177.7 

149.1 

292  223.7  1  187.7 

53 

40  6 

34.1 

113 

86.6 

72.6 

!73 

132.5 

111.2 

233 

178.5 

149.8 

293  224.5  188.3 

54 

41.4 

34.7 

114  87.3 

73.3 

174 

133.3 

111.8 

234 

179.3 

150.4 

294  '  225.2 

189.0 

55 

42.1 

35.4 

ll.T 

88.1 

73.9 

175 

134.1 

112.5 

235 

180.0 

151.1 

295 

22().0 

189.6 

5(> 

42.9 

3().0 

116 

88.9 

74.6 

176 

134.8 

113.1 

236 

180.8 

151.7 

296 

226.7 

190.3 

57 

43.7 

36.6 

117 

89.6 

75.2 

177 

135.6 

113.8 

237 

181.6 

152.3 

297 

227.5 

190.9 

58 

44.4 

37.3 

118 

90.4 

75.8 

178 

136.4 

114.4 

238 

182.3  153.0 

298 

228.3 

191.6 

59 

45.2 

37.9 

119 

91.2 

76.5 

179 

137.1 

115.1 

239 

183.1 

153.6 

299 

229.0 

192.2 

60 

46.0 

38.6 

120 

91.9 

77.1 

180 

!  37.9 

115.7  240 

183.9 

154.3 

300 

229.8 

192.8 

Distl  Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat.   Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

F<ir  50 

3e<^rees. 

.Sii  20'".  1 

f 


TABLE  11.                      67  1 

DIFFERENCE  OF  LATITUDE  AN! 

>  DEPARTURE  FOR  41  DEGREES.   2h  44m.  1 

Dist 

1 

Lat 

Dep. 

Dist. 

Lat. 

Dep. 

Dist.   Lut. 

Dep. 
79.4 

Dist 

Lat 

Dep. 

Dist 
241 

Lat 

Dep. 

00.8 

00.7 

61 

46.0 

40.0 

121   91.3 

181 

136.6 

118.7 

181.9 

158.1 

2 

01.5 

01.3 

62 

46.8 

40.7 

122  92.1 

80.0 

182 

137.4 

119.4 

242 

182.6 

158.8 

3 

02.3 

02.0 

63 

47.5 

41.3 

123  92.8 

80.7 

183 

138.1 

120.1 

243 

183.4 

159.4 

4 

03.0 

02.6 

64 

48.3 

42.0 

124  93.6 

81.4 

184 

138.9 

120.7 

244 

184.1 

160.1 

5 

03.8 

03.3 

65 

49.1 

42.6 

125  94.3 

82.0 

185 

139.6 

121.4 

245 

184.9 

160.7 

6 

04.5 

03.9 

66 

49.8 

43.3 

126 

95.1 

82.7 

186 

140.4 

122.0 

246 

185.7 

161.4 

7 

05.3 

04.() 

67 

50.6 

44.0 

127 

95.8 

83.3 

187 

141.1 

122.7 

247 

186.4 

162.0 

8 

06.0  05.2 

68 

51.3 

44.6 

128 

96.6 

84'.  0 

188 

141.9 

123.3 

248 

187.2 

162.7 

9 

06.8  1  05.9 

69 

52.1 

45.3 

129 

97.4 

84.6 

189 

142.6 

124.0 

249 

187.9 

163.4 

10 

07.5 

06.6 

70 

52.8 

45.9 

130 

98.1 

85.3 

190 
191 

143.4 

124.7 

250 

188.7 

164.0 

11 

08.3 

07.2 

71 

53.6 

46.6 

131 

98.9 

85.9 

144.1 

125.3 

251 

189.4 

164.7 

12 

09.1 

07.9 

72 

54.3 

47.2 

132 

99.6 

86.6 

192 

144.9 

126.0 

252 

1!»0.2 

165.3 

13 

09.8 

08.5 

73 

55.1 

47.9 

133 

100.4 

87.3 

193 

145.7 

126.6 

253 

190.9 

166.0 

14 

10.6 

09.2 

74 

55.8 

48.5 

134 

lOl.l 

87.9 

194 

146.4 

127.3 

254 

191.7 

166.6 

15 

11.3 

09.8 

75 

56.6 

41>.2 

135 

101.9 

88.6 

195 

147.2 

127.9 

255 

192.5 

167.3 

16 

12.1 

10.5 

76 

57.4 

49.9 

136 

102.6 

89.2 

196 

147.9 

128.6 

256 

193.2 

168.0 

17 

12.8 

11.2 

77 

58.1 

50.5 

137 

103.4 

89.9 

197 

148.7 

129.2 

257 

194.0 

168.6 

18 

13.6 

11.8 

78 

58.9 

51.2 

138 

104.1 

90.5 

198 

149.4 

129.9 

258 

194.7 

169.3 

!9 

14.3 

12.5 

79 

59.6 

51.8 

139 

104.9 

91.2 

199 

150.2 

130.6 

259 

195.5 

169.9 

20 
21 

15.1 

15.8 

13.1 

80 

60.4 
61.1 

52.5 
53.1 

140 

105.7 

91.8 

200 

150.9 

131.2 

260 

196.2 

170.6 

13.8 

81 

141 

106.4 

92.5 

201 

151.7 

131.9 

261 

197.0 

171.2 

22 

16.6 

14.4 

82 

61.9 

53.8 

142 

107.2 

93.2 

202 

152.5 

132.5 

262 

197.7 

171.9 

23 

17.4 

15.1 

83 

62.6 

54.5 

143 

107.9 

93.8 

203 

153.2 

133.2 

263 

198.5 

172.5 

24 

18.1 

15.7 

84 

63.4 

55.1 

144 

108.7 

94.5 

204 

154.0 

133.8 

264' 

199.2 

173.2 

25 

18.9 

16.4 

85 

64.2 

55.8 

145 

109.4 

95.1 

205 

154.7 

134.5 

265 

200.0 

173.9 

20 

19.6 

17.1 

86 

64.9 

56.4 

146 

110.2 

95.8 

206 

155.5 

135.1 

266 

200.8 

174.5 

27 

20.4 

17.7 

87 

65.7 

57.1 

147 

110.9 

96.4 

207 

156.2 

135.8 

267 

201.5 

175.2 

28 

21.1 

18.4 

88 

66.4 

57.7 

148 

111.7 

97.1 

208 

157.0 

136.5 

288 

202.3 

175.8 

29 

21.9 

19.0 

89 

67.2 

58.4 

149 

112.5 

97.8 

209 

157.7 

137.1 

269 

203.0 

176.5 

30 
31 

22.6 

.19.7 

90 
91 

67.9 

68.7 

59.0 

150 

113.2 

98.4 

210 

158.5 

137.8 

270 

203.8 

177.1 

23.4 

20.3 

59.7 

151 

114.0 

99.1 

211 

159.2 

138.4 

271 

204.5 

177.8 

32 

24.2 

21.0 

92 

69.4 

60.4 

152 

114.7 

99.7 

212 

160.0 

139.1 

272 

205.3 

178.4 

33 

24.9 

21.6 

93 

70.2 

61.0 

153 

115.5 

100.4 

213 

160.8 

139.7 

273 

206.0 

179.1 

34 

25.7 

22.3 

94 

70.9 

61.7 

154 

116.2 

101.0 

214 

161.5 

140.4 

274 

206.8 

179.8 

35 

26.4 

23.0 

95 

71.7 

62.3 

155 

117.0 

101.7 

215 

102.3 

141.1 

275 

207.5 

180.4 

36 

27.2 

23.6 

96 

72.5 

03.0 

1.56 

117.7 

102.3 

216 

163.0 

141.7 

276 

208.3 

181.1 

37 

27.9 

24.3 

97 

73.2 

03.6 

157 

118.5 

103.0 

217 

163.8 

142.4 

277 

209.1 

181.7 

38 

28.7 

24.9 

98 

74.0 

64.3 

1.58 

119.2 

103.7 

218 

104.5 

143.0 

278 

209.8 

182.4 

39 

29.4 

25.6 

99 

74.7 

64.9 

159 

120.0 

104.3 

219 

165.3 

143.7 

279 

210.6 

183.0 

40 

30.2 

26.2 

100 

75.5 

65.6 

160 

120.8 

io.->.o 

220 

166.0 

144.3 

280 

211.3 

183.7 

41 

30.9 

26.9 

101 

70.2 

66.3 

101 

121.5 

105.6 

221 

166.8 

145.0 

281 

212.1 

184.4 

42 

31.7 

27.6 

102 

77.0 

60.0 

1 02 

122.3 

10(5.3 

222 

16T.5 

145.6 

282 

212.8 

185.0 

43 

32.5 

28.2 

103 

77.7 

07.0 

163 

123.0 

106.9 

223 

168.3 

146.3 

283 

21.3.6 

185.7 

44 

33.2 

28.9 

104 

78.5 

()8.2 

104 

123.8 

107.6 

224 

169.1 

147.0 

284 

214.3 

186.3 

45 

34.0 

29.5 

105 

79.2 

08.9 

105 

124.5 

108.2 

225 

169.8 

147.6 

285 

215.1 

187.0 

46 

34.7 

30.2 

106 

80.0 

09.5 

106 

125.3 

108.9 

226 

170.6 

148.3 

286 

215.8 

187.6 

47 

35.5 

30.8 

107 

808 

70.2 

107 

126.0 

109.6 

227 

171.3 

148.9 

287 

216.6 

188.3 

48 

36.2 

31.5 

108 

81.5 

70.9 

108 

126.8 

110.2 

228 

172.1 

149.0 

288 

217.4 

188.9 

49 

37.0 

32.1 

109 

82.3 

71.5 

109 

127.5 

110.9 

229 

172.8 

150.2 

289 

218.1 

189.6 

50 
51 

37.7 

32.8 

110 

83.0 

72.2 

170 

128.3 

111.5 

230 

173.0 

150.9 

290 

218.9 

190.3 

38.5 

33.5 

111 

83.8 

72.8 

171 

129.1 

112.2 

231 

174.3 

151.5 

291 

219.6 

190.9 

52 

39.2 

34.1 

112 

84.5 

73.5 

172 

129.8 

112.8 

232 

175.1 

1,52.2 

292 

220.4 

191.6 

53 

40.0 

34.8 

113 

85.3 

74.1 

173 

130.6 

113.5 

233 

175.8 

152.9 

293 

221.1 

192.2 

54 

40.8 

35.4 

114 

86.0 

74.8 

174 

131.3 

114.2 

234 

170.6 

153.5 

294 

221.9  1192.9  1 

55 

41.5 

36.1 

115 

86.8 

75.4 

175 

132.1 

114.8 

235 

177.4 

154.2 

295 

222.6 

193.5 

56 

42.3 

36.7 

116 

87.5 

76.1 

170 

132.8 

115.5 

236 

178.1 

154.8 

296 

223.4 

194.2 

57 

43.0 

37.4 

117 

88.3 

76.8 

177 

133.0 

lir,.i 

237 

178.9 

155.5 

297 

224.1 

194.8 

58 

43.8 

38.1 

118 

89.1 

77.4 

178 

134.3 

116.8 

238 

179.6 

156.1 

298 

224.9 

195.5 

59 

44.5 

38.7 

119 

89.8 

78.1 

179 

135.1 

117.4 

239 

180.4 

156.8 

299 

225.7 

196.2 

60 
Dist 

45.3 

Dep. 

39.4 

Lat. 

120 

90.6 

78.7 
Lat. 

180 

135.8 

118.1 

240 

181.1 

157.5 

300 

226.4 

196.8 

Dist. 

Dep. 

Dist. 

Dep. 

Lat 

Dist 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

For  49 

Degrees.                          S^   16"   1 

68                   TABLE  11. 

1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  42  DEGREES.  2^  48ni.  1 

Diflt. 
1 

Lat. 

Dep. 

Dist. 

Lat. 

Dep 

40.8 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

00.7 

00.7 

61 

45.3 

121 

89.9 

81.0 

181 

134.0 

121.1 

241 

179.1 

161.3 

2 

01.5 

01.3 

62 

46.1 

41.5 

122 

90.7 

81.6 

KS2 

135.3 

121.8 

242 

179.8 

161.9 

3 

02.2 

02.0 

63 

46.8 

42.2 

123 

91.4 

82.3 

183 

136.0 

122.5 

243 

180.6 

162.6 

4 

03.0 

02.7 

64 

47.6 

42.8 

124 

92.1 

83.0 

184 

136.7 

123.1 

244 

181.3 

163.3 

5 

03.7 

03.3 

65 

48.3 

43.5 

125 

92.9 

83.6 

185 

137.5 

123.8 

245 

182.1 

163.9 

6 

04.5 

04.0 

66 

49.0 

44.2 

126 

93.6 

84.3 

186 

138.2 

124.5 

246 

182.8 

164.6 

7 

05.2 

04.7 

67 

49.8 

44.8 

127 

94.4 

85.0 

187 

139.0 

125.1 

247 

183.6 

165.3 

8 

05.9 

05.4 

68 

50.5 

45.5 

128 

95.1 

85.6 

188 

139.7  125.8 

248 

184.3 

165.9 

9 

06.7 

06.0 

69 

51.3 

46.2 

129 

95.9 

86.3 

189 

140.5 

126.5 

249 

185.0 

166.6 

10 
11 

07.4 

06.7 

70 

52.0 

46.8 

130 

96.6 

87.0 

190 

141.2 

127.1 

250 

185.8 

167.3 

08.2 

07.4 

71 

52.8 

47.5 

131 

97.4 

87.7 

191 

141.9 

127.8 

251 

186.5 

168.0 

12 

08.9 

08.0 

72 

.^3.5 

48.2 

132 

98.1 

88.3 

192 

142.7 

128.5 

252 

187.3 

168.6 

13 

09.7 

08.7 

73 

54.2 

48.8 

133 

98.8 

89.0 

193 

143.4 

129.1 

253 

188.0 

169.3 

14 

10.4 

09.4 

74  55.0 

49.5 

134 

'99.6 

89.7 

194 

144.2 

129.8 

254 

188.8 

170.0 

15 

11.1 

10.0 

75 

55.7 

50.2 

135 

100.3 

90.3 

195 

144.9 

130.5 

255 

189.5 

170.6 

16 

11.9 

10.7 

76 

56.5 

50.9 

136 

101.1 

91.0 

196 

145.7 

131.1 

256 

190.2 

171.3 

17 

12.6 

11.4 

77 

57.2 

51.5 

137 

101.8 

91.7 

197 

146.4 

131.8 

257 

191.0 

172.0 

18 

13.4 

12.0 

78 

58.0 

52.2 

138 

102.6 

92.3 

198 

147.1 

132.5 

258 

191.7 

172.6 

19 

14.1 

12.7 

79 

58.7 

52.9 

139 

103.3 

93.0 

199 

147.9 

133.2 

259 

192.5 

173.3 

20 

14.9 

13.4 

80 

59.5 

53.5 

140 

104.0 

93.7 

200 

148.6 

133.8 

260 

193.2 

174.0 

21 

15.6 

14.1 

81 

60.2 

54.2 

141 

104.8 

94.3 

201 

149.4 

134.5 

261 

194.0 

174.6 

22 

16.3 

14.7 

82 

60.9 

54.9 

142 

105.5 

95.0 

202 

150.1 

135.2 

262 

194.7 

175.3 

23 

17.1 

15.4 

83 

61.7 

55.5 

143 

106.3 

95.7 

203 

150.9 

135.8 

263 

195.4 

176.0 

24 

17.8 

16.1 

84 

62.4 

56.2 

144 

107.0 

96.4 

204 

151.6 

136.5 

264 

196.2 

176.7 

25 

18.6 

16.7 

85 

63.2 

56.9 

145 

107.8 

97.0 

205 

152.3 

137.2 

265 

196.9 

177.3 

26 

19.3 

17.4 

86 

63.9 

57.5 

146 

108.5 

97.7 

206 

153.1 

137.8 

266 

197.7 

178.0 

27 

20.1 

18.1 

87 

64.7 

58.2 

147 

109.2 

98.4 

207 

153.8 

138.5 

267 

198.4 

178.7 

28 

20.8 

18.7 

88 

65.4 

58.9 

148 

110.0 

99.0 

208 

154.6 

139.2 

268 

199.2 

179.3 

29 

21.6 

19.4 

89 

66.1 

59.6 

149 

110.7 

99.7 

209 

155.3 

139.8 

269  .  199.9 

180.0 

30 

22.3 

20.1 

90 

66.9 

60.2 

150  111.5 

100.4 

210 

156.1 

140.5 

270 

200.6 

180.7 

31 

23.0 

20.7 

91 

67.6 

60.9 

151 

112.-8 

101.0 

211 

156.8 

141.2 

271 

201.4 

181.3 

32 

23.8 

21.4 

92 

68.4 

61.6 

152 

113.0 

iOl.7 

212 

157.5 

141.9 

272 

202.1 

182.0 

33 

24.5 

22.1 

93 

69.1 

62.2 

153 

113.7 

102.4 

213 

158.3 

142.5 

273 

202.9 

182.7 

34 

25.3 

22.8 

94 

69.9 

62.9 

154 

.114.4 

103.0 

214 

159.0 

143.2 

274 

203.6 

183.3 

35 

26.0 

23.4 

95 

70.6 

63.6 

155 

115.2 

103.7 

215 

159.8 

143.9 

275 

204.4 

184.0 

36 

26.8 

24.1 

96 

71.3 

64.2 

156 

115.9 

104.4 

216 

160.5 

144.5 

276 

205.1 

184.7 

37 

27.5 

24.8 

97 

72.1 

64.9 

157 

116.7 

105.1 

217 

161.3 

145.2 

277 

205.9 

185.3 

38 

28.2 

25.4 

98 

72.8 

65.6 

1.58 

117.4 

105.7 

218 

162.0 

145.9 

278 

206.6 

186.0 

39 

29.0 

26.1 

99 

73.6 

66.2 

159 

118.2 

106.4 

219 

162.7 

146.5 

279 

207.3 

186.7 

40 

29.7 

26.8 

100 

74.3 

66.9 

160 

118.9 

107.1 

220 

163.5 

147.2 

280  208.1 

187.4 

41 

30.5 

27.4 

101 

75.1 

67.6 

161 

119.6 

107.7 

221 

164.2 

147.9 

281 

208.8 

188.0 

42 

31.2 

28.1 

102 

75.8 

68.3 

162 

120.4 

108.4 

222 

1*65.0 

148.5 

282 

209.6 

188.7 

43 

32.0 

28.8 

103 

76.5 

68.9 

163 

121.1 

109.1 

223 

165.7 

149.2 

283 

210.3 

189.4 

44 

32.7 

29.4 

104 

77.3 

69.6 

164 

121.9 

109.7 

224 

166.5 

149.9 

284 

211.1 

190.0 

45 

33.4 

30.1 

105 

78.0 

70.3 

165 

122.6 

110.4 

225 

167.2 

150.6 

285 

211.8 

190.7 

46 

34.2 

30.8 

106 

78.8 

70.9 

166 

123.4 

111.1 

226 

168.0 

151.2 

286 

212.5 

191.4 

47 

34.9 

31.4 

107 

79.5 

71.6 

167 

124.1 

111.7 

227 

168.7 

151.9 

287 

213.3 

192.0 

48 

35.7 

32.1 

108 

80.3 

72.3 

1()8 

124.8 

112.4 

228 

169.4 

152.6 

288 

214.0 

192.7 

49 

36.4 

32.8 

109 

81.0 

72.9 

169 

125.6 

113.1 

229 

170.2 

153.2 

289 

214.8 

193.4 

50 

37.2 

33.5 

110 

81.7 

73.6 

170 

126.3 

113.8 

230 

170.9 

153.9 

290 

215.5 

194.0 

51 

37.9 

34.1 

111 

82.5 

74.3 

171 

127.1 

114.4 

231 

171.7 

154.6 

291 

216.3 

194.7 

52 

38.6 

34.8 

112 

83.2 

74.9 

172 

127.8 

115.1 

232 

172.4 

155.2 

292 

217.0 

195.4 

53 

394 

35.5 

113 

84.0 

75.6 

173 

128.6 

115.8 

233 

173.2 

155.9 

293 

217.7 

196.1 

54 

40.1 

36.1 

114 

84.7 

76.3 

174 

129.3 

116.4 

234 

173.9 

156.6 

294 

218.5 

196.7 

55 

40.9 

36.8 

115 

85.5 

77.0 

175 

130.1 

117.1 

235 

174.6 

157.2 

295 

219.2 

197.4 

56 

41.6 

37.5 

116 

86.2 

77.6 

176 

130.8 

117.8 

236 

175.4 

157.9 

296 

220.0 

198.1 

57 

42.4 

38.1 

117 

86.9 

78.3 

177 

131.5 

118.4 

237 

176.1 

158.6 

297 

220.7 

198.7 

58 

43.1 

38.8 

118 

87.7 

79.0 

178 

132.3 

119.1 

238 

176.9 

159.3 

298 

221.5 

199.4 

59 

43.8 

39.5 

119 

88.4 

79.6 

179 

133.0 

119.8 

239 

177.6 

159.9 

299 

222.2 

200.1 

60 
Dist 

44.6 

40.1 

120 

89.2 

80.3 

180 

133.8 

120.4 

240 

178.4 

160.6 

300  222.9 

200.7 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist 

Dep. 

Lat 

F..r  48 

Degrees. 

3h 

12°". 

TABLE  11.                      (9  ' 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  43  DEGREES.   2h  62^. 

1 

Dist 
1 

Lat 

Dep. 

Di8t. 

Lat.  Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 
241 

Lat. 

Dep. 

00.7 

00.7 

61 

44.6 

41.6 

121 

88.5 

82.5 

181 

132.4 

123.4 

176.3 

164.4 

2 

01.5 

01.4 

62 

45.3 

42.3 

122 

89.2 

83.2 

182 

133.1 

124.1 

242 

177.0 

165.0 

3 

02.2 

02.0 

63 

46.1 

43.0 

123 

90.0 

83.9 

183 

133.8 

124.8 

243 

177.7 

165.7 

4 

02.9 

02.7 

64 

46.8 

43.6 

124 

90.7 

84.6 

184 

134.6 

125.5 

244 

178.5 

166.4 

5 

03.7 

03.4 

65 

47.5 

44.3 

125 

91.4 

85.2 

185 

135.3 

126.2 

245 

179.2 

167.1 

6 

04.4 

04.1 

66 

48.3 

45.0 

126 

92.2 

85.9 

186 

136.0 

126.9 

246 

179.9 

167.8 

7 

05.1 

04.8 

67 

49.0 

45.7 

127 

92.9 

86.6 

187 

136.8 

127.5 

247 

180.6 

168.5 

8 

05.9 

05.5 

68 

49.7 

46.4 

128 

93.6 

'  87.3 

188 

137.5 

128.2 

248 

181.4 

169.1 

9 

06.6 

06.1 

69 

50.5 

47.1 

129 

94.3 

88.0 

189 

138.2 

128.9 

249 

182.1 

169.8 

10 

07.3 

06.8 

70 

51.2 

47.7 

130 
131 

95.1 

88.7 

190 

139.0 

129.6 

250 

182.8 

170.5 

11 

08.0 

07.5 

71 

51.9 

48.4 

95.8 

89.3 

191 

139.7 

130.3 

251 

183.6 

171.2 

12 

08.8 

08.2 

72 

52.7 

49.1 

132 

96.5 

90.0 

192 

140.4 

130.9 

252 

184.3 

171.9 

13 

09.5 

08.9 

73 

53.4 

49.8 

133 

97.3 

90.7 

193 

141.2 

131.6 

253 

185.0 

172.5 

14 

10.2 

09.5 

74 

54.1 

50.5 

134 

98.0 

91.4 

194 

141.9 

132.3 

254 

185.8 

173.2 

15 

11.0 

10.2 

75 

54.9 

51.1 

135 

98.7 

92.1 

195 

142.6 

133.0 

255 

186.5 

173.9 

16 

11.7 

10.9 

76 

55.6 

51.8 

136 

99.5 

92.8 

196 

143.3 

133.7 

256 

187.2 

174.6 

17 

12.4 

11.6 

77 

56.3 

52.5 

137 

100.2 

93.4 

197 

144.1 

134.4 

257 

188.0 

175.3 

18 

13.2 

12.3 

78 

57.0 

53.2 

138 

100.9 

94.1 

198 

144.8 

135.0 

258 

188.7 

176.0 

19 

13.9 

13.0 

79 

57.8 

53.9 

139 

101.7 

94.8 

199 

145.5 

135.7 

259 

189.4 

176.6 

20 
21 

14.6 
15.4 

13.6 

80 

58.5 

59.2 

54.6 
55.2 

140 

102.4 

95.5 

200 

146.3 
147.0 

136.4 

260 

190.2 

177.3 

14.3 

81 

141 

103.1 

96.2 

201 

137.1 

261 

190.9 

178.0 

22 

16.1 

15.0 

82 

60.0 

55.9 

142 

103.9 

96.8 

202 

147.7 

137.8 

262 

191.6 

178.7 

23 

16.8 

15.7 

83 

60.7 

56.6 

143 

104.6 

97.5 

203 

148.5 

138.4 

263 

192.3 

179.4 

24 

17.6 

16.4 

84 

61.4 

57.3 

144 

105.3 

98.2 

204 

149.2 

139.1 

264 

193.1 

180.0 

25 

18.3 

17.0 

85 

62.2 

58.0 

145 

106.0 

98.9 

205 

149.9 

139.8 

265 

193.8 

180.7 

26 

19.0 

17.7 

86 

62.9 

58.7 

146 

106.8 

99.6 

206 

150.7 

140.5 

266 

194.5 

181.4 

27 

19.7 

18.4 

87 

63.6 

59.3 

147 

107.5 

100.3 

207 

151.4 

141.2 

267 

195.3 

182.1 

28 

20.5 

19.1 

88 

64.4 

60.0 

148 

108.2 

100.9 

208 

152.1 

141.9 

268 

196.0 

182.8 

29 

21.2 

19.8 

89 

65.1 

60.7 

149 

109.0 

101.6 

209 

152.9 

142.5 

269 

196.7 

183.5 

30 
31 

21.9 

20.5 

90 
91 

65.8 
66.6 

61.4 

150 

109.7 

102.3 

210 

153.6 

143.2 

270 

197.5 

184.1 

22.7 

21.1 

62.1 

151 

110.4 

103.0 

211 

154.3 

143.9 

271 

198.2 

184.8 

32 

23.4 

21.8 

92 

67.3 

62.7 

152 

111.2 

103.7 

212 

155.0 

144.6 

272 

198.9 

185.5 

33 

24.1 

22.5 

93 

68.0 

63.4 

153 

111.9 

104.3 

213 

155.8 

145.3 

273 

199.7 

186.2 

34  24.9 

23.2 

94 

68.7 

64.1 

154 

112.6 

105.0 

214 

156.5 

145.9 

274 

200.4 

186.9 

35  25.6 

23.9 

95 

69.5 

64.8 

155 

113.4 

105.7 

215 

157.2 

146.6 

275 

201.1 

187.5 

36  26.3 

24.6 

96 

70.2 

65.5 

156 

114.1 

106.4 

216 

158.0 

147.3 

276 

201.9 

188.2 

37  27.1 

25.2 

97 

70.9 

66.2 

157 

114.8 

107.1 

217 

158.7 

148.0 

277 

202.6 

188.9 

38  27.8 

25.9 

98 

71.7 

66.8 

158 

115.6 

107.8 

218 

159.4 

148.7 

278 

203.3 

189.6 

39 

28.5 

26.6 

99 

72.4 

67.5 

159 

116.3 

108.4 

219 

160.2 

149.4 

279 

204.0 

190.3 

40 
41 

29.3 

27.3 

100 

73.1 

68.2 

160 

117.0 

109.1 

220 

160.9 

150.0 

280 

204.8 
205.5 

191.0 

30.0 

28.0 

101 

73.9 

68.9 

161 

117.7 

109.8 

221 

161.6 

150.7 

281 

191.6 

42 

30.7 

28.6 

102 

74.6 

69.6 

162 

118.5 

110.5 

222 

162.4 

151.4 

282 

206.2 

192.3 

43 

31.4 

29.3 

103 

75.3 

70.2 

163 

119.2 

111.2 

223 

163.1 

152.1 

283 

207.0 

193.0 

44 

32.2 

30.0 

104 

76.1 

70.9 

164 

119.9 

111.8 

224 

163.8 

152.8 

284 

207.7 

193.7 

45 

32.9 

30.7 

105 

76.8 

71.6 

165 

120.7 

112.5 

225 

164.6 

153.4 

285 

208.4 

194.4 

46 

33.6 

31.4 

106 

77.5 

72.3 

166 

121.4 

113.2 

226 

165.3 

154.1 

286 

209.2 

195.1 

47 

34.4 

32.1 

107 

78.3 

73.0 

167 

122.1 

113.9 

227 

166.0 

154.8 

287 

209.9 

195.7 

48 

35.1 

32.7 

108 

79.0 

73.7 

168 

122.9 

114.6 

228 

166.7 

155.5 

288 

210.6 

196.4 

49 

35.8 

33.4 

lOit 

79.7 

74.3 

169 

123.6 

115.3 

229 

167.5 

156.2 

289 

211.4 

197.1 

50 
51 

36.6 

34.1 

110 

S0.4 

75.0 

170 

124.3 

115.9 

230 

168.2 

156.9 

290 

212.1 

197.8 

37.3 

34.8 

111 

81.2 

75.7 

171 

125.1 

116.6 

231 

168.9 

157.5 

291 

212.8 

198.5 

52 

38.0 

35.5 

112 

81.9 

70.4 

172 

125.8 

117.3 

232 

169.7 

158.2 

292 

213.6 

199.1 

53 

38.8 

36.1 

113 

82.6 

77.1 

173 

126.5 

118.0 

233 

170.4 

158.9 

293 

214.3 

199.8 

54 

39.5 

36.8 

114 

83.4 

77.7 

174 

127.3 

118.7 

234 

171.1 

159.6 

294 

215.0 

200.5 

55 

40.'2 

37.5 

115 

84.1 

78.4 

175 

128.0 

119.3 

235 

171.9 

160.3 

295 

215.7 

201.2 

56 

41.0 

38.2 

116 

84.8 

79.1 

176 

128.7 

120.0 

236 

172.6 

161.0 

296 

216.5 

201.9 

57 

41.7 

38.9 

117 

85.6 

79.8 

177 

129.4 

120.7 

237 

173.3 

161.6 

297 

217.2 

202.6 

58 

42.4 

39.6 

118 

86.3 

80.5 

178 

130.2 

121.4 

238 

174.1 

162.3 

298 

217.9 

203.2 

59 

43.1 

40.2 

119 

87.0 

81.2 

179 

130.9 

122.1 

239 

174.8 

163.0 

299 

218.7 

203.9 

60 

43.9 

40.9 

120 

87.8 

81.8 

180 

131.6 

122.8 

240 

175.5 

163.7 

300 

219.4 

204.6 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat 

Dist. 

Dep. 

Lat 

For  47  Deforces.                           S^  8™.  | 

60                   TABLE  II. 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  44  DEGREES.  2^  BSm. 

Diet 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Diet. 

Lat. 

Dep. 

Dist. 
181 

Lat.   Dep. 

Dist 

Lat 

Dep. 

1 

00.7 

00.7 

61 

43.9 

42.4 

121 

87.0 

84.1 

130.2 

125.7 

241 

173.4 

167.4 

2 

01.4 

01.4 

62 

44.6 

43.1 

122 

87.8 

84.7 

182 

130.9 

126.4 

242 

174.1 

168.1 

3 

02.2 

02.1 

63 

45.3 

43.8 

123 

88.5 

85.4 

183 

131.6 

127.1 

243 

174.8 

168.8 

4 

02.9 

02.8 

64 

46.0 

44.5 

124 

S9.2 

86.1 

184 

132.4 

127.8 

244 

175.5 

169.5 

5 

03.6 

03.5 

65 

46.8 

45.2 

125 

89.9 

86.8 

185 

133.1 

128.5 

245 

176.2 

170.2 

6 

04.3 

04.2 

66 

47.5 

45.8 

126 

90.6 

87.5 

186 

133.8 

129.2 

246 

177.0 

170.9 

7 

05.0 

04.9 

67 

48.2 

46.5 

127 

91.4 

88.2 

187 

134.5 

129.9 

247  177.7 

171.6 

8 

05.8 

05.6 

68 

48.9 

47.2 

128 

92.1 

88.9 

188 

135.2 

130.6 

248  178.4 

172.3 

9 

06.5 

06.3 

69 

49.6 

47.9 

129 

'■92.8 

89.6 

189 

136.0 

131.3 

249 

179.1 

173.0 

10 
11 

07.2 

06.9 

70 

50.4 

48.6 

130 

93.5 

90.3 

190 

136.7 

132.0 

250 

179.8 

173.7 

07.9 

07.6 

71 

51.1 

49.3 

131 

94.2 

91.0 

191 

137.4 

132.7 

251 

180.6 

174.4 

12 

08.6 

08.3 

72 

51.8 

50.0 

132 

95.0 

91.7 

192 

138.1 

133.4 

252 

181.3 

175.1 

13 

09.4 

09.0 

73 

52.5 

50.7 

133 

95.7 

92.4 

193 

138.8 

134.1 

253 

182.0 

175.7 

14 

10.1 

09.7 

74 

53.2 

51.4 

134 

96.4 

93.1 

194 

139.6 

134.8 

254 

182.7 

176.4 

15 

10.8 

10.4 

75 

54.0 

52.1 

135 

97.1 

93.8 

195 

140.3 

135.5 

255 

183.4 

177.1 

16 

11.5 

11.1 

76 

54.7 

52.8 

136 

97.8 

94.5 

196 

141.0 

136.2 

256 

184.2 

177.8 

17 

12.2 

11.8 

77 

55.4 

53.5 

137 

98.5 

95.2 

197 

141.7 

136.8 

257 

184.9 

178.5 

18 

12.9 

12.5 

78 

56.1 

54.2 

138 

99.3 

95.9 

198 

142.4 

137.5 

258 

185.6 

179.2 

19 

13.7 

13.2 

79 

56.8 

54.9 

139 

100.0 

96.6 

199 

143.1 

138.2 

259 

186.3 

179.9 

20 

14.4 

13.9 

80 

57.5 
58.3 

55.6 

140 

100.7 

97.3 

200 

143.9 

138.9 

260 

187.0 

180.6 

21 

15.1 

14.6 

81 

56.3 

141 

101.4 

97.9 

201 

144.6 

139.6 

261 

187.7 

181.3 

22 

15.8 

15.3 

82 

59.0 

57.0 

142 

102.1 

98.6 

202 

145.3 

140.3 

262 

188.5 

182.0 

23 

16.5 

16.0 

83 

59.7 

57.7 

143 

102.9 

99.3 

203 

146.0 

141.0 

263 

189.2 

182.7 

24 

17.3 

16.7 

84 

60.4 

58.4 

144 

103.6 

100.0 

204 

146.7 

141.7 

264 

189.9 

183.4 

25 

18.0 

17.4 

85 

61.1 

59.0 

145 

104.3 

100.7 

205 

147.5 

142.4 

265 

190.61 184.11 

26 

18.7 

18.1 

86 

61.9 

59.7 

146 

105.0 

101.4 

206 

148.2 

143.1 

266 

191.3;  184.8 1 

27 

19.4 

18.8 

87 

62.6 

60.4 

147 

105.7 

102.1 

207 

148.9 

143.8 

267 

192.1 

185.5 

28 

20.1 

19.5 

88 

63.3 

61.1 

148 

106.5 

102.8 

208 

149.6 

144.5 

268 

192.8 

186.2 

29 

20.9 

20.1 

89 

64.0 

61.8 

149 

107.2 

103.5 

209 

150.3 

145.2 

269  193.5 

186.9 

30 

21.6 

20.8 

90 

64.7 

62.5 

150 

107.9 

104.2 

210 

151.1 

145.9 

270 

194.2 

187.6 

31 

22.3 

21.5 

91 

65.5 

63.2 

151 

108.6 

104.9 

211 

151.8 

146.6 

271 

194.9 

188.3 

32 

23.0 

22.2 

92 

66.2 

63.9 

152 

109.3 

105.6 

212 

152.5 

147.3 

272 

195.7 

188.9 

33 

23.7 

22.9 

93 

66.9 

64.6 

153 

110.1 

106.3 

213 

153.2 

148.0 

273 

196.4 

189.6 

34 

24.5 

23.6 

94 

67.6 

65.3 

154 

110.8 

107.0 

214 

153.9 

148.7 

274 

197.1 

190.3 

35 

25.2 

24.3 

95 

68.3 

66.0 

155 

111.5 

107.7 

215 

154.7 

149.4 

275 

197.8 

191.0 

36 

25.9 

25.0 

96 

69.1 

66.7 

156 

112.2 

108.4 

216 

155.4 

150.0 

276 

198.5 

191.7 

37 

26.6 

25.7 

97 

69.8 

67.4 

157 

112.9 

109.1 

217 

156.1 

150.7 

277 

199.3 

192.4 

38 

27.3 

26.4 

98 

70.5 

68.1 

158 

113.7 

109.8 

218 

150.8 

151.4 

278 

200.0 

193.1 

39 

28.1 

27.1 

99 

71.2 

68.8 

159 

114.4 

110.5 

219 

157.5 

152.1 

279 

200.7 

193.8 

40 

28.8 

27.8 

100 

71.9 

69.5 

160 

115.1 

111.1 

220 

158.3 

152.8 

280 

201.4 

194.5 

41 

29.5 

28.5 

101 

72.7 

70.2 

161 

115.8 

111.8 

221 

159.0 

153.5 

281 

202.1 

195.2 

42 

30.2 

29.2 

102 

73.4 

70.9 

162 

116.5 

112.5 

222 

159.7 

154.2 

282 

202.9 

195.9 

43 

30.9 

29.9 

103 

74.1 

71.5 

163 

117.3 

113.2 

223 

100.4 

154.9 

283 

203.6 

196.6 

44 

31.7 

30.6 

104 

74.8 

72.2 

164 

118.0 

113.9 

224 

161.1 

155.6 

284 

204.3 

197.3 

45 

32.4 

31.3 

105 

75.5 

72.9 

165 

118.7 

114.6 

225 

161.9 

156.3 

285 

205.0 

198.0 

46 

33.1 

32.0 

106 

76.3 

73.6 

166 

119.4 

115.3 

226 

162.6 

157.0 

286 

205.7 

198.7 

47 

33.8 

32.6 

107 

77.0 

74.3 

167 

120.1 

116.0 

227 

163.3 

157.7 

287 

206.5 

199.4 

48 

34.5 

33.3 

108 

77.7 

75.0 

168 

120.8 

116.7 

228 

164.0 

158.4 

288 

207.2 

200.1 

49 

35.2 

34.0 

109 

78.4 

75.7 

169 

121.6 

117.4 

229 

164.7 

159.1 

289 

207.9 

200.8 

50 

36.0 

34.7 

110 

79.1 

76.4 

170 

122.3 

118.1 

230 

165.4 

159.8 

290 

208.6 

201.5 

51 

36.7 

35.4 

111 

79.8 

77.1 

171 

12.S.0 

118.8 

231 

166.2 

160.5 

291 

209.3 

202.1 

52 

37.4 

36.1 

112 

80.6 

77.8 

172 

123.7 

119.5 

232 

166.9 

161.2 

292 

210.0 

202.8 

53 

38.1 

36.8 

113 

81.3 

78.5 

173 

124.4 

120.2 

233 

167.6 

161.9 

293 

210.8 

203.5 

54 

38.8 

37.5 

114 

82.0 

79.2 

174 

125.2 

120.9 

234 

168.3 

162.6 

294 

211.5 

204.2 

55 

39.6 

38.2 

115 

82.7 

79.9 

175 

125.9 

121.6 

235 

169.0 

163.2 

295 

212.2 

204.9 

56 

40.3 

38.9 

116 

83.4 

80.6 

176 

126.6 

122.3 

236 

169.8 

163.9 

296 

212.9 

205.6 

57 

41.0 

39.6 

117 

84.2 

81.3 

177 

127.3 

123.0 

237 

170.5 

164.6 

297 

213.6 

206.3 

58 

41.7 

40.3 

118 

84.9 

82.0 

178 

128.0 

123.6 

238 

171.2 

165.3 

298 

214.4 

207.0 

59 

42.4 

41.0 

119 

85.6 

82.7 

179 

128.8 

124.3 

239 

171.9 

166.0 

299 

215.1 

207.7 

60 

43.2 

41.7 

120 

86.3 

83.4 

180 

129.5 

125.0 

240 

172.6 

166.7 

300 

215.8 

208.4 

JDiat 

Dep. 

Lat 

Dist 

Dep. 

Lat. 

Dist. 

Dep. 

Lilt. 

Dist 

Dep. 

Lat 

Dist 

Dep. 

Lat 

1                                For  46  Degrees.                          8h  4m.  | 

TABLE  11.                      ei  1 

DIFFERENCE  OF  LATITUDE  AND  DEPARTURE  FOR  45  DEGREES.   8h  Qm.  | 

Dist- 

1 

Lat.  Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist. 

Lat. 

Dep. 

Dist 

Lat 

Dep. 

00.7  00.7 

61 

43.1 

43.1 

121 

85.6 

85.6 

181 

128.0 

128.0 

241 

170.4 

170.4 

2  01.4  01.4 

62 

43.8 

43.8 

122 

86.3 

86.3 

182 

128.7 

128.7 

242 

171.1 

171.1 

3  02.1  02.1 

63 

44.5 

44.5 

123 

87.0 

87.0 

183 

129.4 

129.4 

243 

171.8 

171.8 

4 

02.8  02.8 

64 

45.3 

45.3 

124 

87.7 

87.7 

184 

130.1 

130.1 

244 

172.5  172.5 

5 

03.5 

03.5 

65 

46.0 

46.0 

125 

88.4 

88.4 

185 

130.8 

130.8 

245 

173.2  1-33.2 

6 

04.2 

04.2 

66 

46.7 

46.7 

126 

89.1 

89.1 

186 

131.5 

131.5 

246 

173.9)173.9 

7 

04.9 

04.9 

67 

47.4 

47.4 

127 

89.8 

,89.8 

187 

132.2 

132.2 

247 

174.7 

174.7 

8 

05.7 

05.7 

68 

48.1 

48.1 

128 

90.5 

90.5 

188 

132.9 

132.9 

248 

175.4 

175.4 

9 

06.4 

06.4 

69 

48.8 

48.8 

129 

91.2 

91.2 

189 

133.6 

133.6 

249 

176.1 

176.1 

10 

07.1 

07.1 

70 

49.5 

4H.5 

130 
131 

91.9 

91.9 

190 

134.4 

134.4 

250 

176.8 

176.8 
177.5 

11 

07.8 

07.8 

71 

50.2 

50.2 

92.6 

92.6 

191 

135.1 

135.1 

251 

177.5 

12 

08.5 

08.5 

72 

50.9 

50.9 

132 

93.3 

93.3 

192 

135.8 

135.8 

252 

178.2 

178.2 

13 

09.2 

09.2 

73 

51.6 

51.6 

133 

94.0 

94.0 

193 

136.5 

136.5 

253 

178.9 

178.9 

14 

09.9 

09.9 

74 

52.3 

52.3 

134 

94.8 

94.8 

194 

137.2 

137.2 

254 

179.6 

179.6 

15 

10.6 

10.6 

75 

53.0 

53.0 

135 

95.5 

95.5 

195 

137.9 

137.9 

255 

180.3 

180.3 

16 

11.3 

11.3 

76 

53.7 

53.7 

136 

96.2 

96.2 

196 

138.6 

138.6 

256 

181.0 

181.0 

17 

12.0 

12.0 

77 

54.4 

54.4 

137 

96.9 

96.9 

197 

139.3 

139.3 

257 

181.7 

181.7 

18 

12.7 

12.7 

78 

55.2 

55.2 

138 

97.6 

97.6 

198 

140.0 

140.0 

258 

182.4 

182.4 

19 

13.4 

13.4 

79 

55.9 

55.9 

139 

98.3 

98.3 

199 

140.7 

140.7 

259 

183.1 

183.1 

20 
21 

14.1 

14J 

80 

56.6 
57.3 

56.6 

140 

99.0 

99.0 

200 

141.4 

141.4 
142.1 

260 

183.8 

183.8 
184.6 

14.8 

14.8 

81 

57.3 

141 

99.7 

99.7 

201 

142.1 

261 

184.6 

22 

15.6 

15.6 

82 

58.0 

58.0 

142 

100.4 

100.4 

202 

142.8 

142.8 

262 

185.3 

185.3 

23 

16.3 

16.3 

83 

58.7 

58.7 

143 

101.1 

101.1 

203 

143.5 

143.5 

263 

186.0 

186..0 

24 

17.0 

17.0 

84 

59.4 

59.4 

144 

101.8 

101.8 

204 

144.2 

144.2 

264 

186.7 

186.7 

25 

17.7 

17.7 

85 

60.1 

60.1 

145 

102.5 

102.5 

205 

145.0 

145.0 

265 

187.4 

187.4 

26 

18.4 

18.4 

86 

60.8 

60.8 

146 

103.2 

103.2 

206 

145.7 

145.7 

266 

188.1 

188.1 

27 

19.1 

19.1 

87 

61.5 

61.5 

147 

103.9 

103.9 

207 

146.4 

146.4 

267 

188.8 

188.8 

28 

19.8 

19.8 

88 

62.2 

62.2 

148 

104.7 

104.7 

208 

147.1 

147.1 

268 

189.5 

189.5 

29 

20.5 

20.5 

89 

62.9 

62.9 

149 

105.4 

105.4 

209 

147.8 

147.8 

269 

190.2 

190.2 

30 

21.2 

21.2 

90 

63.6 

63.6 

150 

106.1 

106.1 

210 

148.5 

148.5 

270 

190.9 

190.9 

31 

21.9 

21.9 

91 

64.3 

64.3 

151 

106.8 

106.8 

211 

149.2 

149.2 

271 

191.6 

191.6 

32 

22.6 

22.6 

92 

65.1 

65.1 

152 

107.5 

107.5 

212 

149.9 

149.9 

272 

192.3 

192.3 

33 

23.3 

23.3 

93 

65.8 

65.8 

153 

108.2 

108.2 

213 

150.6 

150.6 

273 

193.0 

193.0 

34 

24.0 

24.0 

94 

66.5 

66.5 

154 

108.9 

108.9 

214 

151.3 

151.3 

274 

193.7 

193.7 

35 

24.7 

24.7 

95 

67.2 

67.2 

155 

109.6 

109.6 

215 

152.0 

152.0 

275 

194.5 

194.5 

36 

25.5 

25.5 

96 

67.9 

67.9 

156 

110.3 

110.3 

216 

152.7 

152.7 

276 

195.2 

195.2 

37 

26.2 

26.2 

97 

68.6 

68.6 

157 

111.0 

111.0 

217 

153.4 

153.4 

277 

195.9 

195.9 

38 

26.9 

26.9 

98 

69.3 

69.3 

158 

111.7 

111.7 

218 

154.1 

154.  J 

278 

196.6 

196.6 

39 

27.6 

27.6 

99 

70,0 

70.0 

159 

112.4 

112.4 

219 

154.9 

154.9 

279 

197.3 

197.3 

40 

28.3 

28.3 

100 

70.7 

70.7 

160 

113.1 

113.1 

220 

155.6 

155.6 

280 

198.0 

198.0 

41 

29.0 

29.0 

101 

71.4 

71.4 

161 

113.8 

113.8 

221 

156.3 

156.3 

281 

198.7 

198.7 

42 

29.7 

29.7 

102 

72.1 

72.1 

162 

114.6 

114.6 

222 

157.0 

157.0 

282 

199.4 

199.4 

43 

30.4 

30.4 

103 

72.8 

72.8 

163 

115.3 

115.3 

223 

157.7 

157.7 

283 

200.1 

200.1 

44 

31.1 

31.1 

104 

73.5 

73.5 

164 

116.0 

116.0 

224 

158.4 

158.4 

284 

200.8 

200.8 

45 

31.8 

31.8 

105 

74.2 

74.2 

165 

116.7 

116.7 

225 

159.1 

159.1 

285 

201.5 

201.5 

46 

32.5 

32.5 

106 

75.0 

7.5.0 

166 

117.4 

117.4 

226 

159.8 

159.8 

286 

2U2.2 

202.2 

47 

33.2 

33.2 

107 

75.7 

75.7 

167 

118.1 

118.1 

227 

160.5 

160.5 

287 

202.9 

202.9 

48 

33.9 

33.9 

108 

76.4 

76.4 

168 

118.8 

118.8 

228 

161.2 

161.2 

288 

203.6 

203.6 

49 

34.6 

34.6 

109 

77.1 

77.1 

169 

119.5 

119.5 

229 

161.9 

161.9 

289 

204.4 

204.4 

50 
51 

35.4 
36.1 

35.4 

110 

77.8 

77.8 

170 

120.2 

120.2 

230 

162.6 

162.6 

290 

205.1 

205.1 

36.1 

HI 

78.5 

78.5 

171 

120.9 

120.9 

231 

163.3 

163.3 

291 

205.8 

205.8 

52  36.8 

36.8 

112 

79.2 

79.2 

172 

121.6 

121.6 

232 

164.0 

164.0 

292 

206.5 

206.5 

53  37.5 

37.5 

113 

79.9 

79.9 

173 

122.3 

122.3 

233 

164.8 

164.8 

293 

207.2 

207.2 

54 

38.2 

38.2 

114 

80.6 

80.6 

174 

123.0 

123.0 

234 

165.5 

165.5 

294 

207.9 

207.9 

55 

38.9 

38.9 

115 

81.3 

81.3 

175 

123.7 

123.7 

235 

166.2 

166.2 

295 

208.6 

208.6 

56 

39.6 

39.6 

116 

82.0 

82.0 

176 

124.5 

124.5 

236 

166.9 

1H6.9 

296 

209.3 

209.3 

57 

40.3 

40.3 

117 

82.7 

82.7 

177 

125.2 

125.2 

237 

167.6 

167.6 

297 

210.0 

210.0 

58 

41.0 

41.0 

118 

83.4 

83.4 

178 

125.9 

125.1> 

238 

168.3 

168.3 

298 

210.7 

210.7 

59 

41.7 

41.^ 

119 

84.1 

84.1 

179 

126.6 

126.6 

239 

169.0 

169.0 

299 

211.4 

211.4 

60 
Dist 

42.4 

Dep. 

42.4 

120 

84.9 

84.9 

Lat. 

180 
Dist 

127.3 

127.3 

240 

169.7 

169.7 

300 

21'>..1 

212.1 

Lat. 

Dist. 

Dep. 

Dep. 

Lat. 

Dist. 

Dep. 

Lat. 

Dist  Dep. 

Lat 

For  45  Deg:i-ees,                         3^  Om.  | 

62 

TABLE  III. 

MERIDIONAL  PARTS. 

M. 

03 

1° 

2o 

3^ 

40 

50 

6° 

70   go 

90 

10° 

no 

12° 

13° 

M. 

0 

0 

60 

120 

180 

240 

300 

361 

421 

482 

542 

603 

664 

725 

787 

0 

1 

1 

61 

121 

181 

241 

301 

362 

422 

483 

543 

604 

665 

726 

788 

1 

2 

2 

62  122 

182 

242 

302 

363 

423 

484 

544 

605 

666 

727 

789 

2 

3 

3 

63  123 

183 

243 

303 

364 

424 

485 

545 

606 

667 

728 

790 

3 

4 

4 

64 

124 

184 

244 

304 

365 

425 

486 

546 

607 

668 

729 

791 

4 

5 

5 

65 

125 

185 

245 

305 

366 

426 

487 

547 

608 

669 

730 

792 

5 

6 

6 

66 

126 

186 

246 

306 

367 

427 

488 

548 

609 

670 

731 

793 

6 

7 

7 

67 

127 

187 

247 

307 

368 

428 

489 

549 

610 

671 

732 

794 

7 

8 

8 

68 

128 

188 

248 

308 

369 

429 

490 

550 

611 

672 

734 

795 

8 

9 

9 

69 

129 

189 

249 

309 

370 

430 

491 

551 

612 

673 

735 

796 

9 

10 

10 

70 

130 

190 

250 

310 

371 

431 

492 

552 

613 

674 

736 

797 

10 

11 

11 

71 

131 

191 

251 

311 

372 

432 

493 

553 

614 

675  737 

798 

11 

12 

12 

72 

132 

192 

252 

312 

373 

433 

494 

554 

615 

676 

738 

799 

12 

13 

13 

73 

133 

193 

253 

313 

374 

434 

495 

555 

616 

677 

739 

800 

13 

14 

14 

74 

134 

194 

254 

314 

375 

435 

496 

556 

617 

678 

740 

801 

14 

15 

15 

75 

135 

195 

255 

315 

376 

436 

497 

557 

618 

679 

^741 

802 

15 

16 

16 

76 

136 

196 

256 

316 

377 

437 

498 

558 

619 

680 

742 

803 

16 

17 

17 

77 

137 

197 

257 

317 

378 

438 

499 

559 

620 

681 

743 

804 

17 

18 

18 

78 

138 

198 

258 

318 

379 

439 

500 

560 

621 

682 

744 

805 

18 

19 

19 

79 

139 

199 

259 

319 

380 

440 

501 

561 

622 

683 

745 

806 

19 

20 

20 

80 

140 

200 

260 

320 

381 

441 

502 

562 

623 

684 

746 

807 

20  . 

21 

21 

81 

141 

201 

261 

321 

382 

442 

503 

564 

624 

685 

747 

808 

21 

22 

22 

82 

142 

202 

262 

322 

383 

443 

504 

565 

625 

687 

748 

809 

22 

23 

23 

83 

143 

203 

263 

323 

384 

444 

505 

566 

626 

688 

749 

810 

23 

24 

24 

84 

144 

204 

264 

324 

385 

445 

506 

567 

627 

689 

750 

811 

24 

25 

25 

85 

145 

205 

265 

325 

386 

446 

507 

568 

628 

690 

751 

812 

25 

26 

26 

86 

146 

206 

266 

326 

387 

447 

508 

569 

629 

691 

752 

813 

26 

27 

27 

87 

147 

207 

267 

327 

388 

448 

509 

570 

631 

692 

753 

815 

27 

28 

28 

88 

148 

208 

268 

328 

389 

449 

510 

571 

632 

693 

754 

816 

28 

29 

29 

89 

149 

209 

269 

330 

390 

450 

511 

572 

633 

694 

755 

817 

29 

30 

30 

90 

150 

210 

270 

331 

391 

451 

512 

573 

634 

695 

756 

818 

30 

31 

31 

91 

151 

211 

271 

332 

392 

452 

513 

574 

635 

696 

7.57 

819 

31 

32 

32 

92 

152 

212 

272 

333 

393 

453 

514 

575 

636 

697 

758 

820 

32 

33 

33 

93 

153 

213 

273 

334 

394 

454 

515 

576 

637 

698 

759 

821 

33 

34 

34 

94 

154 

214 

274 

335 

395 

455 

516 

577 

638 

699 

760 

822 

34 

35 

35 

95 

155 

215 

275 

336 

396 

456 

517 

578 

639 

700 

761 

823 

35 

36 

36 

96 

156 

216 

276 

337 

397 

457 

51« 

579 

640 

701 

762 

824 

36 

37 

37 

97 

157 

217 

277 

338 

398 

458 

519 

580 

641 

702 

763 

825 

37 

38 

38 

98 

1.58 

218 

278 

339 

399 

459 

520 

581 

642 

703 

764 

826 

38 

39 

39 

99 

159 

219 

279 

340 

400 

460 

521 

582 

643 

704 

765 

827 

39 

40 

40 

100 

160 

220 

280 

341 

401 

461 

522 

583 

644 

705 

766 

828 

40 

41 

41 

101 

161 

221 

281 

342 

402 

462 

523 

584 

645 

706 

767 

829 

41 

42 

42 

102 

162 

222 

282 

343 

403 

463 

524 

585 

646 

707 

768 

830 

42 

43 

43 

103 

163 

223 

283 

344 

404 

464 

525 

586 

647 

708 

769 

831 

43 

44 

44 

104 

164 

224 

284 

345 

405 

465 

526 

587 

648 

709 

770 

832 

44 

45 

45 

105 

165 

225 

285 

346 

406 

466 

527 

588 

649 

710 

771 

833 

45 

46 

46 

106 

166 

226 

286 

347 

407 

467 

528 

589 

650 

711 

772 

834 

46 

47 

47 

107 

167 

227 

287 

348 

408 

468 

529 

590 

651 

712 

773 

835 

47 

48 

48 

108 

168 

228 

288 

349 

409 

469 

530  591 

652 

713 

774 

836 

48 

49 

49 

109 

169 

229 

289 

350 

410 

470 

531  592 

653 

714 

775 

837 

49 

50 

50 

110 

170 

230 

290 

351 

411 

471 

532  593 

654 

715 

777 

838 

50 

51 

51 

111 

171 

231 

291 

352 

412 

472 

533  594 

655 

710 

778 

839 

51 

52 

52 

112 

172 

232 

292 

353 

413 

473 

534  595 

656 

717 

779 

840 

52 

53 

53 

113 

173 

233 

293 

354 

414 1 474 

535  596 

657 

718 

780 

841 

53 

54 

54 

114 

174 

234 

294 

355 

415 1 476 

536  597 

658 

719 

781 

842 

54 

55 

55 

115 

175 

235 

295 

356 

416:477 

537 

598 

659 

720 

782 

843 

55 

56 

56 

116 

176 

236 

296 

357 

417 

478 

538 

599 

660 

721 

783 

844 

56 

57 

57 

117 

177 

237 

297 

358 

418 

479 

539  '600 

661 

722 

784 

845 

57 

58 

58 

lis 

178 

238 

298 

359 

419 

480 

540  601 

662 

723 

785 

846 

58 

59 

59 

119 

179 

239 

299 

360 

420 

481 

541 

602 

663 

724 

786 

847 

59 

M. 

0° 

1° 

2° 

3° 

40 

50 

60 

70 

8° 

90 

10° 

11° 

12° 

130 

M. 

TABLE  III. 
MERIDIONAL  PARTS. 

..  1 

M. 

140  150 

16° 

17° 

18° 

190 

20° 

21° 

22° 

230 

24° 

250 

26° 

27° 

M. 

0 
1 
2 
3 
4 

848 
850 
851 
852 
853 

910 
911 
913 
914 
915 

973 
974 
975 
976 

977 

1035 
1036 
1037 
1038 
1039 

109!s 
1099 
1100 
1101 
1102 

1161 
1163 
1164 
1165 
1166 

1225 
1226 
1227 
1228 
1229 

1289 
1290 
1291 
1292 
1293 

1354 
1355 
1356 
1357 
1358 

1419 
1420 
1421 
1422 
1423 

1484 
1485 
1486 

1487 
1488 

1550 
1551 
1552 
1553 
1554 

1(516 
1618 
1()19 
1620 
1621 

1684 
1685 

168() 

1687 
1688 

0 

1 
2 
3 
4 

5 

6 
7 
8 
9 

854 
855 
856 

857 
858 

916 

917 
918 
919 
920 

978 
979 
980 
981 
982 

1041 
1042 
1043 
1044 
1045 

1103 
1105 
1106 
1107 
llOts 

1167 
116^^ 
1169 
1170 
1171 

1230 
1232 
1233 
1234 
1235 

1295 
1296 
12*97 
1298 
1299 

1359 
1360 
1361 
1362 
1363 

1424 
1425 
1426 
1427 

1428 

1490 
1491 
1492 
1493 
1494 

1556 
1557 
1558 
1559 
1560 

1622 
1623 
1624 
1625 
1626 

1689 
1690 
1691 
1693 
1694 

5 

6 

7 
8 
9 

10 
11 
12 
13 
14 

859 
860 
861 

862 

8H3 

921 
922 
923 
924 
925 

983 
984 
985 
996 

987 

1046 
1047 
1048 
1049 
1050 

1109 
1110 
1111 
1112 
1113 

1172 
1173 
1174 
1175 
1176 

1236 
1237 
1238 
1239 
1240 

1300 
1301 
1302 
1303 
1304 

1364 
1366 
1367 
1368 
1369 

1430 
1431 
1432 
1433 
1434 

1495 
1496 
1497 
1498 
1499 

1561 
1562 
1563 
1564 
1565 

1628 
1629 
1630 
1631 
1632 

1695 
1696 
1697 
1698 
1699 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

864 
865 

866 

867 
868 

926 
927 
928 
929 
930 

988 
989 
990 
991 
993 

1051 
1052 
1053 
1054 
1055 

1114 
1115 
1116 
1117 
1118 

1177 
1178 
1179 
1181 
1182 

1241 
1242 
1243 
1244 
1245 

1305 
1306 
1307 
1308 
1310 

1370 
1371 
1372 
1373 
1374 

1435 
1436 
1437 
1438 
1439 

1500 
1502 
1503 
1504 
1505 

1567 
1568 
1569 
1570 
1571 

1633 
1634 
1635 
1637 
1638 

1700 
1701 
1703 
1704 
1705 

15 

16 
17 

18 
19 

20 
21 
22 
23 
24 

869 

870 
871 
872 
873 

931 
932 
933 
934 
935 

994 
995 
996 
997 

99y 

1056 
1057 
1058 
1059 
1060 

1119 
1120 
1121 
1122 
1123 

1183 

1184 
1185 
1186 
1187 

1246 
1248 
1249 
1250 
1251 

1311 
1312 
1313 
1314 
1315 

1375 
1376 
1377 
1379 
1380 

1440 
1441 
1443 
1444 
1445 

1506 
1507 
1508 
1509 
1510 

1572 
1573 
1574 
1575 
1577 

1639 
1640 
1641 
1642 
1643 

1706 
1707 
1708 
1709 
1711 

20 
21 
22 
23 
24 

25 

26 
27 
28 
29 

874 
875 
876 
877 
878 

93t) 
9D7 
938 
939 
941 

999 
1000 
1001 
1002 
1003 

1061 
1063 
1064 
1065 
1066 

1125 
1126 
1127 
1128 
1129 

1188 
1189 
1190 
1191 
1192 

1252 
1253 
1254 
1255 
1256 

1316 
1317 
1318 
1319 
1320 

1381 
1382 
1383 
1384 
1385 

1446 
1447 
1448 
1449 
1450 

1511 
1513 
1514 
1515 
1516 

1578 
1579 
1580 
1581 
1582 

1644 
1645 
1647 
1648 
1649 

1712 
1713 
1714 
1715 
1716 

25 

26 

27 
28 
29 

30 
31 
32 
33 
34 

879 
880 

882 
883 
884 

942 
943 
944 
945 
946 

1004 
1005 
1006 
1007 
1008 

1067 
1068 
1069 
1070 
1071 

1130 
1131 
U3-2 
1133 
1134 

1193 
1194 
1195 
1196 
1198 

1257 
1258 
1259 
1260 
1261 

1321 
1322 
1324 
1325 
1326 

1386 
1387 

1388 
1389 
1390 

1451 
1452 
1453 
1455 
1456 

1517 
1518 
1519 
1520 
1521 

1583 
1584 
1585 
1586 

1588 

1650 
1651 
1652 
1653 
1654 

1717 

1718 
1720 
1721 
1722 

30 
31 
32 
33 
34 

35 
36 

37 
38 
39 

885 
886 
887 
888 
889 

947 
948 
949 
950 
951 

1009 
1010 
1011 
1012 
1013 

1072 
1073 
1074 
1075 
1076 

1135 
1136 
1137 
1138 
1139 

1199 
1200 
1201 
1202 
1203 

1262 
1264 
1265 
1266 
1267 

1327 
1328 
1329 
1330 
1331 

1392 
1393 
1394 
1395 
1396 

1457 
1458 
1459 
1460 
1461 

1522 
1524 
1525 
1526 
1527 

1589 
1590 
1591 
1592 
1593 

1656 
1657 
1658 
1659 
1660 

1723 
1724 
1725 
1726 
1727 

35 

36 

37 
38 
39 

40 
41 
42 
43 
44 

890 
891 
892 
893 
894 

952 
953 
954 
955 
956 

1014 
1015 
1016 
J018 
1019 

1077 
1078 
1079 
1080 
1081 

1140 
1141 
1142 
1144 
1145 

1204 
1205 
1206 
1207 
1208 

1268 
1269 
1270 
1271 
1272 

1332 
1333 
1334 
1335 
1336 

1397 
1398 
1399 
1400 
1401 

1462 
1463 
1464 
1465 
1467 

1528 
1529 
1530 
1531 
1532 

1594 
1595 
1596 
1598 
1599 

1661 
1662 
1663 
1664 
1666 

1729 
1730 
1731 
1732 
1733 

40 
41 
42 
43 
44 

45 
46 

47 
48 
49 

895 
896 

897 
898 
899 

957 
958 
959 
960 
'.♦61 

1020 
1021 
1022 
1023 
1024 

1082 
1084 
1085 
1086 

1087 

1146 
1147 

1148 
1148 
1150 

1209 
1210 
1211 
1212 
1213 

1273 
1274 
1275 
1276 
1277 

1338 
1339 
1340 
1341 
1342 

1402 
1403 
1405 
1406 
1407 

1468 
1469 
1470 
1471 
1472 

1533 
1535 
1536 
1537 
1538 

1600 
1601 
1602 
1603 
1604 

1667 
1668 
1669 
1670 
1671 

1734 
1735 
1736 

1738 
1739 

45 

46 
47 
48 
49 

50 
51 
52 
53 
54 

900 
901 
902 
903 
904 

962 
963 
964 
965 

966 

1025 
1026 
1027 
1028 
1(^29 

1088 
1089 
1090 
1091 
1092 

1151 
1152 
1153 
1154 
1155 

1215 
1216 
1217 
1218 
1219 

1278 
1280 
1281 
1282 
1283 

1343 
1344 
1345 
1346 
1347 

1408 
1409 
1410 
1411 
1412 

1473 
1474 
1475 
1476 
1477 

1539 
1540 
1541 
1542 
1543 

1605 
1606 
160s 
1609 
1610 

1672 
1673 
1675 
1676 

1677 

1740 
1741 
1742 
1743 
1744 

50 
51 
52 
53 
54 

55 
56 
57 

58 
59 

905 
906 
907 
908 
909 

968 
969 
970 
971 
972 

1030 
1031 
1032 
1033 
1034 

1093 
1094 
1095 
1096 
1097 

1156 
1157 
1158 
115!) 
1160 

1220 
1221 
1222 
1223 
1224 

1284 
1285 
1286 
1287 

1288 

1348 
1349 
1350 
1352 
1353 

1413 
1414 
1415 
1416 
1418 

1479 
1480 
1481 
1482 
1483 

1544 
1546 
1547 
1548 
1549 

1611 
1612 
1613 
1614 
1615 

1678 
1679 
1680 
1681 
1682 

1746 
1747 
1748 
1749 
1750 

55 
56 
57 

58 
59 

M. 

14° 

150 

16° 

170 

18° 

190 

203 

21° 

22=' 

230 

24° 

25° 

26° 

27° 

M. 

64                                               TABLE   III. 

MERIDIONAL  PARTS. 

M. 

28^ 

29^ 

30° 

31° 

32°    33°   34° 

35° 

36° 

37° 

38° 

39°  40° 

41° 

M. 

0 
1 

2 
3 
4 

1751 
1752 
1753 
1755 
1756 

1819 
1821 
1822 
1823 
1824 

1888 
1890 
1891 
1892 
1893 

1958 
1959 
1960 
1962 
1963 

2028 
2030 
2031 
2032 
2033 

2100 
2101 
2102 
2103 
2104 

2171 
2173 
2174 
2175 
2176 

2244 
2246 
2247 
2248 
2249 

2318 
2319 
2320 
2322 
2323 

2393 
2394 
2395 
2396 
2398 

2468 
2470 
2471 
2472 
2473 

2545 
2546 
2548 

2549 
2550 

2623 
2624 
2625 
2627 

2628 

2702 
2703 
2704 
2706 
2707 

0 
1 
2 
3 
4 

5 
6 

7 
8 
9 

1757 

1758 
1759 
1760 
1761 

1825 
1826 

1827 
1829 
1830 

1894 
1895 
1896 

1898 
1899 

1964 
1965 
1966 
1967 
1969 

2034 
2035 
2037 
2038 
2039 

2105 
2107 
2108 
2109 
2110 

2178 
2179 
2180 
2181 
2182 

2250 
2252 
2253 
2254 
2255 

2324 
2325 
2327 
2328 
2329 

2399 
2400 
2401 
2403 
2404 

2475 
2476 

2477 
2478 
2480 

25512629 
25532631 
25542632 
25552633 
2557  2634 

2708 
2710 
2711 
2712 
2714 

5 

6 

7 
8 
9 

10 
11 
12 
13 
14 

1762 
1764 
1765 
1766 
1767 

1831 
1832 
1833 
1834 
1835 

1900 
1901 
1902 
1903 
1905 

1970 
1971 
1972 
1973 
1974 

2040 
2041 
2043 

2044 
2045 

2111 
2113 
2114 
2115 
2116 

2184 
2185 
2186 

2187 
2188 

2257 
2258 
2259 
2260 
2261 

2330 
2332 
2333 
2334 
2335 

2405 
2406 
2408 
2409 
2410 

2481 

2482 
2484 
2485 
2486 

2558 
2559 
2560 
2562 
2563 

2636 
26:!7 
2638 
2640 
2641 

2715 
2716 

2718 
2719 
2720 

10 
11 
-    12 
13 
14 

15 
16 
17 
18 
19 

1768 
1769 
1770 
1772 
1773 

1837 
1838 
1839 
1840 
1841 

1906 
1907 

1908 
1909 
1910 

1976 
1977 

1978 
1979 
1980 

2046 
2047 
2048 
2050 
2051 

2117 
2119 
2120 
2121 
2122 

2190 
2191 
2192 
2193 
2194 

2263 
2264 
2265 
2266 

2268 

2337 
2338 
2339 
2340 
2342 

2411 
2413 
2414 
2415 
2416 

2487 
2489 
2490 
2491 
2492 

2564 
2566 

2567 
2568 
2569 

2642 
2644 
2645 
2646 

2648 

2722 
2723 

2724 
2726 

2727 

15 
16 

17 
18 
19 

20 
21 
22 
23 
24 

1774 
1775 
1776 
1777 

1778 

1842 
1843 
1845 
1846 
1847 

1912 
1913 
1914 
1915 
1916 

1981 

1983 
1984 
1985 

1986 

2052 
2053 
2054 
2056 

2057 

2123 
2125 
2126 
2127 
2128 

2196 
2197 
2198 
2199 
2200 

2269 

2270 
2271 

2272 
2274 

2343 
2344 
2345 
2346 

2348 

2418 
2419 
2420 
2422 
2423 

2494 
2495 
2496 
2498 
2499 

2571 
2572 
2573 

2575 
2576 

2649 
2650 
2651 
2653 
2654 

2728 
2729 
2731 
2732 
2733 

20 
21 
22 
23 
24 

: 

25 
26 
27 

28 
29 

1780 
1781 

1782 
1783 
1784 

1848 
1849 
1850 
1852 
1853 

1917 
1918 
19-^0 
1921 
1922 

1987 
1988 
1990 
1991 
1992 

2058 
2059 
2060 
2061 
2063 

2129 
2131 
2132 
2133 
2134 

2202 
2203 
2204 
2205 

2207 

2275 
2276 
2277 
2279 

2280 

2349 
2350 
2351 
2353 
2354 

2424 
2425 

2427 
2428 
2429 

2500 
2501 
250:; 
2504 
2505 

2577 

2578 
2580 
2581 

2582 

2655 
2657 
2658 
2659 
2661 

2735 
2736 

2737 
2739 
2740 

25 
26 

27 
28 
29 

30 
31 
32 
33 
34 

1785 
1786 
1787 
1789 
1790 

1854 
1855 

1856 

1857 
1858 

1923 
1924 
1925 
1927 
192« 

1993 
1994 
1995 
1997 
1998 

2064 
2065 
2066 
2067 
2069 

2135 
2137 
2138 
2139 
2140 

2208 
2209 
2210 
2211 
2213 

2281 

2282 
2283 
2285 
2286 

2355 
2356 
2358 
2359 
2360 

2430 
2432 
2433 
2334 
2335 

2506 
2508 
2509 
2510 
2512 

2584 
2585 
2586 
2588 
2589 

2662 
2663 
2665 
2666 
2667 

2742 
2743 
2744 
2746 

2747 

30 
31 
32 
33 
34 

i 

35 
36 
37 
38 

39 

1791 
1792 
1793 
1794 
1795 

1860 
1861 
1862 
1863 
1864 

1929 
1930 
1931 
1932 
1934 

1999 
2000 
2001 
2002 
2004 

2070 
2071 
2072 
2073 
2075 

2141 
2143 
2144 
2145 
2146 

2214 
2215 
2216 
2217 
2219 

2287 
2288 
2290 
2291 
2292 

2361 
2363 
2364 
2365 
2366 

2437 
2438 
2439 
2440 
2442 

2513 
2514 
2515 
2517 
2518 

2590 
2591 
2593 
2594 
2595 

2669 
2670 
2671 
2673 
2674 

2748 
2750 
2751 
2752 
2754 

35 
36 
37 

38 
39 

40 
41 
42 
43 
44 

1797 
1798 
1799 
1800 
1801 

1865 
1866 

1868 
1869 
1870 

1935 
1936 
1937 
1938 
1939 

2005 
2006 
2007 

2008 
2010 

2076 
2077 

2078 
2079 
2080 

2147 
2149 
2150 
2151 
2152 

2220 
2221 
2222 
2224 
2225 

2293 
2295 
2296 
2297 

2298 

2368 
2369 
2370 
2371 
2373 

2443 
2444 
2445 
2447 
2448 

2519 
2521 
2522 
2523 
2524 

2597 

2598 
2599 
2601 
2602 

2675 
2676 

2678 
2679 
2680 

2755 
2756 

2758 
2759 
2760 

40 
41 
42 
43 
44 

45 

46 
47 

48 
49 

1802 
1803 
1805 
1806 

1807 

1871 
1872 
1873 
1875 
1876 

1941 
1942 
1943 
1944 
1945 

2011 
2012 
2013 
2014 
2015 

2082 
2083 

2084 
2085 
2086 

2153 
2155 
2156 
2157 

2158 

2226 
2227 
2228 
2230 
2231 

2299 
2301 
2302 
2303 
2304 

2374 
2375 
2376 

2378 
2379 

2449 
2451 
2452 
2453 
2454 

2526 
2527 
2528 
2530 
2531 

2603 
2604 
2606 

2607 
2608 

2682 
2683 
2684 
2686 

2687 

2762 
2763 
2764 
2766 

2767 

45 
46 
47 
48 
49 

1 

50 
51 
52 
53 
54 

180S 
1809 
1810 
1811 
1813 

1«77 
1878 
1879 
1880 
1881 

1946 
1948 
1949 
1950 
1951 

2017 
2018 
2019 
2020 
2021 

2088 
2089 
2090 
2091 
2092 

2159 
2161 
2162 
2163 
2164 

2232 
2233 
2235 
2236 
2237 

230() 
2307 
2308 
2309 
2311 

2380 
2381 
2383 
2384 
3385 

2456 
2457 

2458 
2459 
2461 

2532 
2533 
2535 
2536 
2537 

2610 
2611 
2612 
2614 
2615 

2688 
2690 
2691 
2692 
2694 

2768 
2770 
2771 
2772 
2774 

50 
51 
52 
53 
54 

55 
56 
57 

58 
59 

1814 
1815 
1816 
1817 

1818 

1883 
1884 
1885 
1886 
1887 

1952 
1953 
1955 
1956 
1957 

2022 
2024 
2025 
2026 
2027 

2094 
2095 
2096 
2097 
2098 

2165 
2167 
2168 
2169 
2170 

2238 
2239 
2241 
2242 
2243 

2312 
2313 
3314 
1316 
2317 

2386 
2388 
2389 
2390 
2391 

2462 
2463 
2464 
2466 
2467 

2538 
2540 
2541 
2542 
2544 

2616 
2617 
2619 
2620 
2621 

2695 
2696 
2698 
2699 
2700 

2775 
2776 
2778 
2779 
2780 

55 
56 
57 
58 
59 

M.      28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

40O     410 

M. 

TABLE  111. 

Gti 

MERIDIONAL  PARTS. 

M. 

42° 

43^ 

440 

45" 

46" 

470  48"  49"  50"  51" 

52" 

53" 

54"  55"  i 

M. 

0 

2782 

2863 

,!946 

3030 

3116 

3203 

3292 

3382 

3474 

3569 

3665 

3764 

3865  3968 

0 

1 

783 

804 

947 

031 

117 

204 

293 

384 

476 

570 

667 

765 

866 

970 

1 

2 

784 

866 

949 

033 

118 

206 

295 

385 

478 

572 

668 

767 

868 

971 

2 

3 

786 

867 

950 

034 

120 

207 

296 

387 

479 

574 

670 

769 

870 

973 

3 

4 

787 

869 

951 

036 

121 

209 

298 

388 

481 

575 

672 

770 

871 

975 

4 

5 

2788 

2870 

2953 

3037 

3123 

3210 

3299 

3390 

3482 

3577 

3673 

3772 

3873 

3977 

5 

6 

790 

871 

954 

038 

124 

212 

301 

391 

484 

578 

675 

774 

875 

978 

6 

7 

791 

873 

956 

040 

126 

213 

302 

393 

485 

580 

677 

775 

877 

980 

7 

8 

792 

874 

957 

041 

127 

214 

303 

394 

487 

582 

678 

777 

878 

982 

8 

9 

794 

875 

958 

043 

129 

216 

305 

396 

488 

583 

680 

779 

880 

984 

9 

10 

2795 

2877 

2960 

3044 

3130 

3217 

3306 

3397 

3490 

3585 

3681 

3780 

3882 

3985 

10 

11 

797 

878 

961 

046 

131 

219 

308 

399 

492 

586 

683 

782 

883 

987 

11 

12  . 

798 

880 

963 

047 

133 

220 

309 

400 

493 

588 

685 

784 

885 

989 

12 

13 

799 

881 

964 

048 

134 

222 

311 

402 

495 

590 

686 

785 

887 

991 

13 

14 

801 

882 

965 

050 

136 

223 

312 

403 

496 

591 

688 

787 

889 

992 

14 

15 

2802 

2884 

2967 

3051 

3137 

3225 

3314 

3405 

3498 

3593 

3690 

3789 

3890  3994 

15 

16 

803 

885 

968 

053 

139 

226 

316 

407 

499 

594 

691 

790 

892 

996 

16 

17 

805 

886 

970 

054 

140 

228 

317 

408 

501 

596 

693 

792 

894 

998 

17 

18 

806 

888 

971 

055 

142 

229 

319 

410 

503 

598 

695 

794 

895 

999 

18 

19 

807 

889 

972 

057 

143 

231 

320 

411 

504 

599 

696 

795 

897 

4001 

19 

20 

2809 

2891 

2974 

3058 

3144 

3232 

3322 

3413 

3506 

3601 

3698 

3797 

3899 

4003 

20 

21 

810 

892 

975 

060 

146 

334 

323 

414 

507 

602 

699 

799 

901 

005 

21 

22 

811 

893 

976 

061 

147 

235 

325 

416 

509 

604 

701 

800 

902 

006 

22 

23 

813 

895 

978 

063 

149 

237 

326 

417 

510 

606 

703 

802 

904 

008 

23 

24 

814 

896 

1*79 

064 

150 

238 

328 

419 

512 

607 

704 

804 

906 

010 

24 

25 

2815 

2897 

2981 

3065 

3152 

3240 

3329 

3420 

3514 

3609 

3706 

3806 

3907 

4012 

25 

26 

817 

899 

982 

067 

153 

241 

331 

422 

515 

610 

708 

807 

909 

014 

26 

27 

818 

900 

983 

068 

155 

242 

332 

423 

517 

612 

709 

809 

911 

015 

27 

28 

820 

902 

985 

070 

156 

244 

334 

425 

518 

614 

711 

811 

913 

017 

28 

29 

821 

903 

986 

071 

157 

245 

335 

427 

520 

615 

713 

812 

914 

019 

29 

30 

2822 

2904 

2988 

3073 

3159 

3247 

3337 

3428 

3521 

3617 

3714 

3814 

3916 

4021 

30 

31 

824 

906 

989 

074 

160 

248 

338 

430 

523 

618 

716 

816 

918 

022 

31 

32 

825 

907 

991 

075 

162 

250 

340 

431 

525 

620 

717 

817 

919 

024 

32 

33 

826 

908 

992 

077 

163 

251 

341 

433 

526 

622 

719 

819 

921 

026 

33 

34 

828 

910 

993 

078 

165 

253 

343 

434 

528 

623 

721 

821 

923 

028 

34 

35 

2829 

2911 

2995 

3080 

3166 

3254 

3344 

3436 

3529 

3625 

3722 

3822 

3925 

4029 

35 

36 

830 

913 

996 

081 

168 

256 

346 

437 

531 

626 

724 

824 

926 

031 

36 

37 

832 

914 

998 

083 

169 

257 

347 

439 

532 

628 

726 

826 

928 

033 

37 

38 

833 

915 

999 

084 

171 

259 

349 

440 

534 

630 

727 

827 

930 

035 

38 

39 

834 

917 

3000 

085 

172 

260 

350 

442 

536 

631 

729 

829 

932 

037 

39 

40 

2836 

2918 

3002 

3087 

3173 

3262 

3352 

3443 

3537 

3633 

3731 

3831 

3933 

4038 

40 

41 

837 

919 

003 

088 

175 

263 

353 

445 

539 

634 

732 

832 

935 

040 

41 

42 

839 

921 

005 

090 

176 

265 

355 

447 

540 

636 

734 

834 

937 

042 

42 

43 

840 

922 

006 

091 

178 

266 

356 

448 

542 

638 

736 

836 

938 

044 

43 

44 

841 

924 

007 

093 

179 

268 

358 

450 

543 

639 

737 

838 

940 

045 

44 

45 

2843 

2925 

3009 

3094 

3181 

3269 

3359 

3451 

3545 

3641 

3739 

3839 

3942 

4047 

45 

46 

844 

926 

010 

095 

182 

271 

361 

453 

547 

643 

741 

841 

944 

049 

46 

47 

845 

928 

012 

097 

184 

272 

362 

454 

548 

644 

742 

843 

945 

051 

47 

48 

847 

929 

013 

098 

185 

274 

364 

456 

550 

646 

744 

844 

947 

052 

48 

49 

848 

931 

014 

100 

187 

275 

365 

457 

551 

647 

746 

846 

949 

054 

49 

50 

2849 

2932 

3016 

3101 

3188 

3277 

3367 

3459 

3553 

3649 

3747 

3848 

3951 

4056 

50 

51 

851 

933 

017 

103 

190 

278 

368 

460 

555 

651 

749 

849 

952 

058 

51 

52 

832 

935 

019 

104 

191 

280 

370 

462 

556 

652 

750 

851 

954 

060 

52 

53 

854 

936 

020 

105 

192 

281 

371 

464 

558 

654 

752 

853 

956 

061 

53 

54 

855 

937 

021 

107 

194 

283 

373 

465 

559 

655 

754 

854 

958 

063 

54 

55 

2856 

2939 

3023 

3108 

31953284 

3374 

3467 

3561 

3657 

3755 

3856 

3959 

4065 

55 

56 

858 

940 

024 

110 

197  286 

376 

468 

562 

659 

757 

858 

961 

067 

56 

57 

859 

942 

026 

111 

198  287 

378 

470 

564 

660 

759 

860 

963 

069 

57 

58 

860 

943 

027 

113 

200;  289 

379 

471 

566 

662 

760 

861 

964 

070 

58 

59 

862 

944 

029 

114 

201 

290 

381 

473 

567 

664 

762 

863 

966 

072 

59 

M. 

42° 

430 

440 

450 

46° 

470 

48" 

49" 

50" 

51" 

52" 

53" 

54" 

55" 

M. 

66                   TABLE  III. 

. 

MERIDIONAL  PARTS. 

M. 

56°  157°  58°  1 

590  60°  i 

61° 

62°|63°  64° 

65° 

66°  67° 

68° 

69° 

M. 

0  '- 

4074 

4183 

429444091 

4527  4649  4775'|4905 

5039 

5179 

5324 

54745631 

5795 

0 

1 

076 

184 

296 

411 

529 

651 

777 

907 

042 

181 

326 

477 

633 

797 

1 

2 

077 

186 

298 

413 

531 

653 

779 

909 

044 

184 

328 

479 

636 

800 

2 

3 

079 

188 

300 

415 

533 

655 

781 

912 

046 

186 

331 

482 

639 

803 

3 

4 

081 

190 

302 

417 

535 

657 

784 

914 

049 

188 

333 

484 

742 

806 

4 

5 

4083 

4192 

4304 

4419 

4537 

4660 

4786 

4916 

5051 

5191 

5336 

5487 

5644 

5809 

5 

6 

085 

194 

306 

421 

539 

662 

788 

918 

053 

193 

338 

489 

647 

811 

6 

7 

086 

195 

308 

423 

541 

664 

790 

920 

055 

195 

341 

492 

650 

814 

7 

8 

088 

197 

309  425 

543 

666 

792 

923 

058 

198 

343 

495 

652 

817 

8 

9 

090 

199 

311 

427 

545 

668 

794 

925 

060 

200 

346 

497 

655 

820 

9 

10 

4092 

4201 

4313 

4429 

4547 

4670 

4796 

4927 

5062 

5203 

5348 

5500 

5658 

5823 

10 

11 

094 

203 

315 

431 

549 

672 

798 

929 

065 

205 

351 

502 

660 

825 

11 

12 

095 

205 

317 

433 

551 

674 

801 

931 

067 

207 

353 

505 

663 

828 

12 

13 

097 

207 

319 

434 

553 

676 

803 

934 

069 

210 

356 

507 

666 

831 

13 

14 

099 

208 

321 

436 

555 

678 

805 

936 

071 

212 

358 

510 

668 

834 

14 

15 

4101 

4210 

4323 

4438 

4557 

4680 

4807 

4938 

5074 

5214 

5361 

5513 

5671 

5837 

15 

16 

103 

212 

325 

440 

559 

682 

809 

940 

076 

217 

363 

515 

674 

839 

16 

17 

104 

214 

327 

442 

562 

684 

811 

943 

078 

219 

366 

518 

676 

842 

17 

18 

106 

216 

328 

444 

564 

687 

814 

945 

081 

222 

368 

520 

679 

845 

18 

19 

108 

218 

331) 

446 

566 

689 

816 

947 

08S 

224 

371 

523 

682 

848 

19 

20 

4110 

4220 

4332 

4448 

4568 

4691 

4818 

4949 

5085 

5226 

5373 

5526 

5685 

5851 

20 

21 

112 

221 

334 

450 

570 

693 

820 

951 

088 

229 

376 

528 

687 

854 

21 

22 

113 

223 

336 

452 

572 

695 

822 

954 

090 

231 

378 

531 

690 

856 

22 

23 

115 

225 

338 

454 

574 

697 

824 

956 

092 

234 

380 

533 

693 

859 

23 

24 

117 

227 

340 

456 

576 

699 

826 

958 

095 

236 

383 

536 

695 

862 

24 

25 

kiio 

4229 

4342 

4458 

4578 

4701 

4829 

4960 

5097 

5238 

5385 

5539 

5698 

5865 

25 

26 

121 

231 

344 

460 

580 

703 

831 

963 

099 

241 

388 

541 

701 

868 

26 

27 

122 

232 

346 

462 

582 

705 

833 

965 

102 

243 

390 

544 

704 

871 

27 

28 

124 

234 

347 

464 

584 

707 

835 

967 

104 

246 

393 

546 

706 

874 

28 

29 

126 

236 

349 

466 

586 

710 

837 

969 

106 

248 

395 

549 

709 

876 

29 

30 

4128 

4238 

4351 

4468 

4588 

4712 

4839 

4972 

5108 

5250 

5398 

5552 

5712 

5879 

30 

31 

130 

240 

353 

470 

590 

714 

842 

974 

111 

253 

401 

554 

715 

882 

31 

32 

132 

242 

355 

472 

592 

716 

844 

976 

113 

255 

403 

557 

717 

885 

32 

33 

133 

244 

357 

474 

594 

718 

846 

978 

115 

258 

406 

559 

720 

888 

33 

34 

135 

246 

359 

476 

596 

720 

848 

981 

118 

260 

408 

562 

723 

891 

34 

35 

4137 

4247 

4361 

4478 

4598 

4722 

4850 

4983 

5120 

5263 

5411 

5565 

5725 

5894 

35 

36 

139 

249 

363 

480 

600 

724 

852 

985 

122 

265 

413 

567 

728 

896 

36 

37 

141 

251 

365 

482 

602 

726 

855 

987 

125 

267 

416 

570 

731 

899 

37 

38 

142 

253 

367 

484 

604 

728 

857 

990 

127 

270 

418 

573 

734 

902 

38 

39 

144 

255 

369 

486 

606 

731 

859 

992 

129 

272 

421 

575 

736 

905 

39 

40 

4146 

4257 

4370 

4488 

4608 

4733 

4861 

4994 

5132 

5275 

5423 

5578 

5739 

5908 

40 

41 

148 

259 

372 

490 

610 

735 

863 

996 

134 

277 

426 

580 

742 

911 

41 

42 

150 

260 

374 

492 

612 

737 

865 

999 

136 

280 

428 

5S3 

745 

914 

42 

43 

152 

262 

376 

494 

614 

739 

868 

5001 

139 

282 

431 

586 

747 

917 

43 

44 

153 

264 

378 

495 

616 

741 

870 

503 

141 

284 

433 

588 

750 

919 

44 

45 

4155 

4266 

4380 

4497 

4618 

4743 

4872 

5005 

5143 

5287 

5436 

5591 

5753 

5922 

45 

46 

157 

268 

382 

499 

620 

745 

874 

008 

146 

289 

438 

594 

756 

925 

46 

47 

159 

270 

384 

501 

623 

747 

876 

000 

148 

292 

441 

596 

758 

928 

47 

48 

161 

272 

386 

503 

625 

750 

879 

012 

151 

294 

443 

599 

761 

931 

48 

49 

162 

274 

388 

505 

627 

752 

881 

014 

153 

297 

446 

602 

764 

934 

49 

50 

4164 

4275 

4390 

4507 

4629 

4754 

4883 

5017 

5155 

5299 

5448 

5604 

5767 

5937 

50 

51 

166 

277 

392 

509 

631 

756 

885 

019 

158 

301 

451 

607 

770 

940 

51 

52 

168 

279 

394 

511 

633 

758 

887 

021 

160 

304 

454 

610 

772 

943 

52 

53 

170 

281 

396 

513 

635 

760 

890 

023 

162 

306 

456 

612 

775 

946 

53 

54 

172 

283 

398 

515 

637 

762 

892 

026 

165 

309 

459 

615 

778 

948 

54 

55 

4173 

4285 

4399 

4517 

4639 

4764 

4894 

5028 

5167 

5311 

5461 

5617 

5781 

5951 

55 

56 

175 

287 

401 

519 

641 

766 

896 

030 

169 

314 

464 

620 

783 

954 

56 

57 

177 

289 

403 

521 

643 

769 

898 

033 

172 

316 

466 

623 

786 

957 

57 

58 

179 

291 

405 

523 

645 

771 

901 

035 

174 

319 

469 

625 

789 

960 

58 

59 

181 

292 

407 

525 

647 

773 

903 

037 

176 

321 

471 

628 

792 

963 

59 

M. 

5()0 

570 

58° 

590 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

M. 

TABLE  111. 

67 

MERIDIONAL  PARTS. 

M. 

70° 

71° 

72° 1 73° 

740 

750 

76° 

770  780  17.JO 

80° 

81° 

82^ 

830 

M. 

0 

5966 

6146 

6335 

6534 

6746 

6970 

7210 

7467 

7745 

8046 

8375 

8739 

9145> 

9606 

0 

1 

969 

149 

338 

538 

749 

974 

214 

472 

749 

051 

381 

745 

153 

614 

1 

2 

972 

152 

341 

541 

753 

978 

218 

476 

754 

056 

387 

752 

160 

622 

2 

3 

975 

155 

345 

545 

757 

982 

222 

481 

759 

061 

393 

758 

167 

631 

3 

4 

978 

158 

348 

548 

760 

986 

227 

485 

764 

067 

398 

765 

174 

639 

4 

5 

o981 

6161 

6351  6552 

6764 

6990 

7231 

7490 

7769 

8072 

8404 

8771 

9182 

9647 

5 

6 

984 

164 

354 

555 

768 

994 

235 

494 

774 

077 

410 

788 

189 

655 

6 

7 

986 

167 

358  558 

771  997 

239 

498 

778 

083 

416 

784 

196 

664 

7 

8 

989 

170 

361 

562 

775 

7001 

243 

503 

783 

088 

422 

791 

203 

672 

8 

9 

992 

173 

364 

565 

779 

005 

247 

507 

788 

093 

427 

797 

211 

680 

9 

10 

5995 

6177 

6367 

6569 

6782 

7009 

7252 

7512 

7793 

8099 

8433 

8804 

9218 

9689 

10 

11 

998 

180 

371 

572 

786 

013 

256 

516 

798 

104 

439 

810 

225 

697 

11 

12 

6001 

183 

374 

576 

790 

017 

260 

521 

803 

109 

445 

817 

233 

706 

12 

13 

004 

186 

377 

579 

793 

021 

264 

525 

808 

115 

451 

823 

240 

714 

13 

14 

007 

189 

380 

583 

797 

025 

268 

530 

813 

120 

457 

830 

248 

723 

14 

15 

6010 

6192 

(>384 

6586 

6801 

7029 

7273 

7535 

7817 

8125 

8463 

8836 

9255 

9731 

15 

16 

013 

195 

387 

590 

804 

033 

277 

539 

822 

131 

469 

843 

262 

740 

16 

17 

016 

198 

390 

593 

808 

037 

281 

544 

827 

136 

474 

849 

270 

748 

17 

18 

019 

201 

394 

597 

812 

041 

285 

548 

832 

141 

480 

856 

277 

757 

18 

19 

022 

205 

397 

600 

815 

045 

289 

553 

837 

147 

486 

863 

285 

765 

19 

20 

6025 

6208 

6400 

6603 

6819 

7048 

7294 

7557 

7842 

8152 

8492 

8869 

9292 

9774 

20 

21 

028 

211 

403 

607 

823 

052 

298 

562 

847 

158 

498 

876 

300 

783 

21 

22 

031 

214 

407 

610 

826 

056 

302 

566 

852 

163 

504 

883 

307 

791 

22 

23 

034 

217 

410 

614 

830 

060 

306 

571 

857 

168 

510 

889 

315 

800 

23 

24 
25 

037 

220 

413 

617 

834 

064 

311 

576 

862 

174 

516 

896 

322 

809 

24 

6040 

6223 

6417 

6621 

6838 

7068 

7315 

7580 

7867 

8179 

8522 

8903 

9330 

9817 

25 

26 

043 

226 

420 

624 

841 

072 

319 

585 

872 

185 

528 

909 

337 

.826 

26 

27 

046 

230 

423 

628 

845 

076 

323 

589 

877 

190 

534 

916 

345 

835 

27 

28 

049 

233 

427 

631 

849 

080 

328 

594 

882 

196 

540 

923 

353 

844 

28 

29 

052 

236 

430 

635 

853 

084 

832 

599 

887 

201 

546 

930 

360 

852 

29 

30 

6055 

6239 

6433 

6639 

6856 

7088 

7336 

7603 

7892 

8207 

8552 

8936 

9368 

9861 

30  . 

31 

058 

242 

437 

642 

860 

092 

341 

608 

897 

212 

558 

943 

376 

870 

31 

32 

061 

245 

440 

646 

864 

096 

345 

612 

902 

218 

565 

950 

383 

879 

32 

33 

064 

249 

443 

649 

868 

100 

349 

617 

907 

223 

571 

957 

391 

888 

33 

34 

067 

252 

447 

653 

671 

104 

353 

622 

912 

229 

577 

963 

399 

897 

34 

35 

6070 

6255 

6450 

6656 

6875 

7108 

7358 

7626 

7917 

8234 

8583 

8970 

9407 

9906 

35 

36 

073 

258 

453 

660 

879 

112 

362 

631 

922 

240 

589 

977 

414 

915 

36 

37 

076 

,261 

457 

663 

883 

116 

366 

636 

927 

245 

595 

984 

432 

924 

37 

38 

079 

264 

460 

667 

886 

120 

371 

640 

932 

251 

601 

991 

430 

933 

38 

39 

082 

268 

463 

670 

890 

124 

375 

645 

937 

256 

607 

998 

438 

942 

39 

40 

6085 

6271 

6467 

6674 

6894 

7128 

7379 

7650 

7942 

8262 

8614 

9005 

9445 

9951 

40 

41 

088 

274 

470 

677 

898 

132 

384 

654 

948 

267 

620 

012 

453 

960 

41 

42 

091 

277 

473 

681 

901 

136 

388 

659 

953 

273 

626 

018 

461 

969 

42 

43 

094 

280 

477 

685 

905 

140 

392 

664 

958 

279 

632 

025 

469 

978 

43 

44 

097 

283 

480 

(i88 

909 

145 

397 

668 

963 

284 

638 

032 

477 

987 

44 

45 

6100 

6287 

6483 

6692 

6913 

7149 

7401 

7673 

79()8 

8290 

8644 

9039 

9485 

9996 

45 

46 

103 

290 

487 

695 

917 

153 

406 

678 

973 

295 

651 

046 

493 

10005 

46 

47 

106 

293 

490 

69i» 

920 

157 

410 

683 

978 

301 

657 

053 

501 

015 

47 

48 

101* 

296 

494 

702 

924 

161 

414 

687 

983 

307 

663 

060 

509 

024 

48 

49 

112 

299 

497 

706 

928 

165 

419 

692 

989 

312 

669 

067 

517 

033 

49 

50 

6115 

6303 

6500 

6710 

0932 

7169 

7423 

7697 

7994 

8318 

8676 

9074 

9525 

10043 

50 

51 

118 

306 

004 

713 

936 

173 

427 

702 

999 

324 

682 

081 

533 

052 

51 

52 

121 

309 

007 

717 

940 

177 

432 

706 

8004 

329 

688 

08y 

541 

061 

52 

53 

124 

312 

Oil 

720 

943 

181 

436 

711 

009 

335 

695 

096 

549 

071 

53 

54 

127 

315 

014 

724 

947 

185 

441 

716 

014 

341 

701 

103 

557 

080 

54 

55 

6130 

6319 

6517 

6728 

6951 

7189 

7445 

7721 

8020 

8347 

8707 

9110 

9565 

10089 

55 

56 

133 

322 

521 

731 

955 

194 

449 

725 

025 

352 

714 

117 

573 

099 

56 

57 

136 

3-25 

524 

735 

959 

198 

454 

730 

030 

358 

720 

124 

581 

108 

57 

58 

140 

328 

528 

738 

963 

202 

458 

735 

035 

364 

726 

131 

589 

118 

58 

59 

143 

332 

531 

742 

966 

206 

463 

740 

040 

369 

733 

138 

598 

127 

59 

M. 

70° 

71° 

72° 

73° 

740 

750 

76° 

770 

78° 

790 

80° 

81° 

82° 

830 

M. 

68 

TABLE  IV. 

MEAN  REFRACTION. 

App.  Alt. 

Refrao. 

App.  Alt 

Refrac. 

App.  Alt 

Refrac. 

App.  Alt 

Refraa 

App. 

Alt 

Refrac. 

o   ' 

/   // 

o   ' 

/  ti 

o   ' 

t     ti 

o  ' 

/  n 

o 

/ 

/  // 

0  0 

34  17 

10  0 

5  20 

20  0 

2  39 

30  0 

1  41 

50 

0 

0  49 

10 

32  15 

10 

5  15 

10 

2  37 

20 

1  39 

30 

0  48 

20 

30  23 

20 

5  10 

20 

2  36 

40 

1  38 

51 

0 

0  47 

30 

28  40 

30' 

5  6 

30 

2  35 

,31  0 

1  37 

30 

0  46 

40 

27  27 

40 

5  1 

40 

2  33 

20 

1  35 

52 

0 

0  45 

50 

25  41 

50 

4  56 

50 

2  32 

40 

1  34 

30 

0  44 

1  0 

24  22 

11  0 

4  52 

21  0 

2  31 

32  0 

1  33 

53 

0 

0  44 

10 

23  9 

10 

4  48 

10 

2  29 

20 

1  32 

30 

0  43 

20 

22  2 

20 

4  44 

20 

2  28 

40 

1  31 

54 

0 

0  42 

30 

21  0 

30 

4  40 

30 

2  27 

33  0 

1  30 

30 

0  41 

40 

20  2 

40 

4  36 

40 

2  26 

20 

1  28 

55 

0 

0  40 

50 

19  9 

50 

4  82 

50 

2  25 

40 

1  27 

30 

0  40 

2  0 

18  20 

12  0 

4  28 

22  0 

2  24 

34  0 

1  26 

56 

0 

0  39 

10 

17  34 

10 

4  25 

10 

2  22 

20 

1  25 

30 

0  39 

20 

16  51 

20 

4  21 

20 

2  21 

40 

1  24 

57 

0 

0  38 

30 

16  11 

30 

*  4  18 

30 

2  20 

35  0 

1  23 

30 

0  38 

40 

15  34 

40 

4  14 

40 

2  19 

20 

1  22 

58 

0 

0  37 

50 

14  59 

50 

4  11 

50 

2  18 

40 

1  21 

30 

0  36 

3  0 

14  26 

13  0 

4  8 

23  0 

2  17 

36  0 

1  20 

59 

0 

0  35 

10 

13  55 

10 

4  5 

10 

2  15 

20 

1  19 

30 

0  34 

20 

13  27 

20 

4  2 

20 

2  14 

40 

1  18 

60 

0 

0  33 

30 

13  0 

30 

3  59 

30 

2  13 

37  0 

1  17 

30 

0  33 

40 

12  34 

42 

3  56 

40 

2  12 

20 

1  16 

61 

0 

0  32 

50 

12  10 

50 

3  53 

50 

2  11 

40 

1  15 

30 

0  32 

4  0 

11  47 

14  0 

3  50 

24  0 

2  10 

38  0 

1  14 

62 

0 

0  31 

10 

11  26 

10 

3  47 

10 

2  9 

20 

1  14 

30 

0  31 

20 

11  5 

20 

3  45 

20 

2  8 

40 

1  13 

63 

0 

0  30 

30 

10  46 

30 

3  42 

30 

2  7 

39  0 

1  12 

30 

0  29 

40 

10  28 

40 

3  40 

40 

2  6 

20 

1  11 

64 

0 

0  28 

50 

10  10 

50 

3  37 

50 

2  5 

40 

1  10 

30 

0  28 

5  0 

9  54 

15  0 

3  35 

25  0 

2  5 

40  0 

1  9 

65 

0 

0  27 

10 

9  38 

10 

3  32 

10 

2  4 

20 

1  9 

30 

0  27 

20 

9  23 

20 

3  30 

20 

2  3 

40 

1  8 

66 

0 

0  26 

30 

9  9 

30 

3  28 

30 

2  2 

41  0 

1  T 

30 

0  25 

40 

8  55 

40 

3  25 

40 

2  1 

20 

1  7 

67 

0 

0  24 

50 

8  42 

50 

3  23 

50 

2  0 

40 

1  6 

30 

0  24 

6  0 

8  30 

16  0 

3  21 

26  0 

1  59 

42  0 

1  5 

68 

0 

0  23 

10 

8  18 

10 

3  19 

10 

1  58 

20 

1  4 

30 

0  22 

20 

8  6 

20 

3  17 

20 

1  57 

40 

1  3 

69 

0 

0  21 

30 

7  56 

30 

3  15 

30 

1  56 

43  0 

1  2 

70 

0 

0  20 

40 

7  45 

40 

3  13 

40 

1  56 

20 

1  2 

71 

0 

0  19 

50 

7  35 

50 

3  11 

50 

I  55 

40 

1  1 

72 

0 

0  18 

7  0 

7  25 

17  0 

3  9 

27  0 

1  54 

44  0 

1  0 

73 

0 

0  17 

10 

7  16 

10 

3  7 

10 

1  53 

20 

1  0 

74 

0 

0  16 

20 

7  7 

20 

3  5 

20 

1  52 

40 

0  59 

75 

0 

0  15 

30 

6  59 

30 

3  3 

30 

1  51 

45  0 

0  58 

76 

0 

0  14 

40 

6  50 

40 

3  1 

40 

1  51 

20 

0  58 

77 

0 

0  13 

50 

6  42 

50 

2  59 

50 

1  50 

40 

0  57 

78 

0 

0  12 

8  0 

6  35 

18  0 

2  58 

28  0 

1  49 

46  0 

0  56 

79 

0 

0  11 

10 

6  27 

10 

2  56 

10 

1  49 

20 

0  56 

80 

0 

0  10 

20 

6  20 

20 

2  54 

20 

1  48 

40 

0  55 

81 

0 

0  9 

30 

6  13 

30 

2  53 

30 

1  47 

47  0 

0  54 

82 

0 

0  8 

40 

6  6 

40 

2  51 

40 

1  47 

20 

0  54 

83 

0 

0  7 

50 

6  0 

50 

2  50 

50 

1  46 

40 

0  53 

84 

0 

0  6 

9  0 

5  54 

19  0 

2  48 

29  0 

1  45 

48  0 

0  52 

85 

0 

0  5 

10 

5  48 

10 

2  47 

10 

1  45 

20 

0  52 

86 

0 

0  4 

20 

5  42 

20 

2  45 

20 

1  44 

40 

0  51 

87 

0 

0  3 

30 

5  36 

30 

2  44 

30 

1  43 

49  0 

0  50 

88 

0 

0  2 

40 

5  31 

40 

2  42 

40 

1  43 

20 

0  50 

89 

0 

0  1 

50 

5  25 

50 

2  40 

50 

1  42 

40 

0  49 

90 

0 

0  0 

~ 

TABLES  V, 

VI,  Vll,  Vlll. 

- 

69 

TABLE  V. 

TABLE   Vn. 

niP    Off    THK     HORIZON. 

MOO.l'S    AUGMENTATION. 

])'8       ] 

)'8  Skmidiametkr  by  the  Nautical  Alk 

lANAC. 

Height 

Height 

Height 

App. 

"1  ' 

"1 

'   "1 

f      It 

'   "1 

'   "1 

/      II 

In 
Feet. 

Dip. 

in 
Feet. 

Dip. 

in 

Feet. 

Dip. 

Alt  14.40    15.0015.20 

15.40  16.00  16.20 

16.40 

1    II 

1     II 

1        n 

o 

it 

II 

ti 

II 

II 

II 

It 

1 

0.58 

28 

5.10 

125 

10.56 

0 

0 

0 

0 

0 

0 

0 

?          1 

2 

1.22 

30 

5.21 

\m 

11.  9 

3 

1 

1 

1 

1 

1 

1 

1 

3 

1.40 

32 

5.31 

135 

11.22 

6 

2 

2 

2 

2 

2 

2 

2 

4 

1.55 

34 

5.40 

140 

11.35 

9 

2 

2 

3 

3 

3 

3 

3 

5 

2.  9 

36 

5.50 

145 

11.47 

1^ 

3 

3 

3 

3 

4 

4 

4 

6 

2.22 

38 

6.00 

150 

11.59 

15 

4 

4 

4 

4 

4 

5 

5 

7 

2.33 

40 

6.10 

155 

12.11 

18 

4 

5 

5 

5 

5 

5 

6 

8 

2.44 

42 

6.19 

160 

12.23 

21 

5 

5 

6 

6 

6 

6 

7 

9 

2.54 

44 

6.28 

165 

12.34 

24 

6 

6 

6 

7 

7 

7 

7 

10 

3.03 

46 

6.37 

170 

12.45 

27 

6 

7 

7 

7 

8 

8 

8 

11 

14 
15 

16 
17 
18 
19 
20 

3.12 
3.21 
3.29 
3.37 
3.45 
3.53 
4.  1 
4.  8 
4.15 
4.22 

48 
50 
55 
60 
65 
70 
75 
80 
85 
90 

6.45 
6.53 
7.11 

7.29 
7.47 
8.  5 
8.23 
8.40 
8.57 
9.14 

175 
180 
185 
190 
195 
200 
210 
220 
230 
240 

12.56 
13.  7 
13.18 
13.29 
13.40 
13.50 
14.10 
14.30 
14.50 
15.  9 

30 
33 
36 
39 
42 
45 
48 
51 
54 
57 

7 

8 

8 

9 

9 

10 

10 

11 

11 

12 

7 
8 
8 
9 
10 
10 

11 

12 
12 
13 

8 
8 
9 
10 
10 
11 
11 
12 
12 
13 

8 
8 
9 
10 
11 
11 
12 
12 
13 
13 

8 
9 
10 
11 
11 
12 
12 
13 
13 
14 

9 
9 
10 
11 
12 
12 
13 
13 
14 
14 

9 
10 
11 
11 
12 
13 
13 
14 
14 
15 

21 

4.28 

95 

9.30 

250 

15.27 

60 
65 

12 
13 

13 

14 

13 
14 

14 
15 

14 
15 

15 
16 

lb 
16 

22 

4.34 

100 

9.46 

260 

15.44 

70 

13 

14 

14 

15 

16 

16 

17 

23 

4.40 

105 

10.  1 

270 

16.  0 

75 

14 

14 

15 

15 

16 

16 

17 

24 

4.46 

110 

10.16 

280 

16.16 

80 

14 

14 

15 

16 

16 

17 

18 

25 
26 

4.52 

4.58 

115 

120 

10.30 
10.43 

290 
300 

16.31 
16.46 

90 

14 

15 

15 

16 

17 

17 

18 

' 

1 

TABLE  VIIL 

DIP  OF  THE  HOai7C 

>N — AT  DIFFEAENT  DISTANOXS  FROM  THE  \    \ 

OBSERVER. 

Dista 
of  Lf 
in  M 

nee 

HEIO 

HT    or    THE    «YK    IN    FBET. 

1 

ind       f. 
les.      5 

10 

15 

20 

25    3( 

)   35 

40 

45 

50 

!80 

M. 

0.1     25 

1      1 
\   56 

84 

112] 

1 
14016 

1       1 
9197 

225 

252  S 

TABLE  VL 

0.2     l'^ 

L   28 

42 

56 

70   8 

5   99 

113 

1261 

40 

0.3       i 

)    19 

28 

37 

as:  5 

6   65 

75 

84 

93 
70 

sun's  FARAT.I.AX  IH  ALTTnTDK. 

0.4       ' 

r   14 

21 

28 

35    4 

2   49 

56 

63 

0.5       ( 
0.6       i 
0.7       ^ 
0.8       ^ 

0.9     ; 

5    11 

17 

99, 

28   3 

4   39 

45 

50 

56 

Altitade. 

Parallax. 

)     9 

1     8 
t     7 
I      (5 

14 

12 

10 

9 

19 
16 
14 
12 

23   2 
20    2 
17   2 
15    1 

8  33 

4   28 
,1    25 

9  1-1 

37 
32 

28 
25 

42 

36 
31 

28 

47 
40 
35 
31 

o 

0 

10 

20 

It 

9 
9 
8 

1.0      . 

3      6 

8 

11 

14    1 

7    2C 

23 

25 

27 

1.2       , 

3      5 

7 

.     9 

12    1 

4    K 

^    19 

21 

23 

30 

8 

1.4 

3     4 

6 

8 

10    1 

2    \A 

t    16 

18 

20 

40 

7 

1.6 

3     4 

5 

7 

9    1 

1    15 

.    14 

16 

18 

50 

6 

1.8 

2     3 

5 

6 

8    1 

0    IS 

\    13 

14 

16 

60 

5 

2.0 

2     3 

5 

6 

7 

9    11 

12 

13 

15 

70 

4 

2.2 

2     3 

5 

6 

7 

8    K 

)    11 

12 

14 

80 

2 

2.4 

2     3 

5 

6 

7 

8     £ 

)    11 

12 

13 
11 

90 

0 

2.6 

2.8 

2     3 
2     3 

4 

4 

5 
5 

6 
6 

8     i 
7     6 

)    10 
\    .9 

11 
10 

**■      "*" 

•. 

3.0 

2     3 

4 

5 

6 

7     J 

\     8 

9 

10 

3.5 

2     3 

4 

5 

6 

6     '■ 

r     8 

9 

9 

4.0 

2     3 

4 

4 

5 

6     '■ 

r    7 

8 

8 

4.5 

2     3 

4 

4 

5 

5     ( 

J     6 

7 

8 

5.0 

2     3 

4 

4 

5 

5     ( 

5     6 

7 

7 

6.0 

2     3 

4 

4 

5 

5     ( 

}     6 

7 

7 

7.0 

2     3 

4 

4 

5 

5     ( 

5     6 

7 

71 

70 

TABLE    IX. 

FOB  CORRECTING  THE  OBSERVED  ALTITUDE  OF 

THI 

:  SUN'S  LOWER  LIMB,  WHEN  1 

TAKEN  BY  A  FORE  OBSERVATION. 

Obs. 
Alt 

HEIGHT 

OF   THE 

EYE    ABOVE 

FHE   SEA    IN 

FEET. 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

o     ' 
5    0 

3.8 

1 

3.5 

3.1 

2.8 

2.5 

2. 

3    2.1 

1 
1.8 

1.6 

1.4 

t 
1.2 

1 
1.0 

0.8 

1 
0.6 

0.5 

0.3 

5  20 

4.3 

4.0 

3.6 

3.3 

3.1 

2. 

8    2.6 

2.3 

2.1 

1.9 

1.7 

1.5 

1.3 

1.1 

1.0 

0.8 

5  40 

4.8 

4.5 

4.1 

3.8 

3.5 

3. 

3    3.1 

2.8 

2.6 

2.4 

2.2 

2.0 

1.8 

1.6 

1.5 

1.3 

6    0 

5.3 

4.9 

4.6 

4.3 

4.0 

3. 

7     3.5 

3.3 

3.0 

2.8 

2.6 

2.4 

2.2 

2.1 

1.9 

1.7 

6  20 

5.7 

5.4 

5.0 

4.7 

4.4 

4. 

1     3.9 

3.7 

3.3 

3.2 

3.0 

2.8 

2.6 

2.5 

2.3 

2.0 

6  40 

6.0 

5.7 

5.3 

5.0 

4.7 

4. 

5    4.3 

4.0 

3.8 

3.6 

3.4 

3.2 

3.0 

2.8 

2.7 

2.3 

7    0 

6.4 

6.0 

5.7 

5.4 

5.1 

4. 

8    4.6 

4.4 

4.1 

3.9 

3.7 

3.5 

3.3 

3.2 

3.0 

2.7 

7  20 

6.7 

6.3 

6.0 

5.7 

5.4 

5. 

1     4.9 

4.7 

4.4 

4.2 

4.0 

3.8 

3.6 

3.5 

3.3 

3.1 

7  40 

6.9 

6.6 

6.2 

5.9 

5.7 

5. 

4     5.2 

4.9 

4.7 

4.5 

4.3 

4.1 

3.9 

3.8 

3.6 

3.4 

8    0 

7.2 

6.8 

6.5 

6.2 

5.9 

5. 

7     5.4 

5.3 

5.0 

4.8 

4.6 

4.4 

4.2 

4.0 

3.9 

3.7 

8  20 

7.5 

7.1 

6.7 

6.5 

6.2 

5. 

9     5.7 

5.5 

5.2 

5.0 

4.8 

4.6 

4.4 

4.3 

4.1 

3.9 

8  40 

7.7 

7.3 

7.0 

6.7 

6.4 

6. 

1     5.9 

5.7 

5.5 

5.2 

5.0 

4.8 

4.7 

4.5 

4.3 

4.1 

9    0 

7.9 

7.5 

7.2 

6.9 

6.6 

6. 

4    6.1 

5.9 

5.7 

5.5 

5.3 

5.1 

4.9 

4.7 

4.5 

4.4 

9  20 

8.1 

7.7 

7.4 

7.1 

6.8 

6. 

6    6.3 

6.1 

5.9 

5.7 

5.5 

5.3 

5.1 

4.9 

4.7 

4.6 

9  40 

8.3 

7.9 

7.6 

7.3 

7.0 

6. 

7    6.5 

6.3 

6.1 

5.8 

5.6 

5.4 

5.3 

5.1 

4.9 

4.7 

10    0 

8.5 

8.1 

7.8 

7.5 

7.2 

6. 

9    6.7 

6.5 

6.2 

6.0 

5.8 

5.6 

5.4 

5.3 

5.1 

4.9 

10  30 

8.7 

8.3 

8.0 

7.7 

7.4 

7. 

2    6.9 

6.7 

6.5 

6.3 

6.1 

5.9 

5.7 

5.5 

5.4 

5.2 

11    0 

8.9 

8.6 

8.2 

7.9 

7.6 

7. 

4    7.2 

6.9 

6.7 

6.5 

6.3 

6.1 

5.9 

5.7 

5.6 

5.4 

11  30 

9.1 

8.8 

8.4 

8.1 

7.8 

7. 

6    7.4 

7.1 

6.9 

6.7 

6.5 

6.3 

6.1 

5.9 

5.8 

5.6 

12    0 

9.3 

9.0 

8.7 

8.3 

8.0 

7. 

8    7.6 

7.3 

7.1 

6.9 

6.7 

6.5 

6.3 

6.2 

6.0 

5.8 

13    0 

9.6 

9.3 

9.0 

8.7 

8.4 

8. 

1    7.9 

7.7 

7.4 

7.2 

7.0 

6.8 

6.6 

6.5 

6.3 

6.1 

14    0 

9.9 

9.6 

9.2 

8.9 

8.7 

8. 

4    8.2 

7.9 

7.7 

7.5 

7.3 

7.1 

6.9 

6.8 

6.6 

6.4 

15    0 

10.2 

9.8 

9.5 

9.2 

8.9 

8. 

7     8.4 

8.2 

8.0 

7.8 

7.6 

7.4 

7.2 

7.0 

6.9 

6.7 

16    0 

10.4 

10.1 

9.7 

9.4 

9.1 

8. 

9    8.7 

8.4 

8.2 

8.0 

7.8 

7.6 

7.4 

7.2 

7.1 

6.9 

17    0 

10.6 

10.3 

9.9 

9.6 

9.3 

9. 

1     8.9 

8.6 

8.3 

8.2 

8.0 

7.8 

7.6 

7.4 

7.3 

7.1 

18    0 

10.8 

10.4 

10.1 

9.8 

9.5 

9. 

3    9.0 

8.8 

8.6 

8.4 

8.2 

8.0 

7.8 

7.6 

7.5 

7.3 

19    0 

11.0 

10.6 

10.3 

10.0 

9.7 

9. 

4    9.2 

9.0 

8.8 

8.5 

8.3 

8.1 

8.0 

7.8 

7.6 

7.4 

20    0 

11.1 

10.7 

10.4 

10.1 

9.8 

9. 

6    9.3 

9.1 

8.9 

8.7 

8.5 

8.2 

8.1 

7.9 

7.7 

7.6 

21    0 

11.2 

10.9 

10.5 

10.2 

10.0 

9. 

7    9.5 

9.2 

9.0 

8.8 

8.6 

8.4 

8.2 

8.1 

7.9 

7.7 

22    0 

11.4 

11.0 

10.7 

10.4 

10.1 

9. 

8    9.6 

9.4 

9.1 

8.9 

8.7 

8.5 

8.3 

8.2 

8.0 

7.8 

23    0 

11.5 

11.1 

10.8 

10.5 

10.2 

9. 

9    9.7 

9.5 

9.2 

9.0 

8.8 

8.6 

8.4 

8.3 

8.1 

7.9 

24    0 

11.6 

11.2 

10.9 

10.6 

10.3 

10. 

0    9.8 

9.6 

9.3 

9.1 

8.9 

8.7 

8.5 

8.4 

8.2 

8.0 

25    0 

11.7 

11.3 

11.0 

10.7 

10.4 

10. 

1     9.9 

9.7 

9.4 

9.2 

9.0 

8.8 

8.6 

8.5 

8.3 

8.1 

26    0 

11.7 

11.4 

11.0 

10.7 

10.5 

10. 

2  10.0 

9.7 

9.5 

9.3 

9.1 

8.9 

8.7 

8.6 

8.4 

8.2 

27    0 

11.8 

11.5 

11.1 

10.8 

10.5 

10. 

3  10.1 

9.8 

9.6 

9.4 

9.2 

9.0 

8.8 

8.6 

8.5 

8.3 

28    0 

11.9 

11.6 

11.2 

10.9 

10.6 

10. 

4  10.2 

9.9 

9.7 

9.5 

9.3 

9.1 

8.9 

8.7 

8.5 

8.4 

30    0 

12.0 

11.7 

11.3 

11.0 

10.8 

10. 

5  10.3 

10.0 

9.8 

9.6 

9.4 

9.2 

9.0 

8.9 

8.7 

8.5 

32    0 

12.2 

11.8 

11.5 

11.2 

10.9 

10. 

6  10.4 

10.2 

9.9 

9.7 

9.5 

9.3 

9.1 

9.0 

8.8 

8.6 

34    0 

12.3 

11.9 

11.6 

11.3 

11.0 

10. 

7  10.5 

10.3 

10.1 

9.9 

9.6 

9.4 

9.2 

9.1 

8.9 

8.7 

36    0 

12.4 

12.0 

11.7 

11.4 

11.1 

10. 

8  10.6 

10.4 

10.2 

9.9 

9.7 

9.5 

9.3 

9.2 

9.0 

8.8 

38    0 

12.5 

12.1 

11.8 

11.5 

11.2 

10. 

9  10.7 

10.5 

10.2 

10.0 

9.8 

9.6 

9.4 

9.3 

9.1 

8.9 

40    0 

12.5 

12.2 

11.8 

11.5 

11.3 

11. 

0  10.8 

10.5 

10.3 

10.1 

9.9 

9.7 

9.5 

9.4 

9.2 

9.0 

42    0 

12.6 

12.2 

11.9 

11.6 

11.3 

11. 

1  10.8 

10.6 

10.4 

10.2 

10.0 

9.8 

9.6 

9.4 

9.3 

9.1 

44    0 

12.7 

12.H 

12.0 

11.7 

11.4 

11. 

1   10.9 

10.7 

10.5 

10.2 

10.1 

9.8 

9.7 

9.5 

9.3 

9.1 

46    0 

12.7 

12.4 

12.0 

11.7 

11.5 

11. 

2  11.0 

10.7 

10.5 

10.3 

10.2 

9.9 

9.7 

9.6 

9.4 

9.2 

48    0 

12.8 

124 

12.1 

11.8 

11.5 

11. 

3  11.0 

10.8 

10.6 

10.4 

10.2 

10.0 

9.8 

9.6 

9.5 

9.3 

50    0 

12.8 

12.5 

12.2 

11.9 

11.6 

11. 

3  11.1 

10.9 

10.6 

10.4 

10.3 

10.0 

9.8 

9.7 

9.5 

9.3 

52    0 

12.9 

12.5 

12.2 

11.9 

11.6 

11. 

4  11.1 

10.9 

10.7 

10.5 

10.3 

10.1 

9.9 

9.7 

9.6 

9.4 

54    0 

13.0 

12.6 

12.3 

12.0 

11.7 

11. 

4  11.2 

11.0 

10.7 

10.5 

10.3 

10.1 

9.9 

9.8 

9.6 

9.4 

56    0 

13.0 

12.6 

12.3 

12.0 

11.7 

11. 

5  11.2 

■11.0 

10.8 

10.6 

10.4 

10.2 

10.0 

9.8 

9.7 

9.5 

58    0 

13.0 

12.7 

12.3 

12.0 

11.7 

TT 

5  11.3 

ll.O 

10.8 

10.6 

10.4 

10.2 

10.0 

'9.9 

'  9.7 

9.5 

60    0 

13.1 

12.7 

12.4 

12.1 

11.8 

11. 

6  11.3 

11.1 

10.9 

10.6 

10.4 

10.2 

10.1 

9.9 

9.7 

9.5 

62    0 

13.1 

12.8 

12.4 

12.1 

11.8 

11. 

6  11.4 

11. J 

10.9 

10.7 

10.5 

10.3 

10.1 

9.9 

9.8 

9.6 

64    0 

13.2 

12.8 

12.5 

12.2 

11.9 

11. 

6  11.4 

11.2 

10.9 

10.7 

10.5 

10.3 

10.1 

10.0 

9.8 

9.6 

66    0 

13.2 

12.8 

12.5 

12.2 

11.9 

11. 

7  11.4 

11.2 

11.0 

10.8 

10.6 

10.4 

10.2 

10.0 

9.8 

9.7 

70    0 

13.3 

12.9 

12.0 

12.3 

12.0 

11. 

8  11.5 

11.3 

11.0 

10.8 

10.6 

10.4 

10.2 

10.1 

9.9 

9.7 

80    0 

13.4 

13.1 

12.7 

12.4 

12.1 

11. 

9  11.7 

11.4 

11.2 

11.0 

10.8 

10.6 

10.4 

10.2 

10.1 

9.9 

90    0 

13.6 

13.2 

12.9 

12.6 

12.3 

12. 

0  11.8 

11.6 

11.3 

11.1 

10.9 

10.7 

10.5 

10.4 

10.2 

10.0 

Month. 

Jan. 

Fkb. 

Mab. 

April, 

Mat, 

June, 

Jdlt, 

Auo.  1 

Sept. 

Oct. 

Nov. 

Deo. 

Correction, 

-f0'.3 

4-0'. 

2  4-0 

U 

jO 

— 

-0'.2 

— 0'.2 

— C 

!!£ 

— 

-0'.2 

-0'.] 

[  +0'.l 

+  0'.2  - 

f0'.2 

TABLE  X. 

nl 

SUN'S  DECLINATION  FOR  THE  YEAR  1854  FOR  APPARENT  NOON  AT  GREENWICH.   1 

DATS. 

JAN. 

PBB. 

MARCH. 

APRIL. 

MAY. 

JUNE. 

JULY. 

AUGUST. 

SEPT. 

OCT.   1 

NOV.  1 

DEC    1 

o    ' 

o   ' 

O   ' 

O    ' 

O    ' 

O   ' 

O    ' 

O 

/ 

C    ' 

O 

■ 

O 

/ 

O 

; 

1 

23  IS 

17    as 

7  35S 

4  32N 

15  4N 

22  3N 

23  8N 

18 

4N 

8  19N 

3 

lOS 

14 

26S 

21 

49S 

2 

22  56 

16  49 

7  12 

4  55 

15  22 

22  11 

23  4 

17 

48 

7  57 

3 

33 

14 

45 

21 

58 

3 

22  50 

16  31 

6  49 

5  18 

15  40 

22  19 

22  59 

17 

33 

7  35 

3 

56 

15 

4 

22 

7 

4 

22  44 

16  13 

6  26 

5  41 

15  57 

22  26 

22  54 

17 

17 

7  13 

4 

20 

15 

23 

22 

15 

5 

22  38 

15  55 

6  3 

6  4 

16  14 

22  33 

22  49 

17 

1 

6  51 

4 

43 

15 

41 

22 

23 

6 

22  30 

15  37 

5  40 

6  26 

16  31 

22  40 

22  43 

16 

45 

6  29 

5 

6 

15 

59 

22 

31 

7 

22  23 

15  18 

5  17 

6  49 

16  48 

22  46 

22  37 

16 

28 

6  6 

5 

29 

16 

17 

22 

38 

8 

22  15 

14  59 

4  53 

7  11 

17   5 

22  51 

22  30 

16 

11 

5  44 

5 

52 

16 

35 

22 

44 

9 

22  7 

14  40 

4  30 

7  34 

17  21 

22  56 

22  24 

15 

54 

5  21 

6 

15 

16 

52 

22 

50 

10 

21  58 

14  21 

4  7 

7  56 

17  37 

23  1 

22  16 

15 

37 

4  59 

6 

38 

17 

9 

22 

56 

11 

21  49 

14  1 

3  43 

8  18 

17  52 

23  6 

22  8 

15 

19 

4  36 

7 

0 

17 

26 

23 

1 

12 

21  39 

13  41 

3  19 

8  40 

18  7 

23  10 

22  0 

15 

1 

4  13 

7 

23 

17 

42 

23 

6 

13 

21  29 

13  21 

2  56 

9  2 

18  22 

23  13 

21  52 

14 

43 

3  50 

7 

45 

17 

58 

23 

10 

14 

21  19 

13  1 

2  32 

9  24 

18  37 

23  17 

21  43 

14 

25 

3  27 

8 

8 

18 

14 

23 

14 

15 

21  8 

12  41 

2  9 

9  45 

18  51 

23  19 

21  34 

14 

6 

3  4 

8 

30 

18 

30 

23 

17 

16 

20  57 

12  20 

1  45 

10  6 

19  5 

23  22 

21  24 

13 

47 

2  41 

8 

52 

18 

45 

23 

20 

17 

20  45 

11  59 

1  21 

10  28 

19  19 

23  24 

21  14 

13 

28 

2  17 

8 

14 

19 

0 

23 

23 

18 

20  33 

11  38 

0  57 

10  49 

19  33 

23  25 

21  4 

13 

9 

1  54 

8 

36 

19 

14 

23 

24 

19 

20  20 

11  17 

0  34 

11  9 

19  46 

23  26 

20  53 

12 

49 

1  31 

9 

58 

19 

28 

23 

26 

20 

20  8 

10  55 

0  lOS 

11  30 

19  58 

23  27 

20  42 

12 

30 

1  8 

10 

20 

19 

42 

23 

27 

21 

19  54 

10  34 

0  14N 

11  51 

20  11 

23  28 

20  31 

12 

10 

0  44 

10 

41 

19 

56 

23 

28 

22 

19  41 

10  12 

0  37 

12  11 

20  23 

23  27 

20  19 

11 

50 

0  2lN 

11 

3 

20 

9 

23 

28 

23 

19  27 

9  50 

1   1 

12  31 

20  34 

23  27 

20  7 

11 

29 

0  3S 

11 

24 

21 

22 

23 

27 

24 

19  13 

9  28 

1  25 

12  51 

20  46 

23  26 

19  55 

11 

9 

0  26 

11 

45 

20 

34 

23 

26 

25 

18  58 

9  5 

1  48 

13  11 

20  57 

23  25 

19  42 

10 

48 

0  49 

12 

6 

20 

46 

23 

25 

26 

18  43 

8  43 

2  12 

13  30 

21  7 

23  23 

19  29 

10 

27 

1  13 

12 

26 

20 

57 

23 

23 

27 

18  28 

8  21 

2  35 

13  49 

21  18 

23  21 

19  15 

10 

6 

1  36 

12 

47 

21 

9 

29 

21 

28 

18  12 

7  58 

2  59 

14  8 

21  28 

23  18 

19  2 

9 

45 

2  0 

13 

7 

21 

19 

23 

18 

29 

17  56 

3  22 

14  27 

21  37 

23  15 

18  48 

9 

24 

2  23 

13 

27 

21 

30 

23 

15 

30 

17  40 

3  45 

14  46 

21  46 

23  12 

18  33 

9 

3 

2  46 

13 

47 

21 

40 

23 

11 

31 

17  23 

4  9 

21  55 

18  19 

8 

41 

14 

6 

23 

7 

SUN'S  DECI 

.INATI 

ON  FOR  THE 

YI 

:ar 

1855. 

DAYS. 

JAN. 

FEB. 

MARCH. 

APRIL. 

MAY. 

JUNE. 

JULY. 

AUG. 

SEPT. 

OCT. 

NOV. 

DEC.    1 

O     ' 

O    ' 

O    ' 

O   ' 

O   ' 

O      ' 

O   ' 

O 

/ 

O    ' 

O 

1 

o 

/ 

O 

1 

1 

23  28 

17  US 

7  41S 

4  25N 

14  59N 

22  IN 

23  9N 

18 

8N 

8  25N 

3 

3S 

14 

21S 

21 

47S 

2 

22  57 

16  53 

7  19 

4  49 

15  17 

22  9 

23  5 

17 

53 

8  3 

3 

27 

14 

40 

21 

56 

3 

22  52 

16  36 

6  56 

5  12 

15  35 

22  17 

22  1 

17 

37 

7  42 

3 

50 

14 

59 

22 

5 

4 

22  46 

16  18 

6  33 

5  35 

15  52 

22  24 

22  56 

17 

21 

7  19 

4 

13 

15 

17 

22 

13 

5 

22  39 

16  0 

6  10 

5  57 

16  10 

22  31 

22  50 

17 

5 

6  57 

4 

36 

15 

36 

22 

21 

6 

22  32 

15  42 

5  46 

6  20 

16  27 

22  38 

22  45 

16 

49 

6  35 

4 

59 

15 

54 

22 

29 

7 

22  25 

15  23 

5  23 

6  43 

16  44 

22  44 

22  39 

16 

33 

6  13 

5 

23 

16 

12 

22 

36 

8 

22  17 

15  5 

5  0 

7  5 

17  0 

22  50* 

22  32 

16 

16 

5  50 

5 

46 

16 

30 

22 

42 

9 

22  9 

14  46 

4  36 

7  28 

17  16 

22  55 

22  25 

15 

59 

5  27 

6 

8 

16 

46 

22 

49 

10 

22  0 

14  26 

4  13 

7  50 

17  32 

23  0 

22  18 

15 

41 

5  5 

6 

31 

17 

4 

22 

54 

11 

21  51 

14  7 

3  49 

8  12 

17  48 

23  4 

22  10 

15 

24 

4  42 

6 

54 

17 

21 

23 

0 

12 

21  42 

13  47 

3  26 

8  34 

18  3 

23  9 

22  2 

15 

6 

4  19 

7 

17 

17 

38 

23 

4 

13 

21  32 

13  27 

3  2 

8  56 

18  18 

23  12 

21  54 

14 

48 

3  56 

7 

39 

17 

54 

23 

9 

14 

21  22 

13  7 

2  39 

9  18 

18  33 

23  16 

21  45 

14 

30 

3  33 

8 

2 

18 

10 

23 

13 

15 

21  11 

12  46 

2  15 

9  39 

18  47 

23  19 

21  36 

14 

11 

3  10 

8 

24 

18 

25 

23 

16 

16 

21   0 

12  25 

1  51 

10   1 

19  2 

23  21 

21  27 

13 

52 

2  47 

8 

46 

18 

41 

23 

19 

17 

20  48 

12  5 

1  28 

10  22 

19  15 

23  23 

21  17 

13 

33 

2  24 

9 

8 

18 

56 

23 

22 

18 

20  36 

11  44 

1  4 

10  43 

19  29 

23  25 

21  7 

13 

14 

2  1 

9 

30 

19 

10 

23 

24 

19 

20  24 

11  22 

0  40 

11   4 

19  42 

23  26 

20  56 

12 

55 

1  37 

9 

52 

19 

24 

23 

25 

20 

20  11 

11   1 

0  ITS 

>11  24 

19  55 

23  27 

20  45 

12 

35 

1  14 

10 

14 

19 

38 

23 

27 

21 

19  58 

10  39 

0  71N 

11  45 

20  7 

23  27 

20  34 

12 

15 

0  51 

10 

35 

19 

52 

23 

28 

22 

19  44 

10  18 

0  31 

12  5 

20  19 

23  27 

20  22 

11 

55 

0  27 

11 

57 

20 

5 

23 

27 

23 

19  31 

9  56 

0  54 

12  25 

20  31 

23  27 

20  10 

11 

35 

0  4N 

11 

18 

20 

18 

23 

27 

24 

19  16 

9  34 

1  18 

12  45 

20  43 

23  26 

19  58 

11 

14 

0  20S 

11 

39 

20 

30 

23 

26 

25 

19  2 

9  12 

1  42 

13  5 

20  54 

23  25 

19  45 

10 

54 

0  43 

12 

0 

20 

42 

23 

25 

26 

18  47 

8  49 

2  5 

13  25 

21  4 

23  23 

19  32 

10 

33 

1  6 

12 

21 

20 

54 

23 

23 

27 

18  32 

8  27 

2  29 

13  44 

21  15 

23  21 

19  19 

10 

12 

1  30 

12 

41 

21 

5 

23 

21 

28 

18  16 

8  4 

2  52 

14  3 

21  25 

23  19 

19  5 

9 

51 

1  53 

13 

1 

21 

16 

23 

19 

29 

18  0 

3  16 

14  22 

21  34 

23  16 

18  51 

9 

30 

2  17 

13 

22 

21 

27 

23 

16 

30 

17  44 

3  39 

14  40 

21  44 

23  13 

18  37 

9 

9 

2  40 

13 

41 

21 

37 

2? 

12 

31 

17  27 

4  2, 

21  52 

18  23 

8 

47 

14 

1 

23 

8 

ThiiTal 

>U  will  a 

iiwer  rery  nearly  for  erery  f< 

)ni  yea™ 
take 

iftarwards.  but  if  g 
n  from  Table  XII. 

reater  ace 

uracy  ii  reqtii 

r«d,  < 

b  oor 

rectio 

a  miut  b«  1 

72 

TABLE 

X. 

"n 

SUN'S  DECLINATION  FOR  THE  YEAR  1856  FOR  APPARENT  NOON  AT  GREENWICH.  1 

DAYS. 

JAN. 

FEB. 

MARCH. 

APRIL. 

MAY. 

JUNE. 

JULY. 

AUGUST. 

SEPT. 

OCT. 

NOV. 

DEC.   1 

O     ' 

O 

/ 

O    ' 

O    ' 

O    ' 

O    ' 

O 

/ 

O    ' 

0   ' 

O 

/ 

o 

1 

O 

/ 

1 

23  3S 

17 

15S 

7  25S 

4  42N 

15  12N 

22  7N 

23 

6N 

17  57N 

8  9N 

3 

208 

14 

358 

21 

53S 

2 

22  59 

16 

58 

7  2 

5  5 

15  30 

22  15 

23 

2 

17  41 

7  47 

3 

44 

14 

54 

22 

2 

3 

22  53 

16 

41 

6  39 

5  28 

15  48 

22  22 

«2 

67 

17  26 

7  25 

t 

7 

15 

12 

22 

11 

4 

22  47 

16 

23 

6  16 

5  51 

16  5 

22  29 

22 

52 

17  10 

7  3 

4 

30 

15 

31 

22 

19 

5 

22  41 

16 

5 

5  53 

6  14 

16  22 

22  36 

22 

46 

16  54 

6  41 

4 

53 

15 

49 

22 

27 

6 

22  34 

15 

47 

5  29 

6  37 

16  39 

22  42 

22 

40 

16  37 

6  19 

5 

16 

16 

7 

22 

34 

7 

22  27 

15 

28 

5  6 

6  59 

16  56 

22  28 

22 

34 

16  20 

6  56 

5 

39 

16 

25 

22 

41 

8 

22  19 

15 

10 

4  43 

7  22 

17  12 

22  53 

22 

27 

16  3 

5  34 

6 

2 

16 

42 

22 

47 

9 

22  11 

14 

51 

4  19 

7  44 

17  28 

22  59 

22 

20 

15  46 

5  11 

6 

25 

17 

0 

22 

53 

10 

22  3 

14 

31 

3  56 

8  6 

17  44 

23  3 

22 

13 

15  28 

4  48 

6 

48 

17 

17 

22 

58 

11 

21  54 

14 

12 

3  32 

8  28 

17  59 

23  7 

22 

05 

15  11 

4  25 

7 

11 

17 

33 

23 

3 

12 

21  44 

13 

52 

3  9 

8  50 

18  14 

23  11 

21 

56 

14  53 

4  2 

7 

33 

17 

49 

23 

8 

13 

21  35 

13 

32 

2  45 

9  12 

18  29 

23  15 

21 

48 

14  34 

3  39 

7 

56 

18 

5 

23 

12 

14 

21  24 

13 

12 

2  21 

9  33 

18  44 

23  18 

21 

39 

14  16 

3  16 

8 

18 

18 

21 

23 

15 

15 

21  14 

12 

52 

1  58 

9  55 

18  58 

23  20 

21 

29 

13  57 

2  53 

8 

40 

18 

37 

23 

18 

16 

21  3 

12 

31 

1  34 

10  16 

19  12 

23  23 

21 

20 

13  38 

2  30 

9 

02 

18 

52 

23 

21 

17 

20  51 

12 

10 

1  10 

10  37 

19  25 

23  24 

21 

9 

13  19 

2  7 

9 

24 

19 

6 

23 

23 

18 

20  39 

11 

49 

0  47 

10  58 

19  38 

23  26 

20 

59 

13  0 

1  44 

9 

46 

19 

21 

23 

25 

19 

20  27 

11 

28 

0  23S 

11  19 

19  51 

23^27 

20 

48 

12  40 

1  20 

10 

08 

19 

35 

23 

26 

20 

20  14 

11 

7 

0  IN 

11  39 

20  4 

23  27 

20 

37 

12  20 

0  57 

10 

30 

19 

48 

23 

27 

21 

20  1 

10 

45 

0  24 

12  0 

20  16 

23  27 

20 

25 

12  0 

0  34 

10 

51 

20 

2 

23 

27 

22 

19  48 

10 

23 

0  48 

12  20 

20  28 

23  27 

20 

13 

11  40 

0  IOn 

11 

12 

20 

14 

23 

27 

23 

19  34 

10 

2 

1  12 

12  40 

20  40 

23  26 

20 

1 

11  20 

0  13S 

11 

33 

20 

27 

23 

27 

24 

19  20 

9 

40 

1  35 

13  0 

20  51 

23  25 

19 

49 

10  59 

0  37 

11 

54 

20 

39 

23 

25 

25 

19  6 

9 

17 

1  59 

13  19 

21  1 

23  24 

19 

36 

10  39 

1  0 

12 

15 

20 

51 

23 

24 

26 

18  51 

8 

55 

2  22 

13  39 

21  12 

23  22 

19 

23 

10  18 

1  23 

12 

36 

21 

2 

23 

22 

27 

18  36 

8 

33 

2  46 

13  58 

21  22 

23  20 

19 

9 

9  57 

1  47 

12 

56 

21 

13 

29 

19 

28 

18  20 

8 

10 

3  9 

14  17 

21  32 

27  17 

18 

55 

9  36 

2  10 

13 

16 

21 

24 

23 

16 

29 

18  5 

7 

48 

3  33 

14  35 

21  41 

23  14 

18 

41 

9  14 

2  34 

13 

36 

21 

34 

23 

13 

30 

17  48 

3  56 

14  54 

21  50 

23  10 

18 

27 

8  53 

2  57 

13 

56 

21 

44 

23 

9 

31 

17  32 

4  19 

21  59 

18 

12 

8  31 

14 

15 

23 

5 

SUN'S  DECI 

.INATI 

ON  FO] 

9.  1 

'HE 

YEAR 

1857. 

DAYS. 

JAN. 

FEB. 

MARCH. 

APRIL. 

MAY. 

JUNE. 

JULY. 

AUG. 

SEPT. 

OCT. 

NOV. 

DEC.   1 

O     ' 

r 

O    ' 

O    ' 

O    ' 

O      ' 

0 

/ 

o   / 

O    ' 

o 

/ 

o 

/ 

O 

t 

1 

23  OS 

17 

2S 

7  30S 

4  37N 

15  8N 

22  5N 

23 

7N 

18  ON 

8  15N 

3 

158 

14  308 

21 

51S 

2 

22  54 

16 

45 

7  7 

5  0 

15  26 

22  13 

23 

3 

17  45 

7  53 

3 

38 

14 

49 

22 

0 

3 

22  49 

16 

27 

6  44 

5  23 

15  43 

22  20 

22 

58 

17  30 

7  31 

4 

1 

15 

8 

22 

9 

4 

22  43 

16 

10 

6  21 

5  46 

16  1 

22  28 

22 

53 

17  14 

7  9 

4 

24 

15 

26 

22 

17 

5 

22  36 

15 

51 

5  58 

6  8 

16  18 

22  34 

22 

48 

16  58 

6  46 

4 

48 

15 

45 

22 

25 

6 

22  29 

15 

33 

5  35 

6  31 

16  35 

22  41 

22 

42 

16  41 

6  24 

5 

11 

16 

3 

22 

32 

7 

22  21 

15 

14 

5  12 

6  54 

16  51 

22  47 

22 

36 

16  24 

6  2 

5 

34 

16 

21 

22 

39 

8 

22  13 

14 

55 

4  48 

7  16 

17  8 

22  52 

22 

29 

16  8 

5  39 

5 

57 

16 

38 

22 

45 

9 

22  5 

14 

36 

4  25 

7  38 

17  24 

22  57 

22 

22 

15  50 

5  16 

6 

20 

16 

56 

22 

51 

10 

21  56 

14 

17 

4  1 

8  1 

17  40 

23  2 

22 

14 

15  33 

4  54 

6 

42 

17 

13 

22 

57 

11 

21  47 

13 

57 

3  38 

8  23 

17  56 

23  6 

22 

7 

15  15 

4  31 

7 

5 

17 

29 

23 

2 

12 

21  37 

13 

37 

3  14 

8  45 

18  10 

23  10 

21 

58 

14  57 

4  8 

7 

28 

17 

46 

23 

7 

13 

21  27 

13 

17 

2  51 

9  6 

18  25 

23  14 

21 

50 

14  39 

3  45 

7 

60 

18 

2 

23 

11 

14 

21  16 

12 

57 

2  27 

9  28 

18  40 

23  17 

21 

41 

14  21 

3  22 

8 

13 

18 

17 

23 

14 

15 

21  5 

12 

36 

2  4 

9  50 

18  54 

23  20 

21 

32 

14  2 

2  59 

8 

35 

18 

33 

23 

18 

16 

20  54 

12 

15 

1  40 

10  11 

19  8 

23  22 

21 

22 

13  43 

2  36 

8 

57 

18 

48 

23 

21 

17 

20  42 

11 

54 

1  16 

10  32 

19  22 

23  24 

21 

12 

13  24 

2  12 

9 

19 

19 

3 

23 

23 

18 

20  30 

11 

33 

0  52 

10  53 

19  35 

23  25 

21 

2 

13  5 

1  49 

9 

41 

19 

17 

23 

25 

19 

20  18 

11 

12 

0  29 

11  14 

19  48 

23  26 

20 

51 

12  45 

1  26 

10 

3 

19 

31 

23 

26 

20 

20  5 

10 

50 

0  5S 

.11  34 

20  1 

23  27 

20 

40 

12  23 

1  3 

10 

24 

19 

45 

23 

27 

21 

19  51 

10 

29 

0  19N 

11  55 

20  13 

23  27 

20 

28 

12  5 

0  39 

10 

46 

19 

58 

23 

27 

22 

19  38 

10 

7 

0  42 

12  15 

20  25 

23  27 

20 

16 

11  45 

0  16N 

11 

7 

20 

11 

23 

27 

23 

19  24 

9 

45 

1  6 

12  35 

20  37 

23  27 

20 

4 

11  25 

0  088 

11 

28 

20 

24 

23 

27 

24 

19  9 

9 

23 

1  30 

12  55 

20  48 

23  26 

19 

52 

11  4 

0  31 

11 

49 

20 

36 

23 

26 

25 

18  55 

9 

1 

1  53 

13  15 

20  59 

26  24 

19 

39 

10  44 

0  54 

12 

10 

20 

48 

23 

24 

26 

18  40 

8 

38 

2  17 

13  34 

21  9 

23  22 

19 

26 

10  23 

1  18 

12 

31 

21 

0 

23 

22 

27 

18  24 

8 

16 

2  40 

13  53 

21  20 

23  20 

19 

12 

10  2 

1  41 

12 

51 

21 

11 

23 

20 

28 

18  8 

7 

£3 

3  4 

14  12 

21  29 

23  18 

18 

59 

9  41 

2  5 

13 

11 

21 

21 

23 

17 

29 

17  52 

3  27 

14  31 

21  39 

23  14 

18 

45 

9  19 

2  28 

13 

31 

21 

32 

23 

14 

3U 

17  36 

1 

3  50 

14  49 

21  48 

23  11 

18 

30 

8  58 

2  51 

13 

51 

21 

42 

23 

10 

31 

17  19  ( 

4  14 

21  57 

18 

15 

8  36 

14 

11 

23 

lUt  b* 

TUiTal 

>1«  will  Al 

itrwn  T«rj 

r  nearly  for  vrarj  fo 

nr  years  a 

ifterwardi 

,  but  if  gi 

reatar  aeo 

araoy  ia  raqnired,  a 

o«n 

raotio 

■  m 

^^^ 

takei 

1  from  Ta 

ble 

Xll. 

,^^^^ 

^^ 

^^ 

l,^.. 

n 
TABLE  XI. 

CORRECTION  OF  THE  SUN'S  DECLINATION  AT  SEA  FOR  LONGITUDE  AND  FOR  TIME. 


DECLINATION. 


O 

0 


o 
2 


o 
4 


e 
6 


o 
10 


o 

12 


o 

14 


o 
16 


o 

17 


o 

18 


o 
19 


o 
20 


o 

21 


o 

21i 


o 
22 


22i 


o 

23 


o 
23i 


TIMS 
FROM 
NOON. 


0 
10 
20 
30 
40 
50 


2-0 
2-6 
3-3 


0' 

0-6 
1-2 
1-8 
2-5 
3-1 


0- 

2  0- 

3  0 

4  0 
5 

6|0 


M. 

0 
4C 
20 

0 

40 
20 


60 
70 
80 
90 
100 


3-9 
4-6 
5'2 
5-9 
6-5 


3-9 
4-6 
5-2 
5-9 
6-5 


0 
40 
20 

0 
40 
20 

0 
40 
20 
_0 
40 
2) 

0 


10 
120 
130 
140 
150 


7-2 
7-8 
8-5 
9-1 
9-8 


7-2 
7-8 
8-5 
9-1 

9-8 


160 
170 
180 


10-5 

10-4 

10 

11-1 

11-1 

11 

11-8 

11-7 

11 

10- 
10' 

11- 


9' 
10' 
11' 


IN    WEST    LONOITUDB. 


When  the  Declina.  is  {  Oe^'elTng.llibtract 


TIME    BEFORE    NOON. 


xm.       ^^.    T\    V       •     i  Increasinff,  Subtract 
When  the  Declina.  is  j  decreasing,  Add. 


IN    EAST    LONOITUDE 


^Tn_       .iL     T-»    !•       •      <  Increasing,  Subtract. 
When  the  Declina.  is    j  D^^easing,  Add. 


TIME    AFTERNOON. 


When  the  Declina.  is    \  o^J^elTn^g,  Subtract. 


TABLE    XIL 

CORRECTION  OF  THE  SUN'S  DECLINATION  IN  TABLE  X.,  AFTER  THE  YEARS 

FOLLOWING  1854.  1855    1856,  AND  1857. 


1854 

1858 

1862 

1866 

1870 

1874 

1878 

1855 

1859 

1863 

1867 

1871 

1875 

1879 

1856 

1860 

1864 

1868 

1872 

1876 

1880 

1857 

1861 

1865 

1869 

1873 

1877 

1881 

SUB. 

SUB. 

SUB. 

SUB. 

SUB. 

SUB. 

1 

/ 

1 

t 

/ 

/ 

January  i 

0.1 

0-3 

0-4 

0-6 

0-7 

0-9 

10 

0.2 

0.5 

0-8 

1-0 

1-3 

1-6 

20 

0.4 

0-7 

1-1 

1-4 

1-8 

2-2 

30 

0.5 

1-0 

1-5 

2-0 

2-5 

3-0 

Feb'rt 

10 

0-6 

1-1 

1-6 

2-2 

2-8 

3-4 

20 

0-6 

1-2 

1-9 

2-5 

3-1 

3-7 

28 

0-7 

1-3 

2-0 

2-6 

3-3 

4-0 

March 

10 

0-7 

1-4 

2-1 

2-8 

3-5 

4-2 

20 

0-7 

1-4 

2-1 

2-8 

3-6 

4-3 

ADD. 

ADD. 

ADD. 

ADD. 

ADD. 

ADD. 

30 

0-7 

1-4 

2-1 

2-8 

3-5 

4-2 

April 

10 

0-7 

1-4 

2-1 

2-7 

3-4 

4-1 

20 

0-6 

1-3 

1-9 

2-5 

3-2 

3-9 

30 

0-6 

1-1 

1-7 

2-3 

2-8 

3-4 

Mat 

10 

0-5 

0-9 

1-5 

2-0 

2-5 

3-0 

20 

0-4 

0-8 

1-2 

1-6 

1-9 

2-3 

30 

0-3 

0-5 

0-8 

1-0 

1-4 

1-7 

June: 

10 

0-2 

0-3 

0-4 

0-5 

0-7 

0-9 

20 

0-0 

0-0 

0-1 

0-1 

0-1 

0-1 

SUB. 

SUB. 

SUB. 

SUB. 

SUB. 

SUB. 

30 

0-1 

0-3 

0-4 

0-6 

0-7 

0-8 

1854 
1855 
1856 
1857 


June 
July 


30 
10 
20 
30 


August  10 
20 
30 


Skpt.   10 
20 

30 


Oct. 

10 

0-7 

20 

0-6 

30 

0-5 

Nov. 

10 

0-5 

20 

0-4 

30 

0-2 

1 

Dec. 


10 
20 

30 


1858 
1859 
1860 
1861 


SUB. 

0-1 
0-2 
0-4 
0-5 


0-5 
0-6 
0-7 


0-7 
0-7 

ADD. 

0-7 


0-2 
0-0 

SUb. 

0-1 


1862 
1863 
1864 

1865 


SUB. 
I 

0-3 
0-5 
0-7 
1-0 


1-1 
1-3 
1-4 


1-4 
1-4 

ADD. 

1-4 


1-4 
1-3 
1-1 


1-0 
0-8 
0-5 


0-3 
0-0 

SUB, 

0-3 


1866 
1867 
1868 
1869 


SUB. 

/ 

0-4 
0-8 
1-1 
1-5 


1870 
1871 
1872 
1873 


1-7 
1-9 
2-0 


2-1 
2-1 

ADD. 

2-1 


2-0 
1-9 
1-6 


1-4 
1-2 
0-7 


0-4 
0-1 

SUB. 
0-4 


SUB. 
/ 

0-6 
1-0 
1-4 
2-0 


2-3 
2-5 

2-7 


2-8 
2-9 

ADD. 

2-8 


2-7 
2-5 

2-2 


1-9 
1-5 
I'C 


0-6 
0-1 

SUB. 

0-6 


1874 
1875 
1876 
1877 


SUB. 
/ 

0-7 
1-3 
1-8 
2-5 


2-8 
3-2 
3-4 


1878 
1879 
1880 
1881 


SUB. 

0-8 
1-6 
2-2 
3-0 


3-4 

3-9 
4-1 


3-5      4-2 
3-6      4-3 

ADD.  >    ADD. 

3-5  I  4-2 


3-4 
3-2 

2-8 


4-1 
3-9 
3-4 


2-4 
2-0 
1-3 


2-8 
2-5 
1-6 


0 

7 

0 

2 

SUB.  1 

0 

7  1 

0-8 
0-3 

SUB. 

0-9 


To  apply  the  Correction  in  Table  XII  Rednca  the  proposed  year  by  Subtracting  any  number  of  Fouri  until  it  corresponds 
to  one  of  the  years  for  -which  the  Beclination  is  given  in  Table  X.,  and  take  out  the  Declination  for  that  year  against  the  day 
of  the  month,  and  take  out  the  Correction  from  Table  XII.,  found  opposite  the  «ame  day  of  the  month,  and  under  the  pro 
poaed  year,  vrhich  is  expressed  In  minutes  Hnd  tenths  ;  if  the  tenths  are  more  than  5  increase  the  minutes  by  1,  but  if  less, 
throw  them  away.  This  applied  as  directed  in  the  above  Table,  (add  or  subtract)  to  or  from  the  Declination  taken  from 
Table  X.,  will  give  tne  correct  Decimation  for  the  proposed  year  until  the  year  ISfll.  


74 

TABLE  XIII.— SUN'S  RIGHT  ASCENSION.                                | 

BAYS. 

JAN. 

FEB. 

MARCH. 

APRIL. 

MAY. 

JUNE. 

JULY. 

AUGUST. 

SEPT. 

OCT. 

NOV. 

DEC. 

H.       M 

H.       M. 

H.       M. 

H.    M. 

H.    M. 

H.    M. 

H.    M. 

H.    M. 

U.       H. 

H.       M 

H.       M. 

B.       M. 

1 

18.47 

20.59 

22.49 

0.42 

2.33 

4.36 

6.40 

8.45 

10.41 

12. 2£ 

1    14.25 

16.29 

2 

18.52 

21     3 

22.52 

0.46 

2.37 

4.40 

6.44 

8.49 

10.45 

12.33|   14.29 

16.34 

3 

18.56 

21.   « 

22.56 

0.49 

2.41 

4.44 

6.49 

8.53 

10.48 

12.3^ 

1  14.33 

16.38 

4 

19.   C 

1   21.12 

23.   0 

0.53 

2.45 

4.48 

6.53 

8.57 

10.52 

12.40    14.37 

16.42 

5 

19.   £ 

21.16 

23.   3 

0.57 

2.49 

4.52 

6.57 

9.    1 

10.56 

12.44    14.41 

16.47 

6 

19.   fl 

21.20 

23.    7 

1.    0 

2.53 

4.57 

7.    1 

9.   4 

10.59 

12.47    14.45 

16,51 

7 

19. la 

21.24 

23.11 

1.   4 

2.56 

5.    I 

7.   5 

9.   8 

11.    3 

12.5] 

14.49 

16.55 

8 

19.16 

21.28 

23.15 

1.   8 

3.   0 

5.   5 

7.   9 

9.12 

11.    7 

12.55    14.53 

17.   0 

9 

19.22 

21.32 

23.18 

1.11 

3.   4 

5.   9 

7.13 

9.16 

11.10 

12.58    14.57 

17.    4 

10 

19.27 

21.36 

23.22 

1.15 

3.   8 

5.13 

7.17 

9.20 

11.14 

13.    2    15.    1 

17.   9 

11 

19.3] 

21.39 

23.26 

1.19 

3.12 

5.17 

7.21 

9.23 

11.17 

13.    6    15.    5 

17.13 

12 

19.35 

21.43 

23.29 

1.22 

3.16 

5.21 

7.25 

9.27 

11.21 

13.    9    15.    9 

17.17 

13 

19.40 

21.47 

23.33 

1.26 

3.20 

5.26 

7.30 

9.31 

11.24 

13.13    15.13 

17.22 

14 

19.44 

21.51 

23.37 

1.30 

3.24 

5.30 

7.34 

9.35 

11.28 

13.17    15.18 

17.26 

15 

19.48 

21.55 

23.40 

1.33 

3.28 

5.34 

7.38 

9.39 

11.32 

13.2] 

I    15.22 

17.31 

16 

19.52 

21.59 

23.44 

1.37 

3.32 

5.38 

7.42 

9.42 

11.35 

13.24    15.26 

17.35 

17 

19.57 

22.   3 

23.48 

1.41 

3.36 

5.42 

7.46 

9.46 

11.39 

13.28    15.30 

17.39 

18 

20.    1 

22.   7 

23.51 

1.44 

3.40 

5.46 

7.50 

9.50 

11.42 

13.32    15.34 

17.44 

19 

20.   5 

22.11 

23.55 

1.48 

3.43 

5.50 

7.54 

9.53 

11.46 

13.36    15.38 

17.48 

20 

20.10 

22.14 

23.58 

1.52 

3.47 

5.55 

7.58 

9.57 

11.50 

13.39    15.42 

17.53 

21 

20.14 

22.18 

0.    2 

1.56 

8.51 

5.59 

8.    2 

10.    1 

11.53 

13.43    15.47 

17.57 

22 

20.18 

22.22 

0.    6 

1.59 

3.55 

6.   3 

8.    6 

10.   5 

11.57 

13.47    15.51 

18.   2 

23 

20.22 

22.26 

0.   9 

2.    3 

4.   0 

6.    7 

8.10 

10.   8 

12.   0 

13.51    15.55 

18.   6 

24 

20.26 

22.30 

0.13 

2.    7 

4.   4 

6.11 

8.14 

10.12 

12.   4 

13.55    15.59 

18.11 

25 

20.31 

22.33 

0.17 

2.11 

4.   8 

6.15 

8.18 

10.16 

12.   8 

13.58    16.    4 

18.15 

26 

20.35 

22.37 

0.20 

2.14 

4.12 

6.20 

8.22 

10.19 

12.11 

14.    2    16.    8 

18.19 

27 

20.39 

22.41 

0.24 

2.18 

4.16 

6.24 

8.26 

10.23 

12.15 

14.    ( 

3    16.12 

18.24 

28 

20.43 

22.45 

0.28 

2.22 

4.20 

6.28 

8.30    10.27 

12.18 

14.10    16.16 

18.28 

29 

20.47 

0.31 

2.26 

4.24 

6.32 

8.33    10.30 

12.22 

14.14    16.21 

18.33 

30 

20.51 

0.35 

2.30 

4.28 

6.36 

8.37    10.34 

12.26 

14.18    16.25 

18.37 

31 

20. 5i 

0.38 

4.32 

8.41    10.38 

14.22 

18.42 

The  Rigl 

It  Ascension  given 

in  this  Table  Is  for 
lere  accuracy  is  rec 

he  year  18.54,  and  will  answer  approximately  for  several  years  afterwards,  but 
uired.  it  must  be  biken  from  the  Nautical  Almanac. 

, 

EaUATTC 

)N  OF  TIME  FOI 

I  APPARENT  NC 
NEA 

TA 

>0N  AT 
RLY  FC 

BLE   XIV. 

GREENWICH,  FOR  THE 
)R  1858,  1862,  AND  1866. 

YEAR  1854,  AND  WILL  ANSWER 

V 

DAYS. 

JAN. 

FEB. 

MAR. 

APRIL. 

MAY. 

JUNE. 

JULY. 

AUO. 

SEPT. 

OCT. 

NOV. 

DECEMBER. 

ADD 

ADD 

i 

ItD 

SUB. 

ADD 

ADD 

SUB. 

SUB. 

SUB. 

K         S.  I 

«.        S. 

M. 

s. 

M.        S. 

H.        M. 

M.        S. 

M.        S. 

M.        S 

M.        S. 

M.        S.  1 

I.        3. 

H.        8. 

1 

3.51 

13.55 

12 

.37 

ADD. 

4.    0 

3.    1 

SUB. 

2.32 

3.26 

6.     3 

0.    5 

10.171 

6.16 

SUB. 

10.47 

2 

4.20 

14.   2 

12 

.25 

3.42 

3.    9 

2.23 

3.38 

6.    0 

0.24 

10.361 

6.18 

10.25 

■ 

3 

4.48 

14.   9 

12 

.12 

3.24 

3.16 

2.13 

3.49 

5.55 

0.43 

10.541 

6.18 

10.    1 

4 

5.15 

14.15 

11 

.59 

3.   6 

3.22 

2.   4 

4.00 

5.50 

1.    2 

11.131 

6.17 

9.37 

5 

5.42 

14.20 

11 

.46 

2.48 

3.28 

1.53 

4.11 

5.45 

1.22 

11.31  1 

6.16 

9.12 

6 

6.   9 

14.24 

11 

.32 

2.31 

3.33 

1.43 

4.21 

5.38 

1.42 

11.491 

6.14 

8.47 

7 

6.35 

14.27 

11 

.17 

2.13 

3.37 

1.32 

4.31 

5.32 

2.    2 

12.   61 

6.11 

8.22 

8 

7.    1 

14.30 

11 

.    2 

1.56 

3.42 

?.21 

4.40 

5.24 

2.23 

12.231 

6.   7 

7.55 

9 

7.26 

14.31 

IC 

.47 

1.39 

3.45 

1.10 

4.50 

5.16 

2.43 

12.391 

6.   2 

7.29 

10 

7.50 

14.32 

IC 

►  .32 

1.22 

3.48 

t>  .o» 

4.58 

5.   8 

3.   4 

12.551 

5.57 

7.   2 

11 

8.14 

14.33 

IC 

(.16 

1.    6 

3.51 

0.46 

5.   7 

4.59 

3.25 

13.11  1 

5.50 

6.34 

12 

8.38 

14.32 

c 

1.59 

0.50 

3.52 

0.34 

5.14 

4.49 

3.45 

13.261 

5.43 

6.   6 

13 

9.   0 

14.31 

c 

1.43 

0.34 

3.54 

0.22 

5.22 

4.39 

4.   6 

13.401 

5.35 

5.38 

14 

9.22 

14.29 

c 

(.26 

0.18 

3.54 

0.10 

5.29 

4.28 

4.27 

13.541 

5.25 

5.   9 

15 

9.44 

14.26 

c 

>.    9 

0.    3 

3.54 

ADD. 

0.   3 

5.35 

4.17 

4.50 

14.   81 

5.16 

4.40 

16 

10.    5 

14.22 

i 

5.51 

SOB. 

0.12 

3.53 

0.16 

5.41 

4.   5 

5.10 

14.211 

5.   5 

4.11 

17 

10.25 

14.18 

i 

5.34 

0.26 

3.51 

0.28 

».5.47 

3.53 

5.31 

14.331 

4.53 

3.41 

18 

10.44 

14.13 

{ 

}.16 

0.40 

3.49 

0.41 

5.52 

3. 40 

5.52 

14.441 

4.41 

3.11 

19 

11.    2 

14.    7 

^58 

0.54 

3.46 

0.54 

5.56 

3.27 

6.13 

14.551 

4.27 

2.42 

20 

11.20 

14.    1 

^4o 

1.    7 

3.43 

1.    7 

6.    0 

3.13 

6.34 

15     61 

4.13 

2.12 

21 

11.38 

13.54 

r.22 

1.20 

3   39 

1.20 

6.    4 

2.59 

6.55 

15.151 

3.58 

1.42 

22 

11.54 

13.46 

r.  4 

1.32 

3.34 

1.34 

6.    7 

2.44 

7.16 

15.251 

3.42 

1.12 

23 

12.10 

13.38 

( 

5.45 

1.44 

3.29 

1.47 

6.   9 

2.29 

7  36 

15.331 

3.26 

0.41 

24 

12.24 

13.29 

t 

).27 

1.56 

3.24 

2.   0 

6.11 

2.14 

7  57 

15.411 

3.   9 

0.11 

25 

12.39 

13.20 

( 

5.    8 

2.    7 

3.18 

2.12 

6.12 

1.58 

8.18 

15.481 

2.51 

ADD. 

0.19 

26 

12.52 

13.10 

( 
I 

5.50 

2.17 

3.11 

2.25 

6.12 

1.41 

8.38 

15.541 

2.32 

0.49 

27 

13.    4 

13.    0 

; 

t. 

5.32 

2.27 

3.    4 

2.38 

6.12 

1.25 

8.58 

16.   01 

2.12 

1.18 

28 

13.16 

12.49 

». 

5.13 

2.36 

2.57 

2.50 

6.12 

1.   8 

9.18 

16.    41 

1.52 

1.4S 

29 

13.27 

/ 

1.55 

2.45 

2.49 

3.    3 

6.11 

0.50 

9.38 

16.    91 

1.31 

2.17 

30 

13.37 

^ 

1.36 

2.54 

2.41 

3.15 

6.   9 

0.32 

9.57 

16.121 

1.10 

2.46 

31 

13.46 

4.18 

6.    6 

0.14 

16.15 

3.15 

r 

TABLE  XIV. 

78  • 

|k(1UATI0N  of  time  for  AlPARENT  NOON  A.T  GREENWICH,  FOR 

THE 

YEAR  1855,  AND  WILL  ANSWER 

NEARLY  FOR   1859,  laGi,  AND   1867. 

DATS. 

JAN. 

FEB. 

HAS. 

APRIL.        1 

MAY. 

JUNK. 

JULY. 

AUO. 

SEPT. 

OCT. 

NOV. 

DECBMBRB.    | 

ADD 

ADD 

ADD 

BUB. 

ADD 

ADD 

SUB. 

SUB. 

SUB. 

SI.        8. 

M.        S. 

M.        8. 

M.        8. 

M.        8. 

H.        8. 

U.        S. 

M.        8. 

M.        8. 

M.        S. 

M.        S. 

M.        8. 

1 

3.44 

13.52 

12.40 

ADD. 

4.   4 

2.59 

SUB. 

2.34 

3.23 

6.     3 

0.     0 

10.12 

16.15 

SUB. 

10.52 

2 

4.12 

14.     0 

12.28 

3.46 

3.    7 

2.25 

3.34 

6.     0 

0.19 

10.31 

16.17 

10.30 

3 

4.40 

14.    7 

12.15 

3.28 

3.14 

2.16 

3.46 

5.56 

0.38 

10.49 

16.17 

10.   6 

4 

5.   8 

14.13 

12.    2 

3.11 

3.20 

2.   6 

3.57 

5.51 

0.57 

11.   8 

16.17 

9.42 

5 

5.35 

14.18 

11.49 

2.53 

3.26 

1.56 

4.   8 

5.46 

1.17 

11.26 

16.16 

9.18 

6 

6.    2 

14.23 

11.35 

2.35 

3.31 

1.46 

4.18 

5.40 

1.37 

11.44 

16.14 

8.53 

7 

6.28 

14.26 

11.21 

2.18 

3.36 

1.3S 

4.28 

5.33 

1.57 

12.    1 

16.11 

8.27 

8 

6.54 

14.29 

11.    6 

2.    1 

3.40 

1.24 

4.38 

5.26 

2.17 

12.18 

16.   7 

8.    1 

9 

7.20 

14.31 

10.51 

1.44 

3.44 

1.13 

4.47 

5.18 

2.38 

12.35 

16.   3 

7.35 

10 

7.44 

14.32 

10.36 

1.27 

3.47 

1.    1 

4.56 

5.10 

2.58 

12.51 

15.57 

7.   8 

11 

8.   8 

14.33 

10.20 

1.10 

3.49 

0.49 

5.   4 

5.    1 

3.19 

13.   6 

15.51 

6.40 

12 

8.32 

14.32 

10.   4 

0.54 

3.51 

0.37 

5.12 

4.51 

3.40 

13.21 

15.44 

6.12 

13 

8.55 

14.31 

9.47 

0.38 

3.53 

0.25 

5.20 

4.41 

4.    1 

13.36 

15.36 

5.44 

14 

9.17 

14.29 

9.30 

0.23 

3.54 

0.13 

5.27 

4.30 

4.22 

13.50 

15.27 

5.16 

15 

9.38 

14.26 

9.13 

0.    7 

3.54 

0.   0 

5.33 

4.19 

4.43 

14.    4 

15.18 

4.47 

16 

9.59 

14.23 

8.56 

SOB. 

0.    8 

3.54 

ADD. 

0.12 

5.39 

4.   8 

5.   4 

14.17 

15.    7 

4.18 

17 

10.20 

14.19 

8.39 

0.22 

3.53 

0.25 

5.45 

3.55 

5.26 

14.29 

14.56 

3.48 

18 

10.39 

14.14 

8.21 

0.36 

3.51 

0.38 

5.50 

3.43 

5.47 

14.41 

14.44 

3.19 

19 

10.58 

14.    9 

8.   3 

0.50 

3.49 

0.51 

5.54 

3.30 

6.   8 

14.52 

14.30 

2.49 

20 

11.16 

14.    2 

7.45 

1.   4 

8.47 

1.   4 

5.59 

3.16 

6.29 

15.    3 

14.17 

2.19 

21 

11.33 

13.56 

7.27 

1.16 

3  44 

1.17 

6.    2 

3.   2 

6.50 

15.13 

14.    2 

1.49 

22 

11.50 

13.48 

7.   8 

1.29 

3.40 

1.30 

6.    5 

2.47 

7.11 

15.22 

13.46 

1.19 

23 

12.   5 

13.40 

6.50 

1.41 

3.36 

1.43 

6.    7 

2.32 

7.31 

15.31 

13.30 

0.49 

24 

12.20 

13.31 

6.32 

1.53 

3.31 

1.56 

6.   9 

2.17 

7.52 

15.39 

13.13 

0.19 

25 

12.35 

13.22 

6.13 

2.   4 

3.25 

2.   8 

6.11 

2.    1 

8.12 

15.46 

12.55 

XDD. 

0.11 

26 

12.48 

13. 12 

5.55 

2.14 

3.20 

2.21 

6.11 

1.45 

8.33 

15.52 

12.36 

0.41 

27 

13.    1 

13.    2 

5.36 

2.24 

3.13 

2.34 

6.12 

1.28 

8.53 

15.58 

12.17 

1.11 

28 

13.13 

12.51 

5.18 

2.34 

3.    6 

2.46 

6.11 

1.11 

9.13 

16.   3 

11.57 

1.41 

29 

13.24 

4.59 

2.43 

2.59 

2.59 

6.10 

0.54 

9.33 

16.   7 

11.36 

2.10 

30 

13.34 

4.41 

2.51 

2.51 

3.11 

6.   8 

0.36 

9.52 

16.11 

11.14 

2.40 

31 

13.43 

4.23 

2.43 

6.    6 

0.18 

16.13 

3.   9 

EQUATI 

3N  OF  TIME  FOR  THE  YEAR  18^ 

•6,  AND  WHICH  WILL  AN£ 

5WER 

NEARLY  FOR  1860,  1864,  AND  1868.  | 

DAV8. 

JAN. 

FEB. 

MAR.            APRIL 

MAY. 

JUNE. 

JULY. 

Aua. 

SEPT. 

OCT. 

NOV. 

DECEMBER.    | 

ADD. 

ADD 

ADD 

SUB. 

ADD. 

ADD. 

SUB. 

SUB» 

SUB. 

M.        8. 

M.        S. 

M.        S. 

M.        8. 

M.        S. 

M.        8. 

H.        6. 

M.        S. 

M.        S. 

M.        S. 

H.        6. 

H.        8. 

1 

3-36 

13-50 

12-31 

ADD. 

3-51 

3-   5 

SUB. 

2-28 

3 

31 

6-    0 

0-14 

10-25 

16-16 

SUB. 

10-36 

2 

4-    4 

13-58 

12-19 

3-33 

3-12 

2-19 

3 

42 

5-56 

0-33 

10-44 

16-17 

30-13 

3 

4-33 

14-   5 

12-    6 

3-16 

3-19 

2-    9 

3 

53 

5-52 

0-52 

11-    3 

16-17 

9-49 

4 

5-    0 

14-11 

11-53 

2-58 

3-25 

1-59 

4 

4 

5-47 

1-12 

11-21 

16-16 

9-24 

5 

5-28 

14-17 

11-39 

2-40 

3-30 

1-49 

4 

15 

5-41 

1-31 

11-28 

16-14 

8-59 

6 

5-55 

14-22 

11-25 

2-23 

3-35 

1-38 

4 

25 

5-35 

1-51 

11-56 

16-11 

8-34 

7 

6-21 

14-26 

11-11 

2-    6 

3-39 

1-27 

4 

•35 

5-28 

2-11 

12-13 

16-   8 

8-   8 

8 

6-47 

14-29 

10-56 

1-49 

3-43 

1-16 

4 

44 

5-20 

2-32 

12-30 

16-   4 

7-42 

9 

7-13 

14-31 

10-40 

1-32 

3-46 

1-   4 

4 

53 

5-12 

2-52 

12-46 

15-58 

7-15 

10 

7-38 

14-33 

10-25 

1-15 

3-49 

0-53 

5 

2 

5-    3 

3-13 

13-    2 

15-52 

6-47 

11 

8-    2 

14-33 

10-   9 

0-59 

3-51 

0-41 

5 

10 

4-54 

3-34 

13-17 

15-46 

6-20 

12 

8-26 

14-33 

9-52 

0-43 

3-52 

0-29 

5 

17 

4-44 

3-55 

13-32 

15-38 

5-52 

13 

8-49 

14-32 

9-36 

0-27 

3-53 

0-16 

5 

25 

4-34 

4-16 

13-46 

15-30 

5-23 

14 

9-11 

14-31 

9-19 

0-12 

3-54 

0-   4 

5 

31 

4-23 

4-37 

14-    0 

15-20 

4-55 

15 

9-33 

14-28 

9-   2 

SUB. 

0-    3 

3-54 

ADD. 

0-    9 

5 

38 

4-11 

4-58 

14-13 

15-10 

4-26 

16 

9-54 

14-25 

8-44 

0-18 

3-53 

0-21 

5 

43 

3-59 

5-19 

14-26 

14-59 

3-56 

17 

10-15 

14-21 

8-26 

0-32 

3-52 

0-34 

5 

48 

3-46 

5-41 

14-38 

14-47 

3-27 

18 

10-34 

14-16 

8-   9 

0-46 

3-50 

0-47 

5 

53 

3-33 

6-    2 

14-49 

14-34 

2-57 

19 

10-53 

14-11 

7-51 

0-59 

3-47 

1-    0 

5 

57 

3-20 

6-23 

15-    0 

14-21 

2-517 

20 

11-12 

14-   5 

7-32 

1-13 

3-45 

113 

6 

1 

3-    6 

6-44 

15-10 

14-    6 

1-67 

21 

11-29 

13-58 

7-14 

1-25 

3-41 

1-26 

6 

4 

2-51 

7-    5 

15-20 

13-51 

1-27 

22 

11-46 

13-51 

6-56 

1-38 

3-37 

1-39 

6 

6 

2-36 

7-26 

15-29 

13-35 

0-57 

23 

12-    2 

13-43 

6-37 

1-49 

3-32 

1-52 

6 

8 

2-21 

7-46 

15-37 

13-18 

0-27 

24 

12-17 

13-35 

6-19 

2-    1 

3-27 

2-   4 

6 

10 

2-    5 

8-   7 

15-44 

13-   0 

ADD. 

0.   3 

25 

12-31 

13-25 

6-    0 

2-11 

3-22 

2-17 

6 

11 

1-49 

8-27 

15-51 

12-42 

0-33 

26 

12-45 

13-16 

5-42 

2-22 

3-15 

2-30 

6 

It 

1-33 

8-48 

15-57 

12-22 

1-    3 

27 

12-58 

13-    5 

5-23 

2-31 

3-   9 

2-42 

6 

11 

1-16 

9-   8 

16-    2 

12-    2 

1-33 

28 

13-10 

12-55 

5-    5 

2-41 

3-    2 

2-55 

6 

10 

0-58 

9-27 

16     6 

11  -42 

2-    2 

29 

13-21 

14-43 

4-46 

2-49 

2-54 

3-    7 

6 

8 

0-41 

9-47 

16   10 

11-20 

2-32 

30 

13-31 

4-28 

2-67 

2-46 

3-19 

6 

6 

0-23 

10-   6 

16-13 

10-68 

3-   1 

31 

13-41 

4-10 

1  2-37 

1 

6 

4 

0.    5 

16-15 

3-29 

74  •                                                  TABLE  XIV. 

B<lUATION  OF  TIMB  FOR  APPARENT  NOON  AT  GREENWICH,  FOR  THE  YEAR  1857,  AND  WILL  ANSWER! 

NEARLY  FOR  1861,  1865,  AND  1869.                                                                            1 

DATI. 

JAM. 

FSB. 

MAB. 

APBIL.       1 

MAY. 

JUNE. 

JULY. 

ADO. 

8BPT. 

OCT. 

NOV. 

DECEMBER.     | 

ADD 

ADD 

ADD 

BUB. 

ADD 

ADD 

SOB. 

SUB. 

SUB. 

U.        S. 

M.        B. 

M.        B. 

M.        S. 

M.        8. 

M.        8 

M.        8. 

M.        8. 

w.      s. 

M.        B. 

M.        8. 

M.        8. 

1 

3.58 

13.56 

12.35 

ADD. 

3.56 

3.   3 

SUB. 

2.31 

3.27 

6.     1 

0.10 

]0.21 

16.16 

SUB. 

10.41 

a 

4.26 

14.   4 

12.22 

3.38 

3.11 

2.22 

3.39 

5.57 

0.29 

10.39 

16.17 

10.18 

3 

4.54 

14.10 

12.10 

3.20 

3.17 

2.13 

3.50 

5.52 

0.48 

10.58 

16.17 

9.54 

4 

5.21 

14.16 

11.56 

3.   2 

3.24 

2.   3 

4.    1 

5.47 

1.    7 

11.16 

16.16 

9.30 

5 

5.48 

14.20 

11.43 

2.44 

3.29 

1.53 

4.11 

5.42 

1.27 

11.34 

16.14 

9.   5 

6 

6.15 

14.24 

11.28 

2.26 

3.35 

1.42 

4.21 

5.35 

1.47 

11.52 

16.12 

8.40 

7 

6.41 

14.27 

11.14 

2.   9 

3.39 

1.31 

4.31 

5.28 

2.    7 

12.    9 

16.    8 

8.14 

8 

7.   6 

14.30 

10.59 

1.52 

3.43 

1.20 

4.40 

5.21 

2.28 

12.26 

16.    4 

7.48 

9 

7.31 

14.31 

10.43 

1.35 

3.47 

1.    9 

4.49 

5.13 

2.48 

12.42 

15.59 

7.21 

10 

7.55 

14.32 

10.28 

1.18 

3.50 

0.57 

4.58 

5.   4 

3.   9 

12.58 

15.53 

6.53 

11 

8.19 

14.32 

10.12 

1.   2 

3.52 

0.45 

5.    6 

4.55 

3.29 

13.13 

15.47 

6.26 

12 

8.42 

14.31 

9.55 

0.46 

3.54 

0.33 

5.14 

4.46 

3.50 

13.28 

15.39 

5.58 

13 

9.    5 

14.30 

9.39 

0.30 

3.55 

0.21 

5.22 

4.35 

4.11 

13.42 

15.31 

5.29 

14 

9.27 

14.28 

9.22 

0.15 

3.55 

0.    8 

5.28 

4.25 

4.32 

13.56 

15.21 

5.   0 

15 

9.48 

14.25 

9.   5 

SUB. 

0.    1 

3.55 

ADD. 

0.    4 

5.35 

4.13 

4.53 

14.    9 

15.11 

4.31 

16 

10.   9 

14.21 

8.47 

0.15 

3.54 

0.17 

5.41 

4.    2 

5.14 

14.22 

15.    0 

4.    2 

17 

10.29 

14.17 

8.30 

0.30 

3.53 

O.30 

5.46 

3.49 

5.35 

14.34 

14.48 

3.32 

18 

10.48 

14.12 

8.12 

0.43 

3.51 

0.43 

5.51 

3.37 

5.56 

14.45 

14.35 

3.   3 

19 

11.   6 

14.    6 

7.54 

0.57 

3.49 

o.5e 

5.56 

3.23 

6.17 

14.56 

14.22 

2.33 

20 

11.24 

14.   0 

7.36 

1.10 

3.46 

1.   S 

6.   0 

3.10 

6.38 

15.    6 

14.   8 

2.   3 

21 

11.41 

13.53 

7.18 

1.23 

3  42 

1.22 

6.   3 

2.55 

6.59 

15.16 

13.53 

1.33 

22 

11.58 

13.45 

7.   0 

1.35 

3.38 

1.3t 

1    6.    6 

2.41 

7.20 

15.25 

13.37 

1.   3 

23 

12.13 

13.37 

6.42 

.   47 

3.34 

1.46 

!    6.   8 

2.25 

7.40 

15.33 

13.20 

0.33 

24 

12.28 

13.28 

6.23 

1.58 

3.29 

2.    1 

6.10 

2.10 

8.    1 

15.41 

13.   3 

0.   3 

25 

12.42 

13.18 

6.    5 

2.    9 

3.23 

2.14 

I    6.11 

1.54 

8.21 

15.48 

12.45 

ADD. 

0.27 

26 

12.55 

13.    8 

5.46 

2.19 

3.17 

2.27 

6.11 

1.37 

8.42 

15.54 

12.26 

0.57 

27 

13.   7 

12.58 

5.28 

2.29 

3.10 

2.3£ 

»    6.11 

1.20 

9.    2 

15.59 

12.   6 

1.26 

23 

13.19 

12.46 

5.10 

2.38 

3.   3 

2.5S 

!    6.10 

1.    3 

9.22 

16.    4 

11.46 

1.56 

29 

13.29 

4.51 

2.47 

2.56 

3.   4 

I    6.   9 

0.45 

9.42 

16.    g 

11.25 

2.25 

30 

13.39 

4.33 

2.55 

2.48 

3.16 

.    6.   7 

0.27 

10.    1 

16.11 

11.   3 

2.54 

31 

13.48 

4.14 

2.40 

6.   4 

0.   9 

16.14 

3.23 

TA 

BLE  FOR  CORRECTING  THE  EQUATIO 

LONGITU 

N  OF  TIME  TAKEN  FROM  THE  ABOVE  TABLE  FOR 
DE  AND  FOR  TIME. 

LONO. 

DAILY    CHAN( 

3R    OF 

THE    EQUATION. 

TIME 
FROM 

8. 

8. 

s. 

8. 

8. 

8. 

8. 

8. 

s. 

8. 

8. 

8. 

8. 

s. 

8. 

0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

-• 

NOON. 

Oo 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

H.     M. 

0       0 

8. 

8. 

8. 

8. 

s. 

8. 

8. 

8. 

8. 

8. 

8. 

8. 

s. 

s. 

8. 

10 

0 

0-1 

0-1 

0-2 

0 

•2 

0- 

3    0 

3 

0 

4 

0 

4 

0-5 

0-6 

0- 

6    0-5 

0 

•7 

0 

8 

0 

-8 

0.40 

20 

0 

0-1 

0-2 

0-3 

0 

•4 

0- 

S   0 

7 

0 

8 

0 

9 

1-0 

1-1 

1- 

2    1.5 

1 

4 

1 

5 

1 

-7 

1-20 

30 

0 

0-2 

0-3 

0-5 

0 

•7 

0- 

S    1 

0 

1 

2 

1 

3 

1-5 

1-7 

1- 

8    2-C 

I    2 

2 

2 

3 

2 

•5 

2-    0 

40 

0 

0-2 

0-4 

0-7 

0 

•9 

1- 

1    1 

3 

1 

6 

1 

8 

2-0 

2-2 

2- 

4    2-7 

2 

9 

3 

1 

3 

-3 

2-40 

50 

0 

0-3 

0-6 

0-8 

1 

•1 

1- 

4    1 

7 

1 

9 

2 

2 

2-5 

2-8 

3- 

1    3-S 

3 

6 

3 

9 

4 

•2 

3-20 

60 

0 

0-3 

0-7 

1-0 

1 

•3 

1- 

7    2 

0 

2 

3 

2 

7 

3-0 

3-3 

3- 

7    4C 

1    4 

3 

4 

7 

5 

•0 

4-   0 

70 

0 

0*4 

0-8 

1-2 

1 

•6 

1- 

5    2 

1 

2 

7 

3 

1 

3-5 

3-9 

4- 

3    4-7 

5 

1 

5 

4 

5 

-8 

4-40 

80 

0 

0-4 

0-9 

1-3 

1 

•8 

2- 

2    2 

7 

3 

1 

3 

6 

4  0 

4-4 

4- 

9  5-a 

5 

8 

6 

2 

6 

*7 

5-20 

90 

0 

0*5 

1-0 

1-5 

2 

•0 

2- 

5    3 

0 

3 

5 

4 

0 

4  •> 

5-0 

5- 

5    6'C 

6 

5 

7 

0 

7 

•4 

6-   0 

100 

0 

0-6 

1-1 

1-7 

2 

•2 

2- 

8    3 

3 

3 

9 

4 

4 

5 '  U|  J  •  6 

6- 

I    6-7 

7 

2 

7 

8 

8 

-3 

6-40 

110 

0 

0-6 

1-2 

1-8 

2 

•4 

3- 

1    3 

7 

4 

3 

4 

9 

5-5 

6-1 

6- 

7    7-3 

7 

9 

8 

6 

9 

•2 

7-20 

120 

0 

0-7 

1-3 

2-0 

O 

-J 

•7 

3- 

3    4 

0 

4 

7 

5 

3 

6-0 

6-7 

7  • 

3    8-C 

8 

7 

9 

3 

10 

-0 

8-   0 

130 

0 

0-7 

1-4 

2-2 

2 

•9 

3- 

6    4 

3 

5 

1 

5 

8 

6-5 

7-2 

7- 

9    8-7 

9 

4 

10 

1 

lu 

•8 

8-40 

140 

0 

0-8 

1-6 

2-3 

3 

•1 

3- 

9    4 

7 

5 

4 

6 

2 

7-0 

7-8 

8- 

6    9-3 

10 

1 

10 

9 

11 

•7 

9-20 

150 

0 

0-8 

1-7 

2-5 

3 

•3 

4- 

2   5 

0 

5 

8 

8 

>7 

7-5   8-2 

9- 

210-C 

10 

8 

11 

7 

12 

-5 

10-    0 

160 

0 

0-9 

1-8 

2-7 

3 

•6 

4- 

4    5 

3 

6 

2 

7 

1 

8-0 

8-9 

9- 

810-7 

11 

6 

12 

4 

13 

-3 

10-40 

170 

0 

0-9 

1-9 

2-8 

3 

•8 

4- 

7    5 

7 

6 

6 

7 

6 

8-5 

9-4 

10. 

411-3 

12 

3 

13 

2 

14 

-2 

11-20 

180 

0 

1-0 

2-0 

3-0 

4-0 

5- 

0    6-0 

7-0 

8-0| 

9-0 

10-0 

11- 

012-C 

13-01 

14 

0 

15-0 

12-    0 

IN    WEST    LONGITUDE. 

IN    EAST    LONGITUDE 

1 

Wh 

..     t'          •     S  Increasing  Add. 
en  the  Equa.  is  {  decreasing,  Subtract. 

m.„  .he  Equ..  i.    {  ",3™^- ^;,t-'-          1 

TIME    BEFORE    NOON. 

TIME    AFTERNOON. 

"Wl 

.,     r,          .     <  Increasinsf,  Subtract. 
en  the  Equa.  is  j  j)^„^^i^^^  Add. 

WhentheEqua.i8    5  Increasing,  Add                     1 
^              (  Decreasing,  bublract.            1 

76 


TABLE 

XV.- 

-Part 

First. 

LOGARITHM  OF  THE  SUN'S 

HOUR  ANCfLE, 

OR  THE  TIME  FROM  NOOW 

EXTENDING  TO  64' 

30". 

a     8 

13    4) 

Log. 

cc   ad 

1  s 

Log. 

CD    03 

1  § 

a  u 

Log. 

O}    QO 

1  § 

Log. 

00   m 

1  i 

S  03 

Log. 

s  4 
1  § 

.9  " 

3  02 

Log. 

1. 

4.677 

7.40 

6.446 

14.20 

6.990 

21. 

7.322 

30.20 

7.641 

45. 

7.982 

10 

811 

50 

465 

30 

7.000 

10 

328 

40 

650 

30 

992 

20 

927 

8. 

483 

40 

010 

20 

335 

31. 

660 

46. 

8.001 

30 

5.030 

10 

501 

50 

019 

30 

342 

20 

669 

30 

010 

40 

121 

20 

519 

15. 

029 

40 

349 

40 

678 

47. 

020 

50 

2(»4 

30 

536 

10 

039 

50 

355 

32. 

687 

30 

029 

2. 

279 

40 

553 

20 

048 

22. 

362 

20 

696 

48. 

038 

10 

349 

50 

569 

30 

058 

10 

368 

40 

705 

30 

047 

20 

414 

9. 

586 

40 

067 

20 

375 

33. 

714 

49. 

056 

30 

473 

10 

602 

50 

076 

30 

382 

20 

723 

30 

065 

40 

530 

20 

617 

16. 

085 

40 

388 

40 

731 

50. 

074 

50 

582 

30 

633 

10 

094 

50 

394 

34. 

740 

30 

082 

3. 

632 

40 

648 

20 

103 

23. 

400 

20 

748 

51. 

090 

10 

678 

50 

663 

30 

112 

10 

407 

40 

757 

30 

099 

20 

723 

10. 

677 

40 

121 

20 

413 

35. 

765 

52. 

107 

30 

766 

10 

692 

50 

130 

30 

419 

20 

773 

30 

116 

40 

806 

20 

706 

17. 

138 

40 

425 

40 

781 

53. 

124 

50 

845 

30 

720 

10 

147 

50 

431 

36. 

789 

30 

132 

4. 

881 

40 

734 

20 

155 

24. 

438 

20 

797 

54. 

140 

10 

917 

50 

747 

30 

163 

10 

444 

40 

805 

30 

148 

20 

951 

11. 

760 

40 

172 

20 

449 

37. 

813 

55. 

156 

30 

984 

10 

773 

50 

180 

30 

455 

20 

821 

30 

164 

40 

6.015 

20 

786 

18. 

188 

40 

461 

40 

829 

56. 

172 

50 

046 

30 

798 

10 

190 

50 

467 

38.. 

836 

30 

179 

5. 

075 

40 

811 

20 

204 

25. 

473 

20 

844 

57. 

187 

10 

103 

50 

.824 

30 

212 

20 

484 

40 

851 

30 

194 

20 

132 

12. 

836 

40 

219 

40 

496 

39. 

859 

58. 

202 

30 

158 

10 

848 

50 

227 

26. 

507 

20 

866 

30 

209 

40 

182 

20 

860 

19. 

235 

20 

518 

40 

873 

59. 

217 

50 

209 

30 

871 

10 

242 

40 

529 

40. 

881 

30 

224 

6. 

234 

40 

883 

20 

250 

27. 

540 

20 

888 

60. 

231 

10 

258 

50 

894 

30 

257 

20 

550 

40 

895 

30 

238 

20 

281 

13. 

905 

40 

264 

40 

561 

41. 

902 

61. 

246 

30 

303 

10 

916 

50 

272 

28. 

571 

30 

912 

30 

253 

40 

325 

20 

927 

20. 

279 

20 

582 

42. 

923 

62. 

259 

50 

347 

30 

938 

10 

286 

40 

592 

30 

933 

30 

267 

7. 

367 

40 

949 

20 

294 

29. 

602 

43. 

943 

63. 

274 

10 

388 

50 

959 

30 

301 

20 

612 

30 

953 

30 

280 

20 

408 

14. 

969 

40 

308 

40 

622 

44. 

963 

64. 

287 

30 

427 

10 

980 

50 

315 

30. 

631 

30 

973 

30 

294 

• 

76 

TABLE  XV.— Pak.  Second.                  1 

LOGARITHMS^  OF  THE  LATITUDE  AND  DECLINATION  WHEN  THEY  ARE  OF  THE   | 

SAME  NAMK                             | 

DECLINATION. 

Lat. 

o 
0 

0° 

1° 

2° 

3° 

40 

50 

6° 

70 

8° 

90 

10° 

11° 

12° 

Lat. 

1.359 

1.279 

1.212 

1.153 

1.101 

1.055 

1.012 

0.974 

0 
0 

1 

1 

358 

278 

211 

152 

100 

053 

1.011 

1 

2 

!    1 

357 

277 

209 

151 

098 

051 

2 

3 

356 

276 

208 

149  097 

3 

4 

354 

274 

206  147 

4 

5 

1,359 

352 

272 

204 

5 

6 

279 

1.358 

350 

270 

6 

7 

212 

278 

1.357 

1 

348 

7 

8 

153 

211 

277 

1.356 

1 

8 

9 

101 

152 

209 

276 

1.354 

9 

10 

055 

100 

151 

208 

272 

1.352 

10 

11 

1,012 

1.053 

1.0!>8 

1.149 

1.206 

1.272  1.350 

11 

12 

0.974 

Oil 

051 

097 

147 

204 

270 

1.348 

12 

13 

938 

0.972 

009 

051 

094 

145 

201 

267 

1.345 

13 

14 

904 

936 

0.970 

007 

047 

092 

142 

199 

264 

1.342 

14 

15 

873 

902 

934 

0.967 

004 

045 

089 

139 

196 

261 

1.339 

15 

16 

844 

871 

900 

931 

0.965 

00.2 

042 

086 

136 

193 

258 

1.336 

16 

17 

816 

841 

868 

897 

928 

0.962 

0.999 

039 

083 

133 

189 

254 

1.332 

17 

18 

789 

813 

839 

866 

895 

925 

959 

0.995 

035 

080 

129 

185 

250 

18 

19 

764 

787 

811 

836 

863 

891 

922 

956 

0.992 

032 

076 

125 

181 

19 

20 

740 

761 

784 

807 

833 

859 

888 

919 

952 

0.988 

028 

072 

121 

20 

21 

0.717 

0.737 

0.758 

0.781 

0.804 

0.829 

0.856 

0.884 

0.915 

0.948 

0.984 

1.023 

1.067 

21 

22 

695 

714 

734 

755 

777 

801 

825 

852 

880 

911 

944 

0.980 

019 

22 

23 

673 

691 

710 

730 

752 

773 

807 

821 

848 

876 

906 

939 

0.975 

23 

24 

652 

670 

688 

707 

727 

747 

769 

793 

817 

844 

871 

902 

934 

24 

25 

632 

649 

666 

684 

703 

723 

743 

765 

788 

813 

839 

867 

897 

25 

26 

613 

629 

645 

662 

680 

699 

718 

739 

760 

783 

808 

834 

861 

26 

27 

594 

609 

625 

641 

658 

676 

694 

714 

734 

756 

778 

803 

828 

27 

28 

575 

590 

605 

620 

637 

653 

671 

689 

709 

729 

750  i  773 

797 

28 

29 

557 

571 

586 

600 

616 

632 

649 

666 

684 

703 

724 

745 

767 

29 

30 

540 

553 

567 

581 

596 

611 

627 

643 

661 

679 

698 

718 

739 

30 

31 

0.522 

0.535 

0.548 

0.562 

0.576 

0.591 

0.606 

0.622 

0.638 

0.655 

0.673 

0.692 

0.712 

31 

32 

505 

518 

530 

543 

557 

571 

585 

600 

616 

632 

649 

667 

686 

32 

33 

489 

500 

513 

525 

538 

551 

565 

580 

594 

610 

626 

643 

661 

33 

34 

472 

483 

495 

507 

519 

532 

546 

559 

574 

588 

604 

620 

636 

34 

35 

456 

467 

478 

489 

501 

514 

526 

540 

553 

567 

582 

597 

612 

35 

36 

440 

450 

461 

472 

484 

495 

508 

520 

533 

548 

560 

575 

590 

36 

37 

424 

434 

445 

455 

466 

478 

489 

501 

514 

526 

540 

553 

568 

37 

38 

408 

418 

428 

438 

449 

460 

471 

482 

494 

507 

519 

532 

546 

38 

39 

393 

402 

412 

422 

432 

442 

453 

464 

475 

487 

499 

512 

525 

39 

40 

377 

386 

396 

405 

415 

425 

435 

447 

457 

468 

480 

492 

504 

40 

41 

0.362 

0.371 

0.3H0 

0.389 

0.398 

0.408 

0.418 

0.428 

0.438 

0.449 

0.460 

0.472 

0.484 

41 

42 

347 

355 

364 

373 

382 

391 

400 

410 

420 

431 

441 

452 

464 

42 

43 

331 

340 

348 

358 

365 

374 

383 

393 

402 

412 

422 

433 

444 

43 

44 

316 

324 

332 

340 

349 

357 

366 

375 

384 

394 

404 

414 

424 

44 

45 

301 

309 

316 

324 

333 

341 

349 

358 

367 

376 

385 

395 

405 

45 

46 

286 

293 

301 

308 

316 

324 

332 

341 

349 

358 

367 

376 

386 

46 

47 

271 

278 

285 

292 

300 

308 

315 

323 

331 

340 

349 

358 

367 

47 

48 

255 

262 

269 

276 

284 

291 

299 

306 

314 

322 

331 

339 

348 

48 

49 

240 

247 

254 

260 

267 

275 

282 

289 

297 

305 

312 

321 

329 

49 

50 

225 

231 

238 

244 

251 

258 

265 

272 

2^9 

287 

294 

302 

310 

50 

51 

209  0.216 

0.222 

0.228 

0.235 

0.241 

0.248 

0.255 

0.262 

0.269 

0.276 

0.284 

0.291 

51 

52 

194  200 

206 

212 

218 

225 

231 

238  244 

251 

258 

265 

273 

52 

53 

178  184 

190 

196 

202 

208 

214 

220  227 

233 

240 

247 

254 

53 

54 

162  168 

173 

179 

185 

191 

197 

203  209 

215 

222 

228 

235 

54 

55 

146  152 

157 

162 

168 

174 

179 

185   191 

197 

204 

210 

216 

55 

56 

130  135 

140 

146 

151 

156 

162 

168   173 

179 

185 

191 

197 

56 

57 

•114  118 

124 

129 

134 

139 

144 

150 

155 

160 

166 

172 

178 

57 

58 

097  100 

106 

111 

116 

121 

126 

131 

137 

142 

148 

153 

159 

58 

59 

080 

084 

089 

094 

098 

103 

108 

113 

118 

123 

128 

134 

139 

59 

60 

062 

067 

071 

076 

080 

085 

090 

094 

099 

104 

109 

114 

119 

60 

77               TABLE  XV.— Part  Second. 

LOGARITHMS  OF  THE  LATITUDE  AND  DECLINATION  WHEN  THEY  ARE  OF  THE 

SAME  NAMK 

DKCLINATION. 

Lat. 

0 

0 

13° 

14° 

15° 

16° 

170 

18° 

190 

20°  21° 

22° 

230 

24° 

250 

Lat. 

0.938 

0.904 

0.873 

0.844 

0.816 

0.789 

0.764 

0.740 

0.717 

0.695 

0.673 

0.652 

0.632 

0 
0 

I 

1 

972 

936 

902 

871 

841 

813 

787 

761 

737 

714 

691 

660 

649   ll 
666  '  2 1 

' 

2 

1.009 

970 

934 

900 

868 

839 

811 

784 

758 

734 

710 

687 

3 

049 

1.007 

967 

931 

897 

866 

836 

807 

781 

755 

730 

707 

683 

3 

! 

4 

094 

047 

1.004 

965 

928 

895 

863 

832 

804 

777 

751 

726 

703 

4 

5 

145 

092 

045 

1.002 

962 

925 

891 

'  859 

829 

801 

773 

747 

722 

5 

6 

201 

142 

089 

042 

999 

959 

922 

888 

856 

825 

797 

770 

743 

6 

^ 

7 

267 

199 

139 

086 

1.039 

995 

956 

919 

884 

852 

821 

7'93 

765 

7 

8 

345 

264 

196 

136 

083 

1.035 

992 

952 

915 

880 

848 

818 

788 

8 

9 

342 

261 

191 

133 

080 

1.032 

988 

948 

911 

876 

844 

813 

9 

. 

10 

339 

258 

189 

129 

076 

1.028 

984 

944 

906 

871 

y38 

10 

11 

1.336 

1.254 

1.185 

1.125 

1.072 

1.023 

0.980 

0.939 

0.902 

0.866 

11 

12 

332 

250 

181 

121 

067 

1.019 

975 

934 

896 

12 

13 

328 

246 

177 

116 

063 

1.014 

970 

929 

13 

14 

323 

242 

172 

112 

058 

1.009 

964 

14 

15 

319 

237 

167 

106 

053 

1.003 

15 

16 

314 

232 

162 

101 

047 

16 

17 

308 

226 

157 

095 

17 

18 

1.S28 

303 

221 

150 

18 

19 

246 

1.323 

298 

215 

19 

20 

177 

242 

1.319 

' 

291 

20 

21 

1.116 

1.172 

1.237 

1.314 

21 

22 

063 

112 

167 

232 

1.308 

1 

1 

22 

23 

014 

058 

106 

162 

226 

1.303 

23 

24 

0.970 

009 

052 

101 

156 

221 

1.297 

24 

25 

929 

0.965 

004 

047 

095 

151 

215 

1.291 

25 

26 

890 

924 

0.959 

0.998 

041 

090 

144 

208 

1.285 

26 

^ 

27 

856 

886 

918 

953 

0.992 

035 

083 

138 

202 

1.278 

27 

28 

823 

850 

880 

912 

947 

0.986 

028 

076 

131 

195 

1.271 

28 

29 

791 

817 

844 

874 

906 

940 

0.979 

021 

069 

124 

188 

1.264 

29 

30 

761 

785 

811 

838 

867 

899 

934 

0.972 

014 

062 

117 

181 

1.256 

30 

31 

0.733 

0.755 

0.779 

0.804 

0.831 

0.860 

0.892 

0.926 

0.965 

1.007 

1.055 

1.109 

171 

31 

32 

706 

726 

748 

772 

797 

824 

853 

885 

919 

0.957 

0.999 

046 

100 

32 

' 

33 

679 

699 

720 

742 

765 

790 

817 

846 

877 

911 

949 

0.992 

038 

33 

34 

654 

672 

692 

712 

734 

757 

782 

809 

838 

869 

903 

941 

0.983 

34 

35 

630 

647 

665 

685 

705 

727 

750 

774 

801 

829 

861 

894 

931 

35 

36 

606 

622 

640 

658 

677 

697 

719 

742 

766 

792 

821 

852 

885 

36 

37 

583 

598 

615 

632 

650 

669 

689 

710 

733 

758 

784 

812 

842 

37 

38 

560 

575 

591 

607 

624 

642 

661 

681 

702 

724 

749 

775 

803 

38 

39 

538 

552 

507 

582 

599 

615 

633 

652 

672 

693 

715 

740  765 

39 

40 

517 

530 

544 

559 

574 

590 

607 

624 

643 

662 

683 

706 

729 

40 

41 

0.496 

0.509 

0.522 

0.536 

0.550 

0.565 

0.581 

0.597 

0.615 

0.633 

0.653 

0.674 

696 

41 

42 

475 

487 

500 

513 

527 

541 

556 

572 

588 

605 

623 

643 

663 

42 

43 

455 

466 

478 

491 

504 

517 

532 

546 

562 

578 

595 

613 

632 

43 

44 

435 

446 

457 

469 

482 

494 

508 

522 

536 

552 

568 

585 

602 

44 

45 

415 

426 

436 

448 

460 

472 

484 

498 

511 

526 

541 

557 

573 

45 

46 

395 

405 

416 

427 

438 

449 

461 

474 

487 

501 

515 

530 

545 

46 

47 

376 

386 

396 

406 

416 

427 

439 

451 

463 

476 

490 

504 

518 

47 

48 

357 

366 

375 

385 

395 

406 

417 

428 

440 

452 

465 

479 

492 

48 

49 

337 

346 

355 

365 

374 

384 

395 

405 

417 

428 

440 

453 

407 

49 

50 
51 

318 

327 

335 

344 

354 

362 

373 

383 

394 

405 

416 

428 

440 

50 

0.299 

0.307 

0.316 

0.324 

0.333 

0.342 

)0.351 

0.361 

0.371 

0.381 

0.392 

0.404 

0.415 

51 

52 

280 

288 

296 

304 

312 

321 

330 

339 

349 

359 

369 

379 

390 

52 

53 

261 

269 

276 

284 

292 

300 

309 

317 

326 

336 

346 

355 

365 

53 

54 

242 

249 

257 

264 

271 

279 

287 

296 

304 

313 

322 

332 

341 

54 

55 

223 

230 

236 

244 

251 

258 

266 

274 

282 

291 

299 

309 

318 

55 

56 

204 

210 

217 

223 

230 

237 

245 

252 

260 

268 

277 

286 

294 

56 

57 

184 

190 

197 

203 

210 

216 

223 

231 

238 

246 

254 

262 

270 

57 

58 

164 

170 

176 

183 

189 

195 

202 

209 

216 

223 

231 

238 

246 

58 

59 

145 

150 

156 

162 

168 

174 

180 

187 

194 

201 

208 

215 

222 

59 

60 

125 

130 

135 

141 

147 

153 

159 

165 

171 

178 

185 

192 

198  60 1 

78                TABLE  XV.— Part  Third. 

LOGARITHMS  OF  THE  LATITUDE  AND  DECLINATION  WHEN  THEY  ARE  OP 

CONTRARY  NAMES. 

DECLINATION.                                      ; 

Lat. 

0° 

1° 

2° 

3° 

40 

50 

6° 

70 

8° 

90 

10° 

11° 

12° 

Lat. 

o 

0 

1.359 

1.279 

1.212  1.153 

1.101 

1.055 

1.012 

0.979 

0 
0 

1 

1.360 

280 

213 

154 

102 

056 

014 

0.975 

931 

1 

2 

1.360 

281 

213 

155 

103 

057 

015 

0.976 

941 

907 

2 

3 

1.360 

281 

213 

155 

104 

058 

016 

0.977 

942 

909 

878 

3 

4 

1.360 

280 

213 

155 

104 

058 

016 

0.978 

943 

910 

879 

850 

4 

5 

1.359  j  280 

213 

155 

104 

058 

016 

0.978 

943 

910 

880 

851 

824 

5 

6  2791 

213 

155 

104 

058 

016 

0.979 

943 

911 

880 

852 

825 

799 

6  ' 

7 

219 

154 

103 

058 

016 

0.978 

943 

911 

881 

851 

825 

800 

776 

7I 

8 

153 

102 

057 

016 

0.978 

943 

911 

881 

852 

825 

800 

776 

753 

8 

9 

101 

056 

015 

0.977 

943 

910 

880 

852 

825 

800 

776 

754 

732 

9 

10 

055 

014 

0.976 

942 

910 

880 

852 

825 

800 

776 

754 

732 

711 

10 
ll 

11 

1.012 

0.975 

0.941 

0.9U9 

0.879 

0.851 

0.825 

0.800 

0.776 

0.754 

0.732 

0.711 

0.692 

12 

0.974 

939 

907 

878 

850 

824 

799 

775 

753 

732 

711 

692 

673 

12 

13 

938 

906 

876 

849 

823 

798 

775 

752 

731 

711 

691 

672 

654 

13 

14 

904 

875 

847 

822 

797 

774 

751 

730 

710 

691 

672 

654 

636 

14 

15 

873 

846 

820 

795 

772 

750 

729 

709 

690 

671 

653 

636 

619 

15 

16 

844 

818 

794 

772 

749 

728 

708 

689 

670 

653 

635 

619 

603 

16 

17 

816 

792 

769 

747 

726 

706 

687 

669 

651 

634 

617 

~602 

586 

17 

18 

789 

767 

745 

724 

705 

686 

668 

650 

633 

617 

601 

586 

571 

18 

19 

764 

743 

722 

703 

684 

666 

648 

632 

615 

600 

584 

570 

555 

19 

20 

740 

720 

700 

682 

664 

646 

630 

614 

598 

583 

568 

554 

540 

20 
21 

21 

0.717 

0.698 

0.679 

0.661 

0.644 

0.628 

0.612 

0.596 

0.581 

0.567 

0.553 

0.539 

0.525 

22 

695 

676 

659 

642 

625 

609 

594 

579 

565 

551 

537 

524 

511 

22 

23 

673 

656 

639 

623 

607 

592 

577 

563 

549 

535 

522 

509 

497 

23 

24 

652 

636 

621 

604 

589 

575 

560 

547 

533 

520 

508 

495 

483 

24 

25 

632 

616 

601 

586 

572 

558 

544 

531 

518 

505 

493 

481 

469 

25 

26 

613 

598 

583 

569 

555 

541 

528 

515 

503 

491 

479 

467 

456 

26 

27 

594 

579 

565 

551 

538 

525 

512 

500 

488 

476 

465 

454 

442 

27 

28 

575 

561 

548 

535 

522 

509 

497 

485 

473 

462 

451 

440 

429 

28 

29 

557 

544 

531 

518 

506 

494 

482 

470 

459 

448 

437 

427 

416 

29 

30 

540 

527 

514 

502 

490 

478 

467 

456 

445 

434 

425 

414 

403 

30 
31 

31 

0.522 

0.510 

0.498 

0.486 

0.474 

0.463 

0.452 

0.442 

0.431 

0.421 

0.411 

0.401 

0.391 

32 

505 

493 

482 

470 

459 

448 

438 

427 

417 

407 

397 

388 

378 

32 

33 

489 

477 

466 

455 

444 

434 

423 

413 

403 

394 

384 

375 

366 

33 

34 

472 

461 

450 

440 

429 

419 

409 

399 

390 

380 

371 

362 

353 

34 

35 

456 

445 

435 

424 

414 

405 

395 

386 

376 

367 

358 

349 

341 

35 

36 

440 

429 

419 

410 

400 

390 

381 

372 

363 

354 

345 

337 

328 

36 

37 

424 

414 

404 

395 

385 

376 

367 

358 

350 

341 

333 

324 

316 

37 

38 

408 

399 

389 

380 

371 

362 

353 

345 

336 

328 

320 

312 

304 

38 

39 

393 

384 

374 

365 

357 

348 

340 

331 

323 

315 

307 

299 

291 

39 

40 

377 

368 

360 

351 

342 

334 

326 

318 

310 

302 

294 

287 

279 

40 

41 

0.362 

0.353 

0.345 

U.336 

0.328 

0.320 

0.312 

0.304 

0.297 

0.289 

0.282 

0.274 

0.267 

41 

42 

347 

338 

330 

322 

314 

306 

299 

291 

284 

276 

269 

262 

255 

42 

43 

331 

323 

315 

308 

300 

292 

285 

278 

270 

263 

256 

249 

242 

43 

44 

316 

308 

301 

2!»3 

286 

279 

271 

264 

257 

250 

243 

237 

230 

44 

45 

301 

294 

286 

279 

272 

265 

258 

251 

244 

237 

231 

224 

217 

45 

46 

286 

279 

271 

264 

257 

251 

244 

237 

231 

224 

218 

211 

205 

46 

47 

271 

264 

257 

250 

243 

237 

230 

224 

217 

211 

205 

198 

192 

47 

48 

255 

249 

242 

235 

229 

223 

216 

210 

204 

198 

191 

185 

179 

48 

49 

240 

234 

227 

221 

215 

208 

202 

196 

190 

184 

178 

172 

167 

49 

50 
51 

225 

219 

212 

206 

200 

194 

188 

182 

176 

171 

165 

159 

154 

50 

0.209 

0.203 

0.197 

0.191 

0.185 

0.180 

0.174 

0.168 

0.163 

0.157 

0.151 

0.145 

0.140 

51 

52 

194 

188 

182 

175 

171 

165 

160 

154 

149 

143 

138 

132 

127 

52 

53 

178 

172 

167 

161 

156 

150 

145 

140 

134 

129 

124 

119 

114 

53 

54 

162 

157 

151 

^  146 

141 

136 

130 

125 

120 

115 

110 

105 

100 

54 

55 

146 

141 

136 

131 

125 

120 

115 

110 

105 

101 

096 

091 

086 

55 

56 

130 

125 

120 

115 

no:  105 

100 

095 

091 

086 

081 

077 

072 

56 

57 

114 

109 

104 

099 

094 

090 

085 

080 

076 

071 

066 

062 

057 

57 

58 

097 

092 

087 

083 

078 

074 

069 

065 

060 

056 

051 

047 

043 

58 

59 

080 

075 

071 

066 

062 

058  053 

049  045 

040 

036 

032 

028 

59 

60 

062 

058  054 

0501  045 

041   037 

033  029!  024 

020 

016 

012 

60 

TAliLK  XV.— Part  Third.                  19     1 

LOaARlTHMS  OF  THE  LATITUDE  AND  DECLINATION  WHEN  THEY  ARE  OF     | 

CONTRARY  NAMES. 

I 

DECLINATION.                                     | 

Lat, 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

Lat 

o 

0 

0.938 

0.904 

0.873 

0.844 

0.816 

0.789 

0.764 

0.740 

0.717 

0.695 

0.673 

0.653 

0.632 

'1 
0 

1 

906 

875 

846 

818 

792 

767 

743 

720 

698 

676 

656 

636 

616 

1 

2 

876 

847 

820 

794 

769 

745 

722 

700 

679 

659 

639 

620 

604 

2 

3 

849 

821 

795 

771 

747 

724 

703 

682 

661 

642 

623 

604 

586 

3 

4 

823 

797 

772 

749 

726 

705 

684 

,664 

644 

625 

607 

589 

571 

4 

5 

798 

774 

750 

728 

706 

686 

666 

646 

628 

609 

592 

574 

557 

5 

6 

775 

751 

721> 

70S 

687 

668 

648 

630 

612 

594 

577 

561 

544 

6 

7 

752 

730 

709 

689 

669 

650 

632 

614 

596 

579 

563 

547 

531 

7 

8 

731 

710 

690 

670 

651 

633 

615 

598 

581 

565 

549 

534 

518 

8 

9 

711 

691 

671 

653 

634 

617 

600 

583 

567 

551 

535 

521 

505 

9 

10 

691 

672 

653 

635 

618 

601 

584 

568 

553 

537 

522 

508  493 

10 

11 

0.672 

0.654 

0.636 

0.619 

0.602 

0.5S6 

0.570 

0.554 

0.539 

0.524 

0.509 

0.495 

0.481 

ll 

12 

654 

636 

619 

603 

586 

571 

555 

540 

525 

511 

497 

483 

469 

12 

13 

637 

620 

603 

587 

571 

556 

541 

527 

512 

498 

485 

471 

457 

13 

14 

620 

603 

587 

572 

557 

542 

527 

513 

499 

486 

473 

460 

446 

14 

15 

602 

587 

572 

557 

542 

528 

514 

500 

487 

474 

461 

449 

435 

15 

16 

587 

572 

557 

542 

528 

515 

501 

488 

475 

462 

449 

438 

424 

16 

17 

571 

557 

542 

528 

515 

501 

488 

475 

463 

450 

438 

427 

413 

17 

18 

556 

542  I  528 

515 

501 

488 

475 

463 

451 

438 

426 

416 

402 

18 

19 

541 

527!  514 

501 

488 

475 

463 

451 

439 

427 

415 

405 

392 

19 

20 

527 

513:  500 

488 

475 

463 

451 

439 

427 

416 

404 

394 

382 

20 
21 

21 

0.512 

0.499 

0.487 

0.475 

0.462 

0.451 

0.439 

0.427 

0.416 

0.405 

0.393 

0.383 

0.372 

22 

498 

486 

474 

462 

450 

438 

427 

416 

405 

394 

383 

372 

362 

22 

23 

485 

472 

461 

449 

438 

426 

415 

404 

393 

383 

372 

361 

352 

23 

24 

471 

459 

448 

437 

425 

414 

404 

393 

382 

372 

362 

351 

342 

24 

25 

458 

446 

435 

424 

413 

403 

392 

382 

372 

361 

351 

341 

332 

25 

26 

445 

434 

423 

412 

402 

391 

381 

371 

361 

351 

341 

331 

322 

26 

27 

432 

421 

410 

400 

390 

380 

370 

360 

350 

340 

331 

321 

312 

27 

28 

419 

408 

398 

388 

378 

368 

358 

349 

339 

330 

320 

311 

302 

28 

29 

406 

396 

386 

376 

367 

357 

347 

338 

329 

320 

310 

302 

292 

29 

30 

394 

384 

374 

364 

355 

346 

336 

327 

318 

309 

300 

293 

283 

30 

31 

0.381 

0.372 

0.362 

0.353 

0.344 

0.335 

0.326 

0.317 

0.308 

0.299 

0.290 

0.282 

0.273 

31 

32 

369 

359 

350 

341 

332 

323 

315 

306 

297 

289 

280 

272 

263 

32 

33 

356 

347 

338 

330 

321 

312 

304 

295 

287 

278 

270 

262 

253 

33 

34 

344 

335 

327 

318 

310 

301 

293 

285 

276 

268 

260 

252 

243 

34 

35 

332 

324 

315 

307 

298 

290 

282 

275 

,  266 

258 

250 

242 

233 

35 

36 

320 

312 

303 

295 

287 

279 

271 

263 

256 

248 

240 

232 

224 

36 

37 

308 

300 

292 

284 

276 

268 

260 

253 

245 

237 

230 

222 

214 

37 

38 

296 

288 

280 

272 

265 

257 

250 

242 

235 

227 

220 

212 

204 

38 

39 

2s4 

276 

269 

261 

,254 

246 

239 

231 

224 

217 

210 

202 

194 

39 

40 

272 

264 

257 

250 

242 

235 

228 

221 

214 

207 

199 

192 

185 

40 

41 

0.260 

0.252 

0.245 

0.238 

0.231 

0.224 

0.217 

0210 

0.203 

0.196 

0.188 

0.182 

0.175 

41 

42 

247 

240 

233 

227 

220 

213 

206 

199 

192 

186 

178 

172 

165 

42 

43 

235 

228 

222 

215 

208 

202 

195 

188 

182 

175 

168 

162 

155 

43 

44 

223 

216 

210 

203 

197 

190 

184 

177 

171 

164 

158 

152 

145 

44 

45 

211 

204 

198 

192 

185 

179 

173 

166 

160 

154 

147 

142 

135 

45 

46 

198 

192 

186 

180 

174 

167 

161 

155 

149 

143 

136 

132 

125 

46 

47 

48 

186 

180 

174 

168 

162 

156 

150 

144 

138 

132 

126 

121 

114 

47 

173 

168 

162 

156 

150 

144 

138 

132 

127 

121 

115 

110 

103 

48 

49 

161 

155 

149 

144 

138 

132 

126 

121 

115 

109 

104 

099 

092 

49 

50 

148 

142 

137 

131 

126 

120 

115 

109 

104 

098 

093 

087 

081 

50 

51 

0.135 

0.130 

0.121 

0.119 

0.113 

0.108 

0.103 

0.097 

0.092 

0.086 

0.081. 

0.076 

0.070 

51 

52 

122 

117 

111 

106 

101 

096 

090 

085 

080 

075 

069 

064 

058 

52 

53 

108 

103 

098 

093 

088 

083 

078 

073 

068 

063 

058 

052 

047 

53 

54 

095 

090 

085 

080 

075 

070 

065 

060 

055 

051 

046 

041 

035 

54 

55 

081 

076 

072 

067 

062 

057 

052 

048 

043 

038 

033 

029 

024 

55 

56 

067 

063 

058 

053 

049 

044 

039 

035 

030 

025 

021 

017 

Oil 

56 

57 

053 

048 

044 

039 

035 

030 

026 

021 

017 

012 

008 

004 

9.998 

57 

58 

038 

034 

030 

025 

021 

017 

013 

008 

003 

9.999 

9.995 

9.990 

985 

58 

59 

023 

019 

015 

Oil 

007 

002 

9.998 

9.994 

9.990 

985 

981 

977 

972 

59 

60 

008 

004 

000 

9.996 

9.992 

9.988 

984 

980 

976 

971 

967 

963 

959 

60j 

so 

TABLE 

XV. 

PART  FOURTa 

PART  FIFTH. 

OONTAININO  THE 

8DM   OK 

THE   TWO    LOGS  AND   THE  | 

CONTAINING    THE 

LIMITS   OF   THE   TIME   FUOM 

OOBJIEOTION 

FOE    ALTITUDE. 

NOON 

AT   WHICH   THE    OB3EBVATION 

SHOULD  BE    MADE.                                   1 

, 

, 

, 

.2    s 

1      a 

.11 

II 

2  !> 

DEO.  OF  THE  SAME  NAME  AS  THE  LATITUDE.        | 

1  H 

•S  -:i 

12 

•o    -J 

12 

"3  3 

1 

&  o 

a  g 

%    -^ 

i      1 

1  < 

a  2 

3i 

3      P 

^    J 

^M 

3       ^ 

03    ^ 

Lat 

0° 

5° 

10° 

15° 

20^ 

24° 

o      ' 
0.  1 

6.464 

O        ' 

0.51 

8.171 

O       1 

1.41 

8.468 

o 

h    m 

b    m 

h   m 

h   m 

h    m 

b     m 

2 

765 

52 

180 

1.42 

472 

0 

0.0 

0.4 

0.6 

0.9 

0.12 

0.15 

3 

941 

53 

189 

1.43 

476 

5 

3 

1 

4 

6 

9 

12 

4 

7.066 

54 

196 

1.44 

481 

10 

6 

4 

1 

5 

7 

10 

5 

163 

55 

204 

1.45 

485 

15 

9 

7 

4 

2 

4 

8 

6 

242 

56 

212 

1.46 

489 

20 

12 

10 

7 

5 

2 

5 

7 

309 

57 

220 

1.47 

493 

25 

16 

13 

10 

8 

5 

2 

8 

367 

58 

227 

1.48 

497 

30 

19 

16 

13 

12 

9 

6 

9 

418 

59 

235 

1.49 

501 

35 

24 

21 

18 

15 

13 

10 

10 

464 

1.  0 

242 

1.50 

505 

40 

28 

25 

22 

20 

17 

15 

11 

505 

1.  1 

249 

1.51 

509 

44 

32 

29 

26 

24 

21 

20 

12 

543 

1.  2 

256 

1.52 

513 

48 

36 

33 

30 

30 

27 

25 

13 

578 

1.  3 

263 

1.53 

516 

52 

44 

41 

36 

36 

34 

32 

14 

610 

1.  4 

270 

1.54 

521 

56 

55 

47 

44 

42 

38 

36 

15 
16 

640 

668 

1.  5 
1.  6 

277 
283 

1.55 
1.56 

524 

528 

60 

58 

54 

52 

50 

^ 

44 

17 

694 

1.  7 

290 

1.57 

532 

DEOUNATIO 

N    OF   THE   CONTKAET  NAME   TO   THE 

18 

719 

1.  8 

296 

1.58 

536 

LATITUDE. 

19 

20 

742 
765 

1.  9 
1.10 

303 
309 

1.59 
2.  0 

539 
543 

h    m 

b    m 

h   m 

b    m 

b    m 

b    m 

21 

786 

1.11 

315 

2.  1 

546 

0 

0.0 

0.4 

0.   7 

0.10 

0.13 

0.16 

22 

806 

1.12 

321 

2.  2 

549 

5 

3 

7 

9 

13 

16 

18 

23 

825 

1.13 

327 

2.  3 

553 

10 

7 

10 

13 

17 

19 

21 

24 

844 

1.14 

333 

2.  4 

557 

15 

10 

13 

17 

20 

21 

24 

25 

862 

1.15 

339 

2.  5 

560 

20 

13 

16 

19 

23 

25 

28 

26 

879 

1.16 

345 

2.  6 

564 

25 

18 

20 

23 

26 

28 

31 

27 

895 

1.17 

350 

2.  7 

567 

30 

21 

23 

26 

30 

32 

35 

28 

911 

1.18 

356 

2.  8 

571 

35 

25 

27 

30 

34 

36 

39 

29 

926 

1.19 

361 

2.  9 

574 

40 

30 

32 

33 

38 

40 

43 

30 

941 

1.20 

367 

2.10 

578 

44 

34 

37 

38 

43 

46 

48 

31 

955 

1.21 

372 

2.11 

581 

48 

38 

42 

45 

48 

51 

53 

32 

969 

1.22 

377 

2.12 

584 

52 

44 

48 

52 

55 

58 

1.  0 

33 

982 

1.23 

383 

2.13 

587 

56 

50 

54 

57 

1.  0 

1.  3 

1.  5 

34 
35 

995 

8.008 

1.24 
1.25 

389 
393 

2.14 
2.15 

591 
594 

60 

58 

57 

1.  4 

1.  6 

1.  9 

1.12 

36 

020 

1.26 

398 

2.1-6 

597 

. 

37 

032 

1.27 

403 

2.17 

600 

38 

044 

1.28 

408 

2.18 

603 

39 

054 

1.29 

413 

2.19 

606 

40 

066 

1.30 

419 

2.20 

610 

41 

077 

1.31 

423 

2.21 

613 

42 

087 

1.32 

427 

2.22 

616 

43 

097 

1.33 

432 

2.23 

619 

44 

107 

1.34 

437 

2.24 

622 

45 

117 

1.35 

441 

2.25 

625 

46 

126 

1.36 

446 

2.26 

628 

47 

136 

1.37 

450 

2.27 

631 

48 

145 

1.38 

455 

2.28 

634 

. 

49 

154 

1.39 

459 

2.29 

637 

60 

163 

1.40 

464 

2.30 

640 

J 

TABLE   XVI. 

" 

APPARENT  TIME 

0?  THE  SUTS   RISING  AND  SETTING.                               | 

1 

DECLINATION    OP    THE 

SAME    NAME   AS 

fHE    LATITUDE.                                                                        1 

0° 

2° 

40 

6° 

8°          1 

90 

10° 

Ris. 

SetL 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett. 

Ris. 

Sett 

Ris.     Sett 

H.  M. 

H.  M. 

H.     M. 

H.     M. 

■J.    M. 

H.     M. 

H.     M. 

H.     M. 

H.     M. 

H.    M 

H.    M. 

H.     M. 

a.    M. 

H.     M. 

0 

6.0 

6.0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

2     6.0 

6.0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

5.59 

6.   1 

5.59 

6.   1 

5.59 

6.  1 

4     tJ.O 

6.0 

6.  0 

6.  Q 

5.59 

6.  1 

5.59 

6.   1 

5.58 

6.  2 

5.58 

6.  2 

5.57 

6.  3 

6     6.0 

6.0 

6.  0 

6.  0 

5.58 

6.  2 

5.58 

6.  2 

5.57 

6.  3 

5.57 

6.  3 

5.56 

6.  4 

8     6.0 

6.0 

5.59 

6.   I 

5.58 

6.  2 

5.57 

6.  3 

5.56 

6.  4 

5.55 

6.  5 

5.55 

6.  5 

10 

6.0 

6.0 

5.59 

6.  1 

5.57 

6.  3 

5.56 

6.  4 

5.54 

6.  6 

5.54 

6.  6 

5.53 

6.  7 

12 

6.0 

6.0 

5.58 

6.  2 

5.57 

6.  3 

5.55 

6.  5 

5.53 

6.  7 

5.53 

6.  7 

5.52 

6.  8 

14 

6.0 

6.0 

5.58 

6.  2 

5.56 

6.  4 

5.54 

6.  6 

5.52 

6.  8 

5.51 

6.  9 

5.51 

6.  9 

16 

6.0 

6.0 

5.58 

6.  2 

5.55 

6.  5 

5.53 

6.  7 

5.51 

6.  9 

5.50 

6.10 

5.48 

6.12 

18 

6.0 

6.0 

5.58 

6.  2 

5.55 

6.  5 

5.52 

6.  8 

5.50 

6.10 

5.48 

6.12 

5.47 

6.13 

20 

6.0 

6.0 

5.57 

6.  3 

5.54 

6.  6 

5.51 

6.  9 

5.48 

6.12 

5.47 

6.13 

5.45 

6.13 

21 

6.0 

6  0 

5.57 

6.  3 

5.54 

6.  6 

5.51 

6.  9 

5.48 

6.12 

5.46 

6.14 

5.44 

6.16 

22 

6.0 

6.0 

5.57 

6.  3 

5.54 

6.  6 

5.50 

6.10 

5.47 

6.13 

5.45 

6.15 

5.44 

6.16 

23 

6.0 

6.0 

5.57 

6.  3 

5.53 

6.  7 

5.50 

6.10 

5.46 

6.14 

5.44 

6.16 

5.43 

6.17 

24 

6.0 

6.0 

5.57 

6.  3 

5.53 

6.  7 

5.49 

6.11 

5.46 

6.14 

5.43 

6.17 

5.42 

6.18 

25 

6.0 

6.0 

5.56 

6.  4 

.5.53 

6.  7 

5.49 

6.11 

5.45 

6.15 

5.42 

6.18 

5.41 

6.19 

26 

6.0 

6.0 

5.56 

6.  4 

5.52 

6.  8 

5.48 

6.12 

5.44 

6.16 

5.41 

6.19 

5.40 

6.20 

27 

6.0 

6.0 

5.56 

6.  4 

5.52 

6.  8 

5.48 

6.12 

5.44 

6.16 

5.41 

6.19 

5.39 

6.21 

28 

6.0 

6.0 

5.56 

6.  4 

5.51 

6.  9 

5.47 

6.13 

5.43 

6.17 

5.40 

6.20 

5.38 

6.22 

29 

6.0 

6.0 

5.56 

6.  4 

5.51 

6.  9 

5.47 

6.13 

5.42 

6.18 

5.39 

6.21 

5.38 

6.22 

30 

6.0 

6.0 

5.55 

S.  5 

5.51 

6.  9 

5.46 

6.14 

5.41 

6.19 

5.38 

6.22 

5.37 

6.23 

31 

6.0 

6.0 

5.55 

6.  5 

5.50 

6.10 

5.46 

6.14 

5.41 

6.19 

5.37 

6.23 

5.36 

6.24 

32 

6.0 

6.0 

5.55 

6.  5 

5.50 

6.10 

5.45 

6.15 

5.40 

6.20 

5.36 

6.24 

5.35 

6.25 

33 

6.0 

6.0 

.^.55 

6.  5 

5.50 

6.10 

5.44 

6.16 

5.39 

6.21 

5.35 

6.25 

5.34 

6.26 

34 

6.0 

6.0 

5..55 

6.  5 

5.49 

6.11 

5.44 

6.16 

5.38 

6.22 

5.35 

6.25 

5.33 

6.27 

35 

6.0 

6.0 

.^.55 

6.  5 

5.49 

6.11 

5.43 

6.17 

5.37 

6.23 

5.34 

6.26 

5.32 

6.28 

36 

6.0 

6.0 

5.55 

6.  5 

5.48 

6.12 

5.42 

6.18 

5.37 

6.23 

5.33 

6.27 

5.31 

6.29 

37 

6.0 

6.0 

.5.55 

6.  5 

5.48 

6.12 

5.42 

6.18 

5.36 

6.24 

5.32 

6.28 

5.29 

6.31 

38 

6.0 

6.0 

5.55 

6.  5 

5.47 

6.13 

5.41 

6.19 

5.35 

6.25 

5.31 

6.29 

5.28 

6.32 

39 

6.0 

6.0 

5.55 

6.  5 

5.47 

6.13 

5.40 

6.20 

5.34 

6.26 

5.29' 

6.31 

5.27 

6.33 

40 

0.0 

6.0 

5.54 

6.  6 

5.47 

6.13 

5.40 

6.20 

5.33 

6.27 

5.28 

6.32 

5.26 

6.34 

41 

6.0 

6.0 

5.54 

6.  6 

5.46 

6.14 

5.39 

6.21 

5.32 

6.28 

5.27 

6.33 

5.25 

6.35 

42 

6.0 

6.0 

5.54 

6.  6 

5.46 

6.14 

5.38 

6.22 

5.31 

6.29 

5.26 

6.34 

5.23 

6.37 

43 

6.0 

6.0 

5.53 

6.  7 

5.45 

6.15 

5.38 

6.22 

5.30 

6.30 

5.25 

6.35 

5.22 

6.38 

44 

6.0 

6.0 

5.53 

6.  7 

5.45 

6.15 

5.37 

6.23 

5.29 

6.31 

5.24 

6.36 

5.21 

6.39 

45 

6.0 

6.0 

5.52 

6.  8 

5.44 

6.16 

5.36 

6.24 

5.28 

6.32 

5.22 

6.38 

5.19 

6.41 

46 

6.0 

6.0 

5.52 

6.  8 

5.43 

6.17 

5.35 

6.25 

5.27 

6.33 

5.21 

6.39 

5.18 

6.42 

47 

6.0 

6.0 

5.51 

6.  9 

5.43 

6.17 

5.34 

6.26 

5.25 

6.35 

5.19 

6.41 

5.16 

6.44 

48 

6.0 

6.0 

5.51 

6.  9 

5.42 

6.18 

5.33 

6.27 

5.24 

6.36 

5.18 

6.42 

5.15 

6.45 

49 

6.0 

6.0 

5.51 

6.  9 

5.42 

6.18 

5.32 

6.28 

5.23 

6.37 

5.16 

6.44 

5.13 

6.47 

50 

6.0 

6.0 

5.50 

6.10 

5.41 

6.19 

5.31 

6.29 

5.21 

6.39 

5.15 

6.45 

5.11 

6.49 

51 

6.0 

6.0 

5.50 

6.10 

5.40 

6.20 

5.30 

6.30 

5.20 

6.40 

5.13 

6.47 

5.10 

6.50 

52 

6.0 

6.0 

5.50 

6.10 

5.39 

6.21 

5.29 

6.31 

5.19 

6.41 

5.11 

6.49 

5.  8 

6.52 

53 

6.0 

6.0 

5.49 

6.11 

5.39 

6.21 

5.28 

6.32 

5.17 

6.43 

5.10 

6.50 

5.  6 

6.54 

54 

6.0 

6.0 

5.49 

6.11 

5.38 

6.22 

5.27 

6.33 

5.15 

6.45 

5.  8 

6.52 

5.  4 

6.56 

55 

6.0 

6.0 

5.49 

6.11 

5.37 

6.23 

5.25 

6.35 

5.14 

6.46 

5.  6 

6.54 

5.  2 

6.58 

56 

6.0 

6.0 

5.48 

6.12 

5.36 

6.24 

5.24 

6.36 

5.12 

6.48 

5.  5 

6.55 

4.59 

7.  1 

57 

6.0 

6.0 

5.48 

6.12 

5.35 

6.25 

5.23 

6.37 

5.10 

6.50 

5.  4 

6.56 

4.57 

7.  3 

58 

6.0 

6.0 

5.47 

6.13 

5.34 

6.26 

5.21 

6.39 

5.  8 

6.52 

5.  0 

6.58 

4.54 

7.  6 

59 

6.0 

6.0 

5.47 

6.13 

5.33 

6.27 

5.20 

6.40 

5.  6 

6.54 

4.59 

7.   1 

4.52 

7.  8 

60 

6.0 

6.0 

5.46 

6.14 

5.32 

6.28 

5.18 

6.40 

5.  4 

6.56 

4.56 

7.  4 

4.49 

7.11 

61 

6.0 

6.0 

5.46 

6.14 

5.31 

6.29 

5.16 

6.44 

5.   1 

6.59 

4.54 

7.  6 

4.46 

7.14 

62 

6.0 

6.0 

5.45 

6.15 

5.30 

6.30 

5.14 

6.46 

4.59 

7.  1 

4.51 

7.  9 

4.43 

7.17 

63 

6.0 

6.0 

5.44 

6.16 

5.28 

6.32 

5.12 

6.48 

4.56 

7.  4 

4.48 

7.12 

4.39 

7.21 

64 

6.0 

6,0 

5.44 

6.16 

5.27 

6.33 

5.10 

6.50 

4.53 

7.  7 

4.44 

7.16 

4.35 

7.25 

65 

6.0 

6.0 

5.43 

6.17 

5.26 

6.34 

5.  8 

6.52 

4.50 

7.10 

4.41 

7.19 

4.31 

7.29 

66 

6.0 

6.0 

5.42 

6.18 

5.24 

6.35 

5.  5 

6.54 

4.47 

7.13 

4.37 

7.23 

4.27 

7.33 

661 

6.0 

6.0 

5.42 

6.18 

5.23 

6.36 

5.  4 

6.56 

4.44 

7.16 

4.34 

7.26 

4.24 

7.36 

Lat 

Sett 

Ris. 

Sett 

Ris. 

Sett. 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ria. 

Sett. 

Rio. 

LATITUDE   A] 

ND    DECI 

JNATION   OF    COI 

JTBABT 

NAMES.                         .                                         1 

82 

TABLE   XVI. 

1 

APPARENl'  TIME 

Oi"  THE  SUN'S  RISING  AND  SETTING.                              | 

1 

DECLINATION    OF   THE   SAME    NAME   A3   THE    LATITUDE.                                                                          1 

no    1 

12°        1 

13° 

14°       1 

15° 

16° 

170      1 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett. 

Ris. 

Sett 

Ria. 

Sett 

o 

H.  M. 

H.  M. 

H.     M. 

H.     U. 

H.    M. 

H.    M. 

H.     M. 

H.     M. 

H      M. 

H.    M. 

H.    M. 

B.     H. 

H.     M. 

H.     K. 

0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

2 

5.59 

6.  1 

5.58 

6.  2 

5.58 

6.  2 

5.58 

6.  2 

5.58 

6.  2 

5.58 

6.  2 

5.58 

6.  2 

4 

5.57 

6.  3 

5.57 

6.  3 

5.56 

6.  4 

5.56 

6.  4 

5.56 

6.  4 

5.56 

6.  4 

5.55 

6.  5 

6 

5.56 

6.  4 

5.55 

6.  5 

5.55 

6.  5 

5.54 

6.  6 

5.54 

6.  6 

5.53 

6.  7 

5.53 

6.  7 

8 

5.54 

6.  6 

5.53 

6.  7 

5.53 

6.  7 

5.52 

6.  8 

5.51 

6.  9 

5.51 

6.  9 

5.50 

6.10 

10 

5.52 

6.  8 

5.52 

•6.  8 

5.51 

6.  9 

5.50 

6.10 

5.49 

6.11 

5.49 

6.12 

5.48 

6.12 

12 

5.51 

6.  9 

5.50 

6.10 

5.49 

6.11 

5.48 

6.12 

5.47 

6.13 

5.46 

6.14 

5.45 

6.15 

14 

5.50 

6.10 

5.48 

6.12 

5.48 

6.12 

5.46 

6.14 

5.45 

6.15 

5.44 

6.16 

5.43 

6.17 

16 

5.47 

6.13 

5.46 

6.14 

5.45 

6.15 

5.44 

6.16 

5.42 

6.18 

5.41 

6.19 

5.40 

6.20 

18 

5.46 

6.14 

5.44 

6.16 

5.43 

6.17 

5.41 

6.19 

5.40 

6.20 

5.39 

6.21 

5.37 

6.23 

20 

5.44 

6.16 

5.42 

6.18 

5.41 

6.19 

5.39 

6.21 

5.38 

6.22 

5.36 

6.24 

5.34 

6.26 

21 

5.43 

6.17 

5.41 

6.19 

5.40 

6.20 

5.38 

6.22 

5.36 

6.24 

5.35 

6.25 

5.33 

6.27 

22 

5.42 

6.18 

5.40 

6.20 

5.39 

6.21 

5.37 

6.23 

5.35 

6.25 

5.33 

6.27 

5.32 

6.28 

23 

5.41 

6.19 

5.39 

6.21 

5.38 

6.22 

5.36 

6.24 

5.34 

6.26 

5.32 

6.28 

5..30 

6.30 

24 

5.40 

6.20 

5.38 

6.22 

5.36 

6.24 

5.34 

6.26 

5.33 

6.27 

5.31 

6.29 

5.29 

6.31 

25 

5.39 

6.21 

5.37 

6.23 

5.35 

6.25 

5.33 

6.27 

5.31 

6.29 

5.29 

6.31 

5.27 

6.33 

26 

5.38 

6.22 

5.36 

6.24 

5.34 

6.26 

5.32 

6.28 

5.30 

6.30 

5.28 

6.32 

5.26 

6.34 

27 

5.37 

6.23 

5.35 

6.25 

5.33 

6.27 

5.31 

6.29 

5.29 

6.31 

5.26 

6.34 

5.24 

6.36 

28 

5.36 

6.24 

5.34 

6.26 

5.32 

6.28 

5.30 

6.30 

5.27 

6.33 

5.25 

6.35 

5.23 

6.37 

29 

5.35 

6.25 

5.33 

6.27 

5.31 

6.29 

5.28 

6.32 

5.26 

6.34 

5.23 

6.37 

5.21 

6.39 

30 

5.34 

6.26 

5.32 

6.28 

5.29 

6.31 

5.27 

6.33 

5.24 

6.36 

5.22 

6.38 

5.19 

6.41 

31 

5.33 

6.27 

5.31 

6.29 

5.28 

6.32 

5.26 

6.34 

5.23 

6.37 

5.20 

6.40 

5.18 

6.42 

32 

5.32 

6.28 

5.29 

6.31 

5.27 

6.34 

5.24 

6.36 

5.21 

6.39 

5.19 

6.41 

5.16 

6.44 

33 

5.31 

6.29 

5.28 

6.32 

5.24 

6.36 

5.23 

6.37 

5.20 

6.40 

5.17 

6.43 

5.14 

6.46 

34 

5.30 

6.30 

5.27 

6.33 

5.23 

6.37 

5.21 

6.39 

5.18 

6.42 

5.15 

6.45 

5.12 

6.48 

35 

5.29 

6.31 

5.26 

6.34 

5.21 

6.39 

5.20 

6.40 

5.17 

6.43 

5.14 

6.46 

5.11 

6.49 

36 

5.28 

6.32 

5.24 

6.36 

5.20 

6.40 

5.18 

6.42 

5.15 

6.45 

5.12 

6.48 

5.  9 

6.51 

37 

5.26 

().34 

5.25 

6.37 

5.18 

6.42 

5.17 

6.43 

5.13 

6.47 

5.10 

6.50 

5.  7 

6.53 

38 

5.25 

6.35 

5.22 

6.38 

5.17 

6.43 

5.15 

6.45 

5.12 

6.48 

5.  8 

6.52 

5    5 

6.55 

39 

5.24 

6.36 

5.20 

6.40 

5.15 

6.45 

5.13 

6.47 

5.10 

6.50 

5.  6 

6.54 

5.  3 

6.57 

40 

5.22 

6.38 

5.19 

6.41 

5.14 

6.46 

5.12 

6.48 

5.  8 

6.52 

5.  4 

6.56 

5.  1 

6.59 

41 

5.21 

6.39 

5.17 

6.43 

5.12 

6.48 

5.10 

6.50 

5.  6 

6.54 

5.  2 

6.58 

4.48 

7.  2 

42 

5.20 

6.40 

5.16 

6.44 

5.10 

6.50 

5.  8 

6.52 

5.  4 

6.56 

5.  0 

7.  0 

4.56 

7.  4 

43 

5.18 

6.42 

5.14 

6.46 

5.  8 

6.52 

5.  6 

6.54 

5.  2 

6.58 

4.48 

7.  2 

4.54 

7.  6 

44 

5.17 

6.43 

5.13 

6.47 

5.  7 

6.53 

5.  4 

6.56 

5.  0 

7.  0 

4.56 

7.  4 

4.51 

7.  9 

45 

5.15 

6.45 

5.11 

6.49 

5.  5 

6.55 

5.  2 

6.58 

4.58 

7.  2 

4.53 

7.  7 

4.49 

7.11 

46 

5.14 

6.46 

5.  9 

6.51 

5.  4 

6.56 

5.  0 

7.  0 

4.56 

7.  4 

4.51 

7.  9 

4.46 

7.14 

47 

5.12 

6.48 

5.  7 

6.53 

5.  3 

6.57 

4.58 

7.  2 

4.53 

7.  7 

4.48 

7.12 

4.43 

7.17 

48 

5.10 

6.50 

5.  5 

6.55 

5.   1 

6.59 

4.56 

7.  4 

4.51 

7.  9 

4.46 

7.14 

4.41 

7.19 

49 

5.  8 

6.52 

5.  3 

6.57 

4.58 

7.  2 

4.53 

7.  7 

4.48 

7.12 

4.43 

7.17 

4.38 

7.22 

50 

5.  6 

6.54 

5.  1 

6.59 

4.56 

7.  4 

4.51 

7.  9 

4.46 

7.14 

4.40 

7.20 

4.35 

7.25 

51 

5.  4 

6.56 

4.59 

7.  1 

4.54 

7.  6 

4.58 

7.12 

4.43 

7.17 

4.37 

7.23 

4.31 

7.29 

52 

5.  2 

6.58 

4.57 

7.  3 

4.51 

7.  9 

4.46 

7.14 

4.40 

7.20 

4.34 

7.26 

4.28 

7.32 

53 

5.  0 

7.  0 

4.54 

7.  6 

4.49 

7.11 

4.43 

7.17 

4.37 

7.23 

4.31 

7.29 

4.24 

7.36 

54 

4.58 

7.  2 

4.52 

7.  8 

4.46 

7.14 

4.40 

7.20 

4.33 

7.27 

4.27 

7.33 

4.20 

7.40 

55 

4.56 

7.  4 

4.49 

7.11 

4.43 

7.17 

4.37 

7.23 

4.30 

7.30 

4.23 

7.37 

4.16 

7.44 

56 

4.53 

7.  7 

4.47 

7.13 

4.40 

7.20 

4.33 

7.27 

4.26 

7.34 

4.19 

7.41 

4.12 

7.48 

57 

4.50 

7.10 

4.44 

7.16 

4.37 

7.23 

4.30 

7.30 

4.23 

7.37 

4.15 

7.45 

4.  8 

7.52 

58 

4.47 

7.13 

4.40 

7.20 

4.33 

7.27 

4.26 

7.34 

4.18 

7.42 

4.11 

7.49 

4.  3 

7.57 

59 

4.44 

7.16 

4.37 

7.23 

4.30 

7.30 

4.22 

7.38 

4.14 

7.46 

4.  6 

7.54 

3.58 

8.  2 
8.  8 

60 

4.41 

7.19 

4.34 

7.26 

4.26 

7.34 

4.18 

7.42 

4.  9 

7.51 

4.  1 

7.59 

3.52 

61 

4.38 

7.22 

4.30 

7.30 

4.22 

7.38 

4.13 

7.47 

4.  4 

7.56 

3.55 

8.  5 

3.46 

8.14 

62 

4.34 

7.26 

4.26 

7.34 

4.17 

7.43 

4.  8 

7.52 

3.59 

8.  1 

3.49 

8.11 

3.40 

8.20 

63 

4.30 

7.30 

4.21 

7.39 

4.12 

7.48 

4.  3 

7.57 

3.53 

8.  7 

3.43 

8.17 

3.33 

8.27 

64 

4.26 

7.34 

4.17 

7.43 

4.  7 

7.53 

3.57 

8.  3 

3.47 

8.13 

3.36 

8.24 

3.25 

8.35 

65 

4.21 

7.39 

4.12 

7.48 

4.   1 

7.59 

3.51 

8.  9 

3.40 

8.20 

3.28 

8.32 

3.16 

8.44 

66 

4.18 

7.42 

4.  6 

7.54 

3.55 

8.  5 

3.44 

8.16 

3.32 

8.28 

3.20 

8.40 

3.  7 

8.53 

m\ 

4.14 

7.46 

4.  3 

7.57 

3.52 

8.  8 

3.40 

8.20 

3.28 

8.32 

3.15 

8.45 

3.  1 

8.59 

Lat 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett. 

Ria. 

LATITUDE   A] 

so    DECLINATION    OF    CONTRARY 

NAMES.                                                                        1 

TABLE    XVI.                                                       83 

APPARENT  TIME  OF  THE  SUN'S  RISING  AND  SETTING. 

3 

at 

DECLINATION    OF   THE   SAME    NAME   AS   THE    LATITUDE.                                                                            1 

18°      1 

19° 

20° 

21° 

22° 

23° 

2310      1 

Ris. 

SetL 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

o 

H.  M. 

H.  M. 

B.     M. 

H.     M. 

H.    M. 

H.     M. 

H.     M. 

H.      M. 

H.     M. 

H.     M. 

H.     M. 

H.    M 

H       M. 

H.      U. 

0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

6.  0 

2 

5.58 

6.  2 

5.58 

6.  2 

5.58 

6.  2 

5.57 

6.  3 

5.57 

6.  3 

5.57 

6.  3 

5.57 

6.  3 

4 

5.55 

6.  5 

5.55 

6.  5 

5.55 

6.  5 

5.54 

6.  6 

5.54 

6.  6 

5.53 

6.  7 

5.53 

6.  7 

6 

5.52 

6.  8 

5.52 

6.  8 

5.52 

6.  8 

5.51 

6.  9 

5.51 

6.  9 

5.50 

6.10 

5.50 

6.10 

8 

5.50 

6.10 

5.49 

6.11 

5.49 

6.12 

5.48 

6.12 

5.47 

6.12 

5.47 

6.13 

5.46 

6.14 

10 

5.47 

6.13 

5.46 

6.14 

5.46 

6.15 

5.45 

6.16 

5.44 

6.16 

5.43 

6.17 

5.43 

6.17 

12 

5.44 

6.16 

5.44 

6.17 

5.43 

6.18 

5.42 

6.19 

5.41 

6.20 

5.40 

6.20 

5.39 

6.21 

14 

5.41 

6.19 

5.40 

6.20 

5.39 

6.21 

5.38 

6.22 

5.37 

6.23 

5.36 

6.24 

5.35 

6.25 

16 

5.39 

6.21 

5.37 

6.23 

5.36 

6.24 

5.35 

6.25 

5.33 

6.27 

5.32 

6.28 

5.31 

6.29 

18 

5.36 

6.24 

5.34 

6.26 

5.33 

6.27 

5.31 

6.29 

5.30 

6.30 

5.28 

6.32 

5.28 

6.32 

20 

5.33 

6.27 

5.31 

6.29 

5.30 

6.30 

5.28 

6.32 

5.26 

6.34 

5.24 

6.36 

5.24 

6.36 

21 

5.31 

6.29 

5.30 

6.30 

5.28 

6.32 

5.26 

6.34 

5.24 

6.36 

5.22 

6.38 

5.22 

6.38 

22 

5.30 

6.30 

5.28 

6.32 

5.26 

6.34 

5.24 

6.36 

5.22 

6.38 

5.21 

6.39 

5.20 

6.40 

23 

5.28 

6.32 

5.26 

6.34 

5.24 

6.36 

5.22 

6.38 

5.21 

6.39 

5.19 

6.41 

5.18 

6.42 

24 

5.27 

6.33 

5.25 

6.35 

5.23 

6.37 

5.21 

6.39 

5.19 

6.41 

5.16 

6.44 

5.15 

6.45 

25 

5.25 

6.35 

5.23 

6.37 

5.21 

6.39 

5.19 

6.41 

5.17 

6.43 

5.14 

6.46 

5.13 

6.47 

26 

5.24 

6.36 

5.21 

6.39 

5.19 

6.41 

5.17 

6.43 

5.15 

6.45 

5.12 

6.48 

5.11 

6.49 

27 

5.22 

6.38 

5.20 

6.40 

5.17 

6.43 

5.15 

6.45 

5.12 

6.48 

5.10 

6.50 

5.  9 

6.51 

28 

5.20 

6.40 

5.18 

6.42 

5.15 

6.45 

5.13 

6.47 

5.10 

6.50 

5.  8 

6.52 

5.  7 

6.53 

29 

5.18 

6.42 

5.16 

6.44 

5.13 

6.47 

5.11 

6.49 

5.  8 

6.52 

5.  6 

6.54 

5.  4 

6.56 

30 

5.17 

6.43 

5.14 

6.46 

5.11 

6.49 

5.  9 

6.51 

5.  6 

6.54 

5.  3 

6.57 

5.  2 

6.58 

31 

5.15 

6.45 

5.12 

6.48 

5.  9 

6.51 

5.  7 

6.53 

5.  4 

6.56 

5.  1 

6.59 

5.  0 

7.  0 

32 

5.13 

6.47 

5.10 

6.50 

5.  7 

6.53 

5.  4 

6.56 

5.  2 

6.58 

4.59 

7.   1 

4.57 

7.  3 

33 

5.11 

6.49 

5.  8 

6.52 

5.  5 

6.55 

5.  2 

6.58 

4.59 

7.  1 

4.56 

7.  4 

4.55 

7.  5 

34 

5.  9 

6.51 

5.  6 

6.. 54 

5.  3 

6.57 

5.  0 

7.  0 

4.57 

7.  3 

4.53 

7.  7 

4.52 

7.  8 

35 

5.  7 

6.53 

5.  4 

6.56 

5.    1 

6.59 

4.58 

7.  2 

4.54 

7.  6 

4.51 

7.  9 

4.49 

7.11 

36 

5.  5 

6.55 

5.  2 

6.58 

4.59 

7.   1 

4.55 

7.  5 

4.52 

7.  8 

4.48 

7.12 

4.46 

7.14 

37 

5.  3 

6.5» 

5.  0 

7.  0 

4.56 

7.  4 

4.53 

7.  7 

4.49 

7.11 

4.45 

7.15 

4.44 

7.16 

38 

5.   1 

6.59 

4.58 

7.  2 

4.53 

7.  7 

4.50 

7.10 

4.46 

7.14 

4.43 

7.17 

4.41 

7.19 

39 

4.59 

7.   1 

4.55 

7.  5 

4.51 

7.  9 

4.48 

7.12 

4.44 

7.16 

4.40 

7.20 

4.38 

7.22 

40 

4.57 

7.  3 

4.53 

7.  7 

4.49 

7.11 

4.45 

7.15 

4.41 

7.19 

4.37 

7.23 

4.35 

7.25 

41 

4.54 

7.  6 

4.50 

7.10 

4.46 

7.14 

4.42 

7.18 

4.38 

7.22 

4.33 

7.27 

4.31 

7.29 

42 

4.52 

7.  8 

4.48 

7.12 

4.43 

7.17 

4.39 

7.21 

4.35 

7.25 

4.30 

7.30 

4.28 

7.32 

43 

4.49 

7.11 

4.45 

7.15 

4.41 

7.19 

4.36 

7.24 

4.31 

7.29 

4.27 

7.33 

4.24 

7.36 

44 

4.47 

7.13 

4.42 

7.18 

4.38 

7.22 

4.33 

7.27 

4.28 

7.32 

4.23 

7.37 

4.21 

7.39 

45 

4.44 

7.16 

4.39 

7.21 

4.35 

7.25 

4.30 

7.30 

4.25 

7.35 

4.20 

7.40 

4.17 

7.43 

46 

4.41 

7.19 

4.36 

7.24 

4.31 

7.29 

4.26 

7.34 

4.21 

7.39 

4.16 

7.44 

4.13 

7.47 

47 

4.3S 

7.22 

4.33 

7.27 

4.28 

7.32 

4.23 

7.37 

4.17 

7.43 

4.12 

7.48 

4.  9 

7.51 

48 

4.35 

7.25 

4.30 

7.30 

4.25 

7.35 

4.19 

7.41 

4.13 

7.47 

4.  7 

7.53 

4.  5 

7.55 

49 

4.32 

7.28 

4.27 

7.33 

4.21 

7.39 

4.15 

7.45 

4.  9 

7.51 

4.  3 

7.57 

4.  0 

8.  0 

50 

4.29 

7.31 

4.23 

7.37 

4.17 

7.43 

4.11 

7.49 

4.  5 

7.55 

3.58 

8.  2 

3.55 

8.  5 

51 

4.25 

7.35 

4.19 

7.41 

4.13 

7.47 

4.  7 

7.53 

4.  0 

8.  0 

3.54 

8.  6 

3.50 

8.10 

52 

4.22 

7.38 

4.15 

7.45 

4.  9 

7.51 

4.  2 

7.58 

3.55 

8.  5 

3.48 

8.12 

3.45 

8.15 

53 

4.18 

7.42 

4.11 

7.49 

4.  4 

7.56 

3.58 

8.  2 

3.50 

8.10 

3.43 

8.17 

3.39 

8.21 

54 

4.14 

7.46 

4.  7 

7.53 

4.  0 

8.  0 

3.52 

8.  8 

3.45 

8.15 

3.37 

8.23 

3.33 

8.27 

55 

4.  9 

7.51 

4.  2 

7.5S 

3.55 

8.  5 

3.47 

8.13 

3.39 

8.21 

3.31 

8.29 

3.27 

8.33 

56 

4.  5 

7.55 

3.57 

8.  3 

3.49 

8.11 

3.41 

8.19 

3.33 

8.27 

3.24 

8.36 

3.20'  8.40 

57  '4.  0 

8.  0 

3.52 

8.  8 

3.44 

8.16 

3.35 

8.25 

3.26 

8.34 

3.17 

8.43 

3.12    8.18 

58    3.55 

8.  5 

3.46 

8.14 

3.38 

8.22 

3.28 

8.32 

3.19 

8.41 

3.  9 

8.51 

3.  4    8.56 

59 

3.49 

8.11 

3.40 

8.20 

3.31 

8.29 

3.21 

8.39 

3.11 

8.49 

2.  0 

9.  0 

2.55 

9.  5 

60 

3.43 

8.17 

3.34 

8.26 

3.24 

8.36 

3.13 

8.47 

3.  2 

8.58 

2.51 

9.  9 

2.45 

9.15 

61 

3.36 

8.24 

3.26 

8.34 

3.16 

8.44 

3.  5 

8.55 

2.53 

9.  7 

2.40 

9.20 

2.34 

9.26 

62 

3.29 

8.31 

3.18 

8.42 

3.  7 

8.53 

2.55 

9.  5 

2.42 

9.18 

2.28 

9.32 

2.21 

9.39 

63 

3.22 

8.38 

3.10 

8.50 

2.58 

9.  2 

2.44 

9.16 

2.30 

9.30 

2.14 

9.46 

2.  6    9.54 

64 

3.13 

8.47 

3.  0 

9.  0 

2.47 

9.13 

2.32 

9.28 

2.16 

9.44 

1.58 

10.  2 

1.48  10.12 

65 

3.  3 

8.57 

2.50 

9.10 

2.35 

9.25 

2.18 

9.42 

2.  0 

10.  0 

1.38 

10.22 

1.26  10.34 

66 

2.53 

9.  7 

2.37 

9.23 

2.21 

9.39 

2.  2 

9.58 

1.39 

10.21 

1.10 

10.50 

0.51  ill.  9 

66 

^2.46 

9.14 

2.30 

9.30 

2.12 

9.48 

1.51 

10.  9 

1.26 

10.34 

0.48 

11.12 

0.  0 

12. 

Lat. 

Sett 

Ris. 

Sett. 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

Sett 

Ris. 

LATITUDE   AND    DECLINATION    OF    OOKTBAKY   NAMES. 

84                  TABLE  XVII. 

ALTITUDES  BY  WHICH  THE  APPARENT  TIME  MAY  BE  FOUND  WITH  THE  GREATEST  ACCURACY. 

Lat 

DBCLINXTTON  OF  THE  OBJECT,  OF  THE  SAME  NJIME  AS  THE  LA.TITUDE.                          1 

Lat 

2° 

40 

6° 

8°  ] 

10°] 

12°] 

[40 

[6° 

1 8°  20°; 

12°  240 ', 

260  28°; 

30°; 

32°  34° ; 

36°. 

38° 

10° 

o 
0 

o 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

0 
0 

1 

30 

14 

10 

7 

6 

5 

4 

4 

3 

3 

3 

2 

2 

2 

2 

2 

2 

2 

2 

2 

1 

2 

90 

30 

19 

15 

12 

10 

8 

7 

6 

6 

5 

5 

5 

4 

4 

4 

4 

3 

3 

3 

2 

3 

42 

49 

30 

22 

18 

15 

12 

11 

10 

9 

8 

7 

7 

6 

6 

6 

5 

5 

5 

5 

3 

4 

30 

90 

42 

30 

24 

20 

17 

15 

13 

12 

11 

10 

9 

9 

8 

8 

7 

7 

7 

6 

4 

5 

24 

53 

56 

39 

30 

25 

21 

18 

16 

15 

13 

12 

11 

11 

10 

9 

9 

9 

8 

8 

5 

6 

20 

42 

90 

49 

37 

30 

26 

22 

20 

18 

16 

15 

14 

13 

12 

11 

11 

10 

10 

9 

6 

7 

17 

35 

59 

61 

45 

36 

30 

26 

23 

21 

19 

17 

16 

15 

14 

13 

13 

12 

11 

11 

7 

8 

15 

30 

49 

90 

53 

42 

35 

30 

27 

24 

22 

20 

19 

17 

16 

15 

14 

14 

13 

13 

8 

9 

12 

26 

42 

63 

64 

49 

40 

34 

30 

27 

25 

23 

21 

20 

18 

17 

16 

15 

15 

14 

9 

10 

11 

24 

37 

53 

90 

57 

46 

39 

34 

30 

28 

25 

23 

22 

20 

19 

18 

17 

16 

16 

10 

11 

10 

22 

33 

47 

66 

67 

52 

44 

38 

34 

31 

28 

26 

24 

22 

21 

20  19 

18 

17 

11 

12 

10 

20 

30 

42 

59 

90 

59 

49 

42 

37 

34 

31 

28 

26 

25 

23 

22  21 

20 

19 

12 

13 

9 

18 

28 

38 

51 

68 

68 

55 

47 

41 

37 

34 

31 

29 

27 

25 

24 

23 

21 

20 

13 

14 

8 

17 

20 

35 

46 

59 

90 

61 

52 

45 

40 

37 

33 

31 

29 

27 

26 

24 

23 

22 

14 

15 

8 

16 

24 

33 

42 

53 

69 

70 

57 

49 

44 

40 

36 

34 

31 

29 

28 

26 

25 

24 

15 

16 

7 

15 

22 

30 

39 

49 

61 

90 

63 

54 

47 

43 

39 

36 

33 

31 

30 

28 

27 

25 

16 

17 

7 

14 

21 

28 

36 

45 

56 

71 

71 

59 

51 

46 

42 

39 

36 

34 

32 

30 

28 

27 

17 

18 

6 

13 

20 

27 

34 

42 

52 

63 

90 

65 

56 

49 

45 

41 

38 

36 

34 

32 

30 

29 

18 

19 

6 

12 

19 

25 

32 

40 

48 

58 

72 

72 

60 

53 

48 

44 

41 

38 

36 

34 

32 

30 

19 

20 

6 

12 

18 

24 

31 

37 

45 

54 

65 

90 

66 

57 

51 

47 

43 

40 

38 

36 

34 

32 

20 

21 

6 

11 

17 

23 

29 

35 

42 

50 

60 

73 

73 

62 

55 

50 

46 

43 

40 

38 

36 

34 

21 

22 

5 

11 

16 

22 

28 

34 

40 

47 

56 

66 

90 

67 

59 

53 

49 

45 

42 

40 

38 

36 

22 

23 

5 

10 

16 

21 

26 

32 

38 

45 

52 

61 

73 

74 

63 

57 

51 

48 

44 

42 

39 

37 

23 

24 

5 

10 

15 

20 

25 

31 

36 

43 

49 

57 

67 

90 

68 

60 

54 

50 

47 

44 

41 

39 

24 

25 

5 

9 

14 

19 

24 

29 

35 

41 

47 

54 

62 

74 

75 

64 

58 

53 

49 

46 

43 

41 

25 

26 

5 

9 

14 

19 

23 

28 

33 

39 

45 

51 

59 

68 

90 

69 

61 

56 

52 

48 

45 

43 

26 

27 

4 

9 

13 

18 

22 

27 

32 

37 

43 

49 

56 

64 

75 

76 

65 

59 

54 

51 

48 

45 

27 

28 

4 

9 

13 

17 

22 

26 

31 

36 

41 

47 

53 

60 

69 

90 

70 

62 

57 

53 

50 

47 

28 

29 

4 

8 

12 

17 

21 

25 

30 

35 

40 

45 

51 

57 

65 

76 

76 

66 

60 

56 

52 

49 

29 

30 

4 

8 

12 

16 

20 

25 

29 

34 

38 

43 

49 

54 

61 

70 

90 

71 

64 

58 

54 

51 

30 

31 

4 

8 

12 

16 

20 

24 

28 

33 

37 

42 

47 

52 

58 

66 

76 

77 

67 

61 

57 

53 

31 

32 

4 

8 

11 

15 

19 

23 

27 

32 

36 

40 

45 

50 

56 

62 

71 

90 

71 

64 

60 

56 

32 

33 

4 

7 

11 

15 

19 

22 

26 

31 

35 

39 

43 

48 

54 

60 

67 

77 

77 

68 

62 

58 

33 

34 

4 

7 

11 

14 

18 

22 

26 

30 

34 

38 

42 

47 

52 

57 

63 

72 

90 

72 

65 

61 

34 

35 

3 

7 

10 

14 

18 

21 

25 

29 

33 

37 

41 

45 

50 

55 

61 

68 

77 

78 

69 

63 

35 

36 

3 

7 

10 

14 

17 

21 

24 

28 

32 

36 

40 

44 

48 

53 

58 

65 

72 

90 

73 

66 

36 

37 

3 

7 

10 

13 

17 

20 

24 

27 

31 

35 

39 

43 

47 

51 

56 

62 

68 

78 

78 

70 

37 

38 

3 

7 

10 

13 

16 

20 

23 

27 

30 

34 

38 

41 

45 

50 

54 

59 

65 

73 

90 

74 

38 

39 

3 

6 

10 

13 

16 

19 

23 

26 

29 

33 

37 

40 

44 

48 

53 

57 

62 

69 

78 

78 

39 

40 

3 

6 

9 

12 

16 

19 

22 

25 

29 

32 

36 

39 

43 

47 

51 

55 

60 

66 

73 

90 

40 

42 

3 

6 

9 

12 

15 

18 

21 

24 

28 

31 

34 

37 

41 

45 

48 

52 

57 

62 

67 

74 

42 

44 

3 

6 

9 

12 

15 

17 

20 

23 

26 

29 

33 

36 

39 

43 

46 

50 

54 

58 

62 

68 

44 

46 

3 

6 

8 

11 

14 

17 

20 

23 

25 

28 

31 

34 

38 

41 

44 

48 

51 

55 

59 

63 

46 

48 

3 

5 

8 

11 

14 

16 

19 

22 

24 

27 

30 

33 

36 

39 

42 

46 

49 

52 

56 

60 

48 

50 

3 

5 

8 

10 

13 

16 

18 

21 

24 

27 

29 

32 

35 

38 

41 

44 

47 

50 

54 

57 

50 

52 

3 

5 

8 

10 

13 

15 

18 

20 

23 

26 

28 

31 

34 

37 

39 

42 

45 

48 

51 

55 

52 

54 

2 

5 

7 

10 

12 

15 

17 

20 

22 

25 

28 

30 

33 

36 

38 

41 

43 

46 

49 

53 

54 

56 

2 

5 

7 

10 

12 

15 

17 

19 

22 

24 

27 

29 

32 

35 

37 

40 

42 

45 

48 

51 

56 

68 

2 

5 

7 

9 

12 

14 

17 

19 

21 

24 

26 

29 

31 

34 

36 

39 

41 

44 

47 

49 

58 

60 

2 

5 

7 

9 

12 

14 

16 

19 

21 

23 

26 

28 

30 

33 

35 

38 

40 

43 

45 

48 

60 

62 

2 

5 

7 

9 

11 

14 

16 

18 

20 

23 

25 

27 

80 

32 

35 

37 

39 

42 

44 

47 

62 

64 

2 

4 

7 

9 

11 

13 

16 

18 

20 

22 

25 

27 

29 

31 

34 

36 

39 

41 

43 

46 

64 

6Q 

2 

4 

7 

9 

11 

13 

15 

18 

20 

22 

24 

26 

29 

31 

33 

35 

38 

40 

42 

45 

66 

68 

2 

4 
4 

6 
6 

9 

11 

13 

15 

17 

19 

22 

24 

26 

28 

30 

33 

35 

37 

39 

42 

44 

68 

70 

2 

9 

11 

13 

15 

17 

19 

21 

23 

26 

28 

30 

32 

34 

36 

39 

41 

43 

70 

72 

2 

4 

6 

8 

11 

13 

15 

17 

19 

21 

23 

25 

28 

30 

32 

34 

35 

38 

40 

42 

72 

74 

2 

4 

6 

8 

10 

12 

15 

17 

19 

21 

23 

25 

27 

29 

31 

33 

35 

38 

40 

42 

74 

76 

2 

4 

6 

8 

10 

12 

14 

16 

19 

21 

23 

25 

27 

29 

31 

33 

35 

37 

39 

42 

76 

80 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

35 

37 

39 

41 

80 

^ 

2° 

40 

6° 

8° 

10° 

12° 

14° 

16° 

18° 

•20° 

22° 

24° 

26° 

28° 

30° 

32° 

34° 

36° 

38° 

40° 

TABLE  XVIII. 

86     1 

FOR  FINDING  THE  APPARENT  TIME  OF  24  OF  THE  PRINCIPAL  STARS  PASSING       | 

THE  MERIDIAN  THROUGHOUT  THE  YEAR. 

JANUARY. 

DAT. 

DAT. 

DAT. 

DAY. 

DAT.         DAT. 

DAT. 

DAT. 

DAT.         DAT. 

DAT. 

NAMES. 

1 

3 

6 

9 

12 

15 

18 

21 

24 

27 

30 

H.    M. 

H.    M. 

H.    M. 

H.    M. 

H.  ;u. 

H.    M. 

H.    M. 

H.    M. 

B.    M. 

H.    M. 

H.     M. 

Polar  Stab,  .  .  . 

6.2D 

6.12 

5.58 

5.45 

5.32 

5.19 

5.  6 

4.54 

4.41 

4.29 

4.16 

ACHERNAR,  .... 

6.46 

6.38 

6.24 

6.11 

5.58 

5.45 

5.32 

5.20 

5.  7 

4.55 

4.42 

Aldebaran,  .  .  . 

9.42 

9.34 

9.20 

9.  7 

8.54 

8.41 

8.28 

8.16 

8.  3 

7.51 

7.38 

Capella, 

10.20 

10.12 

9.58 

9.45 

9.32 

9.19 

9.  6 

8.54 

8.41 

8.29 

8.16 

RiGEL, 

10.22 

10.14 

10.  0 

9.47 

9.34 

9.21 

9.  8 

8.56 

8.43 

8.31 

8.18 

Betelguese,  .  .  . 

11.   1 

10.53 

10.39 

10.26 

10.13 

10.  0 

9.47 

9.35 

9.22 

9.10 

8.57 

Canopus, 

11.35 

11.27 

11.13 

11.  0 

10.47 

10.34 

10.21 

10.  9 

9.56 

9.44 

9.31 

SiRIUS, 

11.53 

11.45 

11.31 

11.18 

11.  5 

10.52 

10.39 

10.27 

10.14 

10.  2 

9.49 

Castor, 

12.39 

12.31 

12.17 

12.  4 

11.51 

11.38 

11.25 

11.13 

11.  0 

10.48 

10.35 

Pollux, 

12.50 

12.42 

12.28 

12.15 

1202 

11.49 

11.36 

11.24 

11.11 

10.59 

10.46 

■' 

Argus, 

14.25 

14.10 

14.  3 

13.50 

13.37 

13.24 

13.11 

12.59 

12.46 

12.34 

13.21 

Regulus, 

15.15 

15.  6 

14.53 

14.40 

14.27 

14.14 

14.   1 

13.49 

13.36 

13.24 

13.11 

Dubhe, 

16.  9 

16.  0 

15.47 

1.5.34 

15.21 

15.  8 

14.55 

14.43 

14.30 

14.18 

14.  5 

Cross,  foot  Star. 

17.33 

17.25 

17.11 

16.58 

16.45 

16.32 

16.19 

16.  7 

15.54 

15.42 

15.29 

Spica, 

18.31 

18.23 

18.  9 

17.56 

17.43 

17.30 

17.17 

17.  5 

16.52 

16.40 

16.27 

Arcturus,  .... 

19.23 

19.14 

19.  1 

18.48 

18.35 

18.22 

18.  9 

17.57 

17.44 

17.32 

17.19 

Antares, 

21.34 

21.25 

21.12 

20.59 

20.46 

20.33 

20.20 

20.  8 

19.55 

19.43 

19.30 

Vega, 

23.46 

23.37 

23.24 

23.11 

22.58 

22.45 

22.32 

22.20 

22.  7 

21.55 

21.42 

Altair, 

0.58 

0.49 

0.36 

0.23 

0.10 

23.57 

23.44 

23.32 

23.19 

23.  7 

22.54 

Pavonis, 

1.28 

1.19 

1.  6 

0.53 

0.40 

0.27 

0.14 

0.  2 

23.49 

23.37 

23.24 

Ctgni, 

1.50 

1.41 

1.28 

1.15 

1.  2 

0.49 

0.36 

0.24 

0.11 

23.59 

23.46 

Gruis, 

3.14 

3.  5 

2.52 

2.39 

2.26 

2.13 

2.  0 

1.48 

1.35 

1.23 

1.10 

Fomalhaut,  .  .  . 

4.  4 

3.55 

3.42 

3.29 

3.16 

3.  3 

2.50 

2.38 

2.25 

2.13 

2.  0 

Pegasi, 

4.12 

4.  3 

3.50 

3.37 

3.24 

3.11 

2.58 

2.46 

2.33 

2.21 

2.  8 

FEBRUARY. 

I 

names. 

1 

3 

6 

9 

12 

15 

18 

21 

24 

27 

30 

H.    M. 

H.    M. 

B.    M. 

H.    M. 

H.    U. 

H.    M. 

H.    M. 

H.    M. 

H.    M. 

B.    H. 

H.     M. 

Polar  Star,  .  .  . 

4.  8 

4.  0 

3.48 

3.36 

3.24 

3.12 

3.  1 

2.49 

2.38 

2.26 

0.  0 

Achernar,  .  .  .  . 

4.34 

4.26 

4.14 

4.  2 

3.50 

3.38 

3.27 

3.15 

3.  4 

2.52 

0.  0 

Aldebaran,  .  .  . 

7.30 

7.22 

7.10 

6.58 

6.46 

6.34 

6.23 

6.11 

6.  0 

5.48 

0.  0 

Capella, 

8.  8 

8.  0 

7.48 

7.36 

7.24 

7.12 

7.  1 

6.49 

6.38 

6.26 

RiGEL, 

8.10 

8.  2 

7.50 

7.38 

7.26 

7.14 

7.  3 

6.51 

6.40 

6.28 

Betelguesk,  .  .  . 

8.49 

8.41 

8.29 

8.17 

8.  5 

7.53 

7.42 

7.30 

7.19 

7.  7 

Canopus, 

9.23 

9.15 

9.  3 

8.51 

8.39 

8.27 

8.16 

8.  4 

7.53 

7.41 

SiRIUS, 

9.41 

9.33 

9.21 

9.  9 

8.57 

8.45 

8.34 

8.22 

8.11 

7.59 

Castor, 

10.27 

10.19 

10.  7 

9.55 

9.43 

9.31 

9.20 

9.  8 

8.57 

8.45 

Pollux, 

10.38 

10.30 

10.18 

10.  6 

9.54 

9.42 

9.31 

9.19 

9.  8 

8.56 

Argus, 

12.14 

12.  6 

11.54 

11.42 

11.30 

11.18 

11.  7 

10.55 

10.44 

10.32 

Regulus, 

13.  3 

12.55 

12.43 

12.31 

12.19 

12.  7 

11.56 

11.44 

1133 

11.21 

Dubhe, 

13.57 

13.49 

13.37 

13.25 

13.13 

13.   1 

12.50 

12.38 

12.27 

12.15 

Cross,  foot  Star, 

15.21 

15.13 

15.   1 

14.49 

14.37 

14.25 

14.14 

14.  2 

13.51 

13  39 

Spica, 

16.19 

16.11 

15.51) 

1 5.47 

15.35 

15.23 

lo.l2 

15.  0 

14.49 

14.37 

Arcturus,  .... 

17.11 

17.  3 

16.51 

16.39 

16.27 

16.15 

16.  4 

15.52 

15.41 

15.29 

Antares, 

19.22 

19.14 

19.  2 

18.50 

ls.38 

18.26 

18.15 

18.  3 

17.52 

17.40 

Vega, 

21.34 

21.26 

21.14 

21.  2 

20.50 

20.38 

20.27 

20.15 

20.  4 

19.52 

Altair, 

22.46 

22.38 

22.26 

22.14 

22.  2 

21.50 

21.39 

21.27 

21.16 

21.  4 

Pavonis, 

23.16 

23.  8 

22.56 

22.44 

22.32 

22.20 

22.  9 

21.57 

21.46 

21.34 

Ctgni, 

23.38 

23.30 

23.18 

23.  6 

22.54 

22.42 

22.31 

22.19 

22.  8 

21.56 

Gruis, 

1.  1 

0.53 

0.41 

0.29 

0.17 

0.  5 

23.54 

23.42 

23.31 

23.19 

Fomalhaut,  .  .  . 

1.52 

1.44 

1.32 

1.20 

1.  8 

0.56 

0.45 

0.33 

0.22 

0.10 

Pegasi, 

2.  0 

1..52 

1.40 

1.28 

l.ic, 

1.  4 

0..53 

0.41 

0.30 

0.18 

86 


TABLE   XVIII. 


FOR  FINDING  THE  APPARENT  TIME  OF  24  OF  THE  PRINCIPAL  3TARS  PASSING 
THE  MERIDIAN  THROUGHOUT  THE  YEAR. 


MARCH. 


NAMSS. 


Polar  Star, 
achernar, . 
Aldebaran, 
Capella,  . 

RiGEL,    .    . 

Betelguese 


Canopus,  . 

SiRIUS,   .    . 

Castor,  , 
Pollux,  . 
Argus,  .  . 
Regulus, 


Dubhe,    , 
Cross,  foot 
Spica,   .  , 
Arcturus, 
Antares,  . 
Veoa,    .  . 


Altair,  . 
Pavonis,  , 
Cygni,  . 
Gruis,  . 
Fomalhaut, 
Peoasi,  .  .   . 


Star 


DAT. 


1 


H.    M. 

2.18 
2.44 
5.39 
6.17 
6.19 
6.56 


7.30 
7.48 
8.34 
8.45 
10.21 
11.13 


12.  7 
13.31 
14.29 
15.21 
17.33 
19.45 


20.57 
20.27 
21.4!> 
23.12 
0.  3 
0.11 


DAT. 

3 


H.    M 

2.10 
2.36 
5.31 
6.  9 
6.11 
6.48 


7.22 
7.40 
8.26 
8.37 
10.13 
11.  5 


11.59 
13.23 
14.21 
15.13 
17.25 
19.37 


20.49 
21.19 
21.41 
23.  4 
23.55 
0.  3 


DAY. 
6 


H.    M. 

1..59 
2.25 

5.20 
5.58 
6.  0 
6.37 


7.11 

7.29 

8.15 

8.26 

10.  2 

10.54 


11. 4S 
13.12 
14.10 
15.  2 
17.14 
19.26 


20.38 
21.  8 
21.30 
22.53 
23.44 
23.52 


DAr. 
9 


DAY. 

12 


H.    M. 

1.48 
2.14 
5.  9 
5.47 

5.49 
6.27 


7.  1 
7.19 

8.  4 
8.15 
9.51 

10.43 


11.37 
13.  1 
13.59 
14.51 
17.  3 
19.15 


20.27 
20.57 
21.19 
22.42 
23.33 
23.41 


H. 

1.37 
2.  3 

4.58 
5.36 
5.38 
6.15 


6.49 

7.  7 
7.53 

8.  4 
9.40 

10.32 


11.26 
12.50 
13.48 
14.40 
16.52 
19.  4 


20.16 
20.46 
21.  8 
22.31 
23.22 
23.30 


DAY. 

15 


H.    M. 

1.26 
1.52 
4.47 
5.25 
5.27 
6.  4 


6.38 
6.56 
7.42 
7.53 
9.29 
10.21 


11.15 
12.39 
13.37 
14.29 
16.41 
18.53 


20.  5 
20.35 
20.57 
22.20 
23.11 
23.19 


DAY. 

18 


H.    M. 

1.15 
1.41 
4.36 
5.14 
5.16 
5.53 


6.27 
6.45 
7.31 
7.42 

9.18 
10.10 


11.  4 
12.28 
13.26 
14.18 
16.30 
18.42 


19.54 
20.24 
20.46 

22.  9 

23.  0 
23.  8 


DAY. 
21 


H.  M 
1.    4 

1.30 
4.25 
5.  3 
5.  5 
5.42 


6.16 
6.34 

7.20 
7.31 
9.  7 
9.59 


10.53 
12.17 
13.15 
14.  7 
16.19 
18.31 


19.43 
20.13 
20.35 
21.58 
22.49 
22.57 


DAY. 

24 


H.    M. 

0.53 
1.19 
4.14 
4.52 
4.54 
5.31 


6.  5 
6.23 

7.  9 
7.20 
8.56 
9.49 


10.42 

12.  6 

13.  4 
13.56 
16.  8 
18.20 


19.32 
20.  2 
20.24 
21.47 
22.38 
22.46 


DAY.         DAY. 

27        30 


B.    M 

0.43 
1.  9 
4.  4 
4.42 
4.44 
5.21 


5.55 
6.13 
6.. 59 
7.10 

8.46 
9.38 


10.32 
11.56 
12.54 
13.46 
15.58 
18.10 


19.22 
19.52 
20.14 
21.37 

22.28 
22.36 


H.    I 

0.32 
0.58 
3.53 
4.31 
4.33 
5.10 

5.44 
6.  2 
6.48 
6.59 
8.35 
9.27 


10.21 
11.45 
12.43 
l;^.35 
15.47 
17.59 


19.11 
19.41 
20.  3 
21.26 
22.17 
22.25 


APRIL, 


NAMES. 


Polar  Star,  . 

AcHERNAR,  .    . 

Aldebaram,  . 
Capella,  .  .  . 

RiGEL,   .... 
Betelguese,  . 


Canopus,  . 

SiRIUS,  .    . 

Castor,  . 
Pollux,  . 
Argus,  .  . 
Regulus,  , 


1 


Dubhe, 

Cross,  foot  Star, 

Spica, 

Arcturus,  .  .  .  . 
Antares,  .  .  .  . 
Vega, 


Altair,  .  . 
Pavonis,  .  . 
Cygni,  .  .  . 
Gruis,  .  .  . 
Fomalhaut, 
Pegasi,    .  . 


B.    M 

0.24 
0.50 
3.46 
4.24 
4.26 
5.  5 


5.39 
5.57 
6.43 
6.54 
8.30 
9.19 


10.13 
11.37 
12.35 
13.27 
15.38 
17.50 


19.  2 
19.32 
19.54 
21.17 
22.  7 
22.15 


B.    M. 

0.17 
0.43 
3.39 
4.17 
4.19 
4.58 


5.32 

5.50 
6.36 
6.47 
8.23 
9.12 


10.  6 
11.30 
12.28 
13.20 
15.31 
17.43 


18.55 
19.25 
19.47 
21.10 
22.  0 
22.  8 


B.    M 

0.  6 
0.32 
3.28 
4.  6 
4.  8 
4.47 


5.21 
5.39 
6.25 
6.36 

8.12 
9.   1 


9.55 
11.19 
12.17 
13.  9 
15.20 
17.32 


18.44 
19.14 
19.36 
20.59 
21.49 
21.57 


B.    M. 

23.55 
0.21 
3.17 
3.55 
3.57 
4.36 


5.10 
5.28 
.6.14 
6.25 
8. 
8.50 


9.44 

11.  8 

12.  6 
12.58 
1.5.  9 
17.21 


18.32 
19.  3 
19.25 
20.48 

21.38 
21.46 


12 


B.    M 

23.44 
0.10 
3.  6 
3.44 
3.46 
4.25 


4.59 
5.17 
6.  3 
6.14 
7.50 
8.39 


9.33 
10.57 
11.55 
12.47 
14.58 
17.10 


18.22 
18.52 
19.14 
20.37 
21.27 
21.35 


15 


B. 

23.33 
23.59 
2.55 
3.33 
3.35 
4.14 


4.48 

5.  6 
5.52 

6.  3 
7.39 
8.28 


9.22 
10.46 
11.44 
12.36 
14.47 
16.59 


18.11 
18.41 
19.  3 
20.26 
21.16 
21.24 


18 


B.    M. 

23.22 
23.48 
2.44 
3.22 
3.24 
4.  3 


4.37 
4.55 
5.41 
5.52 

7.28 
8.17 


21 


B.    M. 

23.11 
23.37 
2.33 
3.11 
3.13 
3.52 


9.11 
10.35 
11.33 
12.25 
14.36 
16.48 


18.  0 
18.30 
18.52 
20.15 
21.  5 
21.13 


4.26 
4.44 
5.30 
5.41 
7.17 
8.  6 


9.  0 
10.24 
11.22 
12.14 
14.25 
16.37 


17.49 
18.19 
18.41 

20.  4 
20.54 

21.  2 


24 


B.    M 

23.  0 
23.26 
2.22 
3.  0 
3.  2 
3.41 


4.15 

4.33 
5.19 
5.30 
7.  6 
7.55 


8.49 
10.13 
11.11 
12.  3 
14.14 
16.26 


17.38 
18.  8 
18,30 
19.53 
20.43 
20.52 


27 


a.  M. 

22.48 
23.14 
2.10 
2.48 
2.50 
3.29 


4.  3 
4.21 

5.  7 
5.18 
6.54 
7.43 


30 


a.  M. 

22.37 
23.  3 
1.59 
2.37 
2.39 
3.18 


8.37 
10.  1 
10.59 
11.51 
14.  2 
16.14 


17.26 
17.56 
18.18 
19.41 
20.31 
20.39 


3.52 
4.10 
5.56 
5.  7 
6.43 
7.32 


8.26 
9.50 
10.48 
11.40 
13.51 
16. 


17.15 
17.45 

18.  7 
19.30 
20.20 

20.28 


TABLE  XVIII. 


87 


FOR  FINDING  THE  APPARENT  TIME  OF  24  OF  THE  PRINCIPAL  STARS  PASSING 
THE  MERIDIAN  THROUGHOUT  THE  YEAR. 


MAY. 


NAMES. 


Polar  Star,  . 
achernar,  .  . 
Aldebaran,  . 
Capella,  .  .  . 
RiOEL,    .... 

Betelotjese,  . 


Canopus,  , 
Sirius,  .  , 
Castor,  , 
Pollux,  , 
Argus,  .  , 
Reoulus, 


DAT. 


H.     M. 

22.33 
22.59 
1.55 
2.33 
2.35 
3.14 


DAY. 

3 


H.    M. 

22.26 

22.52 

1.48 

2.26 

2.28 
3.  7 


DUBHE, 

Cross,  foot  Star. 

Spica, 

Arcturus,  .  .  .  . 

Antares, 

Vega, 

Altair, 

Pavonis, 

Cygni, 

Gruis, 

fomalhaut,  .  .  . 
Pegasi, 


3.48 

4.  6 
4.52 

5.  3 
6.39 
7.28 


8.22 
9.46 
10.44 
11.36 
13.47 
15.59 


17.11 
17.41 

18.  3 
19.26 
20.17 
20.25 


DAY. 

6 


H.    M. 

22.14 
22.40 
1.36 
2.14 
2.16 
2.55 


3.41 
3.59 
4.45 
4.56 
6.32 
7.21 


8.15 
9.39 
10.37 
11.29 
13.40 
15.52 


17.  4 
17.34 
17.56 
19.19 
20.10 
20.18 


3.29 
3.47 
4.33 
4.44 

6.20 

7.  9 


8.  o 
9.27 
10.25 
11.17 
13.28 
15.40 


DAY. 
9 


DAY. 

12 


H.    M. 

22.  2 
22.28 
1.24 
2.  2 
2.  4 
2.43 


3.17 
3.35 
4.21 
4.30 

6.  8 
6.57 


7.51 

9.15 
10.13 
11.  5 
13.16 
15.28 


H.    M. 

21.51 
22.17 
1.13 
1.5 
1.53 
2.32 


3.  6 
3.24 
4.10 
4.21 
5.57 
6.46 


DAY. 

15 


H.    M. 

21.39 
22.06 
1.01 
1.39 
1.41 
2.20 


DAY. 

18 


H.    I 

21.27 
21.53 
0.49 
1.27 
1.29 
2.  8 


DAY. 

21 


16.52 

17.22 
17.34 

19.  7 
19.58 

20.  6 


16.40 
17.10 
17.22 
18.55 
19.46 
19.54 


7.40 
9.  4 
10.  2 
10.54 
13.  5 
15.17 


10.29 
16.59 
17.11 
18.44 
19.35 
19.43 


2.54 
3.12 
3.58 
4.  9 
5.45 
6.34 


7.28 

8.52 

9.50 

10.42 

12.53 

1.5.  5 


16.17 
16.47 
16.59 
18.32 
19.23 
19.31 


2.42 
3.  0 
3.46 
3.57 
5.33 
6.22 


7.16 

8.40 

9.38 

10.30 

12.41 

14.53 


H.    M 

21.15 
21.41 
0.37 
1.15 
1.17 
1.56 


DAT. 
24 


H.    M 

21.  3 
21.29 
0.25 
1.  3 
1.  5 
1.44 


DAY. 

27 


2.30 
2.58 
2.34 
3.45 
5.21 
6.10 


7.  4 

8.28 

9.26 

10.18 

12.29 

14.41 


16.  5 
16.35 
16.47 
18.20 
19.11 
19.19 


2.18 
2.46 
2.22 
3.33 
5.  9 
5.58 


6.52 

8.16 

9.14 

10.  6 

12.17 

14.29 


H.    M. 

20.51 
21.17 
0.13 
0.51 
0.53 
1.32 


DAT. 

30 


H.    M. 

20.39 
21.05 
0.01 
0.39 
0.41 
1.20 


2.  6 
2.34 
2.10 
3.21 
4.57 
5.46 


6.40 

8.  4 

9.  2 
9.54 

12.  5 
14.17 


15.53 
16.23 
16.35 

18.  8 
18.59 

19.  7 


15.41 
16.11 
16.23 
17.56 

18.47 
18.55 


1.54 
2.22 
1.58 
3.  9 
4.45 
5.34 


6.28 
7.52 
8.50 
9.42 
11.53 
14.  5 


15.29 
15.59 
16.11 
17.44 
18.35 
18.43 


15.17 
15.47 
15.59 
17.32 
18.23 
18.31 


JUNE. 


NAMES. 


Polar  Star,  . 
Aohernar,  .  . 
Aldebaran,  . 
Capella,  .  .  . 
RiGEL,  .... 
Betelguese,  . 


Canopus, 
Sirius,  . 
Castor, 
Pollux, 
Argus,  . 
Regulus, 


1 


H.    M. 

20.31 

20.57 

23.53 

0.31 

0.33 

1.12 


H.    M. 

20.22 

20.48 

23.44 

0.22 

0.24 

1. 


DuBHE, 

Cross,  foot  Star, 

Spica, 

Arcturus,  .  .  .  . 

Antares, 

Vega, 


Altair,  .  . 
Pavonis,  .  . 
Cygni,  .  .  . 
Gruis,  .  .  . 
Fomalhaut, 
Pkgasi,.  .  . 


1 .46 

2.  4 
2.50 

3.  1 
4.37 
5.26 


6.20 
7.44 
8.42 
9.34 
11.45 
13.57 


15.  9 
15.39 

16.  1 
17.24 
18.15 
18.23 


1.39 
1.55 
2.41 
2.52 

4.28 
5.17 


6.11 

7.35 

8.:- 

9.25 
11.36 
13.48 


15.  0 
15.30 
15.52 
17.15 
18.  6 
18.14 


H.    M. 

20.10 

20.36 

23.32 

0.10 

0.12 

0.51 


1.25 
1.43 
2.29 
2.40 
4.16 
5.  5 


5.59 
7.23 
8.21 
9.13 
11.24 
13.36 


14.48 
15.18 
15.40 

17.  3 
17.54 

18.  2 


H.    M. 

19.58 
20.24 
23.22 
23.58 

0.  0 

0.39 


12 


H.  M. 

19.45 
20. 1 1 
23.  9 
23.45 
23.49 
0.26 


1.13 
1.31 
2.17 

2.28 
4.  4 
4.53 


5.47 
7.11 

8.  9 

9.  1 
11.12 
13  24 


14.36 
15.  6 
15.28 
16.51 
17.42 
17.50 


1.  0 
1.18 

2.  4 
2.15 
3.51 
4.40 


5.34 

6.58 

7.56 

8.58 

10.59 

13.11 


14.23 
14.53 
15.15 
16.38 
17.29 
17.37 


15 


H.    M. 

19.33 
1 9.59 
22.57 
23.33 
23.37 
0.14 


0.48 

1.  6 
1.52 

2.  3 
3.39 
4.28 


5.22 
6.46 

7.44 

8.46 

10.47 

12.59 


14.11 
14.41 
15.  3 
16.26 
17.17 
17.25 


18 


H.    M. 

19.20 
19.46 
22.44 
23.20 
23.24 
0.   1 


0.35 
0.53 
1.39 
1.50 
3.26 
4.15 


5.  9 
6.33 
7.31 
8.33 
10.  S4 
12.46 


13.58 
14.28 
14.50 
16.13 
17.  4 
17.12 


21 


H.    M. 

19.  8 
19.34 
22.32 
23.  8 
23.12 
23.59 


0.23 
0.41 
1.27 
1.38 
3.14 
4.  3 


4.57 
6.21 
7.19 
8.21 
10.22 
12.34 


13.46 
14.16 
14.38 

16.  1 
16.52 

17.  0 


24 


H.    M. 

18.55 
19.21 
22.19 
22.55 
22.59 
23.46 


0.10 
0.28 
1.14 
1.25 
3.  1 
3.50 


4.44 

6.  8 

7.  6 

8.  8 
10.10 
12.21 


13.33 
14.  3 
14.25 
15.48 
16.39 
16.47 


27 


H.    M. 

18.43 
19.  9 
22.  7 
22.43 
22.47 
23.34 


23.48 
0.16 
1.  2 
1.13 
2.49 
3.38 


4.32 
5.56 
6.54 
7.56 
9.57 
12.  9 


13.21 
13.51 
14.13 
15.36 
16.27 
16.35 


30 


H.     M. 

18.30 
18.56 
21.54 
22.30 
22.34 
23.21 


23.35 

0.  3 
0.49 

1.  0 
2.36 
3.25 


4.19 
5.43 
6.41 
7.43 
9.44 
11.56 


13.  8 
13.38 

14.  0 
15.23 
16.14 
16.22 


88 


TABLE   XVIII. 


FOR  FINDING  THE  APPARKNT  TIME  OF  24  OF  THE  PRINCIPAL  STARS  PASSING 
THE  MERIDIAN  THROUGHOUT  THE  YEAR 


JULY. 


NAMES. 


Polar  Star, 
achkrnar, . 
Aldebaran, 
Capella,  , 

RlOEL,    .    , 

Betelguese 


Canopus,  . 

SiRIUS,   .    . 

Castor,  , 
Pollux,  , 
Argus,  .  . 
Regulus, 


DUBHK, 

Cross,  foot 
Spica,   .  . 
Arcturus, 
Antares,  . 
Vega,   .  . 


Altair,  .  . 
Pavonis,  . 
Ctgni,  .  . 
Gruis,  .  . 
fomalhaut, 
Pegasi,  .  .  . 


Star, 


DAT. 
1 


H.    H. 

18.26 
18.52 
21.48 
22.26 

22.28 
23.  7 


23.41 
23.59 
0.45 
0.56 
2.32 
3.21 


4.17 
5.39 
6.37 
7.29 
9.40 
11.52 


13.  4 
13.34 
13.56 
15.19 
16.10 
16.18 


DAT. 

3 


H.    M. 

18.18 
18.44 
21.40 
22.18 
22.20 
22.59 


23.33 
23.51 
0.37 
0.48 
2.24 
3.13 


4.  9 
5.31 
6.29 
7.21 
9.32 
11.44 


12.56 
13.26 
13.48 
15.11 
16.  2 
16.  8 


DAT. 
6 


B.    M. 

18.  6 
18.32 
21.28 
22.  6 
22.  8 
22.47 


23.21 
23.39 
0.25 
0.36 
2.12 
3.  1 


3.57 
5.19 
6.17 
7.  9 
9.20 
11.32 


12.44 
13.14 
13.36 
14.59 
15.50 
15.56 


DAT. 
9 


DAT. 

12 


H.    U. 

17.53 
18.19 
21.15 
21.53 
2155 
22.34 


23.  8 
23.26 
0.12 
0.23 
1.59 
2.48 


3.44 

5.  6 

6.  4 
6.56 
9.  7 

11.19 


12.31 
13.  1 
13.23 
14.46 
15.37 
15.43 


H.    M. 

17.41 
18.  7 
21.  3 
21.41 
21.43 
22.22 


22.56 
23.14 
0.  0 
0.11 
1.47 
2.36 


3.32 
4.54 
5.52 
6.44 
8.55 
11.  7 


12.19 
12.49 
13.11 
14.34 
15.25 
15.31 


DAT. 
15 


H.    M 

17.29 
17.55 
20.51 
21.29 
21.31 
22.10 


22.44 
23.  2 
23.48 
23.59 
1.35 
2.24 


3.20 
4.42 
5.40 
6.32 
8.43 
10.55 


12.  7 
12.37 
12.59 
14.22 
15.13 
15.19 


DAT. 

18 


H.    U. 

17.17 
17.43 
20.39 
21.17 
21.19 
21.58 


22.32 
22.50 
23.36 
23.47 
1.23 
2.12 


3.  8 
4.30 
5.28 
6.20 
8.31 
10.43 


11.55 
12.25 
12.47 
14.10 
15.  1 
15.  7 


DAT. 
21 


H.    M 

17.  5 
17.31 
20.27 
21.05 
21.  7 
21.46 


22.20 
22.38 
23.24 
23.35 
1.11 
2.  0 


2.56 
4.18 
5.16 
6.  8 
8.19 
10.31 


11.43 
12.13 
12.35 
13.58 
14.49 
14.55 


DAT. 

24 


16.53 
17.19 
20.15 
20.53 
20.55 
21.34 


22.  8 
22.26 
23.12 
23.23 
0.59 
1.48 


2.44 

4.  6 

5.  4 
5.56 

8.  7 
10.19 


11.31 
12.  1 
12.28 
13.46 
14.37 
14.43 


DAT.         DAT. 
27  30 


H.    H. 

16.41 

17.  7 
20.  3 
20.41 
20.43 
21.22 


21.56 
22.14 
23.  0 
23.11 
0.47 
1.36 


2.32 
3.54 
4.52 
5.44 
7.55 
10.  7 


11.19 
11.49 
12.11 
13.34 
14.25 
14.31 


H.    M. 

16.29 
16.55 
19.51 
20.29 
20.31 
21.10 


21.44 
22.  2 
22.48 
22.59 
0.35 
1.24 


2.20 
3.42 
4.40 
5.32 
7.43 
9.55 


11.  7 
11.37 
11.59 
13.22 
14.13 
14.19 


AUGUST. 


NAMES. 


Polar  Star,  .  .  . 
achernar,  .  .  .  . 
Aldebaran,  .  .  . 

Capella, 

RiGEL, 

Betelguese,  .  .  . 

Canopus, 

SiRIUS,  

Castor, 

Pollux, 

Argus, 

Regulus, 

DUBHB, 

Cross,  foot  Star, 

Spica, 

Arcturus,  .  .  .  . 
Antares,  .  .  .  . 
Vega, 

Altair, 

Pavonis, 

Cyoni, 

Gruis, 

Fomalhaut,  .  .  . 
Pegasi, 


H.    M. 

16.21 
16.47 
19.43 
20.21 
20.23 
21.  2 


21.36 
21.54 
22.40 
22.51 
0.27 
1.16 


2.10 
3.34 
4.32 
5.24 
7.35 
9.47 


10.59 
11.29 
11.51 
13.14 
14.  5 
14.13 


H.    M. 

16.14 
16.40 
19.36 
20.14 
20.16 
20.55 


21.29 
21.47 
22.33 
22.44 
0.20 
1.  9 


2.  3 
3.27 
4.25 
5.17 

7.28 
9.40 


10.52 
11.22 
11.44 

13.  7 
13.58 

14.  6 


H. 

16. 
16.28 
19.24 
20.  2 
20.  4 
20.43 


21.17 
21.35 
22.21 
22.32 

0.  8 
0.57 


1.51 
3.15 
4.13 
5.  5 

7.16 

9.28 


10.40 
11.10 
11.32 
12.55 
13.46 
13.54 


H.    M. 

15.51 
16.17 
19.13 
19.51 
19.53 
20.32 


21.  6 
21.24 
22.10 
22.21 
23.57 
0.46 


1.40 

3.  4 

4.  2 
4.54 

7.  5 
9.17 


10.29 
10.. 59 
11.21 
12.44 
13.35 
13.43 


12 


H.    M 

15.39 
16.  5 
19.01 
19.39 
19.41 
20.20 


20.54 
21.12 
21.58 
22.  9 
2:^45 
0.34 


1.28 
2.52 
3.50 
4.42 
6.53 
9.  5 


10.17 
10.47 
11.  9 
12.32 
13.23 
13.31 


15 


H.    M, 

15.28 
15.54 
18.50 
19.28 
19.30 
20.  9 


20.43 
21.  1 
21.47 
21.58 
23.34 
0.23 


1.17 
2.41 
3.39 
4.31 
6.42 
8.54 


10.  6 
10.36 
10.58 
12.21 
13.12 
i:{.20 


18 


H.    M. 

15.17 
15.43 
18.39 
19.17 
19.19 
19.58 


21 


20.32 
20.50 
21.36 
21.47 
23.23 
0.12 


1.  6 
2.30 

3.28 
4.20 
6.31 
8.43 


9.55 
10.25 
10.47 
12.10 
13,  1 
13.  9 


H.    M. 

15.  6 
15.32 

18.28 
19.  6 
19.  8 
19.47 


24 


20.21 
20.39 
21.25 
21.36 
23.12 
0.  1 


0.55 
2.19 

2.17 
4.  9 
6.20 

8.32 


9.44 
10.14 
10.36 
11.59 
12.50 
12.58 


H.    U. 

14.54 
15.20 
18.16 
18.54 
18.56 
19.35 


27 


20.  9 
20.27 
21.13 
21.24 
23.  0 
23.49 


0.43 
2.  7 
2.  5 
3.57 

6.  8 
8.20 


9.32 
10.  2 
10.24 
11.47 
11.38 
12.46 


H.     M. 

14.44 
15.  9 
18.05 
18.44 
18.45 
19.24 


19.58 
20.16 
21.  2 
21.13 
22.49 
23.38 


0.32 
1.56 
1..54 
3.46 
557 
8.  9 


9.21 
9.51 
10.13 
11.36 
11.27 
12.35 


30 


H.    M. 

14.34 
14.59 
17.54 
18.34 
18.85 
19.14 


19.48 

20.  6 
20.52 

21.  3 
22.39 
23.28 


0.22 
1.46 
1.44 
3.36 
5.47 
7.59 


9.11 
9.41 
10.  3 
11.26 
11.17 
12.25 


TABLE  XVIII. 


89 


FOE  FINDING  THE  APPARENT  TIME  OF  24  OF  THE  PRINCIPAL  STARS  PASSING 
THE  MERIDIAN  THROUGHOUT  THE  YEAR. 


SEPTEMBER. 


NAMES. 


Polar  Star, 
achernar, . 
Aldebaran, 
Capella,  , 

RiGKL,    .    , 

Betelgxtese 


Canopus,  . 
Smius,  .  . 
Castor,  . 
Pollux,  . 
Argus,  .  . 
Regulus,  . 


DUBHE,  . 

Cross,  foot 
Spica,   .  . 
Arcturits, 

Antares,. 

Vega,    .  . 


Altair,  . 
Pavonis,  , 
Cyoni,  .  . 
Gruis,  .  , 
f  jmalhaut, 
Peoasi,  .  .  . 


Star 


DAT. 

1 


H.  M. 

14.25 
14.51 
17.47 

18.25 
18.27 
19.  6 


19.40 
19.58 
20.44 
20.55 
22.32 
23.20 


0.14 
1.38 
2.36 
3.28 
5.39 
7.51 


9.  3 

9.33 

9.55 

11.18 

12.  9 

12.17 


DAT. 
3 


H.    M 

14.18 
14.44 
17.40 
18.18 
18.20 
18.59 


19.33 
19.51 

20.37 
20.48 
22.24 
23.13 


0.  7 
1.31 
2.29 
3.21 
5.32 
7.44 


8.56 

9.26 

9.48 

11.11 

12.  2 

12.10 


DAT. 

6 


H.    M. 

14.  7 
14.33 
17.29 

18.  7 
18.  9 

18.48 


19.22 
19.40 
20.26 
20.37 
22.13 
23.  2 


23.56 
1.20 
2.18 
3.10 
5.21 
7.33 


8.45 

9.15 

9.37 

11.  0 

11.51 

11.59 


DAT. 
9 


a.  M 

13.56 
14.22 
17.18 
17.56 

17.58 
18.37 


19.11 
19.29 
20.15 
20.26 
22.  2 
22.51 


23.45 

1.  9 

2.  7 
2.59 
5.10 
7.22 


8.34 

9.  4 

9.26 

10.49 

11.40 

11.48 


DAT. 

12 


,H.    M. 

13.46 
14.12 

17.  8 
17.46 

17.48 

18.27 


19.  I 
19.19 

20.  5 
20.16 
21.52 
22.41 


23.35 
0.59 
1.57 
2.49 
5.  0 
7.12 


8.24 

8.54 

9.16 

10.39 

11.30 

11.38 


DAT. 
15 


H.    M. 

13.35 
14.  1 
16.57 
17.35 
17.37 
18.16 


18.50 

19.  8 
19.54 

20.  5 
21.41 
22.30 


23.24 

0.48 
1.46 
2.38 
4.49 
7.  1 


8.13 

8.43 

9.  5 

10.28 

11.19 

11.27 


DAT. 

18 


H.    M. 

13.24 
13.50 
16.46 
17.24 
17.26 
18.  5 


18.39 
18.57 
19.43 
19.54 
21.30 
22.19 


23.13 
0.37 
1.35 
2.27 
4.38 
6.50 


8.  2 

8.32 

8.54 

10.17 

11.  8 

11.16 


DAT. 

21 


a.  M. 
13.13 
13.39 
16.35 
17.13 
17.15 
17.54 


P\T. 

24 


a.  1 

13.  2 
13.28 
16.24 
17.  2 
17.  4 
17.43 


18.28 
18.46 
19.32 
19.43 
21.19 
22.  8 


23.  2 
0.26 
1.24 
2.16 
4.27 
6.39 


7.51 
8.21 
8.43 

10.  6 
10.57 

11.  5 


18.17 
18.35 
19.21 
19.32 
21.  8 
21.57 


DAT. 

27 


H.    M 

12.52 
13.18 
16.14 
16.52 
16.54 
17.33 


18.  7 
18.25 
19.11 
19.22 

20.58 
21.47 


22.51  22.41 


0.15 
1.13 
2.  5 

4.16 

6.28 


7.40 
8.10 
8.32 
9.55 
10.46 
10.54 


DAT. 

30 


H.    M. 

12.41 
13.  7 
16.  3 
16.41 
16,43 
17.22 


17.56 
18.14 
19.  0 
19.11 
20.47 
21.36 


0. 
1. 
1.55 
4.  0 
6.18 


7.30 
8.  0 
8.22 
9.45 
10.36 
10.44 


22.30 
23.54 
0.52 
1.44 
3.55 
6.  7 

7.19 
\49 
8.11 
9.34 
10.25 
10.33 


OCTOBER. 


NAMES. 


Polar  Star, 

AcHERNAR, . 

Aldebaran, 
Capella,  . 

RiGEL,   .   . 

Betbloitssk. 


Canopus,  . 

SiRIUS,  .   , 

Castor,  , 
Pollux,  . 
Argus,  .  , 
Regulus,  , 


DuBHE,  .    . 

Cross,  foot 
Spioa,   .  . 
Arcturus, 
Antares,  . 
Vega,    .  . 


Altair,  . 
Pavonis,  . 
Cygni,  .  . 
Gruis,  .  , 
Fomalhaut, 
Pegasi,.  .  . 


Star 


1 


a.  M. 
12.37 
13.  3 
15.59 
16.37 
16.39 
17.18 


17.52 
18.10 
18.56 
19.  7 
20.43 
21.32 


22.26 
23.50 
0.48 
1.40 
3.51 
6.  3 


7.15 
7.45 
8.  7 
9.30 
10.21 
10.29 


H.    M. 

12.30 
12.56 
15.52 
16.30 
16.32 
17.11 


17.45 

18.  3 
18.49 

19.  0 
20.36 
21.25 


22.19 
23.43 
0.41 
1.33 
3.44 
5.56 


7.  8 
7.38 

8.  7 
9.23 

10.14 
10.22 


a.  M 
12.19 
12.45 
15.41 
16.19 
16.21 
17.  0 


17.34 
17.52 

18.38 
18.49 
20.25 
21.14 


22.  8 
23.32 
0.30 
1.22 
3.33 
5.45 


6.57 
7.27 
7.56 
9.12 
10.  3 
10.11 


9 


a.  u. 
12.  8 
12.34 
15.30 
16.  8 
16.10 
16.49 


17.23 
17.41 

18.27 
18.38 
20.14 
21.  3 


21.57 
23.21 
0.19 
1.11 
3.22 
5.34 


6.46 
7.16 
7.45 
9.  1 
9.52 
10.  0 


12 


a.  M 
11.57 
12.23 
15.19 
15.57 
15.59 
16.38 


17.12 
17.30 
18.16 

18.27 
20.  3 
20.52 


21.46 
23.10 

0.  8 

1.  0 
3.11 
5.23 


6.35 
7.  5 
7.34 
8.50 
9.41 
9.49 


15 


a.  M 
11.46 
12.12 
15.  8 
15.46 
15.48 
16.27 


17.  1 
17.19 

18.  5 
18.16 
19.52 
20.41 


21.35 

22.59 

23.57 

0.49 

3.  0 

5.12 


6.24 
6.54 
7.23 
8.39 
9.30 
9.38 


18 


a.  M. 
11.35 
12.  1 
14.57 
15.35 
15.37 
16.16 


16.50 

17.  8 
17.54 

18.  5 
19.41 
20.30 


21.24 

22.48 

23.46 

0.38 

2.49 

5.   1 


6.13 
6.43 
7.12 

8.28 
9.19 
9.27 


21    ,   24 


a.  M. 
11.23 
11.49 
14.45 
15.23 
15.25 
16.  4 


16.38 
16.56 
17.42 
17.53 
19.29 
20.18 


H.    M 

11.12 
11.38 
14.34 
15.12 
15.14 
15.53 


21.12 

22.36 

23.34 

0.26 

2.37 

4.49 


6.  1 
6.31 

7.  0 
8.16 
9.  7 
9.15 


16.27 
16.45 
17.31 
17.42 
19.18 
20.  7 


21.  1 

22.25 

23.23 

0.15 

2.26 

4.38 


5.50 
6.20 
6.49 

8.  5 
8.56 

9.  4 


27 


u. 

0 


a. 
11. 
11.26 
14.22 
15.  0 
15.  2 
15.41 


16.15 
16.33 
17.19 
17.30 
19.  6 
19.55 


20.49 

22.13 

23.11 

0.  3 

2.14 

4.26 


5.38 
6.  8 
6.37 
7.53 
8.44 
8.52 


30 


a.  M. 
10.49 
11.15 
14.11 
14.49 
14.51 
15.30 


16.  4 
16.22 

17.  8 
17.19 
18.55 
19.44 


20.38 

22.  2 

23.  0 
23.52 

2.  3 
4.15 


5.27 
5.57 
6.26 
7.42 
8.33 
8.41 


»3 


TABLE   XVIII. 


FOR  FINDING   THE  APPARENT  TIME  OF  24  OF  THE  PRINCIPAL  STARS  PASSING 
THE  MERIDIAN  THROUGHOUT  THE  YEAR. 


NOVEMBER. 


NAMES. 


Polar  Star, 
achernab, . 
Aldebaran, 
Capblla,  , 

RiGEL,    .    , 

Betelguese 


Canopus,  . 
Sirius,  .  . 
Castor,  . 
Pollux,  . 
Argus,  .  . 
Regulus, 


DUBHE,     . 

Cross,  foot 
Spica,   .  . 
Arctubus, 
Antares,  . 
Vega,   .  . 


Alt  air,  .  . 
Pavonis,  . 
Ctgni,  .  . 
Gbuis,  .  . 
fomalhaut, 
Pegasi,  .  .  . 


Stab 


DAT. 
1 


H.    M. 

10.41 
11.  7 
14.  3 
14.41 
14.43 
15.22 


15.56 
16.14 
17.  0 
17.11 

18.47 
19.36 


20.30 
21.54 
22.52 
23.44 
1.55 
4.  7 


5.19 
5.49 
6.11 
7.34 

8.25 
8.33 


DAY. 

3 


H.    M. 

10.33 
10.59 
13.55 
14.33 
14.35 
15.14 


15.48 

16.  6 
16.52 

17.  3 
18.39 
19.28 


20.22 
21.46 
22.44 
23.36 
1.47 
3.59 


5.11 
5.41 
6.  3 

7.26 

8.17 
8.25 


DAT. 

6 


DAf. 

9 


H.     M. 

10.21 
10.47 
13.43 
14.21 
14.23 
15.  2 


4.59 
5.29 
5.51 
7.14 
8.  5 
8.13 


H.    M 

10.  9 
10.35 
13.31 
14.  9 
14.11 
14.50 


15.24 
15.42 
16.28 
16.39 
18.15 
19.  4 


DAY. 

12 


H.    M 

9.57 
10.23 
13.19 
13.57 
13.59 
14.38 


15.12 
15.30 
16.16 
16.27 
18.  3 
18.52 


19.58 
21.22 
22.20 
23.12 
1.23 
3.35 


4.47 
5.17 
5.39 

7.  2 
7.53 

8.  1 


19.46 
21.10 

22.  8 

23.  0 
1.11 
3.23 


4.35 
5.  5 
5.27 
6.50 
7.41 
7.49 


DAY. 

15 


H.    M. 

9.45 
10.11 
13.  7 
13.45 
13.47 
14.26 


15.  0 
15.18 

16.  4 
16.15 
17.51 
18.40 


19.34 
20.58 
21.56 
22.48 
0.59 
3.11 


4.23 
4.53 
5.15 

6.38 
7.29 
7.37 


DAY. 

18 


H.    M. 

9.32 
9.58 
12.54 
13.32 
13.34 
14.13 


14.47 

15.  5 
15.51 

16.  2 

17.38 
18.27 


19.21 
20.45 
21.43 
22.35 
0.46 
2.58 


4.10 
4.40 
5.  2 
6.25 
7.16 
7.24 


DAY, 
21 


H.    M. 

9.20 
9.46 
12.42 
13.20 
13.22 
14.  1 


14.35 
14.53 
15.39 
15.50 
17.26 
18.15 


19.  9 
20.33 
21.31 
22.23 
0.34 
2.46 


3.58 
4.28 
4.50 
6.13 
7.  4 
7.12 


DAY. 

24 


H.    M 

9.  7 
9.33 
12.29 
13.  7 
13.  9 
13.48 


14.22 

14.40 

15.26 

15.37 

17.1 

18.  2 


18.56 
20.20 
21.18 
22.10 
0.21 
2.33 


3.45 
4.15 
4.37 
6.  0 
6.51 
6.59 


DAY. 

27 


H.    M. 

8.54 
9.20 
12.16 
12.54 
12.56 
13.35 


14.  9 
14.27 
15.13 
15.24 
17.  0 
17.49 


18.43 
20.07 
21.  5 
21.57 
0.  8 
2.20 


3.32 
4.  2 
4,24 
5.47 
6.38 
6.46 


DAY, 

30 


H.    H. 

8,41 
9.  7 
12.  3 
12.41 
12.43 
13.22 


13.56 
14.14 
15.  0 
15.11 
16.47 
17.86 


18.30 
19.54 
20.52 
21.44 
23.55 
2.  7 


3.19 

3.49 

4,1J 

5.34 

6.25 

6.33 


DECEMBER. 


names. 


Polar  Stab, 
achebnab,  . 
Aldebaban, 
Capella,  , 
Rigel,  .  , 
Betelgxtese, 


Canopus,  . 

SiBIUS,  .    . 

Castob,  . 
Pollux,  . 
Argus,  .  . 
Regulus,  . 


Dubhe,  . 
Cross,  foot 
Spica,    .  . 
Arcturus, 
Antabes, 
Vega,    .  . 


Altaib,  . 
Pavonis,  , 
Ctgni,  .  . 
Gbuis,  .  . 

FoMALHAUT, 

Pegasi,    .  . 


Star 


1 


H.    M. 

8.37 
9.  3 
11.59 
12.37 
12.39 
13.18 


13.52 
14,10 
14,56 
15.  7 
16.43 
17.32 


18.26 
19.50 
20,48 
21.40 
23.51 
2.  3 

3.15 
3.45 
4.  7 
5.30 
6.21 
6.29 


H.    U 

8.29 
8.55 
11,51 
12.29 
12.31 
13.10 


13.44 
14.  2 
14.48 
14.59 
16.35 
17.24 


18.18 
19.42 
20,40 
21,32 
23.43 
1.55 

3,  7 
3,37 
3.59 
5.22 
6.13 
6.21 


6 


H.    M 

8.15 
8.41 
11.37 
12.15 
12.17 
12.56 


13.30 
13.48 
14.34 
14.45 
16.21 
17.10 


18.  4 
19.28 
20.26 
21.18 
23.29 
1.41 

2.53 
3.23 
3.45 

5.  8 
5.59 

6.  7 


H. 

8. 

8.28 
11.24 
12,  2 
12,  4 
12,43 


13.17 
13.35 
14.21 
14.32 
16.  8 
16.57 


17.51 
19.15 
20.13 
21.  5 
23,16 
1.28 

2.40 
3.10 
3.32 
4.55 
5.46 
5,54 


12 


H.    M. 

7.49 
8.15 
11.11 
11.49 
11.51 
12,30 


13.  4 
13.22 

14.  8 
14.19 
15.55 
16.44 


17.38 

19.  2 

20.  0 
20.52 
23.  3 

1.15 

2.27 
2.57 
3.19 
4.42 
5,33 
5,41 


15 


H.    M. 

7.36 
8.  2 
10.58 
11.36 
11.38 
12.17 


12.51 

13.  9 
13.55 

14.  6 
15.42 
16,31 


17,25 
18.49 
19.47 
20.39 
22.50 
1.  2 

2.14 
2.44 
3.  6 
4.29 
5.20 
5,28 


18 


H.    M. 

7,23 
7.49 
10.45 
11.23 
11.25 
12.  4 


12.38 
12.56 
13.42 
13.53 
15.29 
16.18 


17.12 
18.36 
19.34 
20.26 
22.37 
0.49 

2.  1 
2.31 
2.53 
4.16 
5.  7 
5.15 


21 


H.    M. 

7.  9 
7.35 
10.3 
11.  9 
11.11 
11.50 


12.24 
12.42 
13.28 
13.39 
15.15 
16.  4 


17.00 
18.22 
19.20 
20.12 
22.23 
0.35 

1.47 
2.17 
2.39 

4.  2 
4.53 

5,  1 


24 


H.    M. 

6,56 
7.22 
10.18 
10.56 
10.58 
11,37 


12.11 
12.29 
13.15 
13.26 
15.  2 
15.51 


16.46 

18.  9 

19.  7 
19.59 
22.10 

0.22 

1.34 
2.  4 
2.26 
3.49 
4,40 
4,48 


27 


H.     U 

6.43 
7.  9 
10.  5 
10.43 
10.45 
11.24 


30 


11.58 
12.16 
13.  2 
13.13 
14,49 
15,38 


16,33 
17.56 
18.54 
19.46 
21.57 
0.  9 

1.21 
1.51 
2.13 
3.36 
4.27 
4.35 


H.    M. 

6.29 

6.55 

9.51 

10.29 

10.31 

11.10 


11.44 
12.  2 
12.48 
12.59 
14.35 
15.24 


16.20 
17.42 
18.40 
19.32 
21.43 
23,55 

1.  7 
1.37 
1.59 
3.22 
4.13 
4,2jj 


TABLES  XIX— X: 

s:. 

91 

TABLE    XIX. 

PLACES  OF  24  OF  THE  PRINCIPAL  FLKED  STARS,  FOR  THE  YEAR  1864.          | 

UAO. 

NAME.                                   1 

EIGHT  ASCENSION. 

ANNUAL  VAS. 

DECLINATION,    ANNUAL  VAE. 

2 

Polar  Star, 

H.      M.      8. 

1     6     3 

+17.83 

O          ' 

88  32 N. 

It 
+  19-3 

ACHERNAR,  . 

1  32  15 

2-23 

57  59  S. 

-18-5 

Aldebaran, 

4  27  32 

3-43 

16  13  N. 

+  7-9 

Capella,  .  . 

5     6  55 

4-41 

45  51  N. 

+  4-8 

RiGEL,     .    .    . 

5     7  31 

2-b» 

8  23  S. 

-  4-6 

Betelguesh, 

5  47  17 

3-24 

7  22  N. 

+   1-2 

Canopus,  ,  . 

6  20  44 

1-33 

52  37  S. 

+   1-8 

SiRIUS,    .    .    . 

6  38  43 

2-65 

16  31  S. 

+  4-5 

Castor,  .  .  . 

7  25  17 

3-86 

32  12 N. 

-  7-2 

Pollux,    .  . 

7  36  21 

3-68 

28  22  N. 

-  8-1 

2 

Argus,  .  .  . 

9  11  37 

0-73 

69     4S. 

—  14-8 

Regulus,  .  . 

10     0  35 

3-22 

12  41 N. 

—  17-4 

DUBHE, 

Cross, 

10  54  50 
12  18  31 

3-81 
3-27 

62  32 N. 

62  17  S. 

-19-2 
+20-0 

foot 

Star,  .  . 

Spica,.  .  .  . 

13  17  29 

3-15 

10  24  S. 

+  18-9 

Arcturus,  . 

14     8  59 

2-73 

19  57  N. 

-19-9 

Antares,  .  . 

16  20  24 

3-66 

26     6S. 

+  8-5 

Vega,.  .  .  . 

18  31  57 

201 

38  39  N. 

+  2-8 

Altair,     .  . 

19  43  37 

2-93 

8  29  N. 

+   8-4 

Pavonis,  .  . 

20  14     0 

4-81 

57  12  S. 

-11-0 

2 

Cygni,    .  .  . 

20  36  27 

204 

44  46 N. 

+  12-6 

Gruis,    .  .  . 

21  59     3 

3-82 

47  40  S. 

-17-3 

Fomalhaut, 

22  49  32 

3-31 

30  25  S, 

-191 

2 

Pegasi,  .  .  . 

•     •     •     •     • 

22  57  30 

2-98     1    14  25  N. 

+  19-3 

Sign  -f"  means  add.     Sign  —  me 

ans  subtract. 

TABLE   XX. 

1 

CORRECTION  TO  BE  SUBTRACTED  FROM  THE  OBSERVED  ALTITUDE  OF  A  FIXED      | 

STAR,  OR  A  PLANET,  TO  FIND  THE 

TRUE  ALTITUDE.                                   | 

Obs 

Alt 

HEIGHT    OF   THE    EYE    ABOVE   THE    SEA    KJ    FEET. 

#'s 
Obs. 

AIL 

.      4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

o 
5 

1 
11.8 

12.2 

12.6 

12.9 

1 
13.2 

1 
13.5 

13.7 

1 
14.0 

14.2 

14.4 

14.6 

14.8 

15.0 

/ 

15.1 

o 
5 

6 

10.4 

10.8 

11.2 

11.5 

11.8 

12.1 

12.3 

12.6 

12.8 

13.0 

13.2 

13.4 

13.6 

13.7 

6 

7 

9.3 

9.7 

10.1 

10.4 

10.7 

11.0 

11.2 

11.5 

11.7 

11.9 

12.1 

12.3 

12.5 

12.6 

7 

8 

8.4 

8.8 

9.2 

9.5 

9.8 

10.1 

10.3 

10.6 

10.8 

11.0 

11.2 

11.4 

11.6 

11.7 

8 

9 

7.7 

8.1 

8.5 

8.8 

9.1 

9.4 

9.6 

9.9 

10.1 

10.3 

10.5 

10.7 

10.9 

11.0 

9 

10 

7.2 

7.6 

8.0 

8.3 

8.6 

8.9 

9.1 

9.4 

9.6 

9.8 

10.0 

10.2 

10.4 

10.5 

10 

11 

6.7 

7.1 

7.5 

7.8 

8.1 

8.4 

8.6 

8.9 

9.1 

9.3 

9.5 

9.7 

9.9 

10.0 

11 

12 

6.3 

6.7 

7.1 

7.4 

7.7 

8.0 

8.2 

8.5 

8.7 

8.9 

9.1 

9.3 

9.5 

9.6 

12 

14 

5.7 

6.1 

6.5 

6.8 

7.1 

7.4 

7.6 

7.9 

8.1 

8.3 

8.5 

8.7 

8.9 

9.0 

14 

16 

5.2 

5.6 

6.0 

6.3 

6.6 

6.9 

7.1 

7.4 

7.6 

7.8 

8.0 

8.2 

8.4 

8.5 

16 

18 

4.8 

5.2 

5.6 

5.9 

6.2 

6.5 

6.7 

7.0 

7.2 

7.4 

7.6 

7.8 

8.0 

8.1 

18 

20 

4.5 

4.9 

5.3 

5.6 

5.9 

6.2 

6.4 

6.7 

6.9 

7.1 

7.3 

7.5 

7.7 

7.8 

20 

22 

4.3 

4.7 

5.1 

5.4 

5.7 

6.0 

6.2 

6.5 

6.7 

6.9 

7.1 

7.3 

7.5 

7.6 

22 

26 

3.9 

4.3 

4.7 

5.0 

5.3 

5.6 

5.8 

6.1 

6.3 

6.5 

6.7 

6.9 

7.1 

7.2 

26 

30 

3.6 

4.0 

4.4 

4.7 

5.0 

5.3 

5.5 

•  5.8 

6.0 

6.2 

6.4 

6.6 

6.8 

6.9 

30 

35 

3.3 

3.7 

4.1 

4.4 

4.7    5.0 

5.2 

5.5 

5.7 

5.9 

6.1 

6.3 

6.5 

6.6 

35 

40 

3.1 

3.5 

3.9 

4.2 

4.5    4.8 

5.0 

5.3 

5.5 

5.7 

5.9 

6.1 

6.3 

6.4 

40 

45 

2.9 

3.3 

3.7 

4.0 

4.3    4.6 

4.8 

5.1 

5.3 

5.5 

5.7 

5.9 

6.1 

6.3 

45 

50 

2.7 

3.1 

3.5 

3.8 

4.1     4.4 

4.6 

4.9 

5.1 

5.3 

5.5 

5.7 

5.9 

6.1 

50 

55 

2.6 

3.0 

3.4 

3.7 

4.0 

4.3 

4.5 

4.8 

5.0 

5.2 

5.4 

5.6 

5.8 

6.0 

55 

60 

2.5 

2.9 

3.3 

3.6 

3.9 

.4.2 

4.4 

4.7 

4.0 

5.1 

.5.3 

5.5 

5.7 

5.9 

60 

65 

2.4 

2.8 

3.2 

3.5 

3.8 

4.1 

4.3 

4.6 

4.8 

5.0 

5.2 

5.4 

5.6 

5.8 

65 

70 

2.3 

2.7 

3.1 

3.4 

3.7 

4.0 

4.2 

4.5 

4.7 

4.9 

5.1 

5.3 

5.5 

5.7 

70 

80 

2.1 

2.5 

2.9 

3.2 

3.6 

3.8 

4.0 

4.3 

4.5 

4.7 

4.9 

5.1 

5.3 

5.5 

80 

90 

1.9 

2.3 

2.7 

3.0 

3.3 

3.6 

3.8 

4.1 

4.3 

4.5 

4.7 

4.9 

5.1      5.3 

90 

TABLE   XXI. 

TO  FIND  THE  LATITUDE  BY  AN  ALTITUDE  OF  THE  POLAR  STAR. 

When  the  Right  Ab 
censioD  of  the  Meri- 
dian is  found  in  thin 
column,  the  correction 
is  Subtractive. 

EXPLANATION  OF  THE  TABLE, 

WHICH    18    CALCULATED    FOE    THE    TEAE     1854. 

Enter  the  side  column,  with  the  Right  Ascension 
of  the  Meridian  and  the  Altitude  of  the  Star  at  the 
top,  and  at  the  angle  of  meeting  will  be  the  required 
correction. 

When  the  Right  A»- 
cension  of  the  Meri- 
dian is  found  in  this 
column,  the  correction 
is  Additive. 

<4 

3s 

R.  A-  M. 

APPABENT  ALTITUDE  OF  THE  POLAR  STAE. 

R.  A.  M. 

8 

H.    If. 

H.     U. 

10° 

20° 

30° 

40° 

50° 

60° 

H.    M. 

H.     M. 

SUB. 

O         ' 

o       ' 

O         ' 

O         ' 

O         ' 

O        ' 

f 

1        0 

1     0 

1  28 

1  28 

1  28 

1  28 

1  28 

1  28 

13     0 

13     0 

3 

1  30 

0  30 

1  27 

1  27 

1  27 

1  27 

1  27 

1  27 

12  30 

13  30 

3 

2     0 

24     0 

1  25 

1  25 

1  24 

1  24 

1  24 

1  24 

12     0 

14    0 

3 

2  20 

23  40 

1  23 

1  23 

1  23 

1  22 

1  22 

1  22 

11  40 

14  20 

3 

2  40 

23  20 

1  20 

1  20 

1  20 

1  20 

1   19 

1   19 

11  20 

14  40 

3 

3     0 

23     0 

1   16 

1   16 

1   16 

1   16 

1   15 

1   15 

11   10 

15     0 

3 

3  10 

22  50 

1   14 

1   14 

1   14 

1   14 

1   13 

1   13 

10  50 

15  10 

3 

3  20 

22  40 

1   12 

1   12 

1   12 

1   12 

1  11 

1   10 

10  40 

15  20 

3 

3  30 

22  30 

1   10 

1     9 

1     9 

1     9 

1     8 

1     7 

10  30 

15  30 

3 

3  40 

22  20 

1     8 

1     8 

1     8 

1     8 

1     7 

1     5 

10  20 

15  40 

2 

3  50 

22  10 

1     6 

1     5 

1     5 

1     4 

1     3 

1     1 

10  10 

15  50 

2 

4     0 

22     0 

1     3 

1     2 

1     2 

1     2 

1     1 

1     1 

10     0 

16     0 

2 

4  10 

21  50 

1     0 

1     0 

1     0 

1     0 

1     0 

0  59 

9  50 

16  10 

2 

4  20 

21  40 

0  57 

0  57 

0  57 

0  57 

0  56 

0  55 

9  40 

16  20 

2 

4  30 

21  30 

0  54 

0  54 

0  54 

0  54 

0  53 

0  52 

9  30 

16  30 

2 

4  40 

21  20 

0  51 

0  51 

0  51 

0  51 

0  50 

0  49 

9  20 

16  40 

2 

4  50 

21   10 

0  48 

0  48 

0  48 

0  48 

0  47 

0  46 

9  10 

16  50 

2 

5     0 

21     0 

0  45 

0  44 

0  44 

0  44 

0  44 

0  42 

9     0 

17     0 

2 

5  10 

20  50 

0  41 

0  41 

0  40 

0  40 

0  40 

0  39 

8  50 

17  10 

2 

5  20 

20  40 

0  38 

0  37 

0  37 

0  37 

0  37 

0  35 

^  8  40 

17  20 

1 

5  30 

20  30 

0  35 

0  34 

0  34 

0  33 

0  33 

0  31 

8  30 

17  30 

5  40 

20  20 

0  31 

0  30 

0  30 

0  29 

0  29 

0  27 

8  20 

17  40 

5  50 

20  10 

0  27 

0  26 

0  26 

0  25 

0  25 

0  24 

8  10 

17  50 

6     0 

20    0 

0  23 

0  22 

0  22 

0  21 

0  21 

0  20 

8     0 

18     0 

6  10 

19  50 

0  19 

0  18 

0  18 

0  17 

0  17 

0  16 

7  50 

18  10 

6  20 

19  40 

0  15 

0  14 

0  14 

0  13 

0  13 

0  12 

7  40 

18  20 

1 

6  30 

19  30 

0  12 

0  11 

0  11 

0  10 

0  10 

0     9 

7  30 

18  30 

0 

6  40 

19  20 

0     8 

0     7 

0     7 

0     6 

0     6 

0     5 

7  20 

18  40 

0 

6  50 

19  10 

0     4 

0     3 

0     3 

0     2 

0    2 

0     1 

7  10 

18  50 

0 

6  55 

19     5 

0     1 

0     2 

0     2 

0    2 

0    3 

0     4 

7     0 

19     0 

0 

«t 


1 

TABLE  XXII. 

■ 

OOBBEOTION  OF  THE  TIME  OF  THE  MOON'S  MERIDIAN  PASSAGE,  OVER  THE         | 

MERIDIAN  ( 

OF   GREENWICH,  TO  THE   TIME  OF   HER   PASSAGE 

OVER   ANY  OTHER  MERIDIAN. 

DAILY 

VABIATION    OF   THE    MOON's    PASSING   THK    MERIDIAN. 

x. 

X. 

u. 

M. 

u. 

M. 

u. 

M. 

M. 

u. 

M. 

M. 

K. 

H. 

s 

40 

42 

44 

46 

48 

50 

52 

54 

56 

58 

60 

62 

64 

66 

0 

M. 

M. 

II. 

M. 

II. 

M. 

M. 

M. 

M. 

M. 

H. 

u. 

IL 

H. 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

10 

1 

1 

1 

1 

1 

1 

1 

1 

1 

2 

2 

2 

2 

2 

20 

2 

2 

2 

2 

3 

3 

3 

3 

3 

3 

3 

3 

3 

4 

30 

3 

3 

4 

4 

4 

4 

4 

4 

4 

5 

5 

5 

5 

5 

40 

4 

4 

5 

5 

5 

5 

6 

6 

6 

6 

6 

7 

7 

7 

50 

5 

6 

6 

6 

6 

7 

7 

7 

7 

8 

8 

8 

9 

9 

60 

6 

7 

7 

7 

8 

8 

8 

9 

9 

9 

10 

10 

10 

11 

70 

7 

8 

8 

9 

9 

9 

10 

10 

10 

11 

11 

12 

12 

12 

80 

9 

9 

10 

10 

10 

11 

11 

12 

12 

12 

13 

13 

14 

14 

90 

10 

10 

11 

11 

12 

12 

13 

13 

13 

14 

14 

15 

15 

16 

100 

11 

12 

12 

12 

13 

13 

14 

14 

15 

15 

16 

17 

17 

18 

110 

12 

13 

13 

14 

14 

15 

15 

16 

16 

17 

18 

18 

19 

19 

120 

13 

14 

14 

15 

15 

16 

17 

17 

18 

19 

19 

20 

20 

21 

130 

14 

15 

15 

16 

17 

17 

18 

19 

19 

20 

21 

21 

22 

23 

140 

15 

16 

17 

17 

18 

19 

20 

20 

21 

22 

22 

23 

24 

25 

150 

16 

17 

18 

19 

19 

20 

21 

22 

22 

23 

24 

25 

26 

26 

160 

17 

18 

19 

20 

21 

21 

22 

23 

24 

25 

26 

26 

27 

28 

170 

18 

19 

20 

21 

22 

23 

24 

25 

25 

26 

27 

28 

29 

30 

180 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

Th 

e  Sums 

taken 

from  th 

is  Table  mnet  be  added  to  the  time  of  the  Moon's  Meridian  F 

assage  i 

n  the 

Naut 

ical  Aln 

lanac,  ii 

a  West 

Longitude,  and  subtracted  in  East,  will  give  the  Mean  Time  of 

her  Mei 

■idian 

Passj 

ige  at  t 

le  Ship 

TABLE  XXIII. 

FOR  REDUCING  THE  MOON'S  DECLINATION  TO  THE  GREENWICH  TIME  OF  THE 

OBSERVATION. 

D 

Diff  of 

FOR    OD 

Moon's 

HOURS    FKOM    NOON    OB    MIDNIGHT. 

MINUTES. 

Declina- 
tion in  12 

M. 

M. 

M. 

M 

hours. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

24 

36 

48 

r 

o       ' 

O          ' 

O         ' 

o        ' 

O          ' 

O         ' 

o      ' 

O         ' 

o        ' 

o       ' 

o        ' 

o       ' 

t 

/ 

/ 

0     5 

0     0 

0     1 

0     1 

0     2 

0     2 

0     2 

0     3 

0     3 

0     4 

0     4 

0     5 

0 

0 

0 

0 

0  10 

0     1 

0     2 

0     2 

0     3 

0     4 

0     5 

0     6 

0     7 

0     7 

0     8 

0    9 

0 

0 

0 

1 

0  15 

0     1 

0     2 

0     4 

0     5 

0     6 

0    7 

0     9 

0  10 

0  11 

0  12 

0  14 

0 

0 

1 

1 

0  20 

0    2 

0     3 

0     5 

0     7 

0     8 

0  10 

0  12 

0  13 

0  15 

0  17 

0  18 

0 

1 

1 

0  25 

0     2 

0     4 

0     6 

0     8 

0  10 

0  12 

0  15 

0  17 

0  19 

0  21 

0  23 

0 

1 

2 

0  30 

0     2 

0     5 

0     7 

0  10 

0  12 

0  15 

0  17 

0  20 

0  22 

0  25 

0  27 

0 

1 

2 

0  35 

0     3 

0     6 

0     9 

0  12 

0  15 

0  17 

0  20 

0  23 

0  26 

0  29 

0  32 

2 

2 

0  40 

0     3 

0     7 

0  10 

0  13 

0  17 

0  20 

0  23 

0  27 

0  30 

0  33 

0  37 

2 

3 

0  45 

0     4 

0     7 

0  11 

0  15 

0  19 

0  22 

0  26 

0  30 

0  34 

0  37 

0  41 

2 

3 

0  50 

0     4 

0     8 

0  12 

0  17 

0  21 

0  25 

0  29 

0  33 

0  37 

0  42 

0  46 

2 

2 

3 

0  55 

0     5 

0     9 

0  14 

0  18 

0  23 

0  27 

0  32 

0  37 

0  41 

0  46 

0  51 

2 

3 

4 

1     0 

0     5 

0  10 

0  15 

0  20 

0  25 

0  30 

0  35 

0  40 

0  45 

0  50 

0  55 

2 

3 

4 

1     5 

0     5 

0  11 

0  16 

0  22 

0  27 

0  32 

0  38 

0  43 

0  49 

0  54 

1     0 

2 

3 

4 

1   10 

0     6 

0  12 

0  17 

0  23 

0  29 

0  35 

0  41 

0  47 

0  52 

0  58 

1     4 

2 

3 

5 

1   15 

0     6 

0  12 

0  19 

0  25 

0  31 

0  37 

0  44 

0  50 

0  56 

1     2 

1     9 

2 

4 

5 

1  20 

0     7 

0  13 

0  20 

0  27 

0  33 

0  40 

0  47 

0  53 

1     0 

1     7 

1   13 

3 

4 

5 

1  25 

0     7 

0  14 

0  21 

0  28 

0  35 

0  42 

0  50 

0  57 

1     4 

1   11 

1   18 

3 

4 

6 

1  30 

0     7 

0  15 

0  22 

0  30 

0  37 

0  45 

0  52 

1     0 

1     7 

1   15 

1  22 

3 

4 

6 

1  35 

0    8 

0  16 

0  24 

0  32 

0  40 

0  47 

0  55 

1     3 

1   11 

1   19 

1  27 

2 

3 

5 

6 

1  40 

0     8 

0  17 

0  25 

0  33 

0  42 

0  50 

0  58 

1     7 

1   15 

1  23 

1  32 

2 

3 

5 

7 

1  45 

0     9 

0  17 

0  26 

0  35 

0  44 

0  52 

1     1 

1   10 

1   19 

1  27 

1  36 

2 

3 

5 

7 

1  50 

0     9 

0  18 

0  27 

0  37 

0  46 

0  55 

1     4 

1   13 

1  22 

1  32 

1  42 

2 

4 

5 

7 

1  55 

0  10 

0  19 

0  29 

0  38 

0  48 

0  57 

1     7 

1   17 

1  26 

1  36 

1  45 

2 

4 

6 

8 

2     0 

0  10 

0  20 

0  30 

0  40 

0  50 

1     0 

1   10 

1  20 

1  30 

1  40 

1  50 

2 

4 

6 

8 

2     5 

0  10 

0  21 

0  31 

0  42 

0  52 

1     2 

1   13 

1  23 

1  34 

1  44 

1  55 

2 

4 

6 

8 

2  10 

0  11 

0  22 

0  32 

0  43 

0  54 

1     5 

1   16 

1  27 

1  37 

1  48 

1  59 

2 

4 

6 

9 

2  15 

0  11 

0  22 

0  34 

0  45 

0  56 

1     7 

1   19 

1  30 

1  41 

1  52 

2    4 

2 

4 

7 

9 

2  20 

0  12 

0  23 

0  35 

0  47 

0  58 

1   10 

1  22 

1  33 

1  45 

1  57 

2    8 

2 

5 

7 

9 

2  25 

0  12 

0  24 

0  36 

0  48 

1     0 

1   12 

1  25 

1  37 

1  49 

2     1 

2  13 

2 

5 

7 

10 

2  30 

0  12 

0  25 

0  37 

0  50 

1     2 

1   15 

1  27 

1  40 

1  52 

2     5 

2  17 

2 

5 

7 

10 

2  35 

0  13 

0  26 

0  39 

0  52 

1     5 

1    17 

1  30 

1  43 

1  56 

2     9 

2  22 

3 

5 

8 

10 

2  40 

0  13 

0  27 

0  40 

0  53 

1     7 

1  20 

1  33 

1  47 

2     0 

2  13 

2  27 

3 

5 

8 

11 

2  45 

0  14 

0  27 

0  41 

0  55 

1     9 

1  22 

1  36 

1  50 

2     4 

2  17 

2  31 

3 

5 

8 

11 

2  50 

0  14 

0  28 

0  42 

0  57 

1   11 

1  25 

1  39 

1  53 

2     7 

2  22 

2  36 

3 

6 

8 

11 

2  55 

0  15 

0  29 

0  44 

0  58 

1   13 

1  27 

1  42 

1  57 

2  11 

2  26 

2  40 

3 

6 

9 

12 

3     0 

0  15 
0  15 

0  30 

0  45 

1     0 

1   15 

1  30 

1  45 

2     0 

2  15 

2  30 

2  45 

3 

6 

9 

12 
12 

3     5 

0  31 

0  46 

1     2 

1   17 

1  32 

1  48 

2     3 

2  19 

2  34 

2  50 

3 

6 

9 

3  10 

0  16 

0  32 

0  47 

1     3 

1   19 

1  35 

1  51 

2     7 

2  22 

2  38 

2  54 

3 

6 

9 

13 

3  15 

0  16 

0  32 

0  49 

1     5 

1  21 

1  37 

1   54 

2  10 

2  26 

2  42 

2  59 

3 

6 

10 

13 

3  20 

0  17 

0  33 

0  50 

1     7 

1   23 

1  40 

1   57 

2  13 

2  30 

2  47 

3     3 

3 

7 

10 

13 

3  25 

0  17 

0  34 

0  51 

1     8 

1  25 

1  42 

2     0 

2   17 

2  34 

2  51 

3     8 

3 

7 

10 

14 

3  30 

0  17 

0  35 

0  52 

1   10 

1  27 

1   45 

2     2 

2  20 

2  37 

2  55 

3  12 

3 

7 

10 

14 

3  35 

0  18 

0  36 

0  54 

1   12 

1  30 

1  47 

2     5 

2  23 

2  41 

2  59 

3  17 

4 

7 

11 

14 

3  40 

0  IS 

0  37 

0  55 

1   13 

1  32 

1   50 

2     8 

2  27 

2  45 

3     3 

3  22 

4 

7 

11 

15 

3  45 

0  19 

0  37 

0  56 

1    15 

1  34 

1   52 

2  11 

2  39 

2  49 

3     7 

3  26 

4 

7 

11 

15 

Note. — This  Table  is  constructed  upon  the  following  principle: — Rule.  Say  as  12  hours  is 

to  the 

diflFerence  or  change  in  the  Moon's  Declination  in   12  hours,  so  is  the  time  past  Greenwich  N 

oon  or 

Midnight  to  the  Correction,  which  must  be  applied  to  the  Declination  at  the  preceding  Noon  or  Mi 

doig'bt. 

aooording  as  it  is  increasing  or  decreasing. 

06 

TABLE  XTIV. 

CORRECTION  OF  THE  M00N*3  SEMIDIAMETER,  OR  HORIZONTAL  PARALLAX,  FOR  ANT 

GIVEN  TIME  BETWEEN  NOON  AND  MIDNIGHT,  OR  OF  THE  SUN  OR  A  PLANET'S 

DECLINATION   FOR  A  GIVEN  TIME  FROM  THE  PRECEDING  NOON. 

I  2  2 

a=-a 

VARIATION    OF   THE    Jf  'S   SEMIDIAMETER,    OR    HORIZONTAL    PARALLAX,    IN    12    HOOR8. 

**  o 

a  * 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

fr 

20 

21 

22 

n 

23 

/r 

24 

25 

26 

27 

rf 

28 

H.     M. 

0  30 

1  0 

1  30 

2  0 

2  30 

3  0 

0 
0 
0 
0 
0 
0 

0 
0 
0 
0 
0 
0 

0 
0 
0 
0 

0 
0 
0 

0 
0 
1 
1 

1 
1 

0 

0 
1 

1 

1 
1 

0 
1 
1 
1 
1 
2 

0 
1 
1 

1 
2 
2 

0 
1 
1 
1 
2 
2 

0 

1 
1 

2 
2 

2 

0 

1 
1 

2 

2 
3 

0 
1 
1 
2 
2 
3 

1 
1 
2 
2 
3 
3 

1 
1 
2 
2 
3 

3 

1 
1 
2 
2 
3 
4 

1 
1 
2 
3 
3 
4 

1 
1 
2 
3 
4 
4 

1 
1 
2 
3 
4 
4 

1 
2 
2 
3 
4 
5 

1 
2 
2 
3 
4 
5 

1 
2 
■3 
3 
4 
5 

1 
2 
3 
4 
5 
5 

1 
2 
3 
4 
5 
6 

1 
2 
3 
4 
5 
6 

1 

2 
3 

4 

5 
6 

1 
2 
3 
4 
5 
6 

1 
2 
3 
4 

5 

7 

1 
2 
3 
5 

6 

7 

B. 

1 

2 
3 
4 
5 

6 

3  30 

4  0 

4  30 

5  0 

5  30 

6  0 

0 
0 
0 
0 
0 
0 

2 
2 
2 

1 
2 
2 

2 
2 
2 

2 
2 
2 
2 
3 
3 

2 
2 
3 
3 
3 
3 

2 
3 
3 
3 
4 
4 

3 
3 
3 
4 
4 
4 

3 
3 
4 
4 
5 
5 

3 
4 
4 
5 
5 
5 

3 
4 
4 
5 
5 
6 

4 
4 
5 
5 
6 
6 

4 
5 
5 

6 
6 

7 

4 
5 

6 
6 

7 

7 

5 
5 
6 

7 
7 
8 

5 

6 
6 

7 
8 
8 

5 
6 

7 
7 
8 
9 

6 
6 

7 
8 
9 
9 

6 

7 
7 
8 
9 
10 

6 

7 

8 

9 

10 

10 

6 
7 
8 
9 
10 
11 

7 

8 

9 

10 

11 

11 

7 

8 

9 

10 

11 

12 

7 

8 

9 

10 

11 

12 

8 
9 
10 
11 
12 
13 

8 
9 
10 
11 
12 
13 

8 
9 

10 
12 
18 
14 

7 

8 

9 

10 

11 

12 

6  30 

7  0 

7  30 

8  0 

8  30 

9  0 

2 
2 
2 
2 
2 
2 

2 
2 
2 
3 
3 
3 

3 
3 
3 
3 
4 
4 

3 
3 
4 
4 
4 
4 

4 
4 
4 
5 
5 
5 

4 
5 
5 
5 

6 
6 

5 
5 

6 
6 

6 

7 

5 
6 
6 

7 
7 
7 

6 
6 

7 
7 
8 
8 

6 

7 
7 
8 
8 
9 

7 
8 
8 
9 
9 
10 

8 
8 
9 
9 
10 
10 

8 

9 

9 

10 

11 

11 

9 
9 
10 
11 
11 
12 

9 
10 
11 
11 
12 
13 

10 
11 
12 
13 
13 

10 

n 

12 
13 
13 
14 

11 
12 
12 
13 
14 
15 

11 
12 
13 
14 
15 
10 

17 
17 

18 
19 
20 
21 

12 
13 
14 
15 
16 
16 

17 

18 
19 
20 
21 
22 

12 
13 
14 
15 
16 
17 

18 

19 
20 
21 
22 
23 

13 
14 

15 
16 

17 

18 

14 
15 
16 
17 
18 
19 

14 
15 

16 
17 

18 
19 

15 
16 

17 

18 
19 
20 

15 
16 
17 
19 
20 
21 

13 
14 
15 
16 

17 
18 

9  30 
10    0 

10  30 

11  0 

11  30 

12  0 

2 
2 
2 
2 
2 
2 

2 
2 
3 
3 
3 
3 

3 
3 
3 
4 
4 
4 

4 
4 
4 
5 
5 
5 

5 
5 
5 
5 

6 

6 

6 
6 
6 
6 

7 
7 

6 

7 
7 
7 
8 
8 

7 
7 
8 
8 
9 
9 

8 
8 
9 
9 
10 
10 

9 
9 
10 
10 
11 
11 

9 
10 
10 
11 
11 
12 

10 
11 
11 
12 
12 
13 

11 
12 
12 
13 
13 
14 

12 
12 
13 
14 
14 
15 

13 
13 
14 
15 
15 
16 

13 
14 
15 
16 
16 
17 

14 
15 
16 
16 
17 
18 

15 
16 
17 
17 

18 
19 

16 
17 
17 
18 
19 
20 

19 
20 
21 
5i2 

%'^ 

24 

20 
21 
22 
23 
24 
''25 

21 
22 
23 
24 
25 
26 

21 
22 
24 

25 
26 

27 

22 
23 

24 

26 

27 
28 

19 
20 
21 
22 
23 
24 

TIME  AFTER 
NOON  OR 
MIDNIGHT. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

^ 

26 

27 

28 

VARIATION    OF   THE    0    OR   PLANETS*    DECLINATION    IN    24    HOURS. 

Not 
and  the 
the  ang 
Green-w 
the  ang 

E.— 

dii 
le  0 
ich 
let 

-Ec 
fere 
f  n 

N 

)f  E 

ter 
;nc< 
lee 
oon 
nee 

th 
!  or 
.ing 

an 
ting 

8    '] 

ch 
d  t 

rab 

ing 
ill 
be 
ill 

leT 

e  ii] 
be 
difif 
bel 

vitt 
th 
the 
erei 
the 

tb 

eS 

CO 

ice 
cor 

el 

emi 

rre 

or 

rec 

Mm 
dia 
ctio 
cha 
bion 

sfr 
me 

n; 

nge 
,to 

om 

ter 

or, 

of 

be 

Gr 

anc 

ent 

th< 

ap 

een 
1  E 

er 
J  Si 
plie 

wic 
ori 
the 
in  ( 
d  t 

h  J 

ZOD 

ri^ 
)r  ] 
icec 

fooi 

td 

rht 

Plat 
>rdii 

1  or 
Par 
rd 
lat't 

M 
alls 

.  P 

idn 

IX 

th 
«cli 

igh 

D  1 

eT 

rit 

ar 

I  in 
2h 
abl 
ion, 
i  in 

tl 

our 

e  w 

at 

ere 

s  ai 
ith 
tht 
asii 

itb 

tb< 

)  bo 

igo 

tid 
b  T 

:to 

rd 

e  o< 
*P. 

tift  ' 

eff- 

jlumn, 
and  at 
>  from 
xud  at 
9««iiig. 

M 


TABLE  XXV. 

CONTAINING  THE  CORRECTION  FOR  THE  MOON'S  PARALLAX  IN  ALTITUDE,  GIVEN 
IN  MINUTES  AND  TENTHS,  WHICH  IS  ALWAYS  ADDITIVE  TO  THE 

APPARENT  ALTITUDK 


J) '8 
Ap. 
Alt. 


o 

5 

6 

7 

8 

9 

10 


HORIZONTAL    PARALLAX. 


54' 


43-9 
45-2 
46-2 
4G-9 
47-6 
47-9 


55' 


44-9 
46-2 
47-2 

47-9 
48-6 

48-9 


56' 


45-9 

47-2 
48-2 
48-9 
49-6 
49-8 


57' 


46-9 

48-2 
49-2 
49-9 
50-6 
508 


58' 


47-9 
49-2 
50-2 
50-9 
51-6 
51-8 


59' 


48-9 
50-2 
51-2 
51-9 
52-6 
52-8 


60' 


49-9 
51-2 
52.2 
52-9 
53-6 
53-8 


J) '8 

Ap. 

61  y^it. 


50-9 
52-2 
53-2 
53-9 
54-6 
54.8 


48 
49 
50 
51 
52 
53 


HORIZONTAL    PARALLAX. 


54' 


35-3 
34-6 
33-9 
33-2 
32-5 
31-8 


55' 


35-9 
35-3 
34-6 
33-8 
33-1 
32-4 


56' 


36-6 
35-9 
35-2 
34-5 
33-7 
33-0 


57' 


37-3 
36-6 
35-8 
351 
34-4 
33-6 


58' 


38-0 
37-2 
36-5 
35-7 
350 
34-2 


59' 


38-6 
37-9 
371 
36-4 
35-6 
34-8 


60' 


39-3 

38-5 
36-8 
37-0 
36-2 
35-4 


40-0 
39-2 
38-4 
37-6 

36-8 
36-0 


61' 


11 
12 
13 
14 

15 
16 


48-2 
48-4 
48-5 
48-6 
48-6 
48-6 


49-2 
49  4 
49-5 
49-6 
49-6 
49-5 


50-1 
50-4 
50-5 
50.5 
50-5 
50-5 


51-1 
51-3 
51-4 
51-5 
51-5 
51-5 


521 
52-3 
52-4 
52-5 
52-5 
52-4 


531 
53-3 
53-4 
53-4 
53-4 
53-4 


541 
54-2 
54-4 
54-4 
54-4 
54-4 


550 
55-2 
55-3 
55-4 
55-4 
55-3 


54 
55 
56 

57 
58 
59 


311 
30-3 
29-6 

28-8 
28-0 
27-2 


31-6 
30-9 
301 

29-3 

28-6 

27-8 


32-2 
31-5 
30-7 
29-9 
291 
28-3 


32-8 
320 
31-2 
30-4 
29-6 
28-6 


33-4 

32-6 

31-8 

310 

30 

29-3 


34-0 
33-2 


34-6 
33-8 


32-4  32-9 
31-5|32-1 
30-7  31-2 


29-6 


30-3 


35-2 
34-3 
33-5 
32-6 
31-7 
30-9 


17 
18 
19 
20 
21 
22 


48-5 
48-4 
48-3 
48-1 
47-9 
47-7 


49-5 
49-4 
49-2 
49-1 

4S-9 
48-6 


50-4 
50-3 
50-2 
50-0 

49-8 
49-5 


51-4 
51-3 
511 
50-9 
50-7 
50-5 


52-3 
52-2 
521 
51-9 
51-7 
51-4 


53-3 
53-2 
530 

52-8 
52-6 
52-3 


54-3 
541 
53-9 
53-8 
53-5 
53-3 


55-2 
55-1 
54-9 
54-7 
54-6 
54-2 


60 
61 
62 
63 
64 
65 


26-5 
25-7 
24-9 
24-0 
232 
22-4 


27-0 
26-1 
25-3 
24-5 
23-7 
22-8 


27-5 
26-6 
25-6 
24-9 
24-1 
23-2 


28-0 
27-1 
26-3 
25-4 
24-5 
23-7 


28-5 
27-6 
26-7 
25  9 
25-0 
24-1 


29-01 
281 
27-2 
26-3 
25-4 
24-5 


29-0 

28-6 
27-7 
26-8 
25-8 
24-9 


30-0 
29-1 
28-1 
27  2 
26-3 
25-3 


23 
24 
25 

26 
27 

28 


29 
30 
31 
32 
33 
34 


47-4 
47-2 
46-9 
46-6 
46-2 
45-9 


48-4 
48-1 
47-8 
47-5 
471 
46-8 


49-3 
49  0 

48-7 
48-4 
48-0 
47-6 


50-2 
49-9 
49-6 
49-3 
48-9 
48-5 


511 

50-9 
50-5 
50-2 
49-8 
49-4 


52-1 
51-8 
51-4 
51-] 
50-7 
50-3 


53-0 

52 

52-3 

52  0 

51-6 

51-2 


53-9 
53-6 
52-2 
52-9 
52-5 
52-1 


66 
67 
68 
69 
70 
71 


21-5 
20-7 
19-9 
19-0 
18-1 
17-3 


22-0 

21 

20 

19-4 

18-5 

17-6 


22-4 
21-5 

20-6 
19-7 
18-8 
17-9 


2-2 -8 
21-9 
21-0 
20-1 
19-2 
18-^ 


23  2 
22-3 
21-4 
20-4 
19-5 
18-6 


23-6 
22-7 
21-7 

20-8 
19-8 
18'9 


24-0 
23-0 
22-1 
21-1 
20-2 
19-2 


24-4 
23-4 
22-5 
20-5 
20-5 
19-5 


45-5 
45-1 
44-7 
44-3 
43-8 
43-4 


46-4 
46-0 
45-6 
451 
44-7 
44-2 


47-3 
46-8 
46-4 
45-9 
45-5 
45-0 


481 

47-7 
47-3 
46-8 
46-3 
45-8 


49-0 
48-6 
481 

47-7 
47-2 
46-7 


49-9 
49-4 
49-0 
48-5 
48-0 
47-5 


50-8 
50-3 
49-9 
49-4 
48-9 
48-3 


51-6 
51-2 

50-7 
50-2 
49-7 
49-2 


72 
73 
74 
75 

76 

77 


16-4 
15-5 
14-6 
13-7 
12-8 
11-9 


16-7 
158 
14-9 
140 
13-1 
12-2 


17-0 
16-1 
15-2 
14-2 
13-3 
12-4 


17o 
16-4 
15-4 
14-5 
13-5 
12-6 


17-6 
16-7 
15-7 
14-8 
13-8 
12-8 


17-9 
17-0 
16-0 
15-0 
14-0 
13-1 


18-2 

17 

16-3 

15-3 

14-3 

13-3 


18-5 
17-6 
16-5 
15-5 
14-5 
13-5 


35 
36 

37 
38 
39 
40 


41 
42 
43 
44 
45 
46 
47 


430 
42-3 
41-9 
41-3 
40-8 
40-2 


43-7 
43-2 
42-7 
421 
41-6 
41-0 


44-5 
43-9 
43-5 
42-9 
42-3 
41-8 


45-d 
44-8 
44-3 
43-7 
431 
42-5 


46-1 
45-6 
451 
44-5 
43-9 
43-3 


46-9 
46-4 
45-9 
45-3 
44-7 
441 


47-8 
47-2 
46-8 
461 
45-4 
44-8 


48-6 
48-0 
47-5 
46-9 
46-2 
45-6 


78 
79 

80 
81 
82 
83 


11-0 
10-1 
9-2 
8-3 
7-4 
6-5 


11-2 

lO-o 

9-4 

8-5 
7-5 
6-6 


11-4 

10-5 

9-6 

8-6 
7-7 
6-7 


11-7 

10-7 

9-7 

8-8 
7-8 
6-8 


11-9 
10-9 
9-9 
8-9 
7-9 
6-9 


12-1 

11-1 

10-1 

9-1 

8-1 
7-1 


12-3 

11-3 

10-3 

9-2 

8-2 
7-2 


3if7 
39-1 
38-5 
37-9 
37-2 
36-6 
35-9 


40-4 
39-8 
39-2 
38-6 
37-9 


o/' 


0^.3 


36-6 


41-2 
40-6 
39-9 
39-3 
38-6 
38-0 
37-3 


41-9 
41-3 
40-7 
401 
39-4 
38-7 
38-0 


42-7 
42-0 
41-4 
40-7 
40-1 
39-4 
38-7 


43-4 
42-8 
421 
41-5 
40-8 
40-1 
39-4 


44-2 
43-5 
42-9 
42-2 
41-5 
40-8 
40-0 


44-9 
44-3 
43-6 
42-9 
42-2 
41-5 
40-7 


84 
85 
86 
87 
88 
89 
90 


5-6 
4-6 
3-7 
2-8 
1-9 
0-9 
00 


5-7 
4-7 

3-8 
2-8 
1-9 
0-9 
0-0 


5-8 
4-8 
3-8 
2-9 
1-9 
1-0 
00 


5-9 
4-9 
3-9 
2-9 
2-0 
1-0 
0-0 


6-0 
5-0 
4-0 
3-0 
2-0 
1-0 
00 


6-1 
5-1 

4-0 
3-0 
2-0 
1-0 
0-0 


6-2 
5-2 
4-1 
3-1 
2-1 
1-0 
0-0 


12-5 

11-5 

10-4 

9-4 

8-4 

7-3 


6-3 
5-3 
4-2 
3-1 
2-1 
1-0 
0-0 


Enter  this  Table  with  the  Apparent  Altitude  at  the  side,  and  the  Horizontal  Parallax  at  the  top,  and 
at  the  angle  of  meeting  will  be  the  required  correction ;  and  if  Seconds  be  required,  multiply  the 
Tenths  by  6  will  gire  Seconds. 


TABLE  XXVI. 

[Pag6«7. 

TO  TURN  DEGREES  INTO  TIME,  OR,  TIME  INTO  DEGREES. 

OAfirrA^B. 

Time. 

degrees. 

Time. 

Degrees. 

Time. 

Miuutcs 

of 
Oegrees. 

Time. 

Seconds 

of 
Degrees. 

Tim«. 

A^^ie^B. 

H.  M. 

B.   If. 

H.  M. 

M.  8. 

&   T. 

1 

0.  4 

61 

4.  4 

121 

8.  4 

1 

0.  4 

1 

0.4 

2 

0.  8 

62 

4.  8 

122 

8.  8 

2 

0.  8 

2 

0.  8 

3 

0.12 

63 

4.12 

123 

8.12 

3 

0.12 

3 

0.12 

4 

0.16 

64 

4.16 

124 

8.16 

4 

0.16 

4 

0.16 

5 

0.20 

65 

4.20 

125 

8.20 

5 

0.20 

5 

0.20 

6 

0.24 

66 

4.24 

126 

8.24 

6 

0.24 

6 

0.24 

7 

0.28 

67 

4.28 

127 

8.28 

7 

0.28 

7 

0.28 

8 

0.32 

68 

4.32 

128 

8.32 

8 

0.32 

8 

0.32 

9 

0.36 

69 

4.36 

129 

8.36 

9 

0.36 

9 

0.36 

10 

0.40 

70 

4.40 

130 

8.40 

10 

0.40 

10 

0.40 

11 

0.44 

71 

4.44 

131 

8.44 

11 

0.44 

11 

0.44 

12 

0.48 

72 

4.48 

132 

8.48 

12 

0.48 

12 

0.48 

13 

0.52 

73 

4.52 

133 

8.52 

13 

0.52 

13 

0.52 

14 

0.56 

74 

4.56 

134 

8.56 

14 

0.56 

14 

0.56 

15 

1.  0 

75 

5.  0 

135 

9.  0 

15 

1.  0 

15 

1.  0 

It) 

1.  4 

76 

5.  4 

136 

9.  4 

16 

1.  4 

16 

1.  4 

17 

1.  8 

77 

5.  8 

137 

9.  8 

17 

1.  8 

17 

1.  8 

18 

1.12 

78 

5.12 

138 

9.12 

18 

1.12 

18 

1.12 

19 

1.16 

79 

5.16 

139 

9.16 

19 

1.16 

19 

1.16 

20 

1.20 

80 

5.20 

140 

9.20 

20 

1.20 

20 

1.20 

21 

1.24 

81 

5.24 

141 

9.24 

21 

1.24 

21 

1.24 

22 

1.28 

82 

5.28 

142 

9.28 

22 

1.28 

22 

1.28 

23 

1.32 

83 

5.32 

143 

9.32 

23 

1.32 

23 

1.32 

24 

1.36 

84 

5.36 

144 

9.36 

24 

1.36 

24 

1.36 

25 

1.40 

85 

5.40 

145 

9.40 

25 

1.40 

25 

1.40 

26 

1.44 

86 

5.44 

146 

9.44 

26 

1.44 

26 

1.44 

27 

1.48 

87 

5.48 

147 

9.48 

27 

1.48 

27 

1.48 

28 

1.52 

88 

5.52 

148 

9.52 

28 

1.52 

28 

1.52 

29 

1.56 

89 

5.56 

149 

9.56 

29 

1.56 

29 

1.56 

30 

2.  0 

90 

6.  0 

150 

10.  0 

30 

2.  0 

30 

2.  0 

31 

2.  4 

91 

6.  4 

151 

10.  4 

31 

2.  4 

31 

2.  4 

32 

2.  8 

92 

6.  8 

152 

10.  8 

32 

2.  8 

32 

2.  8 

33 

2.12 

93 

6.12 

153 

10.12 

33 

2.12 

33 

2.12 

34 

2.16 

94 

6.16 

154 

10.16 

34 

2.16 

34 

2.16 

35 

2.20 

95 

6.20 

155 

10.20 

35 

2.20 

35 

2.20 

36 

2.24 

96 

6.24 

156 

10.24 

36 

2.24 

36 

2.24 

37 

2.28 

97 

6.28 

157 

10.28 

37 

2.28 

37 

2.28 

38 

2.32 

98 

6.32 

158 

10.32 

38 

2.32 

38 

2.32 

39 

2.36 

99 

6.36 

159 

10.36 

39 

2.36 

39 

2.36 

40 

2.40 

100 

6.40 

160 

10.40 

40 

2.40 

40 

2.40 

41 

2.44 

101 

6.44 

161 

10.44 

41 

2.44 

41 

2.44 

42 

2.48 

102 

6.48 

162 

10.48 

42 

2.48 

42 

2.48 

43 

2.52 

103 

6.52 

163 

10.52 

43 

2.52 

43 

2.52 

44 

2.56 

104 

6.56 

164 

10.56 

44 

2.56 

44 

2.56 

45 

3.  0 

105 

7.  0 

165 

11.  0 

45 

3.  0 

45 

3.  0 

46 

3.  4 

106 

7.  4 

166 

11.  4 

46 

3.  4 

46 

3.  4 

47 

3.  8 

107 

7.  8 

167 

11.  8 

47 

3.  8 

47 

3.  8 

48 

3.12 

108 

7.12 

168 

11.12 

48 

3.12 

48 

3.12 

49 

3.16 

109 

7.16 

169 

11.16 

49 

3.16 

49 

3.16 

50 

.3.20 

110 

7.20 

170 

11.20 

50 

3.20 

50 

3.20 

51 

3.24 

111 

7.24 

171 

11.24 

51 

3.24 

51 

3.24 

52 

3.28 

112 

7.28 

172 

11.28 

52 

3.28 

52 

3.28 

53 

3.32 

113 

7.32 

173 

11.32 

53 

3.32 

53 

3.32 

54 

3.36 

114 

7.36 

174 

11.36 

54 

3.36 

54 

3.36 

55 

3.40 

115 

7.40 

175 

11.40 

55 

3.40 

55 

3.40 

56 

3.44 

116 

7.44 

176 

11.44 

56 

3.44 

56 

3.44 

57 

3.48 

117 

7.48 

177 

11.48 

57 

3.48 

57 

3.48 

58 

3.52 

118 

7.52 

178 

11.52 

58 

3.52 

58 

3.52 

59 

3  56 

119 

7.56 

179 

11.56 

59 

3.56 

59 

3.56 

60 

4.  0 

120 

8.  0 

180 

12.  0 

60 

4.  0 

60 

4.  0 

38 

TABLE  XXVII. 

LOGARITHMS  OF  THE  LATITUDE  AND 

POLAR  DISTANCE. 

' 

LATITUDE,  OB  POLAR  DISTANCE. 

SECANT. 

o  Ic 

o   c 

o   c 

0  Ic 

o 

3           O    C 

o   ( 

0 

M. 

0 

0  or   90    1 

I    .   91    2   .   92    ; 

J    .   93    4    .    94    5    .    95    6    .    96    ' 

r  .  97  ! 

?   .   98    9    .  99 

0  00000 

00007 

00026 

00060 

00106 

00166 

00239 

00325 

00425 

00538 

60 

1 

00000 

00007 

00027 

00060 

00107 

00167 

00240 

00326 

00426 

00540 

39 

2 

00000 

00007 

00027 

00061 

00108 

00168 

00241 

00328 

00428 

00542 

58 

3 

00000 

00007 

00028 

00062 

00108 

00169 

00243 

00330 

00430 

00544 

57 

4 

00000 

00008 

00028 

00062 

00109 

00170 

00244 

00331 

00432 

00546 

56 

5 

0.00000 

00008 

00029 

00063 

00110 

00171 

00245 

00333 

00434 

00548 

55 

6 

00000 

00008 

00029 

00064 

00111 

00172 

00247 

00334 

00435 

00550 

54 

7 

00000 

00008 

00030 

00064 

00112 

00173 

00248 

00336 

00437 

00552 

53 

8 

00000 

00008 

00030 

00065 

00113 

00175 

00249 

00337 

00439 

00554 

52 

9 

00000 

00009 

00031 

00066 

00114 

00176 

00251 

00339 

00441 

00556 

51 

10 

0.00000 

00009 

00031 

00066 

00115 

00177 

00252 

00341 

00443 

00558 

50 

11 

00000 

00009 

00032 

00067 

00116 

00178 

00253 

00342 

00444 

00560 

49 

12 

00000 

00010 

00032 

00068 

00117 

00179 

00255 

00344 

00446 

00562 

48 

13 

00000 

00010 

00033 

00068 

00118 

00180 

00256 

00345 

00448 

00564 

47 

14 

00000 

00010 

00033 

00069 

00119 

00181 

00258 

00347 

00450 

00566 

46 

15 

0.00000 

00010 

00033 

00070 

00120 

00183 

00259 

00349 

00452 

00568 

45 

16 

00000 

00011 

00034 

00071 

00121 

00184 

00260 

00350 

00454 

00571 

44 

17 

00001 

00011 

00034 

00071 

00121 

00185 

00262 

00352 

00455 

00573 

43 

18 

00001 

00011 

00035 

00072 

00122 

00186 

00263 

00353 

00457 

00575 

42 

19 

00001 

00011 

00036 

00073 

00123 

00187 

00264 

00355 

00459 

00577 

41 

20 

0.00001 

00012 

00036 

00074 

0-)124 

00188 

00266 

00357 

00461 

00579 

40 

21 

00001 

00012 

00037 

00074 

0.»125 

00190 

00267 

00358 

00463 

00581 

39 

22 

00001 

00012 

00037 

00075 

00126 

00191 

00269 

00360 

00465 

00583 

38 

' 

23 

00001 

00013 

00038 

00076 

00127 

00192 

00270 

00362 

00467 

00585 

37 

24 

00001 

00013 

00038 

00077 

00128 

00193 

00272 

00363 

00468 

00587 

36 

25 

0.00001 

00013 

00039 

00077 

00129 

00194 

00273 

00365 

00470 

00589 

35 

26 

00001 

00014 

00039 

00078 

00130 

00196 

00274 

00367 

00472 

00591 

34 

27 

00001 

00014 

00040 

00079 

00131 

00197 

00276 

00368 

00474 

00593 

33 

28 

00001 

00014 

00040 

00080 

00132 

00198 

00277 

00370 

00476 

00596 

32 

29 

00002 

00015 

00041 

00080 

00133 

00199 

00279 

00371 

00478 

00598 

31 

30 

0.00002 

00015 

00041 

00081 

00134 

00200 

00280 

00373 

00480 

00600 

30 

31 

00002 

0C015 

00042 

00082 

00135 

00202 

00282 

00375 

00482 

OOfiOa 

29 

32 

00002 

00016 

00042 

00083 

00136 

00203 

00283 

00376 

00483 

00604 

28 

31 

00002 

00016 

00043 

00083 

00137 

00204 

00284 

00378 

00485 

00606 

27 

34 

00002 

00016 

00044 

00084 

00138 

00205 

00286 

00380 

00487 

00608 

26 

35 

0.00002 

00017 

00044 

00085 

00139 

00207 

00287 

00382 

00489 

00610 

25 

36 

00002 

00017 

00045 

00086 

00140 

00208 

00289 

00383 

00491 

00612 

24 

37 

00003 

00017 

00045 

00087 

00141 

00209 

00290 

00385 

00493 

00615 

23 

38 

00003 

00018 

00046 

00087 

00142 

00210 

00292 

00387 

00495 

00617 

22 

39 

00003 

00018 

00046 

00088 

00143 

00212 

00293 

00388 

00497 

00619 

21 

40 

0.00003 

00018 

00047 

00089 

00144 

00213 

00295 

00390 

00499 

00621 

20 

41 

00003 

00019 

00048 

00090 

00145 

00214 

00296 

00392 

00501 

00623 

19 

■ 

42 

00003 

00019 

00048 

00091 

00146 

00215 

00298 

00393 

00503 

00625 

18 

43 

00003 

00019 

00049 

00091 

00147 

00217 

00299 

00395 

00505 

00628 

17 

44 

00004 

00020 

00049 

00092 

00148 

00218 

00301 

00397 

00506 

00630 

16 

45 

0.00004 

00020 

00050 

00093 

00149 

00219 

00302 

00399 

00508 

00632 

15 

46 

00004 

00021 

00051 

00094 

00150 

00220 

00304 

00400 

00510 

00634 

14 

47 

00004 

00021 

00051 

00095 

00152 

00222 

00305 

00402 

00512 

00636 

13 

48 

00004 

00021 

00052 

00096 

00153 

00223 

00307 

00404 

00514 

00638 

12 

49 

00004 

00022 

00052 

00096 

00154 

00224 

00308 

00405 

00516 

00641 

11 

50 

0.00005 

00022 

00053 

00097 

00155 

00225 

00310 

00407 

00518 

00643 

10 

51 

00005 

00023 

00054 

00098 

00156 

00227 

00311 

00409 

00520 

00645 

9 

52 

00005 

00023 

00054 

00099 

00157 

00228 

00313 

00411 

00522 

00647 

8 

53 

00005 

00023 

00055 

00100 

00158 

00229 

00314 

00412 

00524 

00649 

7 

54 

00005 

00024 

00056 

00101 

00159 

00231 

00316 

00414 

00526 

0O652 

6 

55 

0  00006 

00024 

00056 

00102 

00160 

00232 

00317 

00416 

00528 

00654 

5 

56 

00006 

00025 

00057 

00102 

00161 

00233 

00319 

00418 

00530 

00656 

4 

57 

00006 

00025 

(  J058 

00103 

00162 

00235 

00320 

00419 

00532 

00658 

3 

58 

00006 

00026 

00056 

00104 

00163 

00236 

00322 

00421 

00534 

00660 

2 

59 

00006 

00026 

00059 

00105 

00164 

00237 

00323 

00423 

00536 

00663 

I 

60 

00006 

00026 

00060 

00106 

00165 

00239 

00325 

00425 

00538 

0066" 

0 

M 

89° 

88° 

87° 

86° 

85^ 

84° 

83° 

82° 

81° 

80° 

POLAR  DISTANCE. 

CO-SECAI 

sTT. 

^^" 

TABLE  XXVll. 

»9  1 

LOGARITHMS  OF  THE  LATITUDE  AND  POLAR  DISTANCE. 

LATITUDE,  OR  POLAR  DISTANCE. 

SECANT. 

c      o 

o    o 

o    o 

o    o 

o    o 

o    o  1 

o    o 

o    o 

o    o 

o    o 

M. 

10  or  100 

11.101 

00805 

12  102 

13.103 

14.104  15.105 

16.106  ] 

17.107 

18.108  1 

19.109 

0 

0.00665 

00960 

01128 

01310 

01506 

01716 

01940 

02179 

02433 

60 

1 

00667 

00808 

00962 

01131 

01313 

01509 

01719 

01944 

02183 

02437 

59 

2 

00669 

00810 

00965 

01133 

01316 

01512 

01723 

01948 

02188 

02442 

58 

3 

00672 

00813 

00968 

01136 

01319 

01516 

01727 

01952 

02192 

02446 

57 

4 

00674 

00815 

00970 

01139 

01322 

01519 

01730 

01956 

02196 

02450 

56 
55 

5 

0.00676 

00818 

00973 

01142 

01325 

01523 

01734 

01960 

02200 

02455 

6 

00678 

00820 

00976 

01145 

01329 

01526 

01738 

01964 

02204 

02459 

54 

7 

00681 

00823 

00978 

01148 

01332 

01529 

01741 

01968 

02208 

02464 

53 

8 

00683 

00825 

00981 

01151 

01335 

01533 

01745 

01971 

02212 

02468 

52 

9 

00685 

00828 

00984 

01154 

01338 

01536 

01748 

01975 

02216 

02472 

51 

10 

0.00687 

00830 

00987 

01157 

01341 

01540 

01752 

01979 

02221 

02477 

50 

11 

00690 

00833 

00989 

01160 

01344 

01543 

01756 

01983 

02225 

02481 

49 

12 

00692 

00835 

00992 

01163 

01348 

01547 

01760 

01987 

02229 

02485 

48 

13 

00694 

00838 

00995 

01166 

01351 

01550 

01763 

01991 

02233 

02490 

47 

14 

00696 

00840 

00998 

01169 

01354 

01553 

01767 

01995 

02237 

02494 

46 

15 

0.00699 

00843 

01000 

01172 

01357 

01557 

01771 

01999 

02241 

02499 

45 

16 

00701 

00845 

01003 

01175 

01360 

01560 

01774 

02003 

02246 

02503 

44 

17 

00703 

00848 

01006 

01178 

01364 

01564 

01778 

02007 

02250 

02508 

43 

18 

00706 

00850 

01009 

01181 

01367 

01567 

01782 

02011 

02254 

02512 

42 

19 

00708 

00853 
00855 

01011 
01014 

01184 

01370 

01571 

01785 

02014 

02258 

02516 

41 

20 

0.00710 

01187 

01373 

01574 

01789 

02018 

02262 

02521 

40 

21 

00712 

00858 

01017 

01190 

01377 

01578 

01793 

02022 

02266 

02525 

39 

22 

00715 

00860 

01020 

01193 

01380 

01581 

01796 

02026 

02271 

02530 

38 

23 

00717 

00863 

01022 

01196 

01383 

01585 

01800 

02030 

02275 

02534 

37 

24 

00719 

00865 
00868 

01025 

01199 

01386 

01588 
01591 

01804 

02034 

02279 

02539 

36 

25 

0.00722 

01028 

01202 

01390 

01808 

02038 

02283 

02543 

35 

26 

00724 

00870 

01031 

01205 

01393 

01595 

01811 

02042 

02287 

02547 

34 

27 

00726 

00873 

01033 

01208 

01396 

01598 

01815 

02046 

02292 

02552 

33 

28 

00729 

00876 

01036 

01211 

01399 

01602 

01819 

02050 

02296 

02556 

32 

29 

00731 

00878 

01039 

01214 

01403 

01605 

01823 

02054 

02300 

02561 

31 

30 

0  00733 

00881 

01042 

01217 

.01406 

01609 

01826 

02058 

02304 

02565 

30 

31 

00736 

00883 

01045 

01220 

01409 

01612 

01830 

02062 

02309 

02570 

29 

32 

00738 

00886 

01047 

01223 

01412 

01616 

01834 

02066 

02313 

02574 

28 

33 

00740 

00888 

01050 

01226 

01416 

01619 

01838 

02070 

02317 

02579 

27 

34 

00743 

00891 

01053 

01229 

01419 

01623 

01841 

02074 

02321 

02583 

26 

35 

0.00745 

00894 

01056 

01232 

01422 

01627 

01845 

02078 

02326 

02588 

25 

36 

00748 

00896 

01059 

01235 

01426 

01630 

01849 

02082 

02330 

02592 

24 

37 

00750 

00899 

01062 

01238 

01429 

01634 

01853 

02086 

02334 

02597 

23 

38 

00752 

00901 

01064 

01241 

01432 

01637 

01856 

02090 

02338 

02601 

22 

39 

00755 

00904 

01067 

01244 

01435 

01641 

01860 

02094 

02343 

02S06 

21 

40 

0.00757 

00907 

01070 

01247 

01439 

01644 

01864 

02098 

02347 

02610 

20 

41 

00759 

00909 

01073 

01250 

01442 

01648 

01868 

02102 

02351 

02615 

19 

42 

00762 

00912 

01076 

01254 

01445 

01651 

01871 

02106 

02355 

M2619 

18 

43 

00764 

00914 

01079 

01257 

01449 

01655 

01875 

02110 

02360 

02624 

17 

44 

00767 

00917 

01081 

01260 

01452 

01658 

01879 

02114 

02364 

02628 

IG 

45 

0.00769 

00920 

01084 

01263 

01455 

01662 

01883 

02118 

02368 

02633 

15 

46 

00771 

00922 

01087 

01266 

01459 

01666 

01887 

02122 

02372 

02637 

14 

47 

00774 

00925 

01090 

01269 

01462 

01669 

01890 

02126 

02377 

02642 

13 

48 

00776 

00928 

01093 

01272 

01465 

01673 

01894 

02130 

02381 

02647 

12 

49 

00779 

00930 

01096 

01275 

01469 

01676 

01898 

02134 

02385 

02651 

11 

50 

0.00781 

00933 

01099 

01278 

01472 

01680 

01902 

02139 

02390 

02656 

10 

51 

00783 

00936 

01102 

01281 

01475 

01683 

01906 

02143 

02394 

02660 

9 

52 

00786 

00938 

01104 

01285 

01479 

01687 

01910 

02147 

02398 

02665 

8 

53 

00788 

00941 

0111)7 

01288 

01482 

01691 

01913 

02151 

02403 

02669 

7 

54 

00791 

00944 

OHIO 

01291 

01485 

01694 

01917 

02155 

02407 

02674 

6 

55 

1)  00793 

00946 

01113 

01294 

01489 

01698 

01921 

02159 

02411 

02678 

5 

56 

00796 

00949 

01116 

01297 

01492 

01701 

01925 

02163 

02416 

02683 

4 

57 

00798 

00952 

01119 

01300 

01495 

01705 

01929 

02167 

02420 

02688 

3 

58 

00800 

00954 

01122 

01303 

01499 

01709 

01933 

02171 

02424 

02692 

2 

59 

00803 

00957 

01125 

01306 

01502 

01712 

01937 

02175 

02429 

02697 

1 

60 

00805 

00960 

01128 

01310 

01506 

01716 

01940 

02179 

02433 

02701 

0 

5 

79° 

78° 

77° 

76° 

75 

74° 

73° 

72° 

71' 

TO- 

M. 

L_ 

POLAR  DISTANCE. 

CO-SECANT.   1 

100 

TABLE  XXVII. 

i 

LOGARITHMS  OF  THE  LATITUDE  AND  POLAR  DISTANCE. 

LATITUDE, 

OR  POLAR  DISTANCE. 

SECANT.   1 

o      o 

o    o 

o    o 

0    o 

o    o 

o    o 

o    o 

o   o 

o    o 

o    o 

. 

M. 

20  or  110 

21.111 

02985 

22.112 

23.113 

24.114 

25.115 

26.116 

27  117 

28.1«8 

05407 

29.119 

60 

0 

0.02701 

03283 

03597 

03927 

04272 

04634 

05012 

05818 

1 

02706 

02990 

03289 

03603 

03933 

04278 

04640 

05018 

05413 

05825 

59 

2 

02711 

02995 

03294 

03608 

03938 

04284 

04646 

05025 

05420 

05832 

58 

3 

02715 

02999 

03299 

03613 

03944 

04290 

04652 

05031 

05427 

05839 

57 

4 

02720 

03004 

03304 

03619 

03950 

04296 

04659 

05038 

05433 

05846 

56 
55 

5 

0.02724 

03009 

03309 

03624 

03955 

04302 

04665 

05044 

05440 

05853 

6 

02729 

03014 

03314 

03630 

03961 

04308 

04671 

05051 

05447 

05860 

54 

7 

02734 

03019 

03319 

03635 

03966 

04314 

04677 

05057 

05454 

05867 

53 

8 

02738 

03024 

03324 

03640 

03972 

04320 

04683 

05064 

05460 

05874 

52 

9 

02743 

03029 

03330 

03646 

03978 

04326 

04690 

05070 

05467 

05881 

51 

10 

0.02748 

03034 

03335 

03651 

03983 

04332 

04696 

05077 

05474 

05888 

50 

11 

02752 

03038 

03340 

03657 

03989 

04337 

04702 

05083 

05481 

05895 

49 

12 

02757 

03043 

03345 

03662 

03995 

04343 

04708 

05089 

05487 

05902 

48 

13 

02762 

03048 

03350 

03667 

04000 

04349 

04714 

05096 

05494 

05910 

47 

14 

02766 

03053 

03355 

03673 

04006 

04355 

04721 

05102 

05501 

05917 

46 

15 

0.02771 

03058 

03360 

03678 

04012 

04361 

04727 

05109 

05508 

05924 

45 

16 

02776 

03063 

03366 

03684 

04018 

04367 

04733 

05115 

05515 

05931 

44 

17 

02780 

03068 

03371 

03689 

04023 

04373 

04739 

05122 

05521 

05938 

43 

18 

02785 

03073 

03376 

03695 

04029 

04379 

04746 

05129 

05528 

05945 

42 

19 

20 

02790 

03078 
03083 

03381 
03386 

03700 

04035 

04385 

04752 

05135 

05535 

05952 

41 

0.02794 

03706 

04040 

04391 

04758 

05142 

05542 

05959 

40 

21 

02799 

03088 

03392 

03711 

04046 

04397 

04764 

05148 

05549 

05966 

39 

22 

02804 

03093 

03397 

03716 

04052 

04403 

04771 

05155 

05555 

05973 

38 

23 

02808 

03097 

03402 

03722 

04058 

04409 

04777 

05161 

05562 

05980 

37 

24 

02813 

03102 

03407 

03727 
03733 

04063 

04415 

04783 

05168 

05569 

05988 

36 

25 

0.02818 

03107 

03412 

04069 

04421 

04789 

05174 

05576 

05995 

35 

26 

02822 

03112 

03418 

03738 

04075 

04427 

04796 

05181 

05583 

06002 

34 

27 

02827 

03117 

03423 

03744 

04080 

04439 

04802 

05187 

05590 

06009 

33 

28 

02832 

03122 

03428 

03749 

04086 

04439 

04808 

05194 

05596 

06016 

32 

29 

02837 

03127 

03433 

03755 
03760 

04092 

04445 

04815 

05201 

05603 

06023 

31 

30 

30 

0.02841 

03132 

03438 

04098 

04451 

04821 

05207 

05610 

06030 

31 

02846 

03137 

03444 

03766 

04103 

04457 

04827 

05214 

05617 

06037 

29 

32 

02851 

03142 

03449 

03771 

04109 

04463 

04833 

05220 

05624 

06045 

28 

33 

02855 

03147 

03454 

03777 

04115 

04469 

04840 

05227 

05631 

06052 

27 

34 

02860 

03152 

03459 

03782 

04121 
04127 

04475 

04846 

05233 
05240 

05638 

06059 

26 

35 

0.02865 

03157 

03465 

03788 

04481 

04852 

05645 

06066 

25 

36 

02870 

03162 

03470 

03793 

04132 

04487 

04859 

05247 

05651 

06073 

24 

37 

02874 

03167 

03475 

03799 

04138 

04493 

04865 

05253 

05658 

06080 

23 

38 

02879 

03172 

03480 

03804 

04144 

04500 

04871 

05260 

05665 

06088 

22 

39 

02884 
0.02889 

03177 

03486 

03810 

04150 

04506 
04512 

04878 

05266 

05672 

06095 

21 

40 

03182 

03491 

03815 

04156 

04884 

05273 

05679 

06102 

20 

41 

02893 

03187 

03496 

03821 

04161 

04518 

04890 

05280 

05686 

06109 

19 

42 

02898 

03192 

03502 

03826 

04167 

04524 

04897 

052S6 

05693 

06116 

18 

43 

02903 

03197 

03507 

03832 

04173 

04530 

04903 

05293 

05700 

06124 

17 

44 

02908 
0.02913 

03202 

03512 

03838 

04179 

04536 

04910 

05300 

05707 

06131 

16 

45 

03207 

03517 

03843 

04185 

04542 

04916 

05306 

05714 

06138 

15 

46 

02917 

03212 

03523 

03849 

04190 

04548 

04922 

05315 

05721 

06145 

14 

47 

02922 

03217 

03528 

03854 

04196 

04554 

04929 

05320 

05727 

06153 

13 

48 

02927 

03222 

03533 

03860 

04202 

04560 

04935 

05326 

05734 

06160 

12 

49 

02932 

03228 

03539 

03865 

04208 
04214 

04566 

04941 

05333 

05741 

06167 

11 

50 

0.02937 

03233 

03544 

03871 

04573 

04948 

05340 

05748 

06174 

10 

51 

02941 

03238 

0354,» 

03877 

04220 

04579 

04954 

05346 

05755 

06181 

9 

52 

02946 

03243 

03555 

03882 

04225 

04585 

04961 

05353 

05762 

06189 

8 

53 

02951 

03248 

03560 

03888 

04231 

04591 

04967 

05360 

05769 

06196 

7 

54 

02956 

03253 

03565 
03571 

03893 

04237 

04597 
04603 

04973 

05366 

05776 

06203 

6 

55 

0.02961 

03258 

03899 

04243 

04980 

05373 

05783 

06211 

5 

56 

02965 

03263 

03576 

03905 

04249 

04609 

04986 

05380 

05796 

06218 

4 

57 

02970 

03268 

03581 

03910 

04255 

04616 

04993 

05386 

05797 

06225 

3 

58 

02975 

03273 

03587 

03916 

04261 

04^622 

04999 

05393 

05804 

06232 

2 

'iii 

02980 

03278 

03592 

03921 

04267 

04628 

05005 

05400 

05811 

06240 

1 

6b 

j   02985 

03283 

03597 

03927 

04272 

04634 

05012 

05407 

05818 

06247 

0 

69° 

68° 

67° 

66' 

65 

64 

63* 

62" 

61* 

60' 

M. 



P 

OLAR  DISTANCE. 

< 

30-8KCAh 

fT. 

TABLE  XXVII. 

101 

LOGARITHMS  OF  THE  LATITUDE  AND  POLAR  DISTANCK 

■ 

LATITUDE 

OR  POLAR  DISTANCE. 

SECAN 

T 

o     o 

o    o 

o    o 

o    o 

o    o 

o    o 

o    o 

o    o 

o    o 

o    o 

M. 

30  or  120 

31.121 

32.122 

33.123 

34.124 
08143 

35.125 

36.126 

37.127 

38.128 

39.129 

60 

0 

0.06247 

06693 

07158 

07641 

08664 

09204 

09765 

10347 

10950 

1 

06254 

06701 

07166 

07649 

08151 

08672 

09213 

09775 

10357 

10960 

59 

2 

06262 

06709 

07174 

07657 

08160 

08681 

09223 

09784 

10367 

10970 

58 

3 

06269 

06716 

07182 

07665 

08168 

08690 

09232 

09794 

10376 

10980 

57 

4 

5 

06276 

06724 

07190 

07674 

08177 

08699 

09241 

09803 

10386 

10991 

56 
55 

0.062S3 

06731 

07197 

07682 

08185 

087b8 

09250 

09813 

10396 

11001 

6 

06291 

06739 

07205 

07690 

08194 

08717 

09259 

09822 

10406 

11011 

54 

7 

06298 

06747 

07213 

07698 

08202 

08726 

09269 

09832 

10416 

11022 

53 

8 

06305 

06754 

07221 

07707 

08211 

08734 

09278 

09841 

10426 

11032 

52 

9 
10 

06313 

06762 

07229 

07715 

08219 

08743 

09287 

09851 

10436 

11042 

51 

0.063  20 

06770 

07237 

07723 

08228 

08752 

09296 

09861 

10446 

11052 

50 

11 

06327 

06777 

07245 

07734 

08237 

08761 

09306 

09870 

10456 

11063 

49 

12 

06335 

06785 

07253 

07740 

08245 

08770 

09315 

09880 

10466 

11073 

48 

13 

06342 

06793 

07261 

07748 

08254 

08779 

09324 

09889 

10476 

11083 

47 

14 

06350 

06800 

07269 

07756 

08262 

08788 

09333 

09899 

10486 

11094 

46 
45 

15 

0.06357 

06808 

07277 

07765 

08271 

08797 

09343 

09909 

10496 

11104 

16 

06364 

06816 

07285 

07773 

08280 

08806 

09352 

09918 

10505 

11114 

44 

17 

06372 

06823 

07293 

07781 

08288 

08815 

09361 

09928 

10515 

11125 

43 

18 

06379 

06831 

07301 

07789 

08297 

08824 

09370 

09937 

10525 

11135 

42 

19 

06386 

06839 

07309 
07317 

07798 

08305 

08833 

09380 
09389 

09947 
09957 

10535 

11145 

41 
40 

20 

0.06394 

06846 

07806 

08314 

08842 

10545 

11156 

21 

06401 

06854 

07325 

07814 

08323 

08851 

09398 

09966 

10555 

11166 

39 

22 

06409 

06862 

07333 

07823 

08331 

08859 

09408 

09976 

10565 

11176 

38 

23 

06416 

06869 

07341 

07831 

08340 

08868 

09417 

09986 

10575 

11187 

37 

24 

06423 

06877 

07349 

07839 

08349 

08877 

09426 

09995 

10585 

11197 

36 

25 

0.06431 

06885 

07357 

07848 

08357 

08886 

09435 

10005 

10595 

11207 

35 

26 

06438 

06892 

07365 

07856 

08366 

08895 

09445 

10015 

10605 

11218 

34 

27 

06446 

06900 

07373 

07864 

08375 

08904 

09454 

10024 

10615 

11228 

33 

28 

06453 

06908 

07381 

07873 

08383 

08913 

09463 

10034 

10625 

11239 

32 

29 

06461 

06916 

07389 

07881 
07889 

08392 

08922 

09473 

10044 

10636 

11249 

31 
30 

30 

0.06468 

06923 

07397 

08401 

08931 

09482 

10053 

10646 

11259 

31 

06475 

06931 

07405 

07898 

08409 

08940 

09491 

10063 

10656 

11270 

29 

32 

06483 

06939 

07413 

07906 

08418 

08949 

09501 

10073 

10666 

11280 

28 

33 

06490 

06947 

07421 

07914 

08427 

08958 

09510 

10084 

10676 

11291 

27 

34 

06498 

06954 

07429 

07923 

08435 

08967 

09520 

10092 

10686 

11301 

26 
25 

35 

0.06505 

06962 

07437 

07931 

08444 

08977 

09529 

10102 

10696 

11312 

36 

06513 

06970 

07445 

07940 

08453 

08986 

09538 

10112 

10706 

11322 

24 

37 

06520 

06978 

07454 

07948 

08462 

08995 

09548 

10121 

10716 

11332 

23 

38 

06528 

06986 

07462 

07956 

08470 

09004 

09557 

10131 

10726 

11343 

22 

39 

06535 

06993 

07470 

07965 

08479 

09013 

09566 

10141 

10736 

11353 

21 

40 

0.06543 

07001 

07478 

07973 

08488 

09022 

09576 

10151 

10746 

11364 

20 

41 

06550 

07009 

07486 

07982 

08496 

09031 

09585 

10160 

10756 

11374 

19 

42 

06558 

07017 

07494 

07990 

08505 

09040 

09595 

10170 

10767 

11385 

18 

43 

06565 

07024 

07502 

07998 

08514 

09049 

09604 

10180 

10777 

11395 

17 

44 

06573 

07032 

07510 

08007 

08523 

09058 

09614 

10190 

10787 

11406 

16 

45 

0.06580 

07040 

07518 

08015 

08531 

09067 

09623 

10199 

10797 

11416 

15 

46 

06588 

07048 

07527 

08024 

08540 

09076 

09632 

10209 

10807 

11427 

14 

47 

06595 

07056 

07535 

0S032 

08549 

09085 

09642 

10219 

10817 

11437 

13 

48 

06603 

07064 

07543 

08041 

08558 

09094 

09651 

10229 

10827 

11448 

12 

49 

06610 

07071 

07551 

08049 

08567 
08575 

09104 

09661 

10239 

10838 

11458 

11 

50 

0.06618 

07079 

07559 

08058 

09113 

09670 

10248 

10848 

11469 

10 

51 

06625 

07087 

07567 

08066 

08584 

09122 

09680 

10258 

10858 

11479 

9 

52 

06633 

07095 

07575 

08075 

08593 

09131 

09689 

10268 

10868 

11490 

8 

53 

06640 

07103 

07584 

08084 

08602 

09140 

09699 

10278 

10878 

11501 

7 

54 

06648 

07111 

07592 

08092 

08611 

09149 

09708 

10288 

10888 

11511 

6 
5 

55 

0.06656 

07119 

07600 

08100 

08619 

09158 

09718 

10298 

10899 

11522 

56 

06663 

07126 

07608 

08109 

08628 

09168 

09727 

10307 

10909 

11532 

4 

57 

06671 

07134 

07616 

08117 

08637 

09177 

09737 

10317 

10919 

11543 

3 

58 

06678 

07142 

07624 

08126 

08646 

09186 

09746 

10327 

10929 

11553 

2 

69 

06686 

07150 

07633 

08134 

08655 

09195 

09756 

10337 

10940 

11564 

1 

60 

06693 

07158 

07641 

08143 

08664 

09204 

09765 

10347 
52° 

10950 

11575 

0 

59' 

58° 

57° 

56' 

55°    54° 

53° 

51° 

50° 

M. 

p 

OLAR  DISTANCK. 

CO-SECAI 

fT. 

102                TABLE  XXVII. 

LOGARITHMS  OF  THE  LATITUDE  AND  POLAR  DISTANCE. 

LATITUDE,  OR  POLAR  DISTANCE.                     8KCAST. 

M. 

o     o 
40  or  130 

o    o 

41.131 

12222 
12233 
12244 
12255 
12266 

0    o 

42.132 

o    o 
43.133 

0    o 

44.134 

o    o 
45.135 

o    o 
46.136 

o    o 
47.137 

o    o 
48.138 

17449 
17463 
17177 
17491 
17505 

0     C 

49.139 

0 

1 

2 
3 

4 

0.11575 
11585 
11596 
11606 
11617 

12893 
12904 
12915 
12927 
12938 

13587 
13599 
13611 
13623 
13634 

14307 
14319 
14331 
14343 
14355 

15051 
15064 
15077 
15089 
15102 

15823 
15836 
15849 
15862 
15875 

16622 
16635 
16649 
16662 
.16676 

18306 
18320 
18335 
18349 
18364 

60 
59 
58 

57 
56 

5 

6 

7 
8 
9 

0.11628 
11638 
11649 
11660 
11670 

12277 
12288 
12299 
12310 
12321 

12950 
12961 
12972 
12984 
12995 

13646 
13658 
13670 
13682 
13694 

14368 
14380 
14392 
14404 
14417 

15115 
15127 
15140 
15153 
15165 

15888 
15901 
15915 
15928 
15941 

16689 
16703 
16717 
16730 
16744 

17519 
17533 
17547 
17561 
17576 

18378 
18393 
18408 
18422 
18437 

55 
54 
53 
52 
51 

10 
11 
12 
13 
14 

0.11681 
11692 
11702 
11713 
11724 

12332 
12343 
12354 
12365 
12376 

13007 
13018 
13030 
13041 
13053 

13705 
13717 
13729 
13741 
13753 

14429 
14441 
14453 
14466 
14478 

15178 
15191 
15204 
15216 
15229 

15954 
15967 
15980 
15994 
16007 

16758 
16771 
16785 
16798 
16812 

17590 
17604 
17618 
17632 
17646 

18451 
18466 
18481 
18495 
18510 

50 
49 
48 
47 
46 

15 
16 

17 
18 
19 

0.11734 
11745 
11756 
11766 

11777 

12387 
12399 
12410 
12421 
12432 

12443 
12454 
12465 
12476 
12487 

13064 
13076 
13087 
13098 
13110 

13121 
13133 
13145 
13156 
13168 

13765 
13777 
13789 
13800 
13812 

14490 
14503 
14515 
14527 
14540 

15242 
15255 
15267 
15280 
15293 

16020 
16033 
16046 
16060 
16073 

16826 
16839 
16853 
16867 
16880 

17660 
17674 
17689 
17703 
17717 

18525 
18539 
18554 
18569 
18583 

45 
44 
43 
42 
41 

20 
21 
22 
23 

24 

0.11788 
11799 
11809 
11820 
11831 

13824 
13836 
13848 
13860 
13872 

14552 
14564 
14577 
14589 
14601 

15306 
15318 
15331 
15344 
15357 

16086 
16099 
16113 
16126 
16139 

16894 
16908 
16922 
16935 
16949 

17731 

17745 
17760 
17774 
17788 

18598 
18613 
18628 
18642 
18657 

40 
39 
38 
37 
36 

25 

26 

1  27 

28 
29 

0.11842 
11852 
11863 
11874 
11885 

12499 
12510 
12521 
12532 
12543 

13179 
13191 
13202 
13214 

13225 

13884 
13896 
13908 
13920 
13932 

14614 
14626 
14639 
14651 
14663 

15370 
15382 
15395 
15408 
15421 

16152 
16166 
16179 
16192 
16205 

16963 
16977 
16990 
17004 
17018 

17802 
17816 
17831 
17845 
17859 

18672 
18686 
18701 
18716 
18731 

35 
34 
33 
32 
31 

30 
31 
32 
33 
34 

0.11895 
11906 
11917 
11928 
11939 

12554 
12566 
12577 
12588 
12599 

13237 
13248 
13260 
13272 
13283 

13944 
13956 
13968 
13980 
13992 

14676 
14688 
14701 
14713 

14726 

15434 
15447 
15460 

15472 
15485 

16219 
16232 
16245 
16259 
16272 

17032 
17045 
17059 
17073 
17087 

17874 
17888 
17902 
17916 
17931 

18746 
18760 
18775 
18790 
18805 

30 
29 
28 
27 
26 

35 
36 
37 
38 
39 

0.11949 
11960 
11971 

11982 
11993 

0.12004 
12015 
12025 
12036 
12047 

12610 
12622 
12633 
1264*4 
12655 

13295 
13306 
13318 
13330 
13341 

14004 
14016 
14028 
14040 
14052 

14738 
14750 
14763 
14775 
14788 

15498 
15511 
15524 
15537 
15550 

16285 
16299 
16312 
16326 
16339 

17101 
17115 
17128 
17142 
17156 

17945 
17959 
17974 
17988 
18002 

18820 
18834 
18849 
18864 
18879 

25 
24 
23 
22 
21 

20 
19 
18 
17 
16 

40 
41 
42 
43 
44 

12666 
12678 
12689 
12700 
12712 

13353 
13365 
13376 
13388 
13400 

14064 
14076 
14088 
14100 
14112 

14800 
14813 
14825 
14838 
14850 

15563 
15576 
15589 
15602 
15615 

16352 
16366 
16379 
16392 
16406 

17170 
17184 
17198 
17212 
17225 

18017 
18031 
18045 
18060 
18074 

18894 
18909 
18924 
18939 
18954 

45 
46 
47 
48 
49 

0.12058 
12069 
12080 
12091 
12102 

12723 
12734 
12745 
12757 
12768 

13411 
13423 
13435 
13446 
13458 

14124 
14136 
14149 
14161 
14173 

14863 
14875 
14888 
14900 
14913 

15627 
15640 
15653 
15666 
15679 

16419 
16433 
16446 
16460 
16473 

17239 
17253 
17267 
17281 
17295 

18089 
18103 
18118 
18132 
18146 

18968 
18983 
18998 
19013 
19028 

15 
14 
13 
12 
11 

50 
51 
52 
53 
54 

0.12113 
12123 
12134 
12145 
12156 

12779 
12791 
12802 
12813 
12825 

13470 
13482 
13493 
13505 
13517 

14185 
14197 
14209 
14221 
14234 

14926 
14938 
14951 
14963 
14976 

15692 
15705 
15718 
15731 
15745 

16487 
16500 
16514 
16527 
16541 

17309 
17323 
17337 
17351 
17365 

18161 
18175 
18190 
18204 
18219 

19043 
19058 
19073 
19088 
19103 

10 
9 
8 

7 
6 

55 
56 
57 
58 
59 
60 

0.12167 
12178 
12189 
12200 
12211 
12222 

12836 
12847 
12859 
12870 
12881 
12893 

13528 
13540 
13552 
13564 
13575 
13587 

14246 
14258 
14270 
14282 
14294 
14307 

14988 
15001 
15014 
15026 
15039 
15051 

15758 
15771 
15784 
15797 
15810 
15823 

16554 
16568 
16581 
16595 
16608 
16622 

17379 
17393 
17407 
17421 
17435 
17449 

18233 
18248 
18262 
18277 
18291 
18306 

19118 
19133 
19148 
19163 
19178 
19193 

5 

4 
3 
2 

1 
0 

49° 

48° 

47" 

46° 

45° 

44° 

43° 

42' 

41° 

40° 

M. 

POLAR  DISTANCE.                        CO-SECANT.   | 

TABLE  XXVII. 

108 

LOGARITHMS  OF  THE  LATITUDE  AND  POLAR  DISTANCK 

• 

LATITUDE. 

SECANT. 

■    1 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

1 

M. 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

60 

0 

0.19193 

20113 

21066 

22054 

23078 

24141 

25244 

26389 

27579 

28816 

1 

19208 

20128 

21082 

22070 

23096 

24159 

25263 

26409 

27599 

28837 

59 

2 

19223 

20144 

21098 

22087 

23113 

24177 

25281 

26428 

27619 

28858 

58 

3 

19238 

20160 

21114 

22104 

23130 

24195 

25300 

26448 

27640 

28879 

57 

4 

19254 

20175 

21131 

22121 

23148 

24213 
2<f231 

25319 

26467 

27660 

28900 

56 
55 

5 

0.19269 

20191 

21147 

22138 

23165 

^5338 

26487 

27680 

28921 

6 

19284 

20207 

21163 

22154 

23183 

24249 

25356 

26506 

27701 

28942 

54 

7 

19299 

20222 

21179 

22171 

23200 

24267 

25375 

26526 

27721 

28964 

53 

8 

19314 

20238 

21195 

22188 

23218 

24286 

25394 

26545 

27741 

28985 

52 

9 
10 

19329 

20254 

21212 

22205 
22222 

23235 

24304 

25413 

26565 

27762 

29006 

51 

0.19344 

20269 

21228 

23253 

24322 

25432 

26584 

27782 

29027 

50 

11 

19359 

20285 

21244 

22239 

23270 

24346 

25451 

26604 

27802 

29048 

49 

12 

19374 

20301 

21261 

22256 

23288 

24358 

25469 

26623 

27823 

29069 

48 

13 

19390 

20316 

21277 

22273 

23305 

24376 

25488 

26643 

27843 

29091 

47 

14 

19405 

20332 

21293 

22289 

23323 

24395 

25507 

26663 

27863 

29112 

46 
45 

15 

0.19420 

20348 

21309 

22306 

23340 

24413 

25526 

26682 

27884 

29133 

16 

19435 

20364 

21326 

22323 

23358 

24431 

25545 

26702 

27904 

29154 

44 

17 

19450 

20379 

21342 

22340 

23375 

24449 

25564 

26722 

27925 

29176 

43 

18 

19466 

20395 

21358 

22357 

23393 

24467 

25583 

26741 

27945 

29197 

42 

19 

20 

19481 

20411 

21375 

22374 

23410 

24486 

25602 
25621 

26761 
26781 

27966 

29218 

41 

0.19496 

20427 

21391 

22391 

23428 

24504 

27986 

29239 

40 

21 

19511 

20442 

21408 

22408 

23446 

24522 

25640 

26800 

28006 

292G1 

39 

22 

19527 

20458 

21424 

22425 

23463 

24541 

25659 

26820 

28027 

29282 

38 

23 

19542 

20474 

21440 

22442 

23481 

24559 

25678 

26840 

28048 

29303 

37 

24 

19557 

20490 

21457 

22459   23499 

24577 

25697 

25716 

26860 

28068 

29325 

36 

25 

0.19572 

20506 

21473 

22476   23516 

24595 

26879 

28089 

29346 

35 

26 

19588 

20522 

21490 

22493 

23534 

24614 

25735 

26899 

28109 

29367 

34 

27 

19603 

20537 

21506 

22510 

23552 

24632 

25754 

26919 

28130 

29389 

33 

28 

19618 

20553 

21522 

22257 

23569 

24650 

25773 

26939 

28150 

29410 

32 

29 
30 

19634 

20569 

21539 

22544 
22561 

23587 

24669 

25792 

26959 

28171 

29432 

31 

0.19649 

20585 

21555 

23605 

24687 

25811 

26978 

28191 

29453 

30 

31 

19664 

20601 

21572 

22578 

23622 

24706 

25830 

26998 

28212 

29475 

29 

32 

19680 

20617 

21588 

22595 

23640 

24724 

25849 

27018 

28233 

29496 

28 

33 

19695 

20633 

21605 

22613 

23658 

24742 

25868 

27038 

28253 

29518 

27 

34 

19710 

20649 

2162^ 
21638 

22630 

23676 

24761 

25887 

27058 

28274 

29539 

26 
25 

35 

0.19726 

20665 

22647 

23693 

24779 

25907 

27078 

28295 

29561 

36 

19741 

20681 

21654 

22664 

23711 

24798 

25926 

27098 

28315 

29582 

24 

37 

19756 

20696 

21671 

22681 

23729 

24816 

25945 

27117 

28336 

29604 

23 

38 

19772 

20712 

21687 

22698 

23747 

24835 

25964 

27137 

28357 

29625 

22 

39 

19787 

20728 

21704 

22715 

23764 

24853 

25983 

27157 

28378 

29647 

21 
20 

40 

0.19803 

20744 

21720 

22732 

23782 

24872 

26003 

27177 

28398 

29668 

41 

19818 

20760 

21737 

22750 

23800 

24890 

26022 

27197 

28419 

29690 

19 

42 

19834 

20776 

21754 

22767 

23818 

24909 

26041 

27217 

28440 

29712 

18 

43 

19849 

20792 

21770 

22784 

23836 

24927 

26060 

27237 

28461 

29733 

17 

44 

19864 

20808 

21787 

22801 

23854 

24946 

26079 

27257 

28481 

29755 

16 

45 

0.19880 

20824 

21803 

22819 

23871 

24964 

26099 

27277 

28502 

29776 

15 

46 

19895 

20840 

21820 

22836 

23889 

24983 

26118 

27297 

28523 

29798 

14 

47 

19911 

20856 

21837 

22853 

23907 

25001 

26137 

27317 

28544 

29820 

13 

48 

19926 

20872 

21853 

22870 

23925 

25020 

26157 

27337 

28565 

29841 

12 

49 

19942 

20889 

21870 

22888 

23943 
23961 

25039 

26176 

27350 

28586 

29863 

11 

50 

0.19957 

20905 

21887 

22905 

25057 

26195 

27378 

28607 

29885 

10 

51 

19973 

20921 

21903 

22922 

23979 

25076 

26215 

27398 

28627 

29907   9 

52 

19988 

20937 

21920 

22939 

23997 

25094 

26234 

27418 

28648 

29928   8 

53 

20004 

20953 

21937 

22957 

24015 

25113 

26253 

27438 

28669 

29950 

7 

54 

20019 

20969 

21953 

22974 

24033 

25132 

26273 

27458 

28690 

29972 
29994 

6 
5 

55 

0.20035 

20985 

21970 

22991 

24051 

25150 

26292 

27478 

28711 

56 

20050 

21001 

21987 

23009 

24069 

25169 

26311 

27498 

28732 

30016 

4 

57 

20066 

21017 

22003 

23026 

24087 

25188 

26331 

27518 

28753 

30037 

3 

58 

20082 

21033 

22020 

23043 

24105 

25206 

26350 

27539 

28774 

30059 

2 

69 

20097 

21050 

22037 

23061 

24123 

25225 

26370 

27559 

28795 

30081 

1 

60 

20113 

21066 

22054 

23078 

24141 

25244 

26389 

27579 
32° 

28816 

30103 

0 

M. 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

31° 

30° 

POLAR  DISTANCE. 

CO-SECANT. 

104 

TABXE  XXVn. 

LOGARITHMS  OF  THE  LATITUDE  AND  POLAH  DISTANCE. 

LATITUDE. 

SECAKT.   1 

0 

o 

o 

o 

o 

o 

o 

o 

o 

o 

M. 

60 

61 

62 

63 

64 

65 

66 

67 

68 

69 

1 

0 

0.30103 

31443 

32839 

34295 

35816 

37405 

39069 

40812 

42642 

44567 

60  1 

1 

30125 

31466 

32863 

34320 

35842 

37432 

39097 

40842 

42674 

44600 

59 

2 

30147 

31488 

32887 

34345 

35868 

37459 

39125 

40872 

42705 

44633 

58 

3 

30169 

31511 

32910 

34370 

35894 

37487 

39154 

40902 

42736 

44666 

57 

4 

30191 

31534 

32934 

34395 

35920 

37514 

39182 

40931 

42768 

44699 

56 
55 

5 

0.30213 

31557 

32958 

34420 

35946 

37541 

39211 

40961 

42799 

44732 

6 

30235 

31580 

32982 

34444 

35972 

37568 

39239 

40991 

42831 

44765 

54 

7 

30257 

31603 

33006 

34469 

35998 

37595 

39268 

41021 

42862 

44798 

53 

8 

30279 

31626 

33030 

34494 

36024 

37623 

39296 

41051 

42893 

44831 

52 

9 
10 

30301 

31649 

31672 

33054 

34519 

36050 

37650 

39325 

41081 

42925 

44864 

51 

0.30323 

33078 

34544 

36076 

37677 

39354 

41111 

42956 

44898 

50 

11 

30345 

31695 

33101 

34569 

36102 

37704 

39382 

41141 

42988 

44931 

49 

12 

30367 

31718 

33125 

34594 

36128 

37732 

39411 

41171 

43020 

44964 

48 

13 

30389 

31740 

33149 

34619 

36154 

37759 

39439 

41201 

43051 

44997 

47 

14 

30411 

31763 

33173 

34644 

361S0 

37786 

39468 

41231 

43083 

45031 

46 
45 

15 

0.30433 

31787 

33197 

34669 

36206 

37814 

39497 

41261 

43114 

45064 

16 

30455 

31810 

33221 

34694 

36233 

37841 

39526 

41291 

43146 

45097 

44 

17 

30477 

31833 

33245 

34719 

36259 

37869 

39554 

41322 

43178 

45131 

43 

18 

30499 

31856 

33269 

34745 

36285 

37896 

39583 

41352 

43210 

45164 

42 

19 
20 

30521 

31879 

33294 
33318 

34770 

36311 

37924 

39612 

41382 

43241 

45198 

41 

0.30544 

31902 

34795 

36338 

37951 

39641 

41412 

43273 

45231 

40 

21 

30566 

31925 

33342 

34820 

36364 

37979 

39669 

41443 

43305 

45265 

39 

22 

30588 

31948 

33366 

34845 

36390 

38006 

39698 

41473 

43337 

45298 

38 

23 

30610 

31971 

33390 

34870 

36417 

38034 

39727 

41503 

43369 

45332 

37 

24 

30632 

31994 

33414 

34896 

36443 

38061 

39756 

41533 

43401 

45365 

36 
35 

25 

0.30655 

32018 

33438 

34921 

36469 

38089 

39785 

41564 

43432 

45399 

26 

30677 

32041 

33463 

34946 

36496 

38117 

39814 

41594 

43464 

45433 

34 

27 

30699 

32064 

33487 

34971 

36522 

38144 

39843 

41625 

43496 

45466 

33 

28 

30721 

32087 

33511 

34997 

36549 

38172 

39872 

41655 

43528 

45500 

32 

29 
30 

30744 

32110 

33535 

35022 

35047 

36575 

38200 

39901 

41686 

43560 

45534 

31 
30 

0.30766 

32134 

33559 

36602 

38227 

39930 

41716 

43592 

45567 

31 

30788 

32157 

33584 

35073 

36628 

38255 

39959 

41747 

43625 

45601 

29 

32 

30811 

32180 

33608 

35098 

36655 

38283 

39988 

41777 

43657 

45635 

28 

33 

30833 

32204 

33632 

35123 

36681 

38311 

40017 

41808 

43689 

45669 

27 

34 

30856 

32227 

33657 

35149 

36708 

38338 

40046 

41838 

43721 

45703 

26 
25 

35 

0.30878 

32250 

33681 

35174 

36734 

38366 

40076 

41869 

43753 

45737 

36 

30900 

32274 

33705 

35200 

36761 

38394 

40105 

41899 

43785 

45771 

24 

37 

30923 

32297 

33730 

35225 

36787 

38422 

40134 

41930 

43818 

45805 

23 

38 

30945 

32320 

33754 

35251 

36814 

38450 

40163 

41961 

43850 

45839 

22 

39 

30968 

32344 

33779 
33803 

35276 

36841 

38478 

40192 

41992 

43882 

45873 

21 

40 

0.30990 

32367 

35302 

36867 

38506 

40222 

42022 

43915 

45907 

20 

41 

31013 

32391 

33827 

35327 

36894 

38534 

40251 

42053 

43947 

45941 

19 

42 

31035 

32414 

33852 

35353 

36921 

38562 

40280 

42084 

43979 

45975 

18 

43 

31058 

32438 

33876 

35378 

36948 

38590 

40310 

42115 

44012 

46009 

17 

44 

31080 

32461 

33901 

35404 

36974 

38618 

40339 

42145 

44044 

46043 

16 

45 

0.31103 

32485 

33925 

35429 

37001 

38646 

40368 

42176 

44077 

46078 

15 

46 

31125 

32508 

33950 

35455 

37028 

38674 

40398 

42207 

44109 

46112 

14 

47 

31148 

32532 

33975 

35481 

37055 

38702 

40427 

42238 

44142 

46146 

13 

48 

31171 

32555 

33999 

35506 

37082 

38730 

40457 

42269 

44174 

46181 

12 

49 
50 

31193 

32579 

34024 

35532 

37108 

38758 

40486 

42300 

44207 
44239 

46215 

11 

0.31216 

32602 

34048 

35558 

37135 

38786 

40516 

42331 

46249 

10 

51 

31238 

32626 

34073 

35583 

37162 

38814 

40545 

42362 

44272 

46284 

9 

52 

31261 

32650 

34098 

35609 

37189 

38842 

40575 

42393 

44305 

46318 

8 

53 

31284 

32673 

34122 

35635 

37216 

38871 

40604 

42424 

44337 

46353 

7 

54 
55 

31306 

32697 

34147 
34172 

35661 

37243 

38899 

40634 

42455 

44370 

46387 

6 
5 

0.31329 

32720 

35687 

37270 

38927 

40664 

42486 

44403 

46422 

56 

31352 

32744 

34196 

35712 

37297 

38955 

40693 

42518 

44436 

46456 

4 

57 

31375 

32768 

34221 

35738 

37324 

38984 

40723 

42549 

44468 

46491 

3 

58 

31397 

32792 

34246 

35764 

37351 

39012 

40753 

42580 

44501 

46525 

2 

59 

31420 

32815 

34271 

35790 

37378 

39040 

40782 

42611 

44534 

46560 

1 

60 

31443 

32839 

34295 

35816 

37405 

39069 

40812 

42642 

44567 

46595 

0 

29 

28' 

27° 

•2  6° 

25' 

24 

23° 

22' 

21' 

20° 

M. 

^.^ 

■■■M 

P 

OLAR  DI 

STANCE. 

CO-SECAl 

»T. 

TABLE  XXVII. 

105   1 

LOGARITHMS  OF  THE 

LATITUDE  AND  POLAR  DISTANCE. 

LATITUDE, 

SECANT.   1 

o 

o 

o 

o 

0 

o 

o 

o 

o 

o 

iM. 

70 

71 

72 

73 

74 

75 

76 

77 

78 

79 

0 

0.46595 

48736 

51002 

53406 

55966 

58700 

61632 

64791 

68212 

71940 

60 

1 

46630 

43773 

51041 

53448 

56010 

58748 

61683 

64846 

68272 

72005 

59 

2 

46664 

48809 

51080 

53489 

56054 

58795 

61734 

64901 

68331 

72070 

58 

3 

46699 

48846 

51119 

53531 

56099 

58842 

61785 

64956 

68391 

72136 

57 

4 
5 

46734 

48883 

51158 

53572 

56143 

58890 

61836 

65011 

68451 

72201 

56 

C.  46769 

48920 

51197 

53614 

56187 

58937 

61887 

65066 

68510 

72266 

55 

6 

46804 

48957 

51236 

53655 

56231 

58984 

61938 

65121 

68570 

72332 

54 

7 

46839 

48993 

51275 

53697 

56276 

59032 

61989 

65176 

68630 

72398 

53 

8 

46874 

•49030 

51314 

53738 

56320 

59079 

62040 

65231 

68690 

72463 

52 

9 

46908 

49067 

51353 

53780 

56365 

59127 

62091 

65287 

68750 

72529 

51 

10 

0.46944 

49104 

51393 

53822 

56409 

59175 

62142 

65342 

68811 

72595 

50 

11 

46979 

49142 

51432 

53864 

56454 

59222 

62194 

65398 

68871 

72661 

49 

12 

47014 

49179 

51471 

53905 

56498 

59270 

62245 

65453 

68932 

72727 

48 

13 

47049 

49216 

51510 

53947 

56543 

59318 

62297 

65509 

68992 

72794 

47 

14 

47084 

49253 

51550 

53989 

56588 

59366 

62348 

65564 

69053 

72860 

46 

15 

0.47119 

49290 

51589 

54031 

56633 

59414 

62400 

65620 

69113 

72927 

45 

16 

47154 

49327 

51629 

54073 

56677 

59462 

62451 

65676 

69174 

72993 

44 

17 

47189 

49365 

51668 

54115 

56722 

59510 

62503 

65732 

69235 

73060 

43 

18 

47225 

49402 

51708 

54157 

56767 

59558 

62555 

65788 

69296 

73127 

42 

ly 

47260 
0.47295 

49439 

51748 

54199 

56812 

59606 

62607 

65844 

69357 

73194 

41 
40 

20 

49477 

51787 

54242 

56857 

59654 

62659 

65900 

69418 

73261 

21 

47331 

49514 

51827 

54284 

56902 

59703 

62711 

65957 

69479 

73328 

39 

22 

47366 

49551 

51867 

54326 

56947 

59751 

62763 

66013 

69541 

73395 

38 

23 

47402 

49589 

51906 

54368 

56992 

59800 

62815 

66069 

69602 

73462 

37 

24 

47437 

49626 

51946 

54411 

57038 

59848 

62867 

66126 

69664 

73530 

36 

25 

0.47473 

49t^64 

51986 

54453 

57083 

59897 

62919 

66182 

69725 

73597 

35 

26 

47508 

49702 

52026 

54496 

57128 

59945 

62972 

66239 

69787 

73665 

34 

27 

47544 

49739 

52066 

54538 

57174 

59994 

63024 

66296 

69849 

73733 

33 

28 

47579 

49777 

52106 

54581 

57219 

60042 

63076 

66353 

69910 

73801 

32 

29 

47615 

49815 

52146 

54623 

57265 

60091 

63129 

66409 

69972 

73869 

31 
30 

30 

0.47650 

49852 

52186 

54666 

57310 

60140 

63181 

.66466 

70034 

73937 

31 

47686 

49890 

52226 

54708 

57356 

60189 

63234 

66523 

70097 

74005 

29 

32 

47722 

49928 

52266 

54751 

57401 

60238 

63287 

66580 

70159 

74073 

28 

33 

47758 

49966 

52.S06 

54794 

57447 

60287 

63340 

66638 

70221 

74142 

27 

34 

47793 

50004 

52346 

52387 

54837 

57493 

60336 

63392 

66695 

70284 

74210 

26 

35 

0.47829 

50042 

54880 

57539 

60385 

63445 

66752 

70346 

74279 

25 

36 

47865 

50080 

52427 

54923 

57584 

60434 

63498 

66810 

70409 

74348 

24 

37 

47901 

50118 

52467 

54965 

57630 

60483 

63551 

66867 

70471 

74417 

23 

38 

47937 

50156 

52508 

55008 

57676 

60533 

63605 

66925 

70534 

74486 

22 

39 

47973 

50194 

52548 

55052 

57722 

60582 
60631 

63658 

66982 

70597 

74555 

21 

40 

0.48009 

50232 

52589 

55095 

57768 

63711 

67040 

70660 

74624 

20 

41 

48045 

50270 

52629 

55138 

57814 

60681 

63764 

67098 

70723 

74693 

19 

42 

48081 

50308 

52670 

55181 

57860 

60730 

63818 

67156 

70786 

74763 

18 

43 

48117 

50346 

52710 

55224 

57907 

60780 

63871 

67214 

70850 

74832 

17 

44 

48153 

50385 

52751 

55267 

57953 

60830 

63925 

67272 

70913 

74902 

16 

45 

0.481S9 

50423 

52791 

55311 

57999 

60879 

63978 

67330 

70976 

74972 

15 

4fi 

48226 

50461 

52832 

55354 

58046 

60929 

64032 

67388 

71040 

75042 

14 

47 

48262 

50500 

52873 

55398 

68092 

60979 

64086 

67447 

71104 

75112 

13 

48 

48298 

50538 

52914 

55441 

58139 

61029 

64140 

67505 

71167 

75182 

12 

49 

48334 

50576 

52955 

55484 

58185 

61079 

64194 

67563 

71231 

75252 

11 

50 

0.48371 

50615 

52995 

55528 

58232 

61129 

64248 

67622 

71295 

75323 

10 

51 

48407 

50653 

53036 

55572 

58278 

61179 

64302 

67681 

71359 

75393 

9 

52 

48443 

50692 

53077 

55615 

58325 

61229 

64356 

67739 

71423 

75464 

8 

53 

48480 

50731 

53118 

55659 

58372 

61279 

64410 

67798 

71488 

75534 

7 

54 

48516 

50769 

53159 

55703 

58418 

61330 

64464 

67857 

71552 

75605 

6 
5 

55 

0.48553 

50808 

53200 

55747 

48465 

61380 

64519 

67916 

71616 

75676 

56 

48589 

50847 

53242 

55790 

58512 

61430 

64573 

67975 

71681 

75747 

4 

57 

48626 

50S85 

53283 

55834 

58559 

61481 

64627 

68034 

71746 

75819 

3 

58 

4^662 

50924 

53324 

55878 

58606 

61531 

64682 

68093 

71810 

75890 

2 

59 

48699 

50963 

53365 

55922 

58653 

61582 

64737 

68153 

71875 

75961 

1 

60 

48736 

51002 

53406 

55966 

58700 

61632 

64791 

68212 

71940 

76033 

0 

19° 

18° 

17° 

16° 

15° 

14° 

13° 

12° 

W 

10° 

M. 

I 

'OLAR  D 

[STANCE. 

CO-SKCA> 

fT. 

106 

TABLE  XXVII. 

LOGARITHMS  OF  THE  LATITUDE  AND  POLAR  DISTANCE.           | 

LATITDDE. 

SECANT.   1 

o 

o 

o 

o 

o 

o 

o 

■   o  n 

o 

o 

M. 
0 

80 

81 

82 

83 

84 

85 

86 

87 

88 

89 

60 

0.76033 

80567 

85644 

91411 

0.98077 

1.05970 

1.15642 

1.28120 

1.45716/1.75814 

1 

76105 

80647 

85734 

91514 

98197 

06115 

15823 

28362 

46081 

76544 

59 

2 

76177 

80727 

85825 

91617 

98318 

06260 

16004 

28605 

46448 

77287 

58 

3 

76248 

80807 

85915 

91720 

98439 

06406 

16187 

28849 

46817 

78042 

57 

4 

76321 

80887 

86006 
86096 

91824 

98560 

06552 

16370 

29095 

47190 

78811 

56 
55 

5 

0.76393 

80967 

91928 

0.98682 

1.06699 

1.16554 

1.29342 

1.47566 

1.79593 

6 

76465 

81048 

86187 

92032 

98804 

06846 

16739 

29591 

47945 

80390 

54 

7 

76538 

81129 

86278 

92137 

98926 

06993 

16925 

29841 

48327 

81202 

53 

8 

76610 

81210 

86370 

92242 

99049 

07141 

17112 

30093 

48713 

82029 

52 

9 

76683 

81291 

86461 

92347 

99172 

07290 

17299 

30346 

49103 

82872 

51 

10 

0.76756 

81372 

86553 

92452 

0.99296 

1.07439 

1.17487 

1.30600 

1.49495 

1.83732 

50 

11 

76829 

81453 

86645 

92558 

99419 

07589 

17676 

30856 

49892 

84609 

49 

12 

76902 

81535 

86737 

92663 

99544 

07739 

17866 

31114 

50292 

85505 

48 

13 

76975 

81617 

86829 

92769 

99668 

07890 

18056 

31373 

50696 

86419 

47 

14 
15 

77048 

81698 

86922 

92876 

99793 

08041 
1  08193 

18248 

31633 

51104 

87353 
1.88307 

46 
45 

0.77122 

81780 

87015 

92982 

0.99918 

1.18440 

1.31896 

1.51515 

16 

77195 

81863 

87108 

93089 

1.00044 

08345 

18633 

32159 

51931 

89283 

44 

17 

77269 

81945 

87201 

93196 

00170 

08498 

18827 

32425 

52350 

90282 

43 

18 

77343 

82027 

87294 

93304 

00296 

08651 

19022 

32692 

52774 

91304 

42 

19 

77417 

82110 

87388 
87481 

93411 

00423 

08805 

19218 

32901 

53201 

92350 

41 

20 

0.77491 

82193 

93519 

1.00550 

1.08960 

1.19415 

1  .33231 

1.53633 

1.93422 

40 

21 

77565 

82276 

87576 

93628 

00678 

09115 

19612 

33503 

54070 

94522 

39 

22 

77639 

82359 

87669 

93736 

00806 

09270 

19811 

33777 

54511 

95650 

38 

23 

77714 

82442 

87764 

93845 

00934 

09426 

20010 

34053 

54956 

96808 

37 

24 

77789 

82526 

87858 

93954 

01063 

09583 

20211 

34330 

55406 

97998 

36 
35 

25 

0.77863 

82609 

87953 

94063 

1.01192 

1.09740 

1.20412 

1.34609 

1.55861 

1.99222 

26 

77938 

82693 

88048 

94173 

01321 

09898 

20614 

34890 

56320 

2.00480 

34 

27 

78013 

82777 

88143 

94283 

01451 

10057 

20817 

35173 

56784 

01777 

33 

28 

78088 

82861 

88239 

94393 

01581 

L0216 

21021 

35457 

57254 

03113 

32 

29 
30 

78164 

82945 

88334 

94503 
94614 

01712 

10375 

21226 

35744 

57728 

04492 

31 
30 

0.78239 

83030 

88430 

J. 01843 

1.10536 

1.21432 

1.36032 

1.58208 

2.05916 

31 

78315 

83114 

88526 

94725 

01974 

10696 

21639 

36322 

58693 

07388 

29 

32 

78390 

83199 

88623 

94836 

02106 

10858 

21848 

36615 

59184 

08912 

28 

33 

78466 

83284 

88719 

94948 

02238 

11020 

22057 

36909 

59680 

10491 

27 

34 

78542 

83369 

88816 

95060 

02371 

11183 

22267 

37205 

60182 

12130 
2.13834 

26 
25 

35 

0.78618 

83455 

88913 

95172 

1.02504 

1.11346 

1.22478 

1.37503 

1.60690 

36 

78694 

83540 

89010 

95285 

02637 

11510 

22690 

37804 

61204 

15607 

24 

37 

78771 

83626 

89107 

95397 

02771 

11674 

22903 

38106 

61724 

17455 

23 

38 

78847 

83711 

89205 

95510 

02905 

11839 

23117 

38411 

62250 

19385 

22 

39 

78924 

83797 

89303 

95624 

03040 

12005 

23332 

38718 

62783 

21406 

21 
20 

40 

0.79001 

83884 

89401 

95738 

1.03175 

1.12171 

1.23549 

1.39027 

1.63322 

2.23525 

41 

79078 

83970 

89499 

95851 

03311 

12339 

23766 

39338 

63868 

25752 

19 

42 

79155 

84056 

89598 

95966 

03447 

12506 

23985 

39651 

64422 

28100 

18 

43 

79232 

84143 

89696 

96080 

03583 

12675 

24204 

39967 

64982 

30583 

17 

44 

79309 

84230 

89795 

96195 

03720 

12844 

24425 

40285 

65550 

33216 

16 

45 

0.79387 

84317 

89894 

96310 

1.03857 

1.13013 

1.24647 

1.40605 

1.66125 

2.36018 

15 

46 

79465 

84404 

89994 

96426 

03995 

13184 

24870 

40928 

66708 

39015 

14 

47 

79542 

84492 

90093 

96542 

04133 

13355 

25094 

41253 

67298 

42233 

13 

48 

79620 

84579 

90193 

96658 

04272 

13526 

25320 

41581 

67897 

45709 

12 

49 

79698 

84667 

90293 

96774 

04411 

13699 

25546 

41911 

68505 

49488 

11 
10 

50 

0.79777 

84755 

90394 

96891 

1  04550 

1.13872 

1.25774 

1.42243 

1.69121 

2.53627 

51 

79855 

84843 

90494 

97008 

04690 

14045 

26003 

42579 

69746 

58203 

9 

52 

79933 

84931 

90595 

97126 

04830 

14220 

26233 

42916 

70379 

63318 

8 

53 

80012 

85020 

90696 

97243 

04971 

14395 

26465 

43257 

71023 

69118 

7 

54 

80091 

85109 

90798 
90899 

973(il 

05113 

14571 

26697 

43600 

71676 

75812 

6 
5 

55 

0.80170 

85197 

97480 

1.05254 

1.14748 

1.26931 

1.43946 

1.72339 

2.83730 

56 

80249 

85286 

91001 

97598 

05397 

14925 

27166 

44295 

73012 

93121 

4 

57 

80328 

85376 

91103 

97717 

05539 

15103 

27403 

44646 

73696 

3.05915 

3 

58 

80408 

85465 

91205 

97837 

05683 

15282 

27640 

45001 

74391 

23524 

2 

59 

80487 

85555 

91308 

97957 

05826 

15461 

27880 

45358 

75097 

53627 

1 

60 

80567 

85644 

91411 

98077 

05970 

15642 

28120 

45718 
2" 

75814 

0 

9° 

8° 

7° 

6" 

5° 

4° 

3' 

1° 

0° 

M. 

POLAK  DISTANCE. 

CO-SECaNT.   I 

TABLE  XXVllL 
LOGARITHMS  OF  THE  HALF  SUM  AND  DIFFERENCE. 

HALF  8UM. 


107 


CO-SINK. 


M. 


o 
89 


0 
1 
2 
3 
4 


10 
11 
12 
13 
14 


15 

16 

17 
18 
19 


30 
31 
32 
33 
34 


35 
36 
37 
38 
39 


40 
41 

42 
43 
44 


45 
46 
47 
48 
49 


50 
51 
52 
53 
54 


55 
56 
57 
58 
59 
60 


24186 
23456 
22713 
21958 
21189 

. 20407 
19610 
18799 
17971 
17128 


88 


5  J  282 
53919 
53552 
53183 
52810 

3.52434 

52055 
51673 

51287 
50897 


3.1 


(i268 
15391 
14495 
13581 
12647 


3.11693 
10717 
09718 
08696 
07650 


3 


87 

.71880 
71638 
71395 
71151 
70905 

.70658 
70409 
70159 
69907 
69654 


86 


20 

3 

06578 

21 

05478 

22 

04350 

23 

03192 

24 

02002 

25 

3 

.00779 

26 

2 

.99520 

27 

98223 

28 

96887 

29 

95508 

2.94084 
92612 
91088 
89509 
87870 


505(15 
50108 
49708 
49304 
48896 

48485 
48069 
47650 
47226 
46799 


85 


3.84358 
84177 
83996 
83813 
83630 


3.83446 
83261 
83075 

82888 
82701 


,46367 
45930 
45489 
45044 
44594 


.69400 
69144 
68886 
68627 

_68367 

.68104 
67841 
67575 
67308 
67039 

.66769 
66497 
66223 
65947 
65670 


3.82513 
82324 
82134 
81944 
81752 


3.441393 

43680 
43216 
42746 

42272 


3.41792 
41307 
40816 
40320 
39818 


2.86166 
84393 
82545 
80615 
78594 


3.39310 
38796 
38276 
37750 
37217 


2.76475 

74248 
71900 
69417 
66784 


2.63982 
60985 
57767 
54291 
50512 


.94030 
93885 
93740 
93594 
93448 


3.93301 
93154 
93007 

92859 
_92710 

.92561 
92411 
92261 
92110 
91959 


o 

84 


4. 


01923 

01803 
01682 
01561 
0J440 


.01318 
01196 
01074 
00951 
00828 


o 

83 


4.0S589 
084S6 
08383 
08280 
08176 


o 

82 


.08072 
07968 
07863 
07758 
07653 


3.81560 
81367 
81173 
80978 
80782 


3.91807 
91655 
91502 
91349 
91195 


.00704 
00581 
00456 
00332 
00207 


14356 

14266 
14175 
14085 
13994 

13904 
13813 
13722 
13630 
13539 


81 


19433 
19353 
19273 
19193 
19113 


3. 


80585 
80388 
80189 
79990 
79789 


3.91040 
90885 
90730 
90574 
90417 


.65391 
65110 
64827 
64543 
64256 


.63968 
63678 
63385 
63091 
62795 


3.79588 
79386 
79183 
78979 
78774 

3.78568 
78361 
78152 
77943 
77733 


3. 


3.90260 
90102 
89943 
89784 
89625 


00082 
.99956 
99830 
99704 
99577 


99450 
99322 
99194 
99066 
98937 


.07548 
07442 
07337 
07231 
07124 


3.98808 
98679 
98549 
98419 

98288 


4.05937 
05827 
05717 
05607 
05497 


.62497 
62196 
61894 
61589 
61282 


3.36678 
36132 
35578 
35018 
34450 


3.60973 
60662 
60349 
60033 
59715 


2.46373 

41797 
36682 
30882 
24188 


2.16270 
06579 

1.94085 
76476 
46373 
('0000 


0^ 


,33875 
33292 
32702 
32103 
31495 


.30879 
30255 

29621 

28927 
28324 


3.27661 
26988 
26304 
25609 
24903 
24186 


V 


3.89464 
89304 
89142 
88980 

88817 


3.77522 
77310 
77097 

76883 
76667 


3.76451 
76234 
76015 
75796 
75575 


.59395 
59072 
58747 
58419 
58089 


3. 


3.98157 
98026 
97894 
97762 
97629 


3.88654 
88490 
88326 
88161 
87995 


3.87829 
87661 
87494 
87325 
87156 


75353 
75130 
74906 
74680 
74454 


.57757  3 
57421 
57084 
56743 
56400 


.56054 
55705 
55354 
54999 
54642 
54282 


,74226 
73997 
73767 
73535 
7330 


.73069 
72834 
72597 
72360 
72120 
71880 


.86987 
86816 
86645 
86474 
86301 

.86128 
85955 
85780 
85605 
85429 


3.97496 
97363 
97229 
97095 
96960 


.07018 
06911 
06804 
06696 
06589 

.06481 
06372 
06264 
06155 
06046 


13447 
13355 
13263 
13171 

13078 


12985 
12892 
12799 
12706 
12612 


12519 
12425 
12331 
12236 
12142 


19033 
18952 
18871 
18790 
18709 


o 
80 


23967 
23895 
23823 
23752 
2367f) 


23607 
23535 
23462 
23390 
23317 


18628 
18547 
18465 
18383 
18302 


18220 
18137 
18055 
17973 
17890 


4.05386 
05275 
05164 
05052 
04940 


3.96825 
96689 
96553 
96417 
96280 


.96143 
96005 
95867 
95728 
90589 


.85252 
85075 
84897 
84718 
84539 
84358 


.95450 
95310 
95170 
95029 

94887 


3.94746 
94603 
94461 
94317 
94174 
94030 


.04828 
04715 
04603 
04490 
04376 


.04262 
04149 
04034 
03920 
03805 


12047 
11952 
11857 
11761 
11666 


17807 
17724 
17641 
17558 
17474 


11570 
11474 
11377 
11281 
11184 


17391 
17307 
17223 
17139 
17055 


11087 
10990 
10893 
10795 
10697 


4.03690 
03574 
03458 
Co342 
03226 


4.03109 
02992 
02874 
02757 
02639 


4.02520 
02402 
02283 
02163 
02043 
01923 


10599 
10501 
10402 
10304 
10205 


10106 
10006 
09907 
09807 
09707 


09606 
09506 
09405 
09304 
09202 


16970 
16886 
16801 
16716 
16631 


16545 
16460 
16374 
16289 
16203 


16116 
16030 
15944 
15857 
15770 


15683 
15596 
15508 
1C421 
15233 


09101 
08999 
08897 
08795 
08692 
08589 


15245 
15157 
15069 
14980 
14891 


14803 
14714 
14624 
14535 
14445 
14356 


8° 


23244 
23171 
23098 
23025 
22952 

22878 
22805 
22731 
22657 

22583 


60 
59 

58 
57 
56 


55 

54 
53 

52 
51 


22509 
22435 
22361 
22286 
22211 


50 
49 

48 
47 
46 


22137 

22062 
21987 
21912 
21836 


21761 
21685 
21610 
21534 
21458 


21382 
21306 
21229 
21153 
21076 


45 
44 

43 
42 
_41 

40 
39 
38 
37 
_36 

35 
34 
33 
32 
31 


30 
29 
28 
27 
26 


20999 
20922 
20845 
20768 
20691 


20613 
20535 
20458 
20380 
20302 


20223 
20145 
20067 
19988 
19909 


25 
24 
23 
22 
21 


20 
19 
18 
17 
16 


15 
14 
13 
12 
11 


19830 
19751 
19672 
19592 
19513 
19433 


10 
9 
8 
7 
6 

5 
4 
3 
2 
1 
0 


M. 


DIFFERENCE. 


SINE. 


108 

TABLE  XXVIII. 

-] 

LOGARITHMS  OF  THE  HALF  SUM  AND  DIFFERENCK 

1 

HALF  SUM. 

CO-BINK. 

o 

o 

o 

o 

0 

o 

o 

o 

o 

o 

M. 
0 

79 

78 

77 

76 

75 

74 

73 

46594 

72 

71 

70 

4.28060 

31788 

35209 

38368 

41300 

44034 

48998 

51264 

53405 

60 

1 

27995 

31728 

35154 

38317 

41252 

43990 

46552 

48959 

51227 

53370 

59 

2 

27930 

31669 

35099 

38266 

41205 

43946 

46511 

48920 

51191 

53336 

58 

3 

27864 

31609 

35044 

38215 

41158 

43901 

46469 

48881 

51154 

53301 

57 

4 

5 

27799 

31549 

34989 

38164 

41110 

43857 

46428 

48842 

51117 

53266 

56 
55 

4.27734 

31490 

34934 

38113 

41063 

43813 

46386 

48803 

51080 

53231 

6 

27668 

31430 

34879 

38062 

41016 

43769 

46345 

48764 

51043 

53196 

54 

7 

27602 

31370 

34824 

38011 

40968 

43724 

46303 

48725 

51007 

53161 

53 

8 

27537 

31310 

34769 

37960 

40921 

43680 

46262 

48686 

50970 

53126 

52 

9 

27471 

31250 

34713 

37909 

40873 

43635 

46220 

48647 

50933 

53092 

51 

10 

4.27405 

31189 

34658 

37858 

40825 

43591 

46178 

48607 

50896 

53056 

50 

11 

27339 

31129 

34602 

37806 

40778 

43546 

46136 

48568 

50858 

53021 

49 

12 

27273 

31068 

34547 

37755 

40730 

43502 

46095 

48529 

50821 

52986 

48 

13 

27206 

31008 

34491 

37703 

40682 

43457 

46053 

48490 

50784 

52951 

47 

14 

27140 

30947 

34436 

37652 
37600 

40634 

43412 

46011 

48450 

50747 

52916 

46 

15 

4.27073 

30887 

34380 

40586 

43367 

45969 

48411 

50710 

52881 

45 

16 

27007 

30826 

34324 

37549 

40538 

43323 

45927 

48371 

50673 

52846 

44 

17 

26940 

30765 

34268 

37497 

40490 

43278 

45885 

48332 

50635 

52811 

43 

18 

26873 

30704 

34212 

37445 

40442 

43233 

45843 

48292 

50598 

52775 

42 

19 
20 

26806 

30643 

34156 

37393 

40394 

43188 

45801 

48252 

50561 

52740 

41 

4.26739 

30582 

34100 

37341 

40346 

43143 

45758 

48213 

50523 

52705 

40 

21 

26672 

30521 

34043 

37289 

40297 

43098 

45716 

48173 

50486 

52669 

39 

22 

26605 

30459 

33987 

37237 

40249 

43053 

45674 

48133 

50449 

52634 

38 

23 

26538 

30398 

33931 

37185 

40200 

43008 

45632 

48094 

50411 

52598 

37 

24 

26470 

30336 

33874 

37133 

40152 

42962 

45589 

48054 

50374 

52563 

36 

25 

4.26403 

30275 

33818 

37081 

40103 

42917 

45547 

48014 

50336 

52527 

35 

26 

26335 

30213 

33761 

37028 

40055 

42872 

45504 

47974 

50298 

52492 

34 

27 

26267 

30151 

33704 

36976 

40006 

42826 

45462 

47934 

50261 

52456 

33 

28 

26199 

30090 

33647 

36924 

39958 

42781 

45419 

47894 

50223 

52421 

32 

29 

26131 

30028 

33591 

36871 

39909 

42735 

45377 

47854 

50185 

52385 
52350 

31 
30 

30 

4.26063 

29966 

33534 

36819 

39860 

42690 

45334 

47814 

50148 

31 

25995 

29903 

33477 

36766 

39811 

42644 

45292 

47774 

50110 

52314 

29 

32 

25927 

29841 

33420 

36713 

39762 

42599 

45249 

47734 

50072 

52278 

28 

33 

25858 

29779 

33362 

36660 

39713 

42553 

45206 

47694 

50034 

52242 

27 

34 

25790 

29716 

33305 
33248 

36608 

39664 

42507 

45163 

47654 

49996 

52207 

26 

35 

4.25721 

29654 

36555 

39615 

42461 

45120 

47613 

49958 

52171 

25 

36 

25652 

29591 

33190 

36502 

39566 

42416 

45077 

47573 

49920 

52135 

24 

37 

25583 

29529 

33133 

36449 

39517 

42370 

45035 

47533 

49882 

52099 

23 

38 

25514 

29466 

33075 

36395 

39467 

42324 

44992 

47492 

49844 

52063 

22 

39 
40 

25445 
4.25376 

2940.3 

33018 

36342 

39418 

42278 

44948 

47452 

49806 

52027 

21 

20 

29340 

32960 

36289 

39369 

42232 

44905 

47411 

49768 

51991 

41 

25307 

29277 

32902 

36236 

39319 

42186 

44862 

47371 

49730 

51955 

19 

42 

25237 

29214 

32844 

36182 

39270 

42140 

44819 

47330 

49692 

51919 

18 

43 

•^5168 

29150 

32786 

36129 

39220 

42093 

44776 

47290 

49654 

51883 

17 

44 

25098 

29087 

32728 

36075 

39170 

42047 

44733 

47249 

49615 

51847 

16 

45 

4.25028 

29024 

32670 

36022 

39121 

42001 

44689 

47209 

49577 

51811 

15 

46 

24958 

28960 

32612 

35968 

39071 

41954 

44646 

47168 

49539 

51774 

14 

47 

24888 

28896 

32553 

35914 

39021 

41908 

44602 

47127 

49500 

51738 

13 

48 

24818 

28833 

32495 

35860 

38971 

41861 

44559 

47086 

49462 

51702 

12 

49 

24748 

28769 

32437 

35806 

38921 

41815 

44516 

47045 

49424 

51666 

11 

50 

4.24677 

28705 

32378 

35752 

38871 

41768 

44472 

47005 

49385 

51629 

10 

51 

24607 

28641 

32319 

35698 

38821 

41722 

44428 

46964 

49347 

51593 

9 

52 

24536 

28577 

32261 

35644 

38771 

41675 

44385 

46923 

49308 

51557 

8 

53 

24466 

28511 

32202 

35590 

38721 

41628 

44341 

46882 

49269 

51520 

7 

54 

24395 

28448 

32143 

35536 

38670 

41582 
41535 

44297 
44253 

46841 

49231 

51484 

6 

55 

4.24324 

28384 

32084 

35481 

38620 

46800 

49192 

51447 

5 

56 

24253 

28319 

32025 

35427 

38570 

41488 

44210 

46758 

49153 

51411 

4 

57 

24181 

28254 

31966 

35373 

38519 

41441 

44166 

46717 

49115 

51374 

3 

58 

24110 

28190 

31907 

35318 

38469 

41394 

44122 

46676 

49076 

51338 

2 

59 

24039 

28125 

31847 

35263 

38418 

41347 

44078 

46635 

49037 

51301 

1 

60 

23967 

28060 

3178S 

35209 

38368 

41300 

44034 

46594 

48998 

51264 

0 

10° 

11' 

12° 

13° 

14° 

15° 

16° 

17° 

18* 

19° 

M. 

DIFFER 

ENCE. 

SIN 

E. 

TABLE  XXVIII. 

109   1 

LOGARITHMS 

1  OF  THE  HALF  SUM  AND  DIFFERENCE. 

HALF  SUM. 

CO-SINE.   1 

o 

o 

o 

o 

0 

o 

o 

o 

o 

o 

M. 

69 

68 
57358 

67 

66 

65 

64 

63 

62 

61 

60 

0 

4  55433 

59188 

60931 

62595 

64184 

65705 

67161 

68557 

69897 

60 

1 

55400 

57326 

59158 

60903 

62568 

64158 

65680 

67137 

68534 

69875 

59 

2 

55367 

57295 

59128 

60875 

62541 

64132 

65655 

67113 

68512 

69853 

58 

3 

55334 

57264 

59098 

60846 

62513 

64106 

65630 

67090 

68489 

69831 

57 

4 
5 

55301 

57232 

59069 

60818 

62486 

64080 

65605 

67066 

68466 

69809 

56 
55 

4.55268 

57201 

59039 

60789 

62459 

&4054 

65580 

67042 

68443 

69787 

6 

55235 

57169 

59009 

60761 

62432 

64028 

65556 

67018 

68420 

69765 

54 

7 

55202 

57138 

58979 

60732 

62405 

64002 

65531 

66994 

68397 

69743 

53 

8 

55169 

57107 

58949 

60704 

62377 

63976 

65506 

66970 

68374 

69721 

52 

9 

55136 

57075 

58919 

60675 

62350 

63950 

65481 

66946 

68351 

69699 

51 

10 

4.55102 

57044 

58889 

60646 

62323 

63924 

65456 

66922 

68328 

69677 

50 

11 

55069 

57012 

58859 

60618 

62296 

63898 

65431 

66899 

68305 

69655 

49 

12 

55036 

56980 

58829 

60589 

62268 

63872 

65406 

66875 

68282 

69633 

48 

13 

55003 

56949 

58799 

60561 

62241 

63846 

65381 

66851 

68260 

69611 

47 

14 

54969 

56917 

58769 

60532 

62214 

63820 

65356 

66827 

68237 

69589 

46 

15 

4.54936 

56886 

58739 

60503 

62186 

63794 

65331 

66803 

68213 

69567 

45 

16 

54903 

56854 

58709 

60474 

62159 

63767 

65306 

66779 

68190 

69545 

44 

17 

54869 

56822 

58678 

60446 

62131 

63741 

65281 

66755 

68167 

69523 

43 

18 

54836 

56790 

58648 

60417 

62104 

63715 

65255 

66731 

68144 

69501 

42 

19 

54802 

56759 

58618 

60388 

62076 

63689 

65230 

66706 

68121 

69479 

41 

20 

4.54769 

56727 

58588 

60359 

62049 

63662 

65205 

66682 

68098 

69456 

40 

21 

54735 

56695 

58557 

60331 

62021 

63636 

65180 

66658 

68075 

69434 

39 

22 

54702 

56663 

58527 

60302 

61994 

63610 

65155 

66634 

68052 

69412 

38 

23 

54668 

56631 

58497 

60273 

61966 

63583 

65130 

66610 

68029 

69390 

37 

24 

54635 

56599 

58467 

60244 

61939 

63557 

65104 

66586 

68006 

69368 

36 

25 

4.54601 

56568 

58436 

60215 

61911 

63531 

65079 

66562 

679«2 

69345 

35 

26 

54567 

56536 

58406 

60186 

61883 

63504 

65054 

66537 

67959 

69323 

34 

27 

54^34 

56504 

58375 

60157 

61856 

63478 

65029 

66513 

67936 

69301 

33 

28 

54500 

56472 

58345 

60128 

61828 

63451 

65003 

66489 

67913 

69279 

32 

29 

54466 

56440 

58314 

60099 

61800 

63425 

64978 

66465 

67890 

69256 

31 

30 

4.54433 

56408 

58284 

60070 

61773 

63398 

64953 

66441 

67866 

69234 

30 

31 

54399 

56375 

58253 

60041 

61745 

63372 

64927 

66416 

67843 

69212 

29 

32 

54365 

56343 

58223 

60012 

61717 

63345 

64902 

66392 

67820 

69189 

28 

33 

54331 

56311 

58192 

59983 

61689 

63319 

64877 

66368 

67796 

69167 

27 

34 
35 

54297 
4.54263 

56279 

58162 

59954 

61662 

63292 

64851 

66343 

67773 

69144 

26 

56247 

58131 

59924 

61634 

63266 

64826 

66319 

67750 

69122 

25 

36 

54229 

56215 

58101 

59895 

61606 

63239 

64800 

66295 

67726 

69100 

24 

37 

54195 

56182 

58070 

59866 

61578 

63213 

64775 

66270 

67703 

69077 

23 

38 

54161 

56150 

58039 

59837 

61550 

63186 

64749 

66246 

67680 

69055 

22 

39 
40 

54127 
4.54093 

56118 

58008 

59808 

61522 

63159 

64724 

66221 

67656 

69032 

21 

20 

56085 

57978 

59778 

61494 

63133 

64698 

66197 

67633 

69010 

41 

54059 

56053 

57947 

59749 

61466 

63106 

64673 

66173 

67609 

68987 

19 

42 

54025 

56n21 

57916 

59720 

61438 

63079 

64647 

66148 

67586 

68965 

18 

43 

53991 

55988 

57885 

59690 

61410 

63052 

64622 

66124 

67562 

68542 

17 

44 

53957 

55956 

57855 

59661 

61382 

63026 

64596 

66099 

67539 

68920 
68897 

16 
15 

45 

4.53922 

55923 

57824 

59632 

61354 

62999 

64571 

66075 

67515 

46 

53888 

55891 

57793 

59602 

61326 

62972 

64545 

66050 

67492 

68875 

14 

47 

53854 

55858 

57762 

59573 

61298 

62945 

64519 

66025 

67468 

68852 

13 

48 

53819 

55826 

57731 

59543 

61270 

62918 

64494 

66001 

67445 

68829 

12 

49 
50 

53785 

55793 

57700 

59514 

61242 

62892 
62865 

64468 

65976 

67421 

68807 

11 

4.53751 

55761 

57669 

59484 

61214 

64442 

65952 

67398 

68784 

10 

51 

53716 

55728 

57638 

59455 

61186 

62838 

64417 

65927 

67374 

68762 

9 

52 

53682 

55695 

57607 

59425 

61158 

62811 

64391 

65902 

67350 

68739 

8 

53 

53647 

55663 

57576 

59396 

61129 

62784 

64365 

65878 

67327 

68716 

7 

54 

53613 

55630 

57545 

59366 

61101 

62757 

64339 
64313 

65853 

67303 

68694 

6 

55 

4.53578 

55597 

57514 

59336 

61073 

62730 

65828 

67280 

68671 

5 

56 

53544 

55564 

57482 

59307 

61045 

62703 

64288 

65804 

67256 

68648 

4 

57 

53.509 

55532 

57451 

59277 

61016 

62676 

64262 

65779 

67232 

68625 

3 

58 

53475 

55499 

57420 

59247 

60988 

62649 

64236 

65754 

67208 

68603 

2 

59 

53440 

55466 

57389 

59218 

60960 

62622 

64210 

65729 

67185 

68580 

1 

60 

5340.5 

55433 

57358 

59188 

60931 

62595 

64184 

65705 

67161 

68557 

0 

20' 

2/ 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

M. 

DIFFER] 

ENCE. 

SIN 

E. 

HO 

LOGi 

TABLE  XXVIII. 

LRITHMS  OF  THE  HALF  SUM  AND  DIFFERENCE. 

HALF  SUM. 

C0-8INE.   1 

o 

o 

o 

o 

o 

o 

o 

o 

o 

« 

M. 
0 

59' 

58 

57 

56 

55 

54 

53 

52 

51 

50 

60 

4.71184 

72421 

73611 

74756 

75859 

76922 

77946 

78934 

79887 

80807 

1 

71163 

72401 

73591 

74737 

75841 

76904 

77930 

78918 

79872 

80792 

59 

2 

71142 

72381 

73572 

74719 

75823 

76887 

77913 

78902 

79856 

807^7 

58 

3 

71121 

72360 

73552 

74700 

75805 

76870 

77896 

78886 

79840 

80762 

57 

4 

71100 

72340 

73533 

74681 

75787 

76852 

77879 

78869 

79825 

80746 

56 
65 

5 

4.71079 

72320 

73513 

74662 

75769 

76835 

77862 

78853 

79809 

80731 

6 

71058 

72299 

73494 

74644 

75751 

76817 

77846 

78837 

79793 

80716 

54 

7 

71036 

72279 

73474 

74625 

75733 

76800 

77829 

78821 

79778 

80701 

53 

8 

71015 

72259 

73455 

74606 

75714 

76782 

77812 

78805 

79762 

80686 

52 

9 
10 

70994 

72238 

73435 

74587 

75696 

76765 

77795 

78788 

79746 

80671 

51 
50 

4.70973 

72218 

73416 

74568 

75678 

76747 

77778 

78772 

79731 

80656 

11 

70952 

72198 

73396 

74549 

75660 

76730 

77761 

78756 

79715 

80641 

49 

12 

70931 

72177 

73377 

74531 

75642 

76712 

77744 

78739 

79699 

80625 

48 

13 

70909 

72157 

73357 

74512 

75624 

76695 

77727 

78723 

79684 

80610 

47 

14 

70888 

72137 

73337 

74493 

75605 

76677 

77711 

78707 

79668 

80595 

46 

15 

4.70867 

72116 

73318 

74474 

75587 

76660 

77694 

78691 

79652 

80580 

45 

16 

70846 

72096 

73298 

74455 

75569 

76642 

77677 

78674 

79636 

80565 

44 

17 

70824 

72075 

73278 

74436 

75551 

76625 

77660 

78658 

79621 

80550 

43 

18 

70803 

72055 

73259 

74417 

75533 

76607 

77643 

78642 

79605 

80534 

42 

19 

70782 

72034 

73239 
73219 

74398 

75514 

76590 

77626 

78625 

79589 

80519 

41 

20 

4.70761 

72014 

74379 

75496 

76572 

77609 

78609 

79573 

80504 

40 

21 

70739 

71994 

7320  ) 

74360 

75478 

76554 

77592 

78592 

79558 

80489 

39 

22 

70718 

71973 

73180 

74341 

75459 

76537 

77575 

78576 

79542 

80473 

38 

23 

70697 

71952 

73160 

74322 

75441 

76519 

77558 

78560 

79526 

80458 

37 

24 

70675 

71932 

73140 

74303 

74284 

75423 

76501 

77541 

78543 

78527 

79510 

80443 

36 

25 

4.70654 

71911 

73121 

75405 

76484 

77524 

79494 

80428 

35 

26 

70633 

71891 

73101 

74265 

75386 

76466 

77507 

78510 

79478 

^0412 

34 

27 

70611 

71870 

73081 

74246 

75368 

76448 

77490 

78494 

79463 

80397 

33 

28 

70590 

71850 

73061 

74227 

75350 

76431 

77473 

78478 

79447 

80382 

32 

29 
30 

70568 

71829 

73041 

74208 
74189 

75331 

76413 

77456 

78461 

79431 

80366 

31 
30 

4.70547 

71809 

73022 

75313 

76395 

77439 

78445 

79415 

80351 

31 

70525 

71788 

73002 

74170 

75294 

76378 

77422 

78428 

79399 

80336 

29 

32 

70504 

71767 

72982 

74151 

75276 

76360 

77405 

78412 

79383 

80320 

28 

33 

70482 

71747 

72962 

74132 

75258 

76342 

77387 

78395 

79367 

80305 

27 

34 

70461 

71726 

72'»42 

74113 

75239 

76324 

77370 

78379 

79351 

80290 

26 
25 

35 

4.70439 

71705 

72922 

74093 

75221 

76307 

77353 

78362 

79335 

80274 

36 

70418 

71685 

72902 

74074 

75202 

76289 

77336 

78346 

79319 

80259 

24 

37 

70396 

71664 

72883 

74055 

75184 

76271 

77319 

78329 

79304 

80244 

23 

38 

70375 

71643 

72863 

74036 

75165 

76253 

77302 

78313 

79288 

80228 

22 

39 

70353 

71622 

72843 

74017 

75147 

76236 

77285 

78296 

79272 

80213 

21 
20 

40 

4.70332 

71602 

72823 

73997 

75128 

76218 

77268 

78280 

79256 

80197 

41 

70210 

71581 

72803 

73978 

75110 

76200 

77250 

78263 

79240 

80182 

19 

42 

70288 

71560 

72783 

73959 

75091 

76182 

77233 

78246 

79224 

80166 

18 

43 

70267 

71539 

72763 

73940 

75073 

76164 

77216 

78230 

79208 

80151 

17 

44 

70245 

71519 
71498 

72743 

73921 

75054 

76146 

77199 

78213 

79192 

80136 

16 

45 

4.70224 

72723 

73901 

75036 

76129 

77181 

78197 

79176 

80120 

15 

46 

7^202 

71477 

72703 

73882 

75017 

76111 

77164 

78180 

79160 

80105 

14 

47 

7'^180 

71456 

72683 

73863 

74999 

76093 

77147 

78163 

79144 

80089 

13 

48 

•^1159 

71435 

72663 

73843 

74980 

76075 

77130 

78147 

79128 

80074 

12 

49 

73137 

71414 

72643 

73824 

74961 
74943 

76057 

77112 

78130 

7P111 

80058 

11 
10 

50 

4.70115 

71393 

72622 

73805 

76039 

77095 

78113 

79095 

80043 

51 

70093 

71373 

72602 

73785 

74924 

76021 

77078 

78097 

79079 

80027 

9 

52 

70072 

71352 

72582 

73766 

74906 

76003 

77061 

78080 

79063 

80012 

8 

53 

70050 

71331 

72562 

73747 

74887 

75985 

77043 

78063 

79047 

79996 

7 

54 
55 

70028 

71310 

72542 

72522 

73727 

74868 

75967 

77026 

78047 

79031 

79981 

6 
5 

4.70006 

71289 

73708 

74850 

75949 

77009 

78030 

79015 

79965 

56 

69984 

71268 

72502 

73689 

74831 

75931 

76991 

78013 

78999 

79950 

4 

57 

69963 

71247 

72482 

73669 

74812 

75913 

76974 

77997 

78983 

79934 

3 

58 

69941 

71226 

72461 

73650 

74794 

75895 

76957 

77980 

78967 

79918 

2 

59 

69919 

71205 

72441 

73630 

74775 

75877 

76939 

77963 

78950 

79903 

1 

60 

69897 

71184 

72421 

73611 

74756 

75859 

76922 

77946 
37° 

78934 

79887 

0 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

38° 

39° 

M. 

1^^ 

DIFFER! 

-NCE. 

8IN 

E. 

TABLE  XXVIII. 

u,    1 

LOGARITHMS  OF  THE  HALF  SUM  AND  DIFFERENCK 



HALF  f 

3UM. 

C0-8INE. 

o 

o 

o 

o 

0 

o 

o 

o 

o 

" 
o 

M 
0 

49 

48 
82551 

47 

46 

45 

44 

43 

42 

41 

40 

4  81fi94 

83378 

84177 

84949 

85693 

86413 

87107 

87778 

88425 

60 

1 

SKjSO 

82537 

83365 

84164 

84936 

85681 

86401 

87096 

87767 

88415 

59 

2 

81665 

82523 

83351 

84151 

84923 

85669 

86389 

87085 

87756 

88404 

58 

3 

81651 

82509 

83338 

84138 

84911 

85657 

86377 

87073 

87745 

88394 

57 

4 

5 

81636 

82495 

83324 

84125 

84898 

85645 

86366 

87062 

87734 

88383 

56 

4.81622 

82481 

83311 

84112 

84885 

856S2 

86354 

87050 

87723 

88372 

55 

6 

81607 

82467 

83297 

84099 

84873 

85620 

86342 

87039 

87712 

88362 

54 

7 

SI  592 

82453 

83283 

84085 

84860 

85608 

86330 

87028 

87701 

88351 

53 

8 

81578 

82439 

83270 

84072 

84847 

85596 

86318 

87016 

87690 

88340 

52 

9 

81563 

82424 

83256 

84059 

84835 

85583 

86306 

87005 

87679 

88330 

51 

10 

4.81549 

82410 

83242 

84046 

84822 

85571 

86295 

86993 

87668 

88319 

50 

11 

81534 

82396 

83229 

84033 

84809 

85559 

86283 

86982 

87657 

88308 

49 

12 

81519 

82382 

83215 

84020 

84796 

85547 

86271 

86970 

87646 

88298 

48 

13 

81505 

82368 

83202 

84006 

84784 

85534 

86259 

86959 

87635 

88287 

47 

14 
15 

81490 

82354 

83188 

83993 

84771 

85522 

86247 

86947 

87624 

88276 

46 

4.81475 

82340 

83174 

83980 

84758 

85510 

86235 

86936 

87613 

88266 

45 

16 

81461 

82326 

83161 

83967 

84745 

85497 

86223 

86924 

87601 

88255 

44 

17 

81446 

82311 

83147 

83954 

84733 

85485 

86211 

86913 

87590 

88244 

43 

18 

81431 

82297 

83133 

83940 

84720 

85473 

86200 

86902 

87579 

88234 

42 

19 
20 

81417 

82283 

83120 

83927 

84707 

85460 
85448 

86188 

86890 

87568 

88223 

41 

4.81402 

82269 

83106 

83914 

84694 

86176 

86879 

87557 

88212 

40 

21 

81387 

82255 

83092 

83901 

84682 

85436 

86164 

86867 

87546 

88201 

39 

22 

81372 

82240 

83078 

83887 

84669 

85423 

86152 

86855 

87535 

88191 

38 

23 

SISS'^ 

82226 

83065 

83874 

84656 

85411 

86140 

86844 

87524 

88180 

37 

24 

81343 

82212 

83051 

83861 

84643 

85399 

86128 

86832 

87513 

88169 

36 

25 

4.81328 

82198 

83037 

83848 

84630 

85386 

86116 

86821 

87501 

88158 

35 

26 

81314 

82184 

83023 

83834 

84618 

85374 

86104 

86809 

87490 

88148 

34 

27 

81299 

82169 

83010 

83821 

84605 

85361 

86092 

86798 

87479 

88137 

33 

28 

81284 

82155 

82996 

83808 

84592 

85349 

86080 

86786 

87468 

88126 

32 

29 

81269 

82141 

82982 

83795 

84579 

85337 

86068 

86775 

87457 

88115 

31 

30 

4  81254 

82126 

82968 

83781 

84566 

85324 

86056 

86763 

87446 

88105 

30 

31 

81240 

82112 

82955 

83768 

84553 

85312 

86044 

86752 

87434 

88094 

29 

32 

81225 

82098 

82941 

83755 

84540 

85299 

86032 

86740 

87423 

88083 

28 

33 

81210 

82084 

82927 

83741 

84528 

85287 

86020 

86728 

87412 

88072 

27 

34 

81195 

82069 

82913 

82899 

83728 

84515 

85274 

86008 

86717 

87401 

88061 

26 

35 

4.81180 

82055 

83715 

84502 

85262 

85996 

86705 

87390 

88051 

25 

36 

81166 

82041 

82885 

83701 

84489 

85250 

85984 

86694 

87378 

88040 

24 

37 

81151 

82026 

82872 

83688 

84476 

85237 

85972 

86682 

87367 

88029 

23 

38 

81136 

82012 

82858 

83674 

84463 

85225 

85960 

86670 

87356 

88018 

22 

39 

81121 

81998 

82844 

83661 

84450 

85212 

85948 

86659 

87345 

88007 

21 

20 

40 

4.81106 

81983 

82830 

83648 

84437 

85200 

85936 

86647 

87334 

87996 

41 

81091 

81969 

82816 

83634 

84424 

85187 

85924 

86635 

87322 

87985 

19 

42 

81076 

81955 

82802 

83621 

84411 

85175 

85912 

86624 

87311 

87975 

18 

43 

81061 

81940 

82788 

83608 

84398 

85162 

85900 

86612 

87300 

87964 

17 

44 

81047 

81926 

82775 

83594 

84385 

85150 

85888 

86600 

87288 

87953 

16 

45 

4.81032 

81911 

82761 

83581 

84373 

85137 

85876 

86589 

87277 

87942 

15 

46 

81017 

81897 

82747 

83567 

84360 

85125 

85864 

86577 

87266 

87931 

14 

47 

81002 

81882 

82733 

83554 

84347 

85112 

85851 

86565 

87255 

87920 

13 

48 

80987 

81868 

82719 

83540 

84334 

85100 

85839 

86554 

87243 

87909 

12 

49 

80972 

81854 

82705 

83527 

84321 

85087 

85827 

86542 

87232 

87898 

87887 

11 

10 

50 

4.80957 

81839 

82691 

83513 

84308 

85074 

85815 

86530 

87221 

51 

80942 

81825 

82677 

83500 

84295 

85062 

85803 

86518 

87209 

87877 

9 

52 

80927 

81810 

82663 

83486 

84282 

85049 

85791 

86507 

87198 

87866 

8 

53 

80912 

81796 

82649 

83473 

84269 

85037 

85779 

86495 

87187 

87855 

7 

54 

80897 

81781 

82635 

83459 

84255 

85024 

85766 

86483 

87175 

87844 

6 
5 

55 

4.80882 

81767 

82621 

83446 

84242 

85012 

85754 

86472 

87164 

87833 

56 

80867 

81752 

82607 

83432 

84229 

84999 

85742 

86460 

87153 

87822 

4 

57 

80852 

81738 

82593 

83419 

84216 

84986 

85730 

86448 

87141 

87811 

3 

58 

80837 

81723 

82579 

83405 

84203 

84974 

85718 

86436 

87130 

87800 

2 

59 

80822 

81709 

82565 

83392 

84190 

84961 

85706 

86425 

87119 

87789 

1 

60 

80807 

81694 

82551 

83378 

84177 

84949 

85693 

86413 

87107 

87778 

0 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48- 

49° 

M. 

_^ 

DIFFER 

ENCE. 

SIN 

E. 

8 


112 

TABLE  XXVIII. 

LOGARITHMS 

OF  THE  HALF  SUM  AND  DIFFERENCE. 

HALF  SUM.   . 

JO-SINE.   1 

o 

o 

o 

o 

0 

o 

o 

o 

o 

o 

M. 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

0 

4.89050 

89653 

90235 

90796 

91336 

91857 

92359 

92842 

93307 

93753 

60 

1 

89040 

89643 

90225 

90787 

91328 

91849 

92351 

92834 

93299 

93746 

59 

2 

89030 

89633 

90216 

90777 

91319 

91840 

92343 

92826 

93291 

93738 

58 

3 

89020 

89624 

90206 

90768 

91310 

91832 

92334 

92818 

93284 

93731 

57 

4 
5 

89009 

89614 

90197 

90759 

91301 

91823 

92326 

92810 

93276 

93724 

56 

4.88999 

89604 

90187 

90750 

91292 

91815 

92318 

92803 

93269 

93717 

55 

6 

88989 

89594 

90178 

90741 

91283 

91806 

92310 

92795 

93261 

93709 

54 

7 

88978 

89584 

90168 

90731 

91274 

91798 

92302 

92787 

93253 

93702 

53 

8 

88968 

89574 

90159 

90722 

91266 

91789 

92293 

92779 

93246 

93695 

52 

9 

88958 

89564 

90149 

90713 

91257 

91781 

92285 

92771 

93238 

93687 

51 

10 

4.88948 

89554 

90139 

90704 

91248 

91772 

92277 

92763 

93230 

93680 

50 

11 

88937 

89544 

90130 

90694 

91239 

91763 

92269 

92755 

93223 

93673 

49 

12 

88927 

89534 

90120 

90685 

91230 

91755 

92260 

92747 

93215 

93665 

48 

13 

88917 

89524 

90111 

90676 

91221 

91746 

92252 

92739 

93207 

93658 

47 

14 

88906 

89514 

90101 

90667 

91212 

91738 

92244 

92731 

93200 

93650 

46 

15 

4.88896 

89504 

90091 

90657 

91203 

91729 

92235 

92723 

93192 

93643 

45 

16 

88886 

89495 

90082 

90648 

91194 

91720 

92227 

92715 

93184 

93636 

44 

17 

88875 

89485 

90072 

90639 

91185 

91712 

92219 

92707 

93177 

93628 

43 

18 

88865 

89475 

90063 

90630 

91176 

91703 

92211 

92699 

93169 

93621 

42 

19 
20 

88855 

89465 

90053 

90620 

91167 

91695 

92202 

92691 

93161 

93614 

41 

4.88844 

89455 

90043 

90611 

91158 

91686 

92194 

92683 

93154 

93606 

40 

21 

88834 

89445 

90034 

90602 

91149 

91677 

92186 

92675 

93146 

93599 

39 

22 

88824 

89435 

90024 

90592 

91141 

91669 

92177 

92667 

93138 

93591 

38 

23 

88813 

89425 

90014 

90583 

91132 

91660 

92169 

92659 

93131 

93584 

37 

24 

88803 

89415 

90005 

90574 

91123 

91651 

92161 

92651 

93123 

93577 

36 

25 

4.88793 

89405 

89995 

90565 

91114 

91643 

92152 

92643 

93115 

93560 

35 

26 

88782 

89395 

89985 

90555 

91105 

91634 

92144 

92635 

93108 

93.562 

34 

27 

88772 

89385 

89976 

90546 

91096 

91625 

92136 

92627 

93100 

93554 

id 

28 

88761 

89375 

89966 

90537 

91087 

91617 

92127 

92619 

93092 

93547 

32 

29 

88751 

89364 

89956 

90527 

91078 

91608 

92119 

92611 

93084 

93539 

31 

30 

4.88741 

89354 

89947 

90518 

91069 

91599 

92111 

92603 

93077 

93532 

30 

31 

88730 

89344 

89937 

90509 

91060 

91591 

92102 

92595 

93069 

93525 

29 

32 

88720 

89334 

89927 

90499 

91051 

91582 

92094 

92587 

93061 

93517 

28 

33 

88709 

89324 

89918 

90490 

91042 

91573 

92086 

92579 

93053 

93510 

27 

34 

88699 

89314 

89908 
89898 

90480 

91033 

91565 

92077 

92571 

93046 

93502 

26 

35 

4.88688 

89304 

90471 

91023 

91556 

92069 

92563 

93038 

93495 

25 

36 

88678 

89294 

89888 

90462 

91014 

91547 

92060 

92555 

93030 

93487 

24 

37 

88668 

89284 

89879 

90452 

91005 

91538 

92052 

92546 

93022 

93480 

23 

38 

88657 

89274 

89869 

90443 

90996 

91530 

92044 

92538 

93014 

93472 

22 

39 

88647 

89264 

89859 

90434 

90987 

91521 

92035 

92530 

93007 

93465 

21 

40 

4.88636 

89254 

89849 

90424 

90978 

91512 

92027 

92522 

92999 

93457 

20 

41 

88626 

89244 

89840 

90415 

90969 

91504 

92018 

92514 

92991 

93450 

19 

42 

88615 

89233 

89830 

90405 

90960 

91495 

92010 

92506 

92983 

93442 

18 

43 

88605 

89223 

89820 

90396 

90951 

91486 

92002 

92498 

92976 

93435 

17 

44 

88594 

89213 

89810 

90386 

90942 

91477 

91993 

92490 

92968 

93427 

16 

45 

4.88584 

89203 

89801 

90377 

90933 

91469 

91985 

92482 

92960 

93420 

15 

^  46 

88573 

89193 

89791 

90368 

90924 

91460 

91976 

92473 

92952 

93412 

14 

47 

88563 

89183 

89781 

90358 

90915 

91451 

91968 

92465 

92944 

93405 

13 

48 

88552 

89173 

89771 

90349 

90906 

91442 

91959 

92457 

92936 

93397 

12 

49 
50 

88542 

89162 

«9761 

90339 

90896 

91433 

91951 

92449 

92929 

93390 

11 

4.88531 

89152 

89752 

90330 

90887 

91425 

91942 

92441 

92921" 

93382 

10 

51 

88521 

89142 

89742 

90320 

90878 

91416 

91934 

92433 

92913 

93375 

9 

52 

88510 

89132 

89732 

90311 

90869 

91407 

91925 

92425 

92905 

93367 

8 

53 

88499 

89122 

89722 

90301 

90860 

91398 

91917 

92416 

92897 

93360 

7 

54 

88489 

89112 

89712 

90292 

90851 

91389 

91908 

92408 

92889 

93362 

6 
5 

55 

4.88478 

89101 

89702 

90282 

90842 

91381 

91900 

92400 

92881 

93344 

56 

88468 

89091 

89693 

90273 

90832 

91372 

91891 

92392 

92874 

93337 

4 

57 

88457 

89081 

89683 

90263 

90823 

91363 

91883 

92384 

92866 

93329 

3 

58 

88447 

89071 

89673 

90254 

90814 

91354 

91874 

92376 

92858 

93322 

2 

59 

88436 

89060 

89663 

90244 

90S05 

91345 

91866 

92367 

92850 

93314 

1 

60 

88425 

89050 

89653 

90235 

90796 

91336 

91857 

92359 

92842 

93307 

0 

50° 

sr 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

M. 

DIFFER 

ENCE. 

SIN 

rs. 

c 

TABLE  XXVIII. 

118 

LOGARITHMS  OF  THE  HALF  SUM  AND  DIFFERENCE. 

HALF  SUM. 

CO-SINE. 

M. 

0 

o 
29 

e 
28 

o 
27 

o 

26 

95366' 

o 

25 

95728 

o 
24 

o 
23 

o 

22 

o 

21 

o 
20 

4.94182 

94593 

94988 

96073 

96403 

96717 

97015 

97299   60  1 

I 

94175 

94587 

94982 

95360 

95722 

96067 

96397 

96711   97010 

97294   59  | 

2 

9^4168 

94580 

94975 

95354 

95716 

96062 

96392 

96706   97005 

97289 

58 

3 

94161 

94573 

94969 

95348 

95710 

96056 

96387 

96701   97001 

97285 

57 

4 
5 

94154 

94567 

94962 

95341 

95704 

96050 

96381 

96696   96996 

97280 

56 
55 

4.94147 

94560 

94956 

95335 

95698 

96045 

96376 

96691 

96991 

97276 

6 

94140 

94553 

94949 

95329 

95692 

96039 

96370 

96686 

96986 

97271 

54 

7 

94133 

94546 

94943 

95323 

95686 

96034 

96365 

96681 

96981 

97266 

53 

8 

94126 

94540 

94936 

95317 

95680 

96028 

96360 

96676 

96976 

97262 

52 

9 
10 

94119 

94533 

94930 

95310 

95674 

96022 

96354 

96670 

96971 

97257 

51 

4.94112 

94526 

94923 

95304 

9566S! 

96017 

96349 

96665 

96966 

97252 

50 

11 

94105 

94519 

94917 

95298 

95663 

96011 

96343 

96660 

96962 

97248 

49 

12 

94098 

94513 

94911 

95292 

95657 

96005 

96338 

96655 

96957 

97243 

48 

13 

94090 

94506 

94904 

95286 

95651 

96000 

96333 

96650 

96952 

97238 

47 

14 

94083 

94499 

94898 

95279 

95645 

95994 

96327 

96645 

96947 

97234 

46 
45 

15 

4.94076 

94492 

94891 

95273 

95639 

95988 

96322 

96640 

96942 

97229 

1^ 

94069 

944*5 

94884 

95267 

95633 

95982 

96316 

96634 

96937 

97224 

44 

17 

94062 

94479 

94878 

95261 

95627 

95977 

96311 

96629 

96932 

97220 

43 

18 

94055 

94472 

94871 

95254 

95621 

95971 

96305 

96624 

96927 

97215 

42 

19 

94048 

94465 

94865 

94858 

95248 

95615 

95965 

96300 
96294 

96619 
96614 

96922 

97210 

41 

20 

4.94041 

94458 

95242 

95609 

95960 

96917 

97206 

40 

21 

94034 

94451 

94852 

95236 

95603 

95954 

96289 

96608 

96912 

97201 

39 

22 

94027 

94445 

94845 

95229 

95597 

95948 

96284 

96603 

96907 

97196 

38 

23 

94020 

94438 

94839 

95223 

95591 

95942 

96278 

96598 

96903 

97192 

37 

24 

94012 

94431 

94832 

95217 

95585 

95937 

96273 

96593 

96898 

97187 

36 

25 

4.94005 

94424 

94826 

95211 

95579 

95931 

96267 

96588 

96893 

97182 

35 

26 

93998 

94417 

94S19 

95204 

95573 

95925 

96262 

96582 

96888 

97178 

34 

27 

93991 

94410 

94813 

95198 

95567 

95920 

96256 

96577 

96883 

97173 

33 

28 

93984 

94404 

94806 

95192 

95561 

95914 

96251 

96572 

96878 

97168 

32 

29 
30 

93977 

94397 

94799 

95185 
95179 

95555 

95908 

96245 

96567 

96873 

97163 

31 
30 

4.93970 

94390 

94793 

95549 

95902 

96240 

96562 

96868 

97159 

31 

93963 

94383 

94786 

95173 

95543 

95897 

96234 

96556 

96863 

97154 

29 

32 

93955 

94376 

94780 

95167   95537 

95891 

96229 

96551 

96858 

97149 

28 

33 

93948 

94369 

94773 

95160   95531 

95885 

96223 

96546 

96853 

97145 

27 

34 

93941 

94362 

94767 
94760 

95154 

95525 

95879 

96218 

96541 

96848 

97140 

26 
25 

35 

4.93934 

94355 

95148 

95519 

95873 

96212 

96535 

96843 

97135 

36 

93927 

94349 

94753 

95141 

95513 

95868 

96207 

96530 

96838 

97130 

24 

37 

93920 

94342 

94747 

95135 

95507 

95862 

96201 

96525 

96833 

97126 

23 

38 

93912 

94335 

94740 

95129 

95500 

95856 

96196 

96520 

96828 

97121 

22 

39 

93905 

94328 

94734 

95122 

95494 

95850 

96190 

96514 

96823 

97116 

21 

20 

40 

4.93898 

94321 

94727 

95116 

95488 

95844 

96185 

96509 

96818 

97111 

41 

93891 

94314 

94720 

95110 

95482 

95839 

96179 

96504 

96813 

97107 

19 

42 

93884 

94307 

94714 

95103 

95476 

95833 

96174 

96498 

96808 

97102 

18 

43 

93876  94300 

94707 

95097 

95470 

95827 

96168 

96493 

96803 

97097   17 

44 

93869 

94293 
94286 

94700 

95090 

95464 

95821 

96162 

96488 

96798 

97092 

16 

45 

4.93862 

94694 

95084 

95458 

95815 

96157 

96483 

96793 

97087 

15 

46 

93855 

94279 

94687 

95078 

95452 

95810 

96151 

96477 

96788 

97083 

14 

47 

93847 

94273 

94680 

95071 

95446 

95804 

96146 

96472 

96783 

97078 

13 

48 

93840 

94266 

94674 

95065 

95440 

95798 

96140 

96467 

96778 

97073 

12 

49 

93833 

94259 

94667 

95059 

95434 

95792 

96135 

96461 

96772 

97068 

11 

50 

4.93826 

94252 

94660 

95052 

95427 

95786 

96129 

96456 

96767 

97063 

10 

51 

93819 

94245 

94654 

95046 

95421 

95780 

96123 

96451 

96762 

97059 

9 

52 

93811 

94238 

94647 

95039 

95415 

95775 

96118 

96445 

96757 

97054 

8 

53 

93804 

94231 

94640 

95033 

95409 

95769 

96112 

96440 

96752 

97049 

7 

54 

93797 

94224 

94634 

94627 

95027 

95403 

95763 

96107 

96435 

96747 

97044 

6 
5 

55 

4.93789 

94217 

95020 

95397 

95757 

96101 

96429 

96742 

97039 

56 

93782 

94210 

94620 

95014 

95391 

95751 

96095 

96424 

96737 

97035 

4 

57 

93775 

94203 

94614 

95007 

95384 

95745 

96090 

96419 

96732 

97030 

3 

58 

93768 

94196 

94607 

95001 

95378 

95739 

96084 

96413 

96727 

97025 

2 

59 

93760 

94189 

946)0 

94995 

95372 

95733 

96079 

96408 

96722 

97020 

1 

60 

93753 

94182 

94593 

94988 

95366 

95728 

96073 

96403 
67° 

96717 

97015 

0 

60° 

61°    62° 

63° 

64° 

65° 

66° 

68° 

69° 

M. 

DIFFERENCE. 

SINK. 

114 

TABLE  XXVIIl. 

n 

LOGARITHMS  OF  THE  HALF  SUM  AND  DIFFERENCE. 

1 

HALF  SUM. 

co-anrx. 

o 

o 

o 

o 

o 

o 

O 

o 

o 

o 

M. 

19 

18 

97821 

17 

16 

15 

14 

13 

12 

11 

10 

0 

4.97567 

98060 

98284 

98494 

98690 

98872 

99040 

99195 

99335 

60 

1 

97563 

97817 

98056 

98281 

98491 

98687 

98869 

99038 

99192 

99333 

59 

2 

97558 

97812 

98052 

98277 

98488 

98684 

98867 

99035 

99190 

99331 

5S 

3 

97554 

97808 

98048 

98273 

98484 

98681 

98864 

99032 

99187 

99328 

.^7 

4 
5 

97550 

97804 

98044 

98270 

98481 

98678 

98861 

99030 

99185 

99326 

56 

4.97545 

97800 

98040 

98266 

98477 

98675 

98858 

99027 

99182 

99324 

55 

6 

97541 

97796 

98036 

98262 

98474 

98671 

98855 

99024 

99180 

99322 

54 

7 

97536 

97792 

98032 

98259 

98471 

98668 

98852 

99022 

99177 

99319 

53 

8 

97532 

97788 

98029 

98255 

98467 

98665 

98849 

99019 

99175 

99317 

52 

9 

97528 

97784 

98025 

98251 

98464 

98662 

98846 

99016 

99172 

99315 

51 

10 

4.97523 

97779 

98021 

98248 

98460 

98659 

98843 

99013 

99170 

99313 

50 

11 

97519 

97775 

98017 

98244 

98457 

98656 

98840 

99011 

99167 

99310 

49 

12 

97515 

97771 

98013 

98240 

98453 

98652 

98837 

99008 

99165 

99308 

48 

13 

97510 

97767 

98009 

98237 

98450 

98649 

98834 

99005 

99162 

99306 

47 

14 

97506 

97763 

98005 

98233 

98229 

98447 

98646 

98831 

99002 

99160 

99304 

46 

15 

4.97501 

97759 

98001 

98443 

98643 

98828 

99000 

99157 

99301 

45 

16 

97497 

97754 

97997 

98226 

98440 

98640 

98825 

98997 

99155 

99299 

44 

17 

97492 

97750 

97993 

98222 

98436 

98636 

98822 

98994 

99152 

99297 

43 

18 

97488 

97746 

97989 

98218 

98433 

98633 

98819 

98991 

99150 

99294 

42 

19 

97484 

97742 

97986 

98215 

98429 

98630 

98816 

98989 

99147 

99292 

41 

20 

4.97479 

97738 

97982 

98211 

98426 

98627 

98813 

98986 

99145 

99290 

40 

21 

97475 

97734 

97978 

98207 

98422 

98623 

98810 

98983 

99142 

99288 

39 

22 

97470 

97729 

97974 

98204 

98419 

98620 

98807 

98980 

99140 

99285 

38 

23 

97466 

97725 

97970 

98200 

98415 

98617 

98804 

98978 

99137 

99283 

37 

24 

97461 

97721 

97966 

98196 

98412 

98614 

98801 

98975 

99135 

99281 

36 

25 

4.97457 

97717 

97962 

98192 

98409 

98610 

98798 

98972 

99132 

99278 

35 

26 

97453 

97713 

97958 

98189 

98405 

98607 

98795 

98969 

99130 

99276 

34 

27 

97448 

97708 

97954 

98185 

98402 

98604 

98792 

98967 

99127 

99274 

33 

28 

97444 

97704 

97950 

98181 

98398 

98601 

98789 

98964 

99124 

99271 

32 

29 
30 

97439 

97700 

97946 

98177 

98395 

98597 

98786 

98961 

99122 

99269 

31 

4.97435 

97696 

97942 

98174 

98391 

98594 

98783 

98958 

99119 

99267 

30 

31 

97430 

97691 

97938 

98170 

98388 

98591 

98780 

98955 

99117 

99264 

29 

32 

97426 

97687 

97934 

98166 

98384 

98588 

98777 

98953 

99114 

99262 

28 

33 

97421 

97683 

97930 

98162 

98381 

98584 

98774 

98950 

99112 

99260 

27 

34 

97417 

97679 

97926 

98159 

98377 

98581 

98771 

98947 

99109 

99257 

26 

35 

4.97412 

97674 

97922 

98155 

98373 

98578 

98768 

98944 

99106 

99255 

25 

36 

97408 

97670 

97918 

98151 

98370 

98574 

98765 

98941 

99104 

99252 

24 

37 

97403 

97666 

97914 

98147 

98366 

98571 

98762 

98938 

99101 

99250 

23 

38 

97399 

9766-2 

97910 

98144 

98363 

98568 

98759 

98936 

99099 

99248 

22 

39 

97394 

4.97390 

97657 

97906 

98140 

98359 

98565 

98756 

98933 

99096 

99245 

21 

40 

97663 

97902 

98136 

98356 

98561 

98753 

98930 

99093 

99243 

20 

41 

97385 

97649 

97898 

98132 

98352 

98558 

98750 

98927 

99091 

99241 

19 

42 

97381 

97645 

97894 

98129 

98349 

98555 

98746 

98924 

99088 

99238 

18 

43 

9r376 

97(540 

97890 

98125 

98345 

98551 

98743 

98921 

99086 

99236 

17 

44 

97372 

97636 

97886 

9S121 

98342 

98548 

98740 

98919 

99083 

99233 

16 

45 

4.97367 

97632 

97882 

98117 

98338 

98545 

98737 

98916 

99080 

99231 

15 

46 

97363 

97627 

97878 

98113 

98334 

98541 

98734 

98913 

99078 

99229 

14 

47 

97358 

97623 

97874 

98110 

98331 

98538 

98731 

98910 

99075 

99226 

13 

48 

97353 

97619 

97870 

98106 

98327 

98535 

98728 

98907 

99072 

99224 

12 

49 

97349 

97615 

97866 

98102 

98324 

98531 

98725 

98904 

99070 

99221 

11 

50 

4.97344 

97610 

97861 

98098 

98320 

98528 

98722 

98901 

99067 

99219 

10 

51 

97340 

97606 

97857 

9S094 

98317 

98525 

98719 

98898 

99064 

99217 

9 

52 

97335 

97602 

97853 

98090 

98313 

98521 

98715 

98896 

99062 

99214 

8 

53 

97331 

97597 

97849 

98087 

98309 

98518 

98712 

98893 

99059 

99212 

7 

54 

97326 

97593 

97845 

98083 

98306 

98515 

98709 

98890 

99056 

99209 

6 

55 

4.97322 

97589 

97841 

98079 

98302 

98511 

98706 

98887 

99054 

99207 

5 

56 

97317 

97584 

97837 

98075 

98299 

9S508 

98703 

98884 

99051 

99204 

4 

57 

97312 

97580 

97833 

98071 

98295 

98505 

98700 

98881 

99048 

99202 

3 

58 

97308 

97576 

97829 

98067 

98291 

98501 

98697 

98878 

99046 

99200 

2 

59 

97303 

97571 

97825 

98063 

98288 

98498 

98694 

98875 

99043 

99197 

1 

60 

97299 

97567 

97821 

98060 

98284 

98494 

98690 

98872 

99040 

99195 

0 

70° 

71* 

72' 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

M. 

l_ 

DIFFER 

ENCE. 

8I^ 

rE. 

TABLE  XXVIII.                   116 

LOGARITHMS  OF  THE  HALF  SUM  AND  DIFFERENCE. 

HALF  SUM,                               CO-BINK. 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

M. 
0 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

4.99462 

99575 

99675 

99761 

99834 

99894 

99940 

99974 

99993 

00000 

60 

1 

99460 

99573 

99674 

99760 

99833 

99893 

99940 

99973 

99993 

00000 

59 

2 

99458 

99572 

99672 

99759 

99832 

99892 

99939 

99973 

99993 

00000 

58 

3 

99456 

99570 

99670 

99757 

99831 

99891 

99938 

99972 

99993 

00000 

57 

4 

99454 

99568 

99669 
99667 

99756 

99830 

99^91 

99938 

99972 

99992 

00000 

56 
55 

5 

4.99452 

99566 

99755 

99829 

99890 

99937 

99971 

99992   00000 

6 

99450 

99565 

99666 

99753 

99828 

99889 

99936 

99971 

99992 

00000 

54 

7 

99448 

99563 

99664 

99752 

99827 

99888 

99936 

99970 

99992 

00000 

53 

8 

99446 

99561 

99663 

99751 

99825 

99887 

99935 

99970 

99992 

00000 

52 

9 

99444 

99559 

99661 

99749 

99824 

99886 

99934 

99969 

99991 

00000 

51 

10 

4.99442 

99557 

99659 

99748 

99823 

99885 

99934 

99969 

99991 

00000 

50 

11 

99440 

99556 

99658 

99747 

99822 

99884 

99933 

99968 

99991 

00000 

49 

12 

99438 

99554 

99656 

99745 

99821 

99883 

99932 

99968 

99990 

00000 

48 

13 

99436 

99552 

99655 

99744 

99820 

99882 

99932 

99967 

99990 

00000 

47 

14 

99434 

99550 

99653 

99742 

99819 

99881 

99931 

99967 

99990 

00000 

46 
45 

15 

4.99432 

99548 

99651 

99741 

99817 

99880 

99930 

99967 

99990 

00000 

16 

99429 

99546 

99650 

99740 

99816 

99879 

99929 

99966 

99989 

00000 

44 

17 

99427 

99545 

99648 

99738 

99815 

99879 

99929 

99966 

99989 

99999 

43 

18 

99425 

99543 

99647 

99737 

99814 

99878 

99928 

99965 

99989 

99999 

42 

19 

99423 

99541 

99645 
99643 

99736 

99813 

99877 

99927 
99926 

99964 
99964 

99989 

99999 

41 

40 

20 

4.99421 

99539 

99734 

99812 

99876 

99988 

99999 

21 

99419 

99537 

99642 

99733 

99810 

99875 

99926 

99963 

99988 

99999 

39 

22 

99417 

99535 

99640 

99731 

99809 

99874 

99925 

99963 

99988 

99999 

38 

23 

99415 

99533 

99638 

99730 

99808 

99873 

99924 

99962 

99987 

99999 

37 

24 

99413 

99532 

99637 

99728 
99727 

99807 

99872 

99923 

99962 

99987 

99999 

36 
35 

25 

4.99411 

99530 

99635 

99806 

99871 

99923 

99961 

99987 

99999 

26 

99409 

99528 

99633 

99726 

99804 

99870 

99922 

99961 

99986 

99999 

34 

27 

99407 

99526 

99632 

99724 

99803 

99869 

99921 

99960 

99986 

99999 

33 

28 

99404 

99524 

99630 

99723 

99802 

99868 

99920 

99960 

99986 

99999 

32 

29 
30 

99402 

99522 

99629 

99721 
99720 

99801 

99867 

99920 

99959 

99985 
99985 

99998 

31 

4.99400 

99520 

99627 

99800 

99866 

99919 

99959 

99998 

30 

31 

99398 

99518 

99625 

99718 

99798 

99865 

99918 

99958 

99985 

99998 

29 

32 

99396 

99517 

99624 

99717 

99797 

99864 

99917 

99958 

99984 

99998 

28 

33 

99394 

99515 

99622 

99716 

99796 

99863 

99917 

99957 

99984 

99998 

27 

34 

99392 

99513 

99620 

99714 

99795 

99862 

99916 

99956 

99984 

99998 

26 
25 

35 

4.99390 

99511 

99618 

99713 

99793 

99861 

99915 

99956 

99983 

99998 

36 

99388 

99509 

99617 

99711 

99792 

99860 

99914 

99955 

99983 

99998 

24 

37 

99385 

99507 

99615 

99710 

99791 

99859 

99913 

99955 

99983 

99997 

23 

38 

99383 

99505 

99613 

99708 

,99790 

99858 

99913 

99954 

99982 

99997 

22 

39 

99381 

99503 

99612 

99707 

99788 

99857 

99912 

99954 

99982 

99997 

21 
20 

40 

4.99379 

99501 

99610 

99705 

99787 

99856 

99911 

99953 

99982 

99997 

41 

99377 

99499 

99608 

99704 

99786 

99855 

99910 

99952 

99981 

99997 

19 

42 

99375 

99497 

99607 

99702 

99785 

99854 

99909 

99952 

99981 

99997 

18 

43 

99372 

99495 

99605 

99701 

99783 

99853 

99909 

99951 

99981 

99997 

17 

44 

99370 

99494 

99603 

99699 

99782 

99852 

99908 

99951 

99980 

99996 

16 

45 

4.99368 

99492 

99601 

99698 

99781 

99851 

99907 

99950 

99980 

99996 

15 

46 

99366 

99490 

99600 

99696 

99780 

99850 

99906 

99949 

99979 

99996 

14 

47 

99364 

99488 

99598 

99695 

99778 

99848 

99905 

99949 

99979 

99996 

13 

48 

99362 

99486 

99596 

99693 

99777 

99847 

99904 

99948 

99979 

99996 

12 

49 

99359 

99484 

99595 

99692 

99776 

99846 

99904 
99903 

99948 

99978 

99996 

11 

50 

4.99357 

99482 

99593 

99690 

99775 

99845 

99947 

99978 

99995 

10 

51 

99355 

99480 

99591 

99689 

99773 

99844 

99902 

99946 

99977 

99995 

9 

52 

99353 

99478 

99589 

99687 

99772 

99843 

99901 

99946 

99977 

99995 

8 

53 

99351 

99476 

99588 

99686 

99771 

99842 

99900 

99945 

99977 

99995 

7 

54 
55 

99348 

99474 

99586 
99584 

99684 

99769 

99841 

99899 

99944 

99976 

99995 

6 
6 

4.99346 

99472 

99683 

99768 

99840 

99898 

99944 

99976 

99994 

56 

99344 

99470 

99582 

99681 

99767 

99839 

99898 

99943 

99975 

99994 

4 

57 

99342 

99468 

99581 

99680 

99765 

99838 

99897 

99942 

99975 

99994 

3 

58 

99340 

99466 

99579 

99678 

99764 

99837 

99896 

99942 

99974 

99994 

2 

59 

99337 

99464 

99577 

99677 

99763 

99836 

99895 

99941 

99974 

99994 

1 

60 

99335 

99462 

99575 

99675 

99761 

99834 

99894 

99940 

99974 

99993 

0 

80" 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

M. 

DIFFERENCE.                                   81 

116 

TABLE  XXIX. 

HOUR  AN 

LOGARITHMS  OF  THE  APPARENT  TIME,  OR  HOUR  ANGLE. 

OLE,  0  HOURS,  OB  APP.  TIME  P.  M.     j 

PROPORTIONAL  PARTS  FOR  SECONDS.  1 

B. 

8. 

s. 

8. 

8. 

a 

s. 

S. 

8. 

s. 

s.   s. 

s. 

s. 

s. 

« 

M. 

0 

10 

20 

30 

40 

50 

60 

1 

2 

3 

4   5 

6 

7 

8   9  1 

0 

3 

4  • 

12127 

72333 

07551 

32539 

51921 

67757 

59 

1 

i. 67757 

81147 

92745 

02976 

12127 

20406 

27963 

58 

1 

2 

5.27963 

34916 

41352 

46345 

52951 

58216 

63181 

57 

3 

63181 

67877 

72332 

76570 

80611 

84472 

88168 

56 

4 

1  88168 

91714 

95121 

98399 

01557 

04605 

07550 

55 

5 

6.07550 

10398 

13155 

15828 

18421 

20938 

23385 

54 

6 

23385 

25765 

28081 

30337 

32536 

34681 

36774 

53 

7 

36774 

38817 

40814 

42766 

44675 

46543 

48372 

52 

8 

48372 

50162 

51916 

53636 

55323 

56977 

58600 

51 

9 

58600 

60194 

61759 

63296 

64806 

66291 

67751 

50 

10 

6-67751 

69186 

70598 

71988 

73355 

74702 

76028 

49 

11 

76028 

77334 

78620 

79888 

81137 

82369 

83584 

48 

12 

83584 

84782 

85963 

87129 

88279 

89414 

90535 

47 

13 

90535 

91641 

92733 

93812 

94877 

95930 

96970 

46 

14 

|. 96970 

97997 

99013 

00017 

01009 

01990 

02960 

45 

15 

7  02960 

03920 

04869 

05807 

06736 

07655 

08564 

44 

93 

187 

280 

373 

467 

560 

653 

746 

840 

16 

08564 

09464 

10354 

11236 

12108 

12972 

13827 

43 

87 

175 

263 

350 

438 

526 

614 

702 

789 

17 

13827 

14674 

15513 

16344 

17167 

17982 

18790 

42 

82 

165 

248 

331 

413 

496 

579 

662 

744 

18 

18790 

19590 

20383 

21168 

21947 

22719 

23483 

41 

78 

156 

234 

313 

391 

469 

547 

625 

704 

19 
20 

23483 

24241 

24993 

25738 

26477 

27210 

27936 

40 

74 

148 

222 

296 

370 

444 

518 

592 

666 

7.27936 

28656 

29371 

30079 

30782 

31479 

32171 

39 

70 

140 

211 

281 

352 

422 

492 

563 

633 

21 

32171 

32857 

33538 

34213 

34884 

35549 

36209 

38 

67 

134 

201 

268 

335 

403 

470 

537 

604 

22 

36209 

36864 

37514 

38159 

38800 

39435 

40067 

37 

64 

128 

192 

256 

320 

385 

449 

513 

577 

23 

40067 

40693 

41315 

41933 

42546 

43155 

43760 

36 

61 

123 

184 

245 

306 

368 

430 

491 

552 

24 

43760 

44361 

44957 

45549 

46138 

46722 

47302 

35 

59 

118 

171 

235 

295 

353 

412 

471 

531 

25 

7.47302 

47879 

48452 

49021 

49586 

50148 

50706 

34 

56 

113 

169 

226 

282 

339 

396 

452 

509 

26 

50706 

51260 

51811 

52358 

52902 

53443 

53980 

33 

54 

109 

163 

218 

272 

327 

381 

436 

490 

27 

53980 

54514 

55045 

55572 

56096 

56017 

57135 

32 

52 

105 

157 

209 

262 

314 

367 

420 

472 

28 

57135 

57650 

58162 

58670 

59176 

59679 

60179 

31 

51 

101 

152 

202 

253 

303 

354 

405 

455 

29 

60179 

60676 

61170 

61662 

62151 

62636 

63120 

30 

49 

98 

147 

195 

244 

293 

342 

392 

441 

30 

7.63120 

63600 

64078 

64553 

65026 

65496 

65964 

29 

47 

95 

142 

189 

236 

284 

331 

378 

426 

31 

65964 

66429 

66891 

67351 

67809 

68264 

68717 

28 

46 

92 

137 

183 

229 

275 

321 

366 

412 

32 

68717 

69167 

69616 

70061 

70505 

70946 

71385 

27 

44 

89 

133 

178 

222 

267 

311 

355 

400 

33 

71385 

71822 

72257 

72689 

73119 

73548 

73974 

26 

43 

86 

129 

172 

215 

258 

301 

344 

388 

34 

73974 

74398 

74819 

75239 

75657 

76073 

76487 

25 

42 

83 

125 

167 

209 

251 

293 

334 

377 

35 

7.76487 

76898 

77308 

77716 

78122 

78526 

78929 

24 

41 

81 

122 

162 

203 

243 

284 

325 

366 

36 

78929 

79329 

79728 

80124 

80519 

80912 

81303 

23 

40 

79 

118 

158 

197 

237 

277 

316 

356 

37 

81303 

81693 

82081 

82467 

82851 

83234 

83615 

22 

39 

77 

115 

154 

192 

231 

270 

308 

347 

38 

83615 

83994 

84372 

84747 

85122 

85494 

85866 

21 

38 

75 

112 

150 

187 

225 

263 

300 

338 

39 

85866 

86235 

86603 

86969 

87334 

87697 

88059 

20 

37 

73 

109 

146 

182 

219 

256 

292 

329 

40 

7.88059 

88419 

88778 

89135 

89491 

89846 

90198 

19 

36 

71 

106 

142 

178 

213 

249 

284 

321 

41 

90198 

90550 

90900 

91248 

91596 

91941 

92286 

18 

35 

70 

1-04 

139 

174 

208 

243 

278 

313 

42 

92286 

92629 

92970 

93311 

93650 

93987 

94324 

17 

34 

68 

102 

136 

170 

204 

238 

272 

306 

43 

94324 

94659 

94992 

95325 

95656 

95986 

96315 

16 

33 

66 

100 

133 

166 

199 

232 

265 

299 

44 
45 

.96315 

96642 

96968 

97293 

97617 

97939 

98260 

15 

32 

65 

97 

130 

162 

194 

227 

259 

292 

^.98260 

98580 

98899 

99217 

99534 

99849 

00163 

14 

32 

63 

95 

127 

158 

190 

222 

253 

286 

46 

8.00163 

00476 

00788 

01099 

01409 

01717 

02025 

13 

31 

62 

93 

124 

155 

186 

218 

248 

270 

47 

02025 

02331 

02636 

02941 

03244 

03546 

03847 

12 

30 

61 

91 

121 

152 

182 

212 

243 

273 

48 

03847 

04147 

04446 

04744 

05041 

05336 

05631 

11 

30 

60 

89 

119 

148 

178 

208 

238 

268 

49 

05631 

05925 

06218 

06510 

06800 

07090 

07379 

10 

29 

58 

87 

116 

145 

175 

204 

233 

262 

50 

8.07379 

07667 

07954 

08240 

08525 

08809 

09092 

9 

28 

57 

85 

114 

142 

171 

200 

228 

257 

51 

09092 

09374 

09656 

09936 

10216 

10494 

10772 

8 

28 

56 

84 

112 

140 

.168 

196 

224 

252 

62 

10772 

11048 

11324 

11599 

11873 

12147 

12419 

7 

27 

55 

82 

110 

138 

165 

193 

220 

248 

53 

12419 

12691 

12961 

13231 

13500 

13768 

14035 

6 

27 

54 

81 

108 

135 

162 

189 

216 

243 

54 

14035 

14302 

14567 

14832 

15096 

15359 

05621 

5 

26 

53 

79 

106 

133 

159 

185 

212 

239 

55 

8.15621 

15883 

16144 

16404 

16663 

16921 

17179 

4 

26 

52 

78 

104 

130 

156 

182 

208 

234 

56 

17179 

17436 

17692 

17947 

18202 

18455 

18708 

3 

25  51 

77 

102 

127 

153 

179 

204 

229 

57 

18708 

18961 

19212 

19463 

19713 

19963 

20211 

2 

25  50 

75 

100 

125 

150 

175 

200 

224 

58 

20211 

20459 

20706 

20953 

21198 

21444 

21688 

1 

24  49 

73 

98 

123 

147 

172 

196 

220 

69 

21688 

21932 

22175 

22417 

22658 

22899 

23140 

0 

24 

48 

72 

96 

120 

145 

169 

193 

217 

60s. 

50s.   40s. 

30s. 

20s. 

10s. 

Os.   M.  1 

Is. 

28. 

3s. 

4s. 

5s. 

6s. 

7s. 

8s. 

9s. 

11  OR  23  HOURS,  OR  APP.  TIME  A.  M.       | 

PROPORTIONAL  PARTS  yOR  SRCONDS.  | 

TABLE  XXIX. 

m    1 

LOGABITHMS  OF  THE  APPARENT  TIME  OR  HOUR  ANGLE.            | 

] 

aOUR  ANGLE,  1  HOUR,  OR  APP.  TIME  P.  M. 

PROPORTIONAL  PARTS  FOR  SECONDS.  1 

S. 

8. 

s. 

8. 

8. 

s. 

8. 

8. 

8. 

8. 

8.   e. 

8. 

8. 

s. 

8. 

M. 

0 

10 

20 

30 

40 

50 

60 

1 

2 

3 

4   5 

6 

7 

8 

9 

0 

8.23140 

23379 

23618 

23856 

24094 

24331 

24567 

59 

24 

47 

71 

95 

118 

142 

166 

190 

213 

1 

24567 

24802 

25037 

25272 

25505 

25738 

25971 

58 

23 

47 

70 

93 

116 

140 

163 

187 

210 

2 

25971 

26203 

26434 

26664 

26894 

27123 

27352 

57 

23 

46 

69 

92 

115 

138 

161 

184 

207 

3 

27352 

27580 

27807 

28034 

28260 

28486 

28711 

56 

23 

45 

68 

91 

113 

136 

159 

181 

204 

4 

28711 

28935 

29159 

29383 

29605 

29827 

30049 

5i 

22 

44 

67 

89 

111 

133 

156 

178 

201 

5 

8.30049 

30270 

30490 

30710 

30929 

31148 

31366 

54 

22 

44 

66 

87 

109 

131 

153 

175 

198 

6 

31366 

31583 

31800 

32016 

32233 

32448 

32663 

53 

22 

43 

65 

86 

108 

130 

151 

173 

195 

7 

32663 

32877 

33091 

33304 

33517 

33729 

33940 

52 

21 

43 

64 

85 

106 

128 

149 

170 

192 

8 

33940 

34151 

34362 

34572 

34782 

34991 

35199 

51 

21 

42 

63 

84 

105 

126 

147 

168 

189 

9 

35199 

35407 

35614 

35821 

36028 

36234 

36439 

50 

21 

41 

62 

83 

103 

124 

145 

165 

186 

10 

8.36439 

36644 

36849 

37053 

37256 

37459 

37662 

49 

20 

41 

61 

82 

102 

122 

143 

163 

184 

11 

37662 

37864 

38065 

38266 

38467 

38667 

38866 

48 

20 

40 

60 

81 

100 

120 

141 

161 

181 

12 

38866 

39066 

39264 

39463 

39660 

39858 

40055 

47 

20 

40 

60 

80 

99 

119 

139 

159 

179 

13 

40055 

40251 

40447 

40642 

40837 

41032 

41226 

46 

20 

39 

59 

78 

98 

118 

137 

157 

177 

14 
15 

41226 

41420 

41613 

41806 

41998 

42191 

42382 

45 

19 

39 

58 

77 

96 

116 

135 

154 

174 

8.42382 

42573 

42764 

42954 

43144 

43333 

43522 

44 

19 

38 

57 

76 

95 

114 

133 

152 

171 

16 

43522 

43710 

43898 

44086 

44273 

44460 

44647 

43 

19 

37 

56 

75 

93 

112 

131 

150 

169 

17 

44647 

44833 

45018 

45204 

45388 

45573 

45757 

42 

19 

37 

55 

74 

92 

111 

130 

148 

167 

18 

45757 

45940 

46124 

46306 

46489 

46671 

46852 

41 

18 

37 

55 

73 

91 

110 

128 

146 

165 

19 

46852 

47034 

47215 

47395 

47575 

47755 

47934 

40 

18 

36 

54 

72 

90 

108 

126 

144 

162 

20 

8.47934 

48113 

48292 

48470 

48647 

48825 

49002 

39 

18 

35 

53 

71 

89 

107 

125 

142 

160 

21 

49002 

49179 

49355 

49531 

49706 

49882 

50056 

38 

18 

35 

53 

70 

88 

106 

123 

141 

158 

22 

50056 

50231 

50405 

50579 

50752 

50925 

51098 

37 

17 

35 

52 

70 

87 

104 

122 

139 

157 

23 

51098 

51270 

51442 

51614 

51785 

51956 

52127 

36 

17 

34 

52 

69 

86 

103 

120 

138 

155 

24 

52127 

52297 

52467 

52636 

52805 

52974 

53143 

35 

17 

34 

51 

68 

85 

102 

119 

136 

153 

25 

8.53143 

53311 

53479 

53646 

53814 

53980 

54147 

34 

17 

33 

50 

67 

83 

100 

117 

134 

151 

26 

54147 

54313 

54479 

54645 

54810 

54975 

55139 

33 

17 

33 

50 

66 

82 

99 

116 

132 

149 

27 

55139 

55303 

55467 

55631 

55794 

55957 

56120 

32 

16 

33 

49 

65 

81 

98 

114 

130 

147 

28 

56120 

56282 

56444 

56606 

56767 

56928 

57089 

31 

16 

32 

48 

64 

80 

97 

113 

129 

145 

29 

57089 

57249 

57410 

57569 

57729 

57888 

58047 

30 

16 

32 

48 

63 

80 

96 

111 

127 

143 

30 

8.58047 

58206 

58364 

58522 

58680 

58837 

58994 

29 

16 

32 

47 

63 

79 

95 

110 

126 

142 

31 

58994 

59151 

59308 

59464 

59620 

59776 

59931 

28 

16 

31 

47 

62 

78 

94 

109 

125 

141 

32 

59931 

60086 

60241 

60395 

60550 

60704 

60857 

27 

15 

31 

46 

62 

77 

93 

108 

123 

139 

33 

60857 

61011 

61164 

61317 

61469 

61621 

61773 

26 

15 

30 

46 

61 

77 

92 

107 

122 

138 

34 

61773 

61925 

62076 

62228 

62379 

62529 

62679 

25 

15 

30 

45 

60 

76 

91 

106 

121 

136 

35 

8.62679 

62830 

62979 

63129 

63278 

63427 

63576 

24 

15 

30 

45 

60 

75 

90 

105 

119 

134 

36 

63576 

63724 

63872 

64020 

64168 

64315 

64463 

23 

•15 

30 

45 

59 

74 

89 

104 

118 

133 

37 

64463 

64609 

64756 

64902 

65048 

65194 

65340 

22 

15 

29 

44 

58 

73 

88 

102 

117 

132 

38 

65340 

65485 

65630 

65775 

65920 

66664 

66208 

21 

15 

29 

43 

58 

72 

87 

101 

116 

130 

39 

66208 

66352 

66496 

66639 

66782 

66926 

67067 

20 

14 

29 

43 

57 

72 

86 

100 

115 

129 

40 

8.67067 

67209 

«7352 

67494 

67635 

67777 

67918 

19 

14 

28 

43 

57 

71 

85 

99 

113 

128 

41 

67918 

68059 

68199 

68340 

68480 

68620 

68759 

18 

14 

28 

42 

56 

70 

84 

98 

112 

126 

42 

68759 

68899 

£9038 

69177 

69316 

69454 

69593 

17 

14 

28 

42 

55 

69 

83 

97 

111 

125 

43 

69593 

69731 

69869 

70006 

70144 

70281 

70418 

16 

14 

27 

41 

55 

69 

82 

96 

110 

124 

44 
45 

70418 

70554 

70691 

70827 

70963 

71099 

71234 

15 

14 

27 

41 

54 

68 

82 

95 

109 

123 

8.71234 

71370 

71505 

71640 

71774 

71909 

72043 

14 

14 

27 

40 

54 

67 

81 

95 

108 

122 

46 

72043 

72177 

72311 

72444 

72578 

72711 

72844 

13 

13 

27 

40 

53 

67 

80 

94 

107 

121 

47 

72844 

72977 

73109 

73241 

73374 

73505 

73637 

12 

13 

26 

40 

53 

66 

79 

93 

106 

119 

48 

73637 

73768 

73900 

74031 

74162 

74292 

74423 

11 

13 

26 

39 

52 

65 

78 

92 

105 

118 

49 

74423 

74553 

74683 

74813 

74942 

75072 

75201 

10 

13 

26 

39 

52 

65 

78 

91 

104 

117 

50 

8.75201 

75330 

75458 

75587 

75715 

75843 

75971 

9 

13 

26 

38 

51 

64 

77 

90 

103 

116 

51 

75971 

76099 

76227 

76354 

76481 

76608 

76735 

8 

13 

25 

38 

51 

63 

76 

89 

102 

115 

52 

76735 

76862 

76988 

77114 

77240 

77366 

77492 

7 

13 

25 

38 

50 

63 

76 

88 

101 

114 

53 

77492 

77617 

77742 

77867 

77992 

78117 

78241 

6 

13 

25 

37 

50 

62 

75 

87 

100 

113 

54 

78241 

78365 

78489 

78613 

78737 

78861 

78984 

5 

12 

25 

37 

50 

62 

75 

87 

99 

112 

55 

8.78984 

79107 

79230 

79353 

79475 

79598 

79720 

4 

12 

25 

37 

49 

61 

74 

86 

98 

111 

56 

79720 

79842 

79964 

80085 

80207 

80328 

80449 

3 

12 

25 

37 

49 

61 

73 

85 

98 

110 

57 

80449 

80570 

80691 

80812 

80932 

81052 

81172 

2 

12 

24 

36 

48 

60 

73 

85 

97 

109 

58 

81172 

81292 

81412 

81531 

81651 

81770 

81889 

1 

12 

24 

36 

48 

60 

72 

84 

96 

108 

59 

81889 

82008 

82126 

82245 

82363 

82481 

82599 

0 

12 

24 

36 

48 

60 

72 

83 

95 

107 

60s. 

508. 

408. 

308. 

20s. 

10s. 

Os. 

M. 

Is. 

2s. 

3s. 

4s. 

58. 

68. 

78. 

8s. 

9s. 

_^_ 

10  OR  22  HOURS,  OR  APP.  TIME  A.  M.       | 

PROPOR' 

noN 

AL  PART 

8  FOR  SECONDS.  | 

118 

TABLE  XXIX. 

1 

B 

OFB  'KGLE,  " 

A.RITHMS  OF  THE  APPARENT  TIME,  OR  HOUR  ANGLE. 

1 

HOURS,  OR  APP.  TIME  P.  M. 

PROPORTIONAL  PARTS  FOR  SECONDS. 

e. 

S. 

B. 

s. 

s. 

8. 

s. 

s. 

S. 

S. 

s. 

S. 

g 

Is. 

s. 

B. 

M. 

0 

10 

20 

30 

40 

50 

60 

1 

2 

3 

4 

5 

6 

7 

<3 

9 

105 

0 

8.82599 

82717 

82835 

82952 

83069 

83187 

83303 

59 

12 

23 

35 

47 

59 

70 

82 

93 

1 

83303 

83420 

83537 

83653 

83769 

83885 

84001 

58 

12 

23 

35 

46 

58 

70 

81 

93 

105 

2 

84001 

84117 

84233 

84348 

84464 

84579 

84694 

57 

11 

23 

35 

46 

57 

69 

80 

92 

104 

3 

84694 

84808 

84923 

85037 

85152 

85266 

85380 

56 

11 

23 

34 

45 

57 

68 

80 

91 

103 

4 

85380 

85494 

85607 

85721 

85834 

85947 

86060 

55 

11 

23 

34 

45 

57 

68 

79 

90 

102 

5 

8.86060 

86173 

86286 

86398 

86511 

86623 

86735 

54 

11 

22 

34 

45 

56 

67 

78 

90 

101 

6 

86735 

86847 

86959 

87070 

87182 

87293 

87404 

53 

11 

22 

33 

45 

56 

67 

78 

89 

100 

7 

87404 

87515 

87626 

87736 

87847 

87957 

88068 

52 

11 

22 

33 

44 

55 

66 

78 

89 

100 

8 

88068 

88178 

88288 

88397 

88507 

88616 

88726 

51 

11 

22 

33 

44 

55 

66 

77 

88 

99 

9 
10 

88726 

88835 

88944 

89053 

89162 

89270 

89379 

50 

11 

22 

33 

44 

55 

65 

76 

87 

98 

8.89379 

89487 

89595 

89703 

89811 

89918 

90026 

49 

11 

22 

32 

43 

54 

65 

76 

86 

97 

11 

90026 

90133 

90241 

90348 

90455 

90562 

90668 

48 

11 

21 

32 

43 

54 

64 

75 

86 

96 

12 

90668 

90775 

90881 

90988 

91094 

91200 

91306 

47 

11 

21 

32 

42 

53 

64 

74 

85 

95 

13 

91306 

91411 

91517 

91622 

91728 

91833 

91938 

46 

11 

21 

32 

42 

53 

63 

73 

84 

95 

14 

91938 

92043 

92147 

92252 

92356 

92461 

92565 

45 

10 

21 

32 

42 

53 

63 

73 

84 

94 

15 

8.92565 

92669 

92773 

92877 

92980 

93084 

93187 

44 

10 

21 

31 

42 

52 

62 

73 

83 

93 

16 

93187 

93290 

93393 

93496 

93599 

93702 

93804 

43 

10 

20 

31 

41 

52 

62 

72 

82 

93 

17 

93804 

93907 

94009 

94111 

94213 

94315 

94417 

42 

10 

20 

31 

41 

51 

61 

71 

82 

93 

18 

94417 

94519 

94620 

94722 

94823 

94924 

95025 

41 

10 

20 

30 

40 

51 

61 

71 

81 

91 

19 

95025 

95126 

95227 

95327 

95428 

95528 

95628 

40 

10 

20 

30 

40 

50 

60 

70 

80 

90 
90 

20 

8.95628 

95728 

95828 

95928 

96028 

96128 

96227 

39 

10 

20 

30 

40 

50 

60 

70 

80 

21 

96227 

96326 

96426 

96525 

96624 

96723 

96821 

38 

10 

20 

30 

40 

50 

60 

69 

79 

89 

22 

96821 

96920 

97018 

97117 

97215 

97313 

97411 

37 

10 

20 

30 

39 

49 

59 

69 

79 

88 

23 

97411 

97509 

97607 

97704 

97802 

97899 

97996 

36 

10 

19 

29 

39 

49 

59 

68 

78 

87 

24 

97996 

98094 

98191 

98288 

98384 

98481 

98578 

35 

10 

19 

29 

39 

49 

58 

68 

77 

87 
86 

25 

8.98578 

98674 

98770 

98866 

98963 

99058 

99154 

34 

10 

19 

29 

38 

48 

58 

67 

77 

26 

99154 

99250 

99346 

99441 

99536 

99632 

99727 

33 

10 

19 

29 

38 

48 

57 

67 

76 

86 

27 

1-99727 

99822 

99917 

00012 

00106 

00201 

00295 

32 

9 

19 

28 

38 

47 

57 

66 

76 

85 

28 

9.00295 

00390 

00484 

00578 

00672 

00766 

00860 

31 

9 

19 

28 

38 

47 

56 

66 

75 

85 

29 

00860 

00953 

01047 

01140 

01234 

01327 

01420 

30 

29 

9 

19 

28 

37 

47 

56 

65 

75 

84 
83 

30 

9.01420 

01513 

01606 

01698 

01791 

01884 

01976 

9 

18 

28 

37 

46 

55 

65 

74 

31 

01976 

02068 

02161 

02253 

02345 

02437 

02528 

28 

9 

18 

28 

37 

46 

55 

64 

74 

83 

32 

02528 

02620 

02712 

02803 

02894 

02986 

03077 

27 

9 

18 

27 

37 

46 

55 

64 

73 

82 

33 

03077 

03168 

03259 

03350 

03440 

03531 

03621 

26 

9 

18 

27 

36 

45 

54 

64 

73 

82 

34 

03621 

03712 

03802 

03892 

03982 

04072 

04162 

25 
24 

9 

18 

27 

36 

45 

54 

63 

72 

81 
81 

35 

9.04162 

04252 

04341 

04431 

04520 

04610 

04699 

9 

18 

27 

36 

45 

54 

63 

72 

36 

04699 

04788 

04877 

04966 

05055 

05144 

05232 

23 

9 

18 

27 

36 

45 

53 

62 

71 

80 

37 

05232 

05321 

05409 

05498 

05586 

05674 

05762 

22 

9 

18 

26 

35 

44 

53 

62 

71 

79 

38 

05762 

05850 

05938 

06025 

06113 

06200 

06288 

21 

9 

17 

26 

35 

44 

53 

61 

70 

79 

39 

06288 

06375 

06462 

06550 

06637 

06724 

06810 

20 

9 

17 

26 

35 

43 

52 

61 

70 

78 

40 

9.06810 

06897 

06984 

07070 

07157 

07243 

07329 

19 

9 

17 

26 

35 

43 

52 

61 

69 

78 

41 

07329 

07415 

07501 

07587 

07673 

07759 

07845 

18 

9 

17 

26 

34 

43 

52 

60 

69 

77 

42 

07845 

07930 

08016 

08101 

08186 

08271 

08357 

17 

9 

17 

26 

34 

43 

51 

60 

68 

77 

43 

08357 

08442 

08526 

08611 

08696 

08781 

08865 

16 

8 

17 

25 

34 

42 

51 

59 

67 

76 

44 
45 

08865 

08949 

09034 

09118 

09202 

09286 

09370 

15 

8 

17 

25 

34 

42 

51 

59 

67 

76 

9.09370 

09454 

09538 

09622 

09705 

09789 

09872 

14 

8 

17 

25 

34 

42 

50 

59 

67 

76 

46 

09872 

09955 

10039 

10122 

10205 

10288 

10371 

13 

8 

17 

25 

33 

42 

50 

58 

66 

75 

47 

10371 

10453 

10536 

10619 

10701 

10784 

10866 

12 

8 

16 

25 

33 

41 

50 

58 

66 

74 

48 

10866 

10948 

11030 

11112 

11194 

11276 

11358 

11 

8 

16 

25 

33 

41 

49 

57 

66 

74 

49 

1135^ 

11440 

11521 

11603 

11684 

11765 

11847 

10 

8 

16 

24 

33 

41 

49 

57 

65 

73 

50 

9.11847 

1192!^ 

12009 

12090 

12171 

12252 

12332 

9 

8 

16 

24 

32 

40 

49 

57 

65 

73 

51 

12332 

12413 

12494 

12574 

12655 

12735 

12815 

8 

8 

16 

24 

32 

40 

48 

56 

64 

73 

52 

12815 

12895 

12975 

13055 

13135 

13215 

13295 

7 

8 

16 

24 

32 

40 

48 

56 

64 

72 

53 

13295 

13374 

13454 

13533 

13613 

13692 

13771 

6 

•  8 

16 

24 

32 

40 

48 

56 

64 

72 

54 

55 

13771 

13850 

13929 

14008 

14087 

14166 

14245 

5 

8 

16 

24 

32 

40 

47 

55 

63 

71 

9.14245 

14323 

14402 

14480 

14559 

14637 

14715 

4 

8 

16 

24 

31 

39 

47 

55 

63 

71 

56 

14715 

14793 

14871 

14949 

15027 

15105 

15183 

3 

8 

16 

23 

31 

39 

47 

55 

62 

70 

57 

15183 

15260 

15338 

15415 

15493 

15570 

15647 

2 

8 

15 

23 

31 

39 

47 

54 

62 

70 

58 

15647 

15724i 

15802 

15879 

15955 

16032 

16109 

1 

8 

15 

23 

31 

38 

46 

54 

62 

69 

59 

16109 

16186 

16262 

16339 

16415 

16492 

16568 

0 

8 

15 

2s. 

23 
3s. 

31 

38 

46 

54 

61 

69 

60s. 

50s. 

40s. 

30s. 

20s. 

10s. 

Os. 

M. 

Is., 

4s. 

5s. 

6s. 

7s. 

8s. 

9s 

9  OR  21  HOURS,  OR  APP.  TIME  A.  M.        [ 

PRO 

POR 

noN 

AL  I 

'ART 

S  FC 

)R  S 

ECONDS.  1 

■ 

TABLE  XXIX. 

119   1 

LOGARITHMS  OF  THE  APPARENT  TIME,  OR  HOUR  ANGLE. 

HOUR  ANGLE,  3  HOURS,  OR  APP.  TIME  P.  M.     | 

PROPORTIONAL  PARTS  FOR  SECONDS.  1 

«. 

B. 

8. 

B. 

s. 

B. 

8. 

8. 

B. 

8. 

8. 

s. 

s. 

8. 

S.     8.   1 

M. 

0 

10 

20 

30 

40 

50 

60 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

M6568 

16644 

16720 

16796 

16872 

16948 

17024 

59 

8 

15 

23 

30 

38 

46 

53 

61 

68 

1 

17024 

17100 

17175 

17251 

17326 

17402 

17477 

58 

8 

15 

23 

30 

38 

45 

53 

60 

68 

2 

17477 

17553 

17628 

17703 

17778 

17853 

17928 

57 

7 

15 

22 

30 

37 

45 

52 

60 

67 

3 

17928 

18003 

18077 

18152 

18227 

18301 

18376 

56 

7 

14 

22 

30 

37 

45 

52 

60 

67 

4 

18376 

18450 

18524 

18598 

18673 

18747 

18821 

^5 

7 

14 

22 

30 

37 

44 

52 

59 

67 

5 

9.18821 

18895 

18968 

19042 

19116 

19190 

19263 

54 

7 

14 

22 

30 

37 

44 

52 

59 

67 

6 

19263 

19337 

19410 

19483 

19557 

19630 

19703 

53 

7 

14 

22 

29 

37 

44 

51 

59 

66 

7 

19703 

19776 

19849 

19922 

19995 

20067 

20140 

52 

7 

14 

22 

29 

37 

44 

51 

58 

66 

8 

20140 

20213 

20285 

20358 

20430 

20502 

20574 

51 

7 

14 

22 

29 

36 

44 

51 

58 

65 

9 

20574 

20647 

20719 

20791 

20863 

20935 

21006 

50 

7 

14 

22 

29 

36 

43 

50 

58 

65 

10 

9.21006 

21078 

21150 

21221 

21293 

21364 

21436 

49 

7 

14 

21 

29 

36 

43 

50 

57 

64 

11 

21431S 

21507 

21578 

21650 

21721 

21792 

21863 

48 

7 

14 

21 

28 

36 

43 

50 

57 

64 

12 

2186:^ 

21934 

22004 

22075 

22146 

22216 

22287 

47 

7 

14 

21 

28 

35 

42 

49 

56 

63 

13 

22287 

22358 

22428 

22498 

22569 

22639 

22709 

46 

7 

14 

21 

28 

35 

42 

49 

56 

63 

14 
15 

22709 

22779 

22849 

22919 

22989 

23059 

23128 

45 

7 

14 

21 

28 

35 

42 

49 

56 

63 

9.23128 

23198 

23268 

23337 

23407 

23476 

23545 

44 

7 

14 

21 

28 

35 

42 

49 

56 

63 

16 

23545 

23615 

23684 

23753 

23822 

23891 

23960 

43 

7 

14 

21 

28 

35 

41 

48 

55 

62 

17 

23960 

24029 

24098 

24166 

24235 

24304 

24372 

42 

7 

14 

21 

28 

35 

41 

48 

55 

62 

18 

24372 

24441 

24509 

24577 

24646 

24714 

24782 

41 

7 

14 

21 

27 

34 

41 

48 

55 

62 

19 

24782 

24850 

24918 

24986 

25054 

25122 

25190 

40 

7 

14 

20 

27 

34 

41 

48 

54 

61 

20 

9.25190 

25257 

25325 

25393 

25460 

25527 

25595 

39 

7 

14 

20 

27 

34 

41 

47 

54 

61 

21 

25595 

25662 

25729 

25796 

25864 

25931 

25998 

38 

7 

13 

20 

27 

34 

40 

47 

54 

60 

22 

25998 

26065 

26132 

2tJ198 

26265 

26332 

26398 

37 

7 

13 

20 

27 

34 

40 

47 

54 

60 

23 

2639S 

26465 

26532 

26598 

26664 

26731 

26797 

36 

^7 
4 

13 

20 

27 

33 

40 

47 

53 

60 

24 

25 

26797 

26863 

26929 

26995 

27061 

27127 

27193 

35 

7 

13 

20 

26 

33 

40 

46 

53 

59 

9.27193 

27259 

27325 

27390 

27456 

27521 

27587 

34 

7 

13 

20 

26 

33 

40 

46 

53 

59 

26 

27587 

27652 

27718 

27783 

27848 

27914 

27979 

33 

7 

13 

20 

26 

33 

39 

46 

52 

59 

27 

27979 

28044 

28109 

28174 

28239 

28304 

28368 

32 

6 

13 

20 

26 

32 

39 

46 

52 

59 

28 

28368 

28433 

28498 

28562 

28627 

28691 

28756 

31 

6 

13 

20 

26 

32 

39 

46 

52 

59 

29 

28756 

28820 

28885 

28949 

29013 

29077 

29141 

30 

6 

13 

19 

26 

32 

39 

45 

52 

58 

30 

9.29141 

29205 

29269 

29333 

29397 

29461 

29524 

29 

6 

13 

19 

26 

32 

38 

45 

51 

58 

31 

29524 

29588 

29652 

29715 

29779 

29842 

29905 

28 

6 

13 

19 

25 

32 

38 

45 

51 

57 

32 

29905 

29969 

30032 

30095 

30158 

30221 

30285 

27 

6 

13 

19 

25 

32i  38 

44 

51 

57 

33 

30285 

30347 

30410 

30473 

30536 

30599 

30661 

26 

6 

13 

19 

25 

32 

38 

44 

50 

57 

34 

30661 

30724 

30787 

30849 

30912 

30974 

31036 

25 

6 

12 

19 

25 

31 

38 

44 

50 

56 

35 

9.31036 

31099 

31161 

31223 

31285 

31347 

31409 

24 

6 

12 

19 

25 

31 

37 

43 

50 

56 

36 

31409 

31471 

31533 

31595 

31657 

31719 

31780 

23 

6 

12 

19 

25 

31 

37 

43 

50 

56 

37 

31780 

31842 

31903 

31965 

32026 

32088 

32149 

22 

6 

12 

18 

25 

31 

37 

43 

49 

55 

38 

32149 

32210 

32272 

32333 

32394 

32455 

32516 

21 

6 

12 

18 

24 

31 

37 

43 

49 

55 

39 

32516 

32577 

32638 

32699 

32760 

32820 

32881 

20 

6 

12 

18 

24 

31 

37 

43 

49 

55 

40 

9.32881 

32942 

33002 

33063 

33123 

33184 

33244 

19 

6 

12 

18 

24 

30 

»6 

42 

48 

55 

41 

33244 

33304 

33365 

33425 

33485 

33545 

33605 

18 

6 

12 

18 

24 

30 

36 

42 

48 

54 

42 

33605 

336tij 

33725 

33785 

33845 

33905 

33965 

17 

6 

12 

18 

24 

30 

36 

42 

48 

54 

43 

33965 

34024 

34084 

34143 

34203 

34262 

34322 

16 

6 

12 

18 

24 

30 

36 

42 

48 

54 

44 
45 

34322 

34381 

34441 

34500 

34559 

34618 

34677 

15 

6 

12 

18 

24 

30 

36 

41 

47 

53 

9.34677 

34736 

34795 

34854 

34913 

34972 

35031 

14 

6 

12 

18 

24 

30 

35 

41 

47 

53 

46 

35031 

35O90 

35148 

35207 

35266 

35324 

35383 

13 

6 

12 

18 

24 

30 

35 

41 

47. 

53 

47 

35383 

35441 

35499 

35558 

35616 

35674 

35733 

12 

6 

12 

18 

23 

29 

35 

41 

47 

53 

48 

35733 

35791 

35849 

35907 

35965 

36023 

36081 

11 

6 

12 

17 

23 

29 

35 

41 

46 

52 

49 

36081 

36139 

36196 

36254 

36312 

36369 

36427 

10 

6 

12 

17 

23 

29 

35 

41 

46 

52 

50 

9.36427 

36485 

36542 

36599 

36657 

36714 

36771 

9 

6 

11 

17 

23 

29 

35 

40 

46 

52 

51 

36771 

3682y 

36886 

36943 

37OO0 

37057 

37114 

8 

6 

11 

17 

23 

29 

34 

40 

46 

51 

52 

37114 

37171 

37228 

37285 

37342 

37399 

37455 

7 

6 

11 

17 

23 

29 

34 

40 

46 

51 

53 

3745£ 

i  3751S 

3756S 

37625 

37682 

37738 

37794 

6 

6 

11 

17 

23 

28 

34 

40 

45 

51 

54 

37794 

[  37851 

37907 

37963 

38020 

38076 
38412 

38132 

5 

6 

11 

17 

22 

28 

34 

39 

45 

51 

55 

9.^8131 

!  38186 

S  38244 

38300 

38356 

38468 

4 

6 

11 

17 

22 

28 

34 

39 

45 

50 

56 

38466 

i  38524 

[  38579 

38635 

38691 

38746 

38802 

3 

6 

11 

17 

22 

28 

33 

39 

44 

50 

57 

3880S 

!  38857 

3891S 

38968 

39024 

39079 

39134 

2 

6 

11 

17 

22 

28 

33 

39 

44 

50 

58 

39134 

[  39189 

1  39245 

.  39300 

39355 

39410 

39465 

1 

6 

11 

16 

.  22 

28 

i  33 

39 

1  44 

60 

59 

3946£ 

>  3952C 

1  39575 

i  39630 

39684 

39739 

39794 

0 

6 

11 

le 

;  22 

28 

!  33 

39 

»  44 

[    50 

60s. 

50s. 

40s.  '  'Os.  1  20s. 

10s. 

Os. 

M. 

Is. 

2s. 

3s. 

4s. 

5s. 

6s. 

.7s. 

8s. 

9s. 

; 

8  OR  20  HOURS,  OR  APP.  TIME  A.  M.        ( 

PRC 

•PORTIONAL  PARTS  FOR  SECONDS.  1 

"? 


120                 TABLE  XXIX. 

J 

LOGARITHMS  OP  THE  APPARENT  TIME,  OR  HOUR  ANGLE. 

HOCB  ANGLE,  4  H0UK8,  OR  APP.  TIME  P.  M.        PROPORTIONAL  1 

PARTS  FOR  SECONDS. 

8. 

8. 

s. 

s. 

s. 

8.      8. 

8. 

8. 

8. 

& 

8. 

a 

8. 

8. 

8. 

M. 

0 

10 

20 

30 

40 

50    60 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0 

9.39794 

39849 

39903 

39958 

40012 

40067 

40121 

59    6 

11 

16 

22 

28 

33 

39 

44 

50 

1 

40121 

40176 

40230 

40284 

40339 

40393 

40447 

58    5 

11 

16 

22 

27 

33 

38 

44 

49 

2 

40447 

40501 

40555 

40609 

40663 

40717 

40771 

57    5 

11 

16 

22 

27 

32 

38 

43 

49 

3 

40771 

40825 

40879 

40933 

40986 

41040 

41094 

56    5 

11 

16 

22 

27 

32 

38 

43 

49 

4 

41094 

41147 

41201 

41254 

41308 

41361 

41415 

55    5 

11 

16 

21 

27 

27 

32 

37 

43 

48 

5 

9.41415 

41468 

41521 

41575 

41628 

41681 

41734 

54    5 

11 

16 

21 

32 

37 

43 

48 

6 

41734 

41787 

41840 

41893 

41946 

41999 

42052 

53    5 

11 

16 

21 

27 

32 

37 

43 

48 

7 

42052 

42105 

42157 

42210 

42263 

42315 

42368 

52    5 

10 

16 

21 

26 

31 

37 

42 

47 

8 

42368 

42420 

42473 

42525 

42578 

42630 

42682 

51    5 

10 

16 

21 

26 

31 

37 

42 

47 

9 

42682 

42735 

42787 

42839 

42891 

42943 

42996 

50    5 

10 

16 

21 

26 

31 

36 

42 

47 

10 

9.42996 

43048 

43100 

43151 

43203 

43255 

43307 

49    5 

10 

16 

21 

26 

31 

36 

42 

47 

11 

43307 

43359 

43411 

43462 

43514 

43565 

43617 

48    5 

10 

15 

21 

26 

31 

36 

41 

46 

12 

43617 

43669 

43720 

43771 

43823 

43874 

43925 

47    5 

10 

15 

20 

25 

31 

36 

41 

46 

13 

43925 

43977 

44028 

44079 

44130 

44181 

44232 

46    5 

10 

15 

20 

25 

31 

36 

41 

46 

14 

44222 

44283 

44334 

44385 

44436 

44487 

44538 

45    5 

10 

15 

20 

25 

31 

36 

41 

46 

15 

9.44538 

44589 

44639 

44690 

44741 

44791 

44842 

44    5 

10 

15 

20 

25 

30 

35 

40 

45 

16 

44842 

44892 

44943 

44993 

45044 

45094 

45144 

43    5 

10 

15 

20 

25 

30 

35 

40 

45 

17 

45144 

45195 

45245 

4.'-295 

45345 

45395 

45446 

42    5 

10 

15 

20 

25 

30 

35 

40 

45 

18 

45446 

45496 

45546 

45595 

45645 

45695 

45745 

41    5 

10 

15 

20 

25 

30 

35 

40 

45 

19 

45745 

45795 

45845 

45894 

45944 

45994 

46043 

40    5 

10 

15 

20 

25 

30 

35 
3.^ 

40 

45 

20 

9.46043 

46093 

46142 

46192 

46241 

46291 

46340 

39    5 

10 

15 

20 

25 

30 

40 

45 

21 

46340 

46389 

46439 

46488 

46537 

46586 

46635 

38    5 

10 

15 

20 

25 

29 

34 

39 

44 

22 

46635 

46684 

46733 

46782 

46831 

46880 

46929 

37    5 

10 

15 

20 

24 

29 

34 

39 

44 

23 

46929 

46978 

47027 

47076 

47124 

47173 

47222 

36    5 

10 

15 

20 

24 

29 

34 

39 

44 

24 

47222 

47270 

47319 

47367 

47416 

47464 

47513 

35    5 

10 

15 

19 

24 

29 

34 

39 

44 

25 

9.47513 

47561 

47610 

47658 

47706 

47754 

47803 

34    5 

10 

14 

19 

24 

29 

34 

38 

43 

26 

47803 

47851 

47899 

47947 

47995 

48043 

48091 

33    5 

10 

14 

19 

24 

29 

34 

38 

43 

27 

48091 

48139 

48187 

48235 

48282 

48330 

48378 

32    5 

10 

14 

19 

24 

29 

34 

38 

43 

28 

48378 

48425 

48473 

48521 

48568 

48616 

48664 

31    5 

9 

14 

19 

24 

29 

33 

38 

43 

29 

48664 

48711 

48758 

48806 

48853 

48900 

48948 

30    5 

9 

14 

19 

24 

28 

33 

38 

42 

30 

9.48948 

48995 

49042 

49089 

49137 

49184 

49231 

29    5 

9 

14 

19 

23 

28 

33 

38 

42 

31 

49231 
19512 

49278 

49325 

49372 

49419 

49465 

49512 

28    5 

9 

14 

19 

23 

28 

33 

38 

42 

32 

49559 

49606 

49653 

49699 

49746 

49793 

27    5 

9 

14 

19 

23 

28 

33 

37 

42 

33 

49793 

49839 

49886 

49932 

49979 

50025 

50071 

26    5 

9 

14 

19 

23 

28 

33 

37 

42 

34 

50071 

50118 
50395 

50164 

50211 

50257 

50303 

50349 

25    5 

9 

14 

19 

23 

28 

33 

37 

42 
41 

35 

9.50349 

50441 

50488 

50534 

50580 

50626 

24    '^ 

9 

14 

18 

23 

28 

32 

37 

36 

50626 

50672 

50717 

50763 

50809 

50855 

50901 

23    0 

9 

14 

18 

23 

28 

32 

37 

41 

37 

50901 

50946 

50992 

51038 

51083 

51129 

51174 

22    5 

9 

14 

18 

23 

27 

32 

36 

41 

38 

51174 

51220 

51265 

51311 

51356 

51402 

51447 

21    5 

9 

14 

18 

23 

27 

32 

36 

41 

39 

51447 

51492 

51538 

51583 

51628 

51673 

51718 

20    4 

9 

13 

18 

22 

27 

31 

36 

40 

40 

9.51718 

51763 

51808 

51853 

51898 

51943 

51988 

19    4 

9 

13 

18 

22 

27 

31 

36 

40 

41 

51988 

52033 

32078 

52123 

52168 

52212 

52257 

18    4 

9 

13 

18 

22 

27 

31 

36 

40 

42 

52257 

52302 

52346 

52391 

52435 

52480 

52525 

17    4 

9 

13 

18 

22 

27 

31 

36 

40 

43 

52525 

52569 

52613 

52658 

52702 

52747 

52791 

16    4 

9 

13 

18 

22 

27 

31 

36 

40 
40 

44 

02791 

52835 

52879 

52923 

52968 

53012 

53056 

15    4 

9 

13 

18 

22 

27 

31 

35 

45 

9.53056 

53100 

53144 

53188 

53232 

53276 

53320 

14    4 

9 

13 

18 

22 

26 

31 

35 

40 

46 

,53320 

53364 

53407 

53451 

53495 

53539 

53582 

13    4 

9 

13 

18 

22 

26 

31 

35 

40 

47 

53582 

53626 

53670 

53713 

53757 

53800 

53844 

12    4 

9 

13 

17 

22 

26 

30 

35 

39 

48 

53844 

53887 

53931 

53974 

54017 

54061 

54104 

11    4 

9 

13 

17 

22 

26 

30 

35 

39 

49 

54104 

54147 

54190 

54234 

54277 

54320 

54363 

10    4 

9 

13 

17 

22 

26 

30 

35 

39 

50 

9  54363 

54406 

54449 

54492 

54535 

54578 

54621 

9    4 

9 

13 

17 

22 

26 

30 

34 

39 

51 

54621 

54664 

54707 

54749 

54792 

54835 

54878 

8    4 

9 

13 

17 

22 

26 

30 

34 

39 

52 

54878 

54920 

54963 

55005 

55048 

55091 

55133 

7    4 

8 

13 

17 

21 

26 

30 

34 

38 

53 

55133 

55175 

55218 

55260 

55303 

55345 

55387 

6    4 

8 

13 

17 

21 

26 

30 

34 

38 

54 

55387 

55430 

55472 

55514 

55556 

55598 

55641 

5    4 

8 

13 

17 

21 

25 

29 

34 

38 

55 

9.55641 

55683 

55725 

55767 

55809 

55851 

55893 

4    4 

8 

13 

17 

21 

25 

29 

34 

38 

56 

65893 

55934 

55976 

56018 

56060 

56102 

56144 

3    4 

8 

13 

17 

21 

25 

29 

34 

38 

57 

56144 

56185 

56227 

56269 

56310 

56352 

56393 

2    4 

8 

12 

17 

21 

25 

29 

33 

37 

58 

56393 

56435 

56476 

56518 

56559 

56601 

56642 

1    4 

8 

12 

17 

21 

25 

29 

33 

37 

59 

56642 

56683 

56725 

56766 

56807 

56848 

56889 

0    4 

8 

12 

16 

20 

25 

29 

33 

37 

60s. 

50s. 

40s. 

303. 

20s. 

10s. 

Os.   M.  1  Is. 

2s. 

3s. 

4s. 

5s. 

6s. 

7s. 

Ss. 

9s. 

7  OR  19  HOURS,  OR  APP,  TIME  A.  M.           PRO 

P0R1 

PION 

AL  r 

•ARTS  FC 

R  b 

ECONDS.  ( 

TABLE  XXIX. 
LOGARITHMS  OF  THE  APPARENT  TIME,  OR  HOUR  ANGLE. 


121 


HOITB  ANGLE,  5 

HOURS,  OR  APP.  TIME  P.  M.     | 

PROPORTIONAL  PARTS  FOR  SECONDS.  1 

8. 

& 

8. 

a. 

8. 

8. 

8. 

8. 

8. 

8.  1  8.  1 

8. 

8. 

B.    S 

M. 

0 

10 

20 

30 

40 

50 

60 

1 

2 

3 

4 

0 

6 

7 

8   9 

0  i 

). 56889  56931 

56972 

57013 

57054 

57095 

57136 

59 

4 

8 

12 

16 

20 

25 

29 

33  37 

1 

57136  57177 

57218 

57259 

57299 

57340 

57381 

58 

4 

8 

12 

16 

20 

25 

29 

33 

37 

2 

57381 

57422 

57463 

57503 

57544 

57585 

57625 

57 

4 

8 

12 

16 

20 

25 

29 

33 

37 

3 

57625 

57666 

57706 

57747 

57787 

57828 

57868 

56 

4 

8 

12 

16 

20 

24 

28 

32 

36 

4 

57868 

57909 

57949 

57990 

58030 

58070 

58110 

,.55 

4 

8 

12 

16 

20 

24 

28 

32 

36 

o 

J. 58110 

58151 

58191 

58231 

58271 

58311 

58351 

54 

4 

8 

12 

16 

20 

24 

28 

32 

36 

6 

58351 

58391 

58431 

58471 

58511 

58551 

58591 

53 

4 

8 

12 

16 

20 

24 

28 

32 

36 

7 

58591 

58631 

58671 

58711 

58750 

58790 

58830 

( 

0:d 

4 

8 

12 

16 

20 

24 

28 

32 

36 

8 

58830 

58870 

58909 

58949 

58988 

59028 

59068 

51 

4 

8 

12 

16 

20 

24 

28 

32 

36 

9 
10 

59068 

59107 

59147 

59186 

59225 

59265 

59304 

50 

4 

8 

12 

16 

20 

24 

28 

32 

36 

9.59304 

59344 

59383 

59422 

59461 

59501 

591540 

49 

4 

8 

12 

16 

20 

24 

28 

32 

36 

11 

59540 

59579 

59618 

59657 

59696 

59735 

59774 

48 

4 

8 

12 

16 

20 

23 

27 

31 

35 

12 

59774 

59813 

59852 

59891 

59930 

59969 

60008 

47 

4 

8 

12 

16 

20 

23 

27 

31 

35 

13 

60008 

60047 

60085 

60124 

60163 

60202 

60240 

46 

4 

8 

12 

16 

20 

23 

27 

31 

35 

14 

60240 

60279 

60318 

60356 

60395 

60433 

60472 

45 

4 

8 

12 

16 

20 

23 

27 

31 

35 

15 

9.60472 

60510 

60549 

60587 

60625 

60664 

60702 

44 

4 

8 

12 

15 

19 

23 

27 

31 

35 

16 

60702 

60740 

60779 

60817 

60855 

60893 

60931 

43 

4 

8 

12 

15 

19 

23 

27 

31 

35 

17 

60931 

60970 

61008 

61046 

61084 

61122 

61160 

42 

4 

8 

11 

15 

19 

23 

27 

30 

34 

18 

61160 

61198 

61236 

61274 

61311 

61349 

61387 

41 

4 

8 

11 

15 

19 

23 

27 

30 

34 

19 
20 

61387 

61425 

61463 

61500 

61538 

61576 

61613 

40 

4 

8 

11 

15 

19 

23 

27 

30 

34 

9.61613 

61651 

61689 

61726 

61764 

61801 

61839 

39 

4 

8 

11 

15 

19 

23 

27 

30 

34 

21 

61839 

61876 

61914 

61951 

61988 

62026 

62063 

38 

4 

7 

11 

15 

19 

22 

26 

30 

34 

22 

62063 

62100 

62138 

62175 

62212 

62249 

62287 

37 

4 

7 

11 

15 

19 

22 

26 

30 

34 

23 

62287 

62324 

62361 

62398 

62435 

62472 

62509 

36 

4 

7 

11 

15 

18 

22 

26 

30 

33 

24 

62509 

62546 

62583 

62620 

62657 

62693 

62730 

35 

4 

7 

11 

15 

18 

22 

26 
26 

30 

33 

25 

9.62730 

62767 

62804 

62841 

62877 

62914 

62951 

34 

4 

7 

11 

15 

18 

22 

30 

33 

26 

62951 

62987 

63024 

63061 

63097 

63134 

63170 

33 

4 

7 

11 

15 

18 

22 

26 

29 

33 

27 

63170 

63207 

63243 

63279 

63316 

63352 

63389 

32 

4 

7 

11 

15 

18 

22 

26 

29 

33 

28 

63389 

63425 

63461 

63497 

63534 

63570 

63606 

31 

4 

7 

11 

14 

18 

22 

25 

29 

32 

29 
30 

63606 

63642 

63678 

63715 

63751 

63787 

63823 

30 

4 

7 

11 

14 

18 

22 

25 

29 

32 

9.63823 

63S59 

63895 

63931 

63966 

64002 

64038 

29 

4 

7 

11 

14 

18 

22 

25 

29 

32 

31 

64038 

64074 

64110 

64146 

64181 

64217 

64253 

28 

4 

7 

11 

14 

18 

22 

25 

29 

32 

32 

64253 

64289 

64324 

64360 

64395 

64431 

64467 

27 

4 

7 

11 

14 

18 

21 

25 

28 

32 

33 

64467 

64502 

64538 

64573 

64609 

64644 

64679 

26 

4 

7 

11 

14 

18 

21 

25 

28 

32 

34 

64679 

64715 

64750 

64785 

64821 

64856 

64891 

25 

4 

7 

11 

14 

18 

21 

25 

28 

32 

35 

9.64891 

64926 

64962 

64997 

65032 

65067 

65102 

24 

4 

7 

10 

14 

18 

21 

25 

28 

31 

36 

65102 

65137 

65172 

65207 

65242 

65277 

65312 

23 

3 

7 

10 

14 

18 

21 

25 

28 

31 

37 

65312 

65347 

65382 

65417 

65452 

65486 

65521 

22 

3 

7 

10 

14 

18 

21 

25 

28 

31 

38 

65521 

65556 

65591 

65625 

65660 

65695 

65729 

21 

3 

7 

10 

14 

18 

21 

25 

28 

31 

39 

65729 

65764 

65799 

65834 

65868 

65902 

65937 

20 

3 

7 

10 

14 

17 

21 

24 

28 

31 

40 

9.65937 

6597-1 

66006 

66040 

66074 

66109 

66143 

19 

3 

7 

10 

14 

17 

21 

24 

28 

31 

41 

66143 

66177 

66212 

66246 

66280 

66314 

66348 

18 

3 

7 

IC 

14 

17 

21 

24 

28 

31 

42 

66348 

66383 

66417 

66451 

66485 

66519 

66553 

17 

3 

7 

10 

14 

17 

20 

24 

27 

31 

43 

66553 

66587 

66621 

66655 

'66689 

66723 

66757 

16 

3 

7 

10 

14 

17 

20 

24 

27 

30 

44 

66757 

66791 

66824 

66858 

66892 

66926 

66959 

15 

3 

7 

10 

14 

17 

20 

24 

27 

30 

45 

9.66959 

66993 

67027 

67060 

67094 

67128 

67161 

14 

a 

7 

10 

14 

17 

20 

24 

27 

30 

46 

67161 

67195 

67228 

67262 

67295 

67329 

67362 

13 

J 

7 

10 

13 

17 

20 

23 

27 

30 

47 

67362 

67396 

67429 

67462 

67496 

67529 

67562 

12 

3 

7 

10 

13 

17 

20 

23 

27 

30 

48 

67562 

67596 

67628 

67662 

67695 

67729 

67762 

11 

3 

7 

10 

13 

17 

20 

23 

27 

30 

49 

67762 

67795 

67825 

67861 

67894 

67927 

6796C 

10 

3 

7 

10 

13 

16 

20 

23 

26 

30 

50 

9.6796C 

67993 

68026 

6805S 

68092 

68125 

68158 

9 

3 

7 

10 

13 

16 

20 

23 

26 

30 

'    51 

68158 

681 9C 

68223 

68256 

6828L 

68322 

68354 

8 

? 

7 

10 

13 

16 

20 

23 

26 

30 

52 

68354 

68387 

6842C 

) 68452 

68485 

)  68517 

6855C 

7 

J 

7 

10 

13 

16 

19 

23 

26 

29 

53 

6855C 

68583 

6861.' 

)  68648 

6868C 

)  68713 

68745 

6 

t 

7 

10 

13 

16 

19 

23 

26 

29 

54 
55 

6874.^ 

68777 

6881C 

)  6884[ 
[   ii9036 

68874 

68907 

68939 

5 

3 

7 

10 

13 

16 

19 

23 

26 

29 

9.6893i 

68971 

69004 

69068 

6910C 

69132 

4 

6 

10 

13 

16 

19 

22 

26 

29 

56 

69132 

•  69164 

[  69197 

'  69229 

69261 

6929."] 

69325 

3 

3 

6 

10 

13 

16 

19 

22 

26 

29 

57 

6932c 

)  6935^ 

i  6938C 

1  69421 

69453 

69484 

69516 

2 

3 

6 

10 

13 

16 

19 

22 

26 

29 

58 

69516 

;  6954? 

6958C 

)  69612 

69644 

[  69675 

69707 

1 

3 

6 

10 

13 

16 

19 

22 

26 

29 

59 

69707 

69739 

6977( 

)  69^^02 

69834 

69866 

69897 

0 

3 

6 

10 

13 

16 

19 

22 

26 

29 

60s. 

50s. 

40s. 

308. 

20s. 

10s. 

Os. 

M. 

Is.  2s. 

38. 

4s. 

5s.  6s. 

7s. 

8s. 

9s. 

_ 

6  OR  18  HOURS,  OR  APP.  TIME  A.  M. 

PROPORTIONAL  PARTS  FOR  8ECO 

ND8. 

V 


122                 TABLE  XXIX. 

LOGi 

>LE,  6 

i^RITHMS  OF  THE  APPARENT  TIME,  OR  HOUR  ANGLE.            1 

HOUR  AN( 

HOURS,  OR  APP.  TIME  P.  M. 

PROPORTIONAL  PARTS  FOR  SECONDS.  1 

8. 

8. 

S. 

8. 

s. 

s. 

s. 

S. 

8. 

S. 

6. 

8. 

s. 

S.   S.    d.   1 

M. 

0 

10 

20 

30 

40 

50 

60 

1 

2 

3 

4 

5 

6 

7 

8   9 

0 

J. 69897 

69929 

69960 

69992 

70023 

70055 

70086 

59 

3 

6 

9 

13 

16 

19 

22 

25  28 

1 

70086 

70118 

70149 

70180 

7021V70243 

70274 

58 

3 

6 

9 

13 

16 

19 

22 

25  28 

( 

2 

70274 

70306 

70337 

70368 

7039?  ■'^431 

70462 

57 

3 

6 

9 

13 

16 

19 

22 

25 

28 

• 

3 

70462 

70493 

70524 

70555 

70586 

7v.617 

70648 

56 

3 

6 

9 

12 

15 

19 

22 

25 

28 

4 

70648 

70680 

70710 

70741 

70772 

70803 

70834 

55 

3 

6 

9 

12 

15 

19 

22 

25 

28 

5 

9.70834 

70865 

70896 

70927 

70958 

70988 

71019 

54 

3 

6 

9 

12 

15 

19 

22 

25 

28 

6 

71019 

71050 

71081 

71111 

71142 

71173 

71203 

53 

3 

6 

9 

12 

15 

19 

22 

25 

28 

7 

71203 

71234 

71265 

71295 

71326 

71356 

71387 

52 

3 

6 

9 

12 

15 

18 

21 

24 

27 

8 

71387 

71417 

71448 

71478 

71509 

71539 

71569 

51 

3 

6 

9 

12 

15 

18 

21 

24 

27 

9 
10 

71569 

71600 

71630 

71660 

71691 

71721 

71751 

50 

3 

6 

9 

12 

15 

18 

21 

24 

27 

9.71751 

71781 

71812 

71842 

71872 

71902 

71932 

49 

3 

6 

9 

12 

15 

18 

21 

24 

27 

11 

71932 

71962 

71992 

72022 

72052 

72082 

72112 

48 

3 

6 

9 

12 

15 

18 

21 

24 

27 

12 

72112 

72142 

72172 

72202 

72232 

72262 

72292 

47 

3 

6 

9 

12 

15 

18 

21 

24 

27 

13 

72292 

72322 

72352 

72381 

72411 

72441 

72471 

46 

3 

6 

9 

12 

15 

18 

21 

24 

27 

14 

72471 

72500 

72530 

72560 

72589 

72619 

72648 

45 

3 

6 

9 

12 

15 

18 

21 

24 

27 

15 

9.72648 

72678 

72708 

72737 

72767 

72796 

72825 

44 

3 

6 

9 

12 

15 

18 

21 

24 

27 

16 

72825 

72855 

72884 

72914 

72943 

72972 

73002 

43 

3 

6 

9 

12 

15 

18 

21 

24 

27 

17 

73002 

73031 

73060 

73090 

73119 

73148 

73177 

42 

3 

6 

9 

12 

14 

17 

20 

23 

26 

18 

73177 

73207 

73236 

73265 

73294 

73323 

73352 

41 

3 

6 

9 

12 

14 

17 

20 

23 

26 

19 

73352 

73381 

73410 

73439 

73468 

73497 

73526 

40 

3 

6 

9 

12 

14 

17 

20 

23 

26 

20 

9.73526 

73555 

73584 

73613 

73642 

73671 

73699 

39 

3 

6 

9 

12 

14 

17 

20 

23 

26 

21 

73699 

73728 

73757 

73786 

73815 

73843 

73872 

38 

3 

6 

9 

11 

14 

17 

20 

23 

26 

22 

73872 

73901 

73929 

73958 

73987 

74015 

74044 

37 

3 

6 

9 

11 

14 

17 

20 

23 

26 

23 

74044 

74072 

74101 

74129 

74158 

74186 

74215 

36 

3 

6 

9 

11 

14 

17 

20 

23 

26 

24 

74215 

74243 

74272 

74300 

74328 

74357 

74385 

35 

3 

6 

9 

11 

14 

17 

20 

23 

26 

25 

9.74385 

74413 

74442 

74470 

74498 

74526 

74554 

34 

3 

6 

8 

11 

14 

17 

20 

22 

25 

26 

74554 

74583 

74611 

74639 

74667 

74695 

74723 

33 

3 

6 

8 

11 

14 

17 

20 

22 

25 

27 

74723 

74751 

74779 

74807 

74835 

74863 

74891 

32 

3 

6 

8 

11 

14 

17 

20 

22 

25 

28 

74891 

74919 

74947 

74975 

75003 

75031 

75059 

31 

3 

6 

8 

11 

14 

17 

20 

22 

25 

29 

75059 

75086 

75114 

75142 

75170 

75197 

75225 

30 

3 

6 

8 

11 

14 

17 

20 

22 

25 

30 

9.75225 

75253 

75280 

75308 

75336 

75363 

75391 

29 

3 

5 

8 

11 

14 

16 

19 

22 

25 

31 

75391 

75418 

75446 

75474 

75501 

75528 

75556 

28 

3 

5 

8 

11 

14 

16 

19 

22 

25 

32 

75556 

75583 

75611 

75638 

75666 

75693 

75720 

27 

3 

5 

8 

11 

14 

16 

19 

22 

25 

33 

75720 

75748 

75775 

75802 

75830 

75857 

75884 

26 

3 

5 

8 

11 

14 

16 

19 

22 

25 

34 

75884 

75911 

75938 

75966 

75993 

76020 

76047 

25 
24 

3 

5 

8 

11 

14 

16 

19 

22 
22 

24 

24 

35 

9.76047 

76074 

76101 

76128 

76155 

76182 

76209 

3 

5 

8 

11 

14 

16 

19 

36 

76209 

76236 

76263 

76290 

76317 

76344 

76371 

23 

3 

5 

8 

11 

14 

16 

19 

22 

24 

37 

76371 

76397 

76424 

76451 

76478 

76505 

76531 

22 

3 

5 

8 

11 

14 

16 

19 

21 

24 

38 

76531 

76558 

76585 

76611 

76638 

76665 

76691,  21 

3 

5 

8 

11 

14 

16 

19 

21 

24 

39 

76691 

76718 

76745 

76771 

76798 

76824 

76851 

20 

3 

5 

8 

11 

13 

16 

19 

21 

24 

40 

9.76851 

76877 

76904 

76930 

76957 

76983 

77009 

19 

3 

5 

8 

11 

13 

16 

18 

21 

24 

41 

77009 

77036 

77062 

77089 

77115 

77141 

77167 

18 

3 

5 

8 

11 

13 

16 

18 

21 

24 

42 

77167 

77194 

77220 

77246 

77272 

77298 

77325 

17 

3 

5 

8 

10 

13 

16 

18 

21 

24 

43 

77325 

77351 

77377 

77«)3 

77429 

77455 

77481 

16 

3 

5 

8 

10 

13 

16 

18 

21 

24 

44 

77481 

77507 

77533 

77  59 

77585 

77611 

77637 

15 

3 

t. 

8 

10 

13 

16 

18 

21 

23 

45 

9.77637 

77663 

77689 

77715 

77741 

77766 

77792 

14 

3 

8 

10 

13 

15 

18 

21 

23 

46 

77792 

77818 

77844 

77870 

77895 

77921 

77947 

13 

3 

8 

10 

13 

15 

18 

21 

23 

47 

77947 

77972 

77998 

78024 

78049 

78075 

78101 

12 

3 

t 

8 

10 

13 

1^  18 

21|  23 

48 

78101 

78126 

78152 

78177 

78203 

78228 

78254 

11 

3 

«. 

•   8 

Id  13!  1.^  18 

20  23 

49 

78254 

78279 

78305 

78330 

7835S 

78381 

78406 

10 

3 

«. 

8 

10 

13 

15 

18 

20 

23 

50 

9.78406 

78431 

78457 

78482 

78507 

78533 

78558 

9 

3 

8 

IC 

13 

15 

17 

20 

23 

51 

78558 

78583 

78608 

78633 

78659 

78684 

78709 

8 

3 

tJ 

IC 

13 

15 

17 

20 

23 

52 

78709 

78734 

78759 

78784 

78809 

78834 

78859 

7 

3 

IC 

13 

15 

17 

20 

23 

53 

78859 

78884 

78909 

78934 

78959 

78984 

79009 

6 

3 

A 

10  13 

15 

17 

20 

23 

54 

79009 

79034 

79059 

79084 

79108 

79133 

79158 

!   5 

2 

*- 

IC 

18 

15 

17 

20 

23 

55 

9.7915? 

79183 

7920S 

79232 

79257 

79282 

79306 

.   4 

2 

IC 

13 

15 

17 

20 

23 

56 

79306 

79331 

79356 

79380 

79405 

79430 

79454 

[      3 

2 

IC 

13 

15 

17 

2(1 

22 

57 

79454 

[  79479 

79503 

79528 

79552 

79577 

79601 

2 

2 

f 

IC 

1  12 

15 

17 

20 

22 

58 

79601 

79626 

7965C 

79674 

79699 

79723 

79747 

1 

2 

ft 

IC 

12 

15 

11 

2C 

22 

59 

79747 

79772 

79796 

79821 

79845 

79869 

79893 

0 

2 

( 

IC 

12 

15 

11 

2C 

22 

60.'5. 

50s. 

40s. 

30s. 

20s. 

10s. 

Os. 

M. 

Is. 

2s. 

3s. 

4s. 

5s. 

6s. 

7s. 

8s. 

9s. 

5  OR  17  HOURS,  OR  APP.  TIME  A.  M. 

_ 

PRC 

)POK 

TIONAL  PARTS  FOR  SECONDS 

TABLE  XXIX. 

123   1 

LOGARITHMS  OF  THE  APPARENT  TIME,  OR  HOUR  ANGLE. 

HOUR  ANGLE,  7  HOURS,  OR  APP.  TIME  P.  M. 

PROPORTIONAL  PARTS  FOR  SECONDS.  1 

0. 

S. 

8. 

8. 

8. 

8. 

8. 

8. 

8. 

8. 

8. 

8. 

8. 

8. 

8. 

8. 

M. 

0 

10 

20 

30 

40 

50 

60 

1 

2 

3 

4 

5 

6 

7 

8 

9 

0  i 

). 79893 

79918 

79942 

79966 

79990 

80014 

80038 

59 

2 

5 

7 

10 

12 

14 

17 

19 

22 

1 

80038 

80063 

80087 

80111 

80135 

80159 

80183 

58 

2 

5 

7 

10 

12 

14 

17 

19 

22 

2 

80183 

80207 

80231 

80255 

80279 

80303 

80327 

57 

2 

5 

7 

10 

12 

14 

17 

19 

22 

3 

80327 

80350 

80374 

80398 

80422 

80446 

80470 

56 

2 

5 

7 

10 

12 

14 

17 

19 

22 

4 

80470 

80494 

80517 

80541 

80565 

80588 

80612 

55 

2 

5 

7 

9 

12 

14 

16 

19 

21 

5 

3.80612 

80636 

80660 

80683 

80707 

80730 

80754 

54 

2 

5 

7 

9 

12 

14 

16 

19 

21 

6 

80754 

80778 

80801 

80825 

80848 

80872 

80895 

53 

2 

5 

7 

9 

12 

14 

16 

19 

21 

7 

80895 

80919 

80942 

80966 

80989 

81012 

81036 

,52 

2 

5 

7 

9 

12 

14 

16 

19 

21 

8 

81036 

81059 

81082 

81106 

81129 

81152 

81176 

51 

2 

5 

7 

9 

11 

14 

16 

18 

21 

9 

81176 

81199 

81222 

81245 

81269 

81292 

81315 

50 

2 

5 

7 

9 

11 

14 

16 

18 

21 

10 

9.81315 

81338 

81361 

81384 

81407 

81430 

81454 

49 

2 

5 

7 

9 

11 

14 

16 

18 

21 

11 

81454 

81477 

81500 

81523 

81546 

81569 

81592 

48 

2 

5 

7 

9 

11 

14 

16 

18 

21 

12 

81592 

81614 

81637 

81660 

81683 

81706 

81729 

47 

2 

5 

7 

9 

11 

14 

16 

18 

21 

13 

81729 

81752 

81775 

81797 

81820 

81843 

81866 

46 

2 

5 

7 

9 

11 

14 

16 

18 

21 

1 

14 

81866 

81888 

81911 

81934 

81956 

81979 

82002 

45 

2 

5 

7 

9 

11 

14 

16 

18 

20 

15 

9.82002 

82024 

82047 

82070 

82092 

82115 

82137 

44 

2 

5 

7 

9 

11 

14 

16 

18 

20 

, 

16 

82137 

82160 

82182 

82205 

82227 

82250 

82272 

43 

2 

5 

7 

9 

11 

14 

16 

18 

20 

17 

82272 

82294 

82317 

82339 

82362 

82384 

82406 

42 

2 

5 

7 

9 

11 

14 

16 

18 

20 

18 

82406 

82429 

82451 

82473 

82495 

82518 

82540 

41 

2 

5 

7 

9 

11 

14 

16 

18 

20 

19 

82540 

82562 

82584 

82606 

82629 

82651 

82673 

40 

2 

4 

7 

9 

11 

13 

15 

18 

20 

20 

9.82673 

82695 

82717 

82739 

82761 

82783 

82805 

39 

2 

4 

7 

9 

11 

13 

15 

18 

20 

21 

82805 

82827 

82849 

82871 

82893 

82915 

82937 

38 

2 

4 

7 

9 

11 

13 

15 

18 

20 

22 

82937 

82959 

82981 

83003 

83025 

83046 

83068 

37 

2 

4 

7 

9 

11 

13 

15 

18 

20 

23 

83068 

83090 

83112 

83134 

83155 

83177 

83199 

36 

2 

4 

7 

9 

11 

13 

15 

18 

20 

24 

83199 

83220 

83242 

83264 

83285 

83307 

83329 

35 

2 

4 

6 

9 

11 

13 

15 

17 

19 

25 

9.83329 

83350 

83372 

83393 

83415 

83436 

83458 

34 

2 

4 

6 

9 

11 

13 

15 

17 

19 

26 

83468 

83479 

83501 

83522 

83544 

83565 

83587 

33 

2 

4 

6 

9 

11 

13 

15 

17 

19 

27 

83587 

83608 

83629 

83651 

83672 

83694 

83715 

32 

2 

4 

6 

9 

11 

13 

15 

17 

19 

28 

83715 

83736 

83757 

83779 

83800 

83821 

83842 

31 

2 

4 

6 

9 

11 

13 

15 

17 

19 

29 

83842 

83864 

83885 

83906 

83927 

83948 

83969 

30 

2 

4 

6 

8 

11 

13 

15 

17 

19 

30 

9.83969 

83990 

84011 

84033 

84054 

84075 

84096 

29 

2 

4 

6 

8 

11 

13 

15 

17 

19 

31 

84096 

84117 

84138 

84159 

84179 

84200 

84221 

28 

2 

4 

6 

8 

11 

13 

15 

17 

19 

32 

84221 

84242 

84263 

84284 

84305 

84326 

84346 

27 

2 

4 

6 

8 

11 

13 

15 

17 

19 

33 

84346 

84367 

84388 

84409 

84430 

84450 

84471 

26 

2 

4 

6 

8 

11 

13 

15 

17 

19 

34 

84471 

84492 

84512 

84533 

84554 

84574 

84595 

25 

2 

4 

6 

8 

10 

12 

14 

16 

18 
18 

35 

9.84595 

84616 

84636 

84657 

84677 

84698 

84718 

24 

2 

4 

6 

8 

10 

12 

14 

16 

36 

84718 

84739 

84759 

84780 

84800 

84821 

84841 

23 

2 

4 

6 

8 

10 

12 

14 

16 

18 

37 

84841 

84861 

84882 

84902 

84923 

84943 

84963 

22 

2 

4 

6 

8 

10 

12 

14 

16 

18 

38 

84963 

84984 

85004 

85024 

85044 

85065 

85085 

21 

2 

4 

6 

8 

10 

12 

14 

16 

18 

39 

85085 

85105 
85226 

85125 

85145 

85166 

85186 

85206 

20 

2 

4 

6 

8 

10 

12 

14 

16 

18 

40 

9.85206 

85246 

85266 

85286 

85306 

85326 

19 

2 

4 

6 

8 

10 

12 

14 

16 

18 

41 

85326 

85346 

85366 

85386 

85406 

85426 

85446 

18 

2 

4 

6 

8 

10 

1§ 

14 

16 

18 

42 

85446 

85466 

85486 

85506 

85526 

85546 

85565 

17 

2 

4 

6 

8 

10 

12 

14 

16 

18 

43 

85565 

85585 

85605 

85625 

85645 

85664 

85684 

16 

2 

4 

6 

8 

10 

12 

14 

16 

18 

44 

85684 

85704 

85724 

85743 

85763 

85783 

85802 

15 

2 

4 

6 

8 

10 

12 

14 

16 

18 

45 

9.85802 

85822 

85841 

85861 

85881 

85900 

85920 

14 

2 

A 

6 

8 

10 

12 

14 

16 

18 

46 

85920 

85939 

85959 

85978 

85998 

86017 

86037 

13 

2 

4 

[       6 

fl 

10 

12 

14 

16 

18 

47 

86037 

8605fc 

86076 

86095 

86114 

86134 

86153 

12 

2 

4 

[      6 

S 

IC 

12 

14 

16 

18 

48 

86153 

86172 

86192 

86211 

8623C 

8625C 

86269 

11 

2 

4 

[      6 

8 

10 

12 

14 

16 

18 

49 

86269 

8628S 

86307 

86327 

86346 

86365 

86384 

[    10 

2 

4 

[      6 

? 

IC 

12 

14 

16 

18 

50 

9.86384 

86403,  8642.'^ 

86442 

86461 

8648C 

1  86499 

9 

2 

'      4 

i 

9 

11 

13 

15 

i7 

51 

86499 

8651S 

86537 

86556 

8657t 

i  86594 

[  8661S 

8 

2 

4 

.   S 

9 

11 

13 

15 

17 

52 

86613 

86632 

86651 

86670 

8668C 

1  8670J 

!  86727 

7 

2 

!  4 

;  8 

9 

11 

13 

15 

17 

53 

86727 

8674f 

86764 

[  86783 

86802 

!  86821 

8684C 

)   6 

2 

!  4 

)   ? 

S 

11 

13 

15 

17 

54 

55 

8684C 

8685S 

!  86877 

86896 

8691^ 

)  8693c 

86952 

!   5 

2 

!   4 

1   8 

!   9 

11 

13 

15 

17 

9.8695S 

!  86971 

8699C 

)  87008 

87027 

8704f 

i  87064 

I   4 

2 

!   4 

;  8 

!   9 

11 

13 

15 

17 

56 

87064 

[  8708r 

87101 

87120 

8713E 

!  87157 

87175 

i   3 

2 

'  4 

;  7 

9 

11 

Ic 

15 

17 

57 

8717f 

)  87194 

[  87212 

!  87231 

8724£ 

1  8726J 

!  87286 

)   2 

2 

4 

.   7 

9 

11 

IS 

15 

17 

58 

8728( 

)  8730^ 

)  8732c 

I  87341 

8736C 

I  8737S 

87396 

;  1 

2 

4 

.   7 

9 

11 

Vc 

!  15 

.  17 

59 

8739f 

i  8741^ 

)  8743c 

I  87451 

8747C 

I  8748? 

!  87506 

0 

2 

4 

;  1 

c 

1  11 

U 

!  15 

i  17 

605. 

50s. 

40s. 

308. 

208. 

10s. 

Os. 

M. 

Is. 

2s. 

3s. 

4&. 

5s. 

6s. 

7s. 

8s. 

9s. 

4  OR  16  HOURS,  OR  APP.  TIME  A.  M. 

PROPORTIONAL  PARTS  F 

OR  i 

3ECOND8.  1 

124                 TABLE  XXIX. 

n 

LOGARITHMS  OF  THE  APPARENT  TIME,  OR  HOUR  ANGLE. 

1 

HOUR  AN&I.B,  8  HOURS,  OR  APP.  TIME  P.  M. 

PROPORTIONAL  PARTS  FOR  SECONDS.  | 

8. 

■'  ■ 

s. 

8. 

8. 

6. 

8. 

s. 

S.    8. 

8. 

8. 

8. 

s. 

a   a  1 

M. 

0 

IJ 

20 

30 

40 

50 

60 

1 

2   3 

4 

5 

6 

7 

8 

' 

0 

9.87506 

87524 

87543 

87561 

87579 

87597 

87615 

o9 

2 

4   5 

7 

9 

11 

13 

14 

16  1 

1 

87615 

87633 

87652 

87670 

87688 

87706 

87724 

58 

2 

4   5 

7 

9 

11 

13 

14 

16 

2 

87724 

87742 

87760 

87778 

87796 

87814 

87832 

57 

2 

4   5 

7 

9 

11 

13 

14 

16 

3 

87832 

87850 

87868 

87886 

87904 

87921 

87939 

56 

2 

4   5 

7 

9 

11 

13 

14 

16 

4 

87939 

87957 

87975 

87993 

88011 

88028 

88046 

55 

2 

4   5 

7 

9 

11 

13 

14 

16 

5 

9.88046 

88064 

88082 

88100 

88117 

88135 

88153 

54 

2 

4   5 

7 

9 

11 

13 

14 

16 

6 

88153 

88170 

88188 

88206 

88223 

88241 

88259 

53 

2 

3   5 

7 

9 

11 

12 

14 

16 

7 

88259 

88276 

88294 

88311 

88329 

88346 

88364 

52 

2 

3   5 

7 

9 

11 

12 

14 

16 

8 

88364 

88381 

88399 

88416 

88434 

88451 

88469 

51 

2 

3   5 

7 

9 

11 

12 

14 

16 

9 

88469 

88486 

88503 

88521 

88538 

88556 

88573 

50 

2 

3   5 

7 

9 

11 

12 

14 

16 

10 

9.88573 

88590 

88607 

88625 

88642 

88659 

88677 

49 

2 

3   5 

7 

8 

10 

12 

14 

15 

11 

88677 

88694 

88711 

88728 

88745 

88763 

88780 

48 

2 

3   5 

■  7 

8 

10 

12 

14 

15 

12 

88780 

88797 

88814 

88831 

88848 

88865 

88882 

47 

2 

3   5 

7 

8 

10 

12 

14 

15 

13 

88882 

88899 

88916 

88933 

88950 

88967 

88984 

46 

2 

3   5 

7 

8 

10 

12 

14 

15 

14 

88984 

89001 

89018 

89035 

89052 

89069 

89086 

45 
44 

2 

3   5 

7 

8 

10 

12 

14 

15 

15 

9.89086 

89103 

89120 

89137 

89153 

89170 

89187 

2 

3   5 

7 

8 

10 

12 

14 

15 

16 

89187 

89204 

89221 

89237 

89254 

89271 

89287 

43 

2 

3   5 

7 

8 

10 

12 

14 

15 

17 

89287 

89304 

89321 

89338 

89354 

89371 

89387 

42 

2 

3   5 

7 

8 

10 

12 

14 

15 

18 

89387 

89404 

89421 

89438 

89454 

89470 

89487 

41 

2 

3   5 

7 

8 

10 

12 

13 

15 

19 

89487 

89503 

89520 

89536 

89553 

89569 

89586 

40 

2 

3   5 

7 

8 

10 

12 

13 

15 

20 

9.89586 

89602 

89619 

89635 

89651 

89668 

89684 

39 

2 

3   5 

7 

8 

16 

12 

13 

15 

21 

89684 

89701 

89717 

89733 

89749 

89766 

89782 

38 

2 

3   5 

7 

8 

10 

12 

13 

15 

22 

89782 

89798 

89815 

89831 

89847 

89863 

89879 

37 

2 

3   5 

7 

8 

10 

12 

13 

15 

23 

89879 

89896 

89912 

89928 

89944 

89960 

89976 

36 

2 

3   5 

6 

8 

10 

11 

13 

14 

24 

89976 

89992 

90008 

90024 

90040 

90056 

90072 

35 

2 

3   5 

6 

8 

10 

11 

13 

14 

25 

9.90072 

90088 

90104 

90120 

90136 

90152 

90168 

34 

2 

3   5 

6 

8 

10 

11 

13 

14 

26 

90168 

90184 

90200 

90216 

90232 

90248 

90263 

33 

2 

3   5 

6 

8 

10 

11 

13 

14 

27 

90263 

90279 

90295 

90311 

90327 

90342 

90358 

32 

2 

3   5 

6 

8 

10 

11 

13 

14 

28 

90358 

90374 

90390 

90405 

90421 

90437 

90452 

31 

2 

3   5 

6 

8 

10 

11 

13 

14 

29 

90452 

90468 

90484 

90499 

90515 

90531 

90546 

30 

2 

3   5 

6 

8 

10 

11 

13 

14 

30 

(.90546 

90562 

90577 

90593 

90608 

90624 

90639 

29 

2 

3   5 

6 

8 

9 

11 

12 

14 

31 

90639 

90655 

90670 

90686 

90701 

90717 

90732 

28 

2 

3   5 

6 

8 

9 

11 

12 

14 

32 

90732 

90747 

90763 

90778 

90794 

90809 

90824 

27 

2 

3   5 

6 

8 

9 

11 

12 

14 

33 

90824 

90840 

90855 

90870 

90885 

90901 

90916 

26 

2 

3   5 

6 

8 

9 

11 

12 

14 

34 

90916 

9093) 

90946 

90961 

90977 

90992 

91007 

25 

2 

3   5 

6 

8 

9 

11 

12 

14 

35 

9.91007 

91022 

91037 

91052 

91067 

91083 

91098 

24 

2 

3   4 

6 

7 

9 

10 

12 

14 

36 

91098 

91113 

91128 

91143 

91158 

91173 

91188 

23 

2 

3   4 

6 

7 

9 

10 

12 

14 

37 

91188 

91203 

91218 

91233 

91248 

91262 

91277 

22 

2 

3   4 

6 

7 

9 

10 

12 

14 

38 

91277 

91292 

91307 

91322 

91337 

91352 

91367 

21 

2 

3   4 

6 

7 

9 

10 

12 

14 

39 

91367 

91381 

91396 

91411 

91426 

91440 

91455 

20 

2 

3   4 

6 

7 

9 

10 

12 

14 

40 

9.91455 

91470 

91485 

91499 

91514 

91529 

91543 

19 

3   4 

6 

7 

9 

10 

12 

13 

41 

91543 

91558 

91573 

91587 

91602 

91616 

91631 

18 

3   4 

6 

7 

9 

10 

12 

13 

42 

91631 

91645 

91660 

91674 

91689 

91703 

91718 

17 

3   4 

6 

7 

9 

10 

12 

13 

43 

91718 

91732 

91747 

91761 

91776 

91790 

91805 

16 

3   4 

6 

7 

9 

10 

12 

13 

44 

91805 

91819 

91833 

91848 

91862 

91876 

91891 

15 

— V, 

3   4 

6 

7 

9 

10 

12 

13 

45 

9  9i?91 

91905 

91919 

91934 

91948 

91962 

91976 

14 

1   3   4 

6 

7 

8 

10 

11 

13 

46 

91976 

91991 

92005 

92019 

92033 

92047 

92061 

13 

3   4 

6 

7 

8 

10 

11 

13 

47 

92061 

92076 

92090 

92104 

92118 

92132 

92146 

12 

3   4 

6 

7 

8 

10 

11 

13 

48 

92146 

92160 

92174 

92188 

92202 

92216 

92230 

11 

3   4 

6 

7 

8 

10 

11 

13 

49 

92230 

92244 

92258 

92272 

92286 

92300 

92314 

10 

3   4 

6 

7 

8 

10 

11 

13 

50 

9.92314 

92328 

92342 

92355 

92369 

92383 

92397 

9 

3   4 

6 

7 

8 

10 

11 

13 

51 

92397 

92411 

92425 

92438 

92452 

92466 

92480 

8 

3   4 

6 

7 

8 

10 

11 

13 

52 

92480 

92493 

92507 

92521 

92534 

92548 

92562 

7 

3   4 

5 

7 

8 

9 

11 

12 

53 

92562 

92575 

92589 

92603 

92616 

92630 

92643 

6 

3   4 

5 

7 

8 

9 

11 

12 

54 
55 

92643 

92657 

92670 

92684 

92698 

92711 

92725 

5 
4 

3   4 

5 

7 

8 

9 

11 

12 

9.92725 

92738 

92751 

92765 

92778 

92792 

92805 

3   4 

5 

7 

8 

9 

11 

12 

56 

92805 

92819 

92832 

92845 

92859 

92872 

92885 

3 

3   4 

5 

7 

8 

9 

11 

12 

57 

92885 

92899 

92912 

92925 

92939 

92952 

92965 

2 

3   4 

5 

7 

8 

9 

11 

12 

58 

92965 

92978 

92992 

93005 

93018 

93031 

93044 

1 

3   4 

5 

7 

8 

9 

10 

12 

59 

93044 

93057 

93071 

)30S!4 

93097 

93110 

93123 

0 

3   4 

2s.  3s. 

5 

7 

8 

9 

10 

12 

- 

60s. 

508. 

40s. 

30s. 

20s. 

10s. 

Os. 

M. 

Is. 

4s. 

5s. 

6s. 

78. 

8s. 

9s. 

3  OR  15  HOURS,  OR  APP.  TIME  A.  M.        | 

PRC 

►  PORTION 

AL 

PARTS  FOR  S 

ECONDS.  1 

126 

TABLE  XXX. 

FOR  CORRECTING  THE  LONGITUDE  BY  CHRONOMETER  FR  JM  THE  EFFECT  OF  AN 

ERROR  IN  THE  LATITUDE  USED  IN  FINDING  THE  TIME. 

TABLE   A. 

EitUr  this  Table  %nth  the  Latitude  worked  with  at  the  Side,  and  the  Hour  Angle  at  the  Tap. 

(See  explanation  of  this  Table  at  page  144.)                                                                1 

Lat. 

HOUR    ANOLK. 

HOUR    ANOLE. 

HOUR    ANGLE. 

HOUR.    AN. 

B.    A 

H.    U. 

H.    U 

H.    H 

H.    H 

H.    M 

H.    M. 

H.    H 

H.    M 

H.    M 

H.    U 

H.    M. 

H.    H 

H.    H 

H.    M 

H.    M. 

H.    H 

H.    M. 

H.    11. 

D.R. 

1        0 

1    10 

1   20 

1   30 

1   40 

1   50 

2     0 

2    10 

2  20 

2  30 

2  45 

3       0 

3    15 

3  30 

3  45 

4     0 

4  30 

5     0 

o 

'        // 

/       n 

'      n 

/      // 

/      // 

^      // 

1      n 

/       n 

t       n 

1      n 

*       n 

t        tl 

/      // 

r       tl 

1      tl 

/      II 

1     tl 

t      tl 

2 

0.    8 

0.   7 

0.    6 

0.   5 

0.   4 

0.   4 

0.    4 

0.    3 

0.    3 

0.    2 

0.    2 

0.    2 

0.    2 

0.    1 

0.    1 

0.    1 

0.   0 

0.   0 

4 

0.15 

0.13 

0.12 

0.10 

0.   9 

0.   8 

0.    7 

0.    7 

0.    b 

0.    5 

0.    5 

0.   4 

0.    4 

0.    3 

0.    2 

0.   2 

0.   2 

0.    1 

6 

0.23 

0.20 

0.17 

0.15 

0.13 

0.12 

0.10 

0.10 

0.    9 

0.   8 

0.    7 

0.    7 

0.   6 

0.    5 

0.    4 

0.    3 

0.   2 

0.   2 

8 

0.31 

0.27 

0.23 

0.20 

0.18 

0.16 

0.14 

0.13 

0.12 

0.11 

0.10 

0.    9 

0.    8 

0.   7 

0.    6 

0.    5 

0.    4 

0.   3 

10 

0.40 

0.34 

0.29 

0.25 

0.22 

0.20 
0.25 

0.18 

0.16 

0.15 

0.14 

0.12 

0.11 

0.   9 

0.    8 

0.    7 

0.   6 

0.    5 

0.   3 

12 

0.47 

0.40 

0.35 

0.31 

0.28 

0.22 

0.20 

0.18 

0.16 

0.14 

0.13 

0.11 

0.10 

0.   8 

0.    7 

0.    5 

0,   4 

14 

0.56 

0.47 

0.41 

0.36 

0.32 

0.29 

0.26 

0.23 

0.21 

0.19 

0.17 

0.15 

0.13 

0.11 

0.10 

0.   8 

0.   6 

0.   4 

16 

1.   4 

0.54 

0.47 

0.41 

0.37 

0.33 

0.29 

0.27 

0.25 

0.22 

0.19 

0.16 

0.15 

0.13 

0.11 

0.10 

0.    7 

0.   5 

18 

1.12 

1.   2 

0,53 

0.47 

0.41 

037 

0.34 

0.31 

0.28 

0.25 

0.22 

0.19 

0.17 

0.15 

0.13 

0.11 

0.   8 

0.   6 

20 

1.22 

1.   9 

1.   0 

0.53 

0.47 

0.43 

0.47 

0.38 

0.34 

0.31 

0.28 

0.25 

0.22 

0.19 

0.17 

0.15 

0.13 

0.   9 

0.   6 

22 

1.31 

1.17 

1.   7 

0.58 

0.52 

0.42 

0.38 

0.35 

0.32 

0.28 

0.24 

0.21 

0.19 

0.16 

0.14 

0.10 

0.   7 

24 

1.40 

1.25 

1.13 

1.   4 

0.57 

0.52 

0.46 

0.42 

0.38 

0.35 

0.31 

0.26 

0.23 

0.20 

0.18 

0.15 

0.11 

0.   7 

26 

1.49 

1.33 

1.20 

1.11 

1.   3 

0.56 

0.50 

0.46 

0.42 

0.38 

0.34 

0.29 

0.26 

0.22 

0.20 

0.17 

0.12 

0.   8 

28 

1.59 

1.41 

1.28 

1.17 

1.   8 

1.    1 

0.55 

0.50 

0.46 

0.41 

0.37 

0.32 

0.28 

0.25 

0.22 

0.19 

0.13 

0.    8 

30 

2.    9 

1.50 

1.35 

1.23 

1.14 

1.    7 

1.    0 

0.54 

0.49 

0.45 

0.39 

0.34 

0.31 

0.26 

0.23 

0.20 

0.14 

0.   9 

32 

2.19 

1.59 

1.43 

1.31 

1.20 

1.12 

1.   5 

0.59 

0.53 

0.49 

0.43 

0.37 

0.33 

0.27 

0.25 

0.22 

0.16 

0.10 

34 

2.31 

2.   8 

1.51 

1.30 

1.27 

1.18 

1.10 

1.   4 

0.58 

0.53 

0.46 

0.40 

0.35 

0.31 

0.27 

0.23 

0.17 

0.11 

36 

2.43 

2.18 

2.   0 

1.45 

1.34 

1.24 

1.16 

1.   8 

1.    2 

0.57 

0.59 

0.43 

0.38 

0.34 

0.29 

0.25 

0.18 

0.11 

38 

2.55 

2.29 

2.   9 

1.53 

1.41 

1.30 

1.21 

1.14 

1.   7 

1.    1 

0.53 

0.47 

0.41 

0.36 

0.31 

0.27 

0.19 

0.13 

40 

3.    8 

2  40 

2.19 

2.   2 

1.48 

1.37 

1.27 

1.19 

1.12 

1.    5 

0.57 

O.50 

0.44 

0.39 

0.34 

0.29 

0.21 

0.13 

42 

3.22 

2.52 

2.28 

2.10 

1.56 

1.44 

1.34 

1.25 

1.17 

1.10 

1.    1 

0.54 

0.47 

0.41 

0.36 

0.31 

0.22 

0.14 

44 

3.36 

3.   4 

2.39 

2.20 

2   .4 

1.52 

1.40 

1.31 

1.23 

1.16 

1.    6 

0.58 

0.51 

0.44 

0.39 

0.34 

0.24 

0.16 

46 

3.51 

3.16 

2.5a 

2.30 

2.13 

1.59 

1.47 

1.38 

1.29 

1.21 

1.11 

1.   2 

0.55 

0.47 

0.41 

0.36 

0.25 

0.17 

48 

3.31 

3.    3 

2.41 

2.23 

2.    8 

1.55 

1.44 

1.35 

1.27 

1.16 

1.    7 

0.58 

0.51 

0.44 

0.38 

0.28 

0.18 

50 

3.16 

2.53 

2.34 

2.17 

2.   4 

1.52 

1.43 

1.34 

1.21 

1.11 

1.    3 

0.56 

0.47 

0.41 

0.29 

0.19 

52 

3.   5 

2.44 

2.281 

2.13 

2.   0 

1.50 

1.40 

1.28 

1.17 

1.   7 

0.59 

0.51 

0.44 

0.32 

0.20 

54 

3.19 

2.57 

2.38, 

2.23 

2.10 

2.58 

1.48 

1.34 

1.23 

1.13 

1.   3 

0.65 

0.47 

0.34 

0.22 

56 

3.35 

3.11 

2.50 

2.34 

2.20 

2.    7 

1.56 

1.41 

1.29 

1.18 

1.   8 

0.59 

0.51 

0.37 

0.24 

58 

3.52 

3.26 

3.   4 

2.44 

2.31 

2.17 

2.    5 

1.49 

1.36 

1.24 

1.14 

1.   4 

0.55 

0.40 

0.26 

60 

4.10 

3.43 

3.20 

3.   0 

2.43 

2.29 

2.16 

1.58 

1.44 

1.31 

1.20 

1.10 

1.   0 

0.43 

0.28 

62 

/ 

4.   2 

3.37 

3.14 

2.57 

2.39 

2.27 

2.    8 

1.63 

1.39 

1.26 

1.16 

1.   5 

0.47 

0.30 

64 

3.56 

3.33 

3.13 

2.56 

2.40 

2.20 

2.   3 

1.58 

1.34 

1.22 

1.11 

0.51 

0.33 

66 

3.53 

3.32 

3.13 

2.56 

2.34 

2.15 

1.58 

1.43 

1.30 

1.18 

0.56 

0.36 

68 

1          1 

3.53 

3.32 

3.14 

2.49 

2.28 

2.10 

1.54 

1.39 

1.26 

1.    1 

0.40 

TABLE   B. 

ErUer  this  Table  with  the  Declination  at  the  Side,  and  the  Hour  Angle  at  the  Top. 

Dbo. 

HOOK    ANOLB. 

HOUR    ANOLE. 

HOUR    ANOLE. 

HOUR    AN. 

H.    A. 

H.    M. 

H.    M. 

H.    H. 

H.    H. 

H.    M. 

H.    M. 

H.    M. 

H.    M. 

H.    M. 

H.    M. 

H.    M. 

H.    M 

H.    M. 

H.    M. 

H.    M. 

H.    H. 

H.    M. 

H.    M 

1        0 

1    10 

1   20 

1   30 

1   40 

1   50 

2       0 

2   10 

2  20 

2  30 

2  45 

3       0 

3   15 

3  30 

3  45 

4       0 

4  30 

5     0 

0 

/      n 

f         M 

/      // 

t      n 

t      n 

t     tt 

f        ft 

t      n 

r       n 

/      tt 

/      tt 

/        tt 

t      tt 

t     It 

1     tt 

/        tl 

/      // 

1      n 

2 

0.    8 

0.   7 

0.    6 

0.   5 

0.   5 

0.   5 

0.   4 

0.   4 

0.   4 

0.04 

0.    3 

0.   3 

0.   3 

0.   2 

0.   2 

0.   2 

0.    2 

0.   2 

4 

0.16 

0.14 

0.12 

0.11 

0.10 

0.    9 

0.   8 

0.   8 

0.   7 

0.07 

0.   7 

0.    6 

0.    5 

0.   5 

0.   5 

0.    5 

0.    5 

0.   4 

6 

0.25 

0.21 

0.19 

0.16 

0.15 

0.14 

0.13 

0.12 

0.11 

0.10 

0.10 

0.   9 

0.   8 

0.    8 

0.   8 

0.    7 

0.    7 

0.   7 

8 

0.32 

0.28 

0.25 

0.22 

0.20 

0.18 

0.17 

0.16 

0.14 

0.14 

0.13 

0.12 

0.11 

0.11 

0.10 

0.10 

0.    9 

0.   9 

10 

0.41 

0.35 

0.31 

0.28 

0.25 

0.23 

0.21 

0.20 

0.19 

0.17 

3.16 
3.19 

0.15 

0.14 

0.13 

0.12 

0.12 

o.n 

0.11 

12 

0.49 

0.43 

0.37 

0.33 

0.30 

0.28 

0.25 

0.24 

0.22 

0.21 

0.18 

0.17 

0.16 

0.16 

0.15 

0.14 

0.13 

14 

0.58 

0.50 

0.44 

0.39 

0.35 

0.32 

0.30 

0.28 

0.26 

0.25 

0.23 

0.21 

0.20 

0.19 

0.18 

0.17 

0.16 

0.15 

16 

1.   7 

0.57 

0.50 

0.45 

0.41 

0.37 

0.34 

0.32 

0.30 

0.28 

3.26 

0.25 

0.23 

0.22 

0.21 

0.20 

0.19 

0.18 

18 

1.16 

1.   5 

0.57 

0.51 

0.46 

0.42 

0.39 

D.36 

0.34 

3.32 

3.29 

0.28 

0.26 

0.25 

0.23 

0.22 

0.21 

0.20 

20 

1.25 

1.13 

1.   4 

0.57 

0.52 

0.47 

0.44 

[).41 

D.38 

1.36( 

3.33 

0.31 

0.29 

0.28 

0.26 

0.25 

0.23 

0.22 

f 

22 

1.34 

1.20 

1.11 

1.   4 

0.58 

0.52 

0.49 

[).45 

').42( 

T.40( 

3.37 

0.34 

0.32 

0.31 

0.29 

0.28 

0.26 

0.25 

j 

24 

1.43 

1.27 

1.18 

1.11 

1.    4 

O.b;    0.54] 

T.49 

1.46 

1.44( 

3.41    0.37| 

0.35 

0.34 

0.32 

0.31 

0.29 

0.28 

126 

TABLE  XXXI. 

LOGARITHMS  OF  THE  APPARENT  DISTANCE 

APPARENT  DISTANCE, 

M. 

18» 

19° 

20° 

21° 

22° 

23° 

M. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Loy-.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S.  iLog.  T. 

0 

0.4900 

0.5118 

0.5126 

0.5370 

0.5341 

0.5611 

0.5543 

0.5842 

0.5736 

0.6064 

0.59190.6279 

0 

1 

4904 

5122 

5130 

5374 

5344 

5615 

5547 

5846 

5739 

6068 

5922 

6282 

1 

2 

4908 

5126 

5134 

5378 

5347 

5619 

5550 

5849 

5742 

6071 

5925 

6286 

2 

3 

4911 

5131 

5137 

538i- 

5351 

5622 

5553 

5853 

5745 

6075 

5928 

6289 

3 

4 

4915 

5135 

5141 

5386 

5354 

5626 

5556 

5857 

5748 

6079 

5931 

6293 

4 

5 

0.4919 

0.5139 

0.5145 

0.5390 

0.5358 

0.5630 

0.5560 

0.5861 

0.5751 

0.6082 

0.5934 

0.6296 

5 

6 

4923 

5143 

5148 

5394 

5361 

5634 

5563 

5864 

5754 

6086 

5937 

6300 

6 

7 

4927 

5148 

5152 

5398 

5365 

5638 

5566 

5868 

5758 

6090 

5940 

6303 

7 

8 

4931 

5152 

5156 

5402 

5368 

5642 

5570 

5872 

5761 

6093 

5943 

6307 

8 

9 

4935 

5156 

5159 

5407 

5372 

5646 

5573 

5876 

5764 

6097 

5945 

6310 

9 

10 

0.4939 

0.5161 

0.5163 

0.5411 

0.5375 

0.5650 

0.5576 

0.5879 

0.5767 

0.6100 

0.5948 

0.6314 

10 

11 

4942 

5165 

5167 

5415 

5379 

5654 

5579 

5883 

5770 

6104 

5951 

6317 

11 

12 

4946 

5169 

5170 

5419 

5382 

5658 

5583 

5887 

5773 

6108 

5954 

6321 

12 

13 

4950 

5173 

5174 

5423 

5385 

5662 

5586 

5891 

5776 

6111 

5957 

6324 

13 

14 

4954 

5178 

5177 

5427 

5389 

5665 

5589 

5894 

5779 

6115 

5960 

6328 

14 

15 

0.4958 

0.5182 

0.5181 

0.5431 

0.5392 

0.5669 

0.5592 

0.5898 

0.5782 

0.6118 

0.5963 

0.6331 

15 

16 

4962 

5186 

5185 

5435 

5396 

5673 

5596 

5902 

5785 

6122 

5966 

6334 

16 

17 

4965 

5190 

5188 

5439 

5399 

5677 

5599 

5906 

5789 

6126 

5969 

6338 

17 

18 

4969 

5195 

5192 

5443 

5402 

5681 

5602 

5909 

5792 

6129 

5972 

6341 

18 

19 

4973 

5199 

5196 

5447 

5406 

5685 

5605 

5913 

5795 

6133 

5975 

6345 

19 

20 

0.4977 

0.5203 

0.5199 

0.5451 

0.5409 

0.5689 

0.5609 

0.5917 

0.5798 

0.6136 

0.5978 

0.6348 

20 

21 

4981 

5207 

5203 

5455 

5413 

5693 

5612 

5921 

5801 

6140 

5981 

6352 

21 

22 

4984 

5212 

5206 

5459 

5416 

5696 

5615 

5924 

5804 

6144 

5984 

6355 

22 

23 

4988 

5216 

5210 

5463 

5420 

5700 

5618 

5928 

5807 

6147 

5987 

6359 

23 

24 

4992 

5220 

5213 

5467 

5423 

5704 

5621 

5932 

5810 

6151 

5990 

6362 

24 

25 

0.4996 

0.5224 

0.5217 

0.5471 

0.5426 

0.5708 

0.5625 

0.5935 

0.5813 

0.6154 

0.5992 

0.6366 

25 

26 

5000 

5228 

5221 

5475 

5430 

5712 

5628 

5939 

5816 

6158 

5995 

6369 

26 

27 

5003 

5233 

5224 

5479 

5433 

5716 

5631 

5943 

5819 

6162 

5998 

6373 

27 

28 

5007 

5237 

5228 

5483 

5436 

5720 

5634 

5947 

5822 

6165 

6001 

6376 

28 

29 

5011 

5241 

5231 

5487 

5440 

5724 

5638 

5950 

5825 

6169 

6004 

6380 

29 

*  30 

0.5015 

0.5245 

0.5235 

0.5491 

0.5443 

0.5727 

0.5641 

0.5954 

0.5828 

0.6172 

0.6^7 

0.6383 

30 

31 

5019 

5249 

5239 

5496 

5447 

5731 

5644 

5958 

5831 

6176 

6010 

6386 

31 

32 

5022 

5254 

5242 

5500 

5450 

5735 

5647 

5961 

5834 

6179 

6013 

6190 

32 

33 

5026 

5258 

5246 

5504 

5453 

5739 

5650 

5965 

5838 

6183 

6016 

6393 

33 

34 

5030 

5262 

5249 

5508 

5457 

5743 

5654 

5969 

5841 

6187 

6019 

6397 

34 

35 

0.5034 

0.5266 

0.5253 

0.5512 

0.5460 

0.5747 

0.5657 

0.5972 

0.5844 

0.6190 

0.6022 

0.6400 

35 

36 

5037 

5270 

5256 

5516 

5463 

5750 

5660 

5976 

5847 

6194 

6024 

6404 

36 

37 

5041 

5275 

5260 

5520 

5467 

5754 

5663 

5980 

5850 

6197 

6027 

6407 

37 

38 

5045 

5279 

5263 

5524 

5470 

5758 

5666 

5984 

5853 

6201 

6030 

6411 

38 

39 

5049 

5283 

5267 

5528 

5474 

5762 

5670 

5987 

5856 

6204 

603S 

6414 

39 

40 

0.5052 

0  5287 

0.5270 

0.5531 

0.5477 

0.5766 

0.5673 

0.5991 

0.5859 

0.6208 

0.6036 

0.6417 

40 

' 

41 

5056 

5292 

5274 

5535 

5480 

5770 

5676 

5995 

5862 

6211 

6039 

6421 

41 

42 

5060 

5295 

5278 

5539 

5484 

5773 

5679 

5998 

5865 

6215 

6042 

6424 

42 

43 

5064 

5299 

5281 

5543 

5487 

5777 

5682 

6002 

5868 

6219 

6045 

6428 

43 

44 

5067 

5304 

5285 

5547 

5490 

5781 

5685 

6006 

5871 

6222 

6047 

6431 

44 

45 

0.5071 

0.5308 

0.5288 

0.5551 

0.5494 

0.5785 

0.5689 

0.6009 

0.5874 

0.6226 

0.6050 

0.6435 

45 

46 

5075 

5312 

5292 

5555 

5497 

5789 

5692 

6013 

5877 

6229 

6053 

6438 

46 

47 

5078 

5316 

5295 

5559 

5500 

5792 

5695 

6017 

5880 

6233 

6056 

6441 

47 

48 

5082 

5320 

5299 

5563 

5504 

5796 

5698 

6020 

5883 

6236 

6059 

6445 

48 

49 

5086 

5324 

5302 

5567 

5507 

5800 

5701 

6024 

5886 

6240 

6062 

6448 

49 

50 

0.5090 

0.5329 

0.5306 

0.5571 

0.5510 

0.5804 

0.5704 

0.6028 

0.5889 

0.6243 

0.6065 

0.6452 

50 

51 

5093 

5333 

5309 

5575 

5514 

5808 

5708 

6031 

5892 

6247 

6068 

6455 

51 

52 

5097 

5337 

5313 

5579 

5517 

5811 

5711 

6035 

5895 

6250 

6070 

6459 

52 

53 

5101 

5341 

5316 

5583 

5520 

5815 

5714 

6039 

5898 

6254 

6073 

6462 

53 

54 

5104 

5345 

5320 

5587 

5523 

5819 

5717 

6042 

5901 

6257 

6076 

6465 

54 

55 

0.5108 

0.5349 

0.5323 

0.5591 

0.5527 

0.5823 

0.5720 

0,6046 

0.5904 

0.6261 

0.6079 

0.6469 

55 

56 

5112 

5353 

5327 

5595 

5530 

5827 

5723 

6050 

5907 

6264 

6082 

6472 

56 

57 

5115 

5357 

5330 

5599 

5533 

5830 

5726 

6053 

5910 

6268 

6085 

6476 

57 

58 

5119 

5362 

5334 

5603 

5537 

5834 

5730 

6057 

5913 

6271 

6087 

6479 

58 

59 

5123 

5366 

5337 

5607 

5540 

5838 

5733 

6060 

5916 

6275 

6090 

6482 

59 

60 

5126 

5370 

5341 

5611 

5543 

5842 

5736 

6064 

5919 

6279 

6093 

6486 

60 

M. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  8. 

Log.  T. 

Log.  8. 

Log.  T. 

M. 

18° 

19° 

20° 

2 

I* 

22° 

23° 

APPARENT  DISTANCE. 

1 

TABLE  XXXI.                     '87 

LOGARITHMS  OF  THE  APPARENT  DISTANCE. 

i' 

APPARENT  DISTANCE. 

M. 

2 

25° 

26° 

27° 

28° 

29* 

M 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  8. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  8. 

Log.  T 

0 

0.6093 

0.6486 

0.6259 

0.6687 

0.6418 

0.6882 

0.6570 

0.7072 

0.6716 

0.7257 

0.6856 

0.7438 

0 

1 

6096 

6489 

6262 

6690 

6421 

6885 

6573 

7075 

6718 

7260 

6858 

7441 

1 

2 

6099 

6493 

6265 

6693 

6424 

6888 

6575 

7078 

6721 

7263 

6860 

7443 

2 

3 

6102 

6496 

6268 

6697 

6426 

6891 

6578 

7081 

6723 

7266 

6863 

7446 

3 

4 

6104 

6499 

6270 

6700 

6429 

6895 

6580 

7084 

6726 

7269 

6865 

7449 

4 

5 

0.6107 

0.6503 

0.6273 

0.6703 

0.6431 

0.6898 

0.6583 

0.7087 

0.6728 

0.7272 

0.6867 

0.7452 

5 

6 

6110 

6506 

6276 

6706 

6434 

6901 

6585 

7090 

6730 

7275 

6869 

7455 

6 

7 

6113 

6510 

6278 

6710 

6437 

6904 

6588 

7093 

6733 

7278 

6872 

7458 

7 

8 

6116 

6513 

6281 

6713 

6439 

6907 

6590 

7097 

6735 

7281 

6874 

7461 

8 

9 

6119 

6516 

6284 

6716 

6442 

6911 

6593 

7100 

6737 

7284 

6876 

7464 

9 

10 

0.6121 

0.6520 

0.6286 

0.6720 

0.6444 

0.6914 

0.6595 

0.7103 

0.6740 

0.7287 

0.6878 

0.7467 

11 

6124 

6523 

6289 

6723 

6447 

6917 

6598 

7106 

6742 

7290 

6881 

7470 

11 

12 

bl27 

6527 

6292 

6726 

6449 

6920 

6600 

7109 

6744 

7293 

6883 

7473 

12 

13 

6130 

6530 

6295 

6729 

6452 

6923 

6603 

7112 

6747 

7296 

6885 

7476 

13 

14 

6133 

6533 

6297 

6733 

6455 

6927 

6605 

7115 

6749 

7299 

6887 

7479 

14 
15 

15 

0.6135 

0.6537 

0.6300 

0.6736 

0.6457 

0.6930 

0.6607 

0.7118 

0.6752 

0.7302 

0.6890 

0.7482 

16 

6138 

6540 

6303 

6739 

6460 

6933 

6610 

7121 

6754 

7305 

6892 

7485 

16 

17 

6141 

6543 

6305 

6743 

6462 

6936 

6612 

7125 

6756 

7308 

6894 

7488 

17 

18 

6144 

6547 

6308 

6746 

6465 

6939 

6615 

7128 

6759 

7311 

6896 

7491 

18 

19 

6147 

6550 

6311 

6749 

6467 

6942 

6617 

7131 

6761 

7314 

6899 

7494 

19 

20 

0.6149 

0.6553 

0.6313 

0.6752 

0.6470 

0.6946 

0.6620 

0.7134 

0.6763 

0.7317 

0.6901 

0.7497 

20 

21 

6152 

6557 

6316 

6756 

6472 

6949 

6622 

7137 

6766 

7320 

6903 

7600 

21 

22 

6155 

6560 

6319 

6759 

6475 

6952 

6625 

7140 

6768 

7324 

6905 

7503 

22 

23 

6158 

6564 

6321 

6762 

6477 

6955 

6627 

7143 

6770 

7327 

6908 

7506 

23 

24 

6161 

(1.567 

6324 

6765 

6480 

6958 

6629 

7146 

6773 

7330 

6910 

7509 

24 

25 

0.6163 

0.6570 

0.6327 

0.6769 

0.6483 

0.6962 

0.6632 

0.7149 

0.6775 

0.7333 

0.6912 

0.7512 

25 

26 

6166 

6574 

6329 

6772 

6485 

6965 

6634 

7152 

6777 

7336 

6914 

7515 

26 

27 

6169 

6577 

6332 

6775 

6488 

6968 

6637 

7156 

6780 

7339 

6917 

7518 

27 

28 

6172 

6580 

6335 

6778 

6490 

6971 

6639 

7159 

6782 

7342 

6919 

7521 

28 

29 

6175 

6584 

6337 

6782 

6493 

6974 

6642 

7162 

6784 

7345 

6921 

7523 

29 

30 

0.6177 

0.6587 

0.6340 

0.6785 

0.6495 

0.6977 

0.6644 

0.7165 

0.6787 

0.7348 

0.6923 

0.7526 

30 

31 

6180 

6590 

6342 

6788 

6498 

6981 

6646 

7168 

6789 

7351 

6926 

7529 

31 

32 

6183 

6594 

6345 

6791 

6500 

6984 

6649 

7171 

6791 

7354 

6928 

7632 

32 

33 

6186 

6597 

6348 

6795 

6503 

6987 

6651 

7174 

6794 

7357 

6930 

7535 

33 

34 
35 

6188 

6600 

6350 

6798 

6505 

6990 

6654 

7177 

6796 

7360 

6932 

7538 

34 

0.6191 

0.6604 

0.6353 

0.6801 

0.6508 

0.6993 

0.6656 

0.7180 

0.6798 

0.7363 

0.6935 

0.7541 

35 

36 

6194 

6607 

6356 

6804 

6510 

6996 

6659 

7183 

6801 

7366 

6937 

7544 

36 

37 

6197 

6610 

_6358 

6808 

6513 

6999 

6661 

7186 

6803 

7369 

6939 

7647 

37 

38 

6199 

6614 

6361 

6811 

6515 

7003 

6663 

7189 

6805 

7372 

6941 

7550 

38 

39 

6202 

6617 

6364 

6814 

6518 

7006 

6666 

7192 

6808 

7375 

6943 

7553 

39 

40 

0.6205 

0.6620 

0.6366 

0.6817 

0  6521 

0.7009 

0.6668 

0.7196 

0.6810 

0.7378 

0.6946 

9.7556 

40 

41 

6208 

6624 

6369 

6821 

6523 

7012 

6671 

7199 

6812 

7381 

6948 

7559 

41 

42 

6210 

6627 

6371 

6824 

6526 

7015 

6673 

7202 

6814 

7384 

6950 

7562 

42 

43 

6213 

6630 

6374 

6827 

6528 

7018 

6675 

7205 

6817 

7387 

6952 

7566 

43 

44 

6216 

6634 

6377 

6830 

6531 

7022 

6678 

7208 

6819 

7390 

6954 

7568 

44 

45 

0.6219 

0.6637 

0.6379 

0.6834 

0.6533 

0.7025 

0.6680 

0.7211 

0.6821 

0.7393 

0.6957 

0.7571 

45 

46 

6221 

6640 

6382 

6837 

6536 

7028 

6683 

7214 

6824 

7396 

6959 

7573 

46 

47 

6224 

6644 

6385 

6840 

6538 

7031 

6685 

7217 

6826 

7399 

6961 

7576 

47 

48 

6227 

6647 

6387 

6843 

6541 

7034 

6687 

7220 

6828 

7402 

6963 

7679 

48 

49 

6230 

6650 

6390 

6846 

6543 

7037 

6690 

7223 

6831 

7405 

6966 

7582 

49 

50 

0.6232 

0.6654 

0.6392 

0.6850 

0.6546 

0.7040 

0.6692 

0.7226 

0.6833 

0.7408 

0.6968 

0.7685 

60 

51 

6235 

6657 

6395 

6853 

6548 

7043 

6695 

7229 

6835 

7411 

6970 

7688 

51 

52 

6238 

6660 

6398 

6856 

6551 

7047 

6697 

7232 

6837 

7414 

6972 

7691 

52 

53 

6240 

6664 

6400 

6859 

6553 

7050 

6699 

7235 

6840 

7417 

6974 

7594 

53 

54 

6243 

6667 

6403 

6863 

6556 

7053 

6702 

7238 

6842 

7420 

6977 

7597 

54 

55 

0.6246 

0.6670 

0.6405 

0.6866 

0.6558 

0.7056 

0.6704 

0.7241 

0.6844 

0.7423 

0.6979 

0.7600 

55 

56 

6249 

6674 

6408 

6869 

6561 

7059 

6707 

7245 

6847 

7426 

6981 

7603 

56 

57 

6251 

6677 

6411 

6872 

6563 

7062 

6709 

7248 

6849 

7429 

6983 

7606 

57 

58 

6254 

6680 

6413 

6875 

6566 

7065 

6711 

7251 

6851 

7432 

6985 

7609 

58 

59 

6257 

6683 

6416 

6879 

6568 

7069 

6714 

7254 

6853 

7435 

6988 

7611 

59 

60 

6259 

6687 

6418 

6882 

6570 

7072 

6716 

7257 

6856 

7438 

6990 

7614 

60 

M. 

Log.  8. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  8. 

Loff.  T. 

Log.  S. 

L"g.  T. 

Log.  S. 

Log.  T. 

Log.  8.  Log.  T. 

M. 

24° 

25* 

26° 

27° 

28° 

29° 

APPARENT  DISTANCE.                                  1 

1S8                                         TABLE  XXXI. 

LOGARITHMS  OF  THE  APPARENT  DISTANCE 

APPARENT  DISTANCE. 

M. 

30° 

31" 

32° 

33° 

34°     ,     35° 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  8. 

Log.  T. 

Log.  «. 

Log.  T. 

M 

0 

0.6990 

0.7614 

0.71180.7788 

0.7242 

0.7958 

0.7361 

0.8125 

0.7476 

0.8290 

0.7586 

0.8452 

0 

1 

6992 

7617 

7121 

7791 

7244 

7961 

7363 

8128 

7477 

8293 

7588 

8455 

1 

2 

6994 

7620 

7123,  7793 

7246 

7964 

7365 

8131 

7479 

8295 

7590 

8458 

2 

3 

6996 

7623 

7125 

7796 

7248 

7966 

7367 

8133 

7481 

8298 

7591 

8460 

3 

4 
5 

6998 

7626 

"   27 

7799 

7250 

7969 

7369 

8136 

7483 

8301 

7593 

8463 

4 

0.7001 

0.7629 

0.7129 

0.7802 

0.7252 

0.7972 

0.7371 

0.8139 

0.7485 

0.8303 

0.7595 

0.8466 

5 

6 

7003 

7632 

7131 

7805 

7254 

7975 

7373 

8142 

7487 

8306 

7597 

8468 

6 

7 

7005 

7635 

7133 

7808 

7256 

7978 

7375 

8145 

7489 

8309 

7599 

8471 

7 

8 

7007 

7638 

7135 

7811 

7258 

7980 

7377 

8147 

7491 

8312 

7600 

8474 

8 

9 

7009 

7641 

7137 

7813 

7260 

7983 

7379 

8150 

7492 

8314 

7602 

8476 

9 

10 

0.7012 

0.7644 

0.7139 

0.7816 

0.7262 

0.7986 

0.7380 

0.8153 

0.7494 

0.8317 

0.7604 

0.8479 

10 

11 

7014 

7646 

7141 

7819 

7264 

7989 

7382 

8156 

7496 

8320 

7606 

8482 

11 

12 

7016 

7649 

7144 

7822 

7266 

7992 

7384 

8158 

7498 

8323 

7607 

8484 

12 

13 

7018 

7652 

7146 

7825 

7268 

7994 

7386 

8161 

7500 

8325 

7609 

8487 

13 

14 

7020 

7655 

7148 

7828 

7270 

7997 

7388 

8164 

7502 

8328 

7611 

8490 

14 

15 

0.7022 

0.7658 

0.7150 

0.7831 

0.7272 

0.8000 

0.7390 

0.8167 

0.7504 

0.8331 

0.7613 

0.8493 

15 

16 

7025 

7661 

7152 

7833 

7274 

8003 

7392 

8169 

7505 

8333 

7615 

8495 

16 

17 

7C27 

7664 

7154 

7836 

7276 

8006 

7394 

8172 

7507 

8336 

7616 

8498 

17 

18 

7029 

7667 

7156 

7839 

7278 

8008 

7396 

8175 

7509 

8339 

7618 

8501 

18 

19 

7031 

7670 

7158 

7842 

7280 

8011 

7398 

8178 

7511 

8342 

7620 

8503 

19 

20 

0.7033 

0.7673 

0.7160 

0.7845 

0.7282 

0.8014 

0.7400 

0.8180 

0.7513 

0.8345 

0.7622 

0.8506 

20 

21 

7035 

7675 

7162 

7848 

7284 

8017 

7402 

8183 

7515 

8347 

7624 

8509 

21 

22 

7037 

7678 

7164 

7850 

7286 

8020 

7404 

8186 

7517 

8350 

7625 

8511 

22 

23 

7040 

7681 

7166 

7853 

7288 

8022 

7406 

8189 

7518 

8352 

7627 

8514 

23 

24 

7042 

7684 

7168 

7856 

7290 

8025 

7407 

8191 

7520 

8355 

7629 

8517 

24 

25 

0.7044 

0.7687 

0.7171 

0.7859 

0.7292 

0.8028 

0.7409 

0.8194 

0.7522 

0.8358 

0.7631 

0.8519 

25 

26 

7046 

7690 

7173 

7862 

7294 

8031 

7411 

8197 

7524 

8361 

7632 

8522 

26 

27 

7048 

7693 

7175 

7865 

7296 

8034 

7413 

8200 

7526 

8363 

7634 

8525 

27 

28 

7050 

7696 

7177 

7868 

7298 

8036 

7415 

8202 

7528 

8366 

7636 

8527 

28 

29 

7053 

7699 

7179 

7870 

7300 

8039 

7417 

8205 

7529 

8369 

7638 

8530 

29 

30 

0.7055 

0.7701 

0.7181 

0.7873 

0.7302 

0.8042 

0.7419 

0.8208 

0.7531 

0.8371 

0.7640 

0.8532 

30 

31 

7057 

7704 

7183 

7876 

7304 

8045 

7421 

8211 

7533 

8374 

7641 

8535 

31 

32 

7059 

7707 

7185 

7879 

7306 

8047 

7423 

8213 

7535 

8377 

7643 

8538 

32 

33 

7061 

7710 

7187 

7882 

7308 

8050 

7425 

8216 

7537 

8379 

7645 

8541 

33 

34 

7063 

7713 

7189 

7885 

7310 

8053 

7427 

8219 

7539 

8382 

7647 

8543 

34 

35 

0.7065 

0.7716 

0.7191 

0.7887 

0.7312 

0.8056 

0.7428 

0.8222 

0.7540 

0.8385 

0.7648 

0.8546 

35 

36 

7068 

7719 

7193 

7890 

7314 

8059 

7430 

8224 

7542 

8388 

7650 

8549 

36 

37 

7070 

7722 

7195 

7893 

7316 

8061 

7432 

8227 

7544 

8390 

7652 

8551 

37 

38 

7072 

7725 

7197 

7896 

7318 

8064 

7434 

8230 

7546 

8393 

7654 

8554 

38 

39 

7074 

7727 

7199 

7899 

7320 

8067 

7436 

8233 

7548 

8396 

7655 

8557 

39 

40 

0.7076 

0.7730 

0.7201 

0.7902 

0.7322 

0.8070 

0.7438 

0.8235 

0.7550 

0.8398 

0.7657 

0.8559 

40 

41 

7078 

7733 

7203 

7904 

7324 

8072 

7440 

8238 

7551 

8401 

7659 

8562 

41 

42 

7080 

7736 

7205 

7907 

7326 

8075 

7442 

8241 

7553 

8404 

7661 

8565 

42 

43 

7082 

7739 

7208 

7910 

7328 

8078 

7444 

8243 

7555 

8406 

7662 

8567 

43 

44 

7085 

7742 

7210 

7913 

7330 

8081 

7446 

8246 

7557 

8409 

7664 

8570 

44 

45 

0.7087 

0.7745 

0.7212 

0.7916 

0.7332 

0.8084 

0.7447 

0.8249 

0.7559 

0.8412 

0.7666 

0.8573 

45 

46 

7089 

7748 

7214 

7918 

7334 

8086 

7449 

8252 

7561 

8415 

7668 

8575 

46 

47 

7091 

7750 

7216 

7921 

7336 

8089 

7451 

8254 

7562 

8417 

7669 

8578 

47 

48 

7093 

7753 

7218 

7924 

7338 

8092 

7453 

8257 

7564 

8420 

7671 

8581 

48 

49 

7095 

7756 

7220 

7927 

7340 

8095 

7455 

8260 

7566 

8423 

7673 

8583 

49 

50 

0.7097 

0.7759 

0.7222 

0.7930 

0.7342 

0.8097 

0.7457 

0.8263 

0.7568 

0.8425 

0.7675 

0.8586 

50 

51 

7099 

7762 

7224 

7933 

7344 

8100 

7459 

8265 

7570 

8428 

7676 

8589 

51 

52 

7102 

7765 

7226 

7935 

7345 

8103 

7461 

8268 

7571 

8431 

7678 

8591 

52 

53 

7104 

7768 

7228 

7938 

7347 

8106 

7462 

8271 

7573 

8433 

7680 

8594 

53 

54 

7106 

7771 

7230 

7941 

7349 

8109 

7464 

8274 

7575 

8436 

7682 

8597 

54 

55 

0.7108 

0.7773 

0.7232 

0.7944 

0.7351 

0.8111 

0.7466 

0.8276 

0.7577 

0.8439 

0.7683 

0.8599 

55 

56 

7110 

7776 

7234 

7947 

7353 

8114 

7468 

8279 

7579 

8442 

7685 

8602 

56 

57 

7112 

7779 

7236 

7949 

7355 

8117 

7470 

8282 

7581 

8444 

7687 

8605 

67 

58 

7114 

7782 

7238 

7952 

7357 

8120 

7472 

8284 

7582 

8447 

7689 

8607 

58 

59 

7116 

7785 

7240 

7955 

7359 

8122 

7474 

8287 

7584 

8450 

7690 

8610 

59 

60 

7118 

7788 

7242 

7958 

7361 

8125 

7476 

8290 

7586 

8452 

7692 

8613 

60 

M. 

Loe.  S. 

Lop.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

L..g.  T. 

Log.  9. 

Log.  T. 

Log.  S. 

Log.  T. 

M 

30° 

31"         32° 

33° 

34°     1 

35° 

APPARENT  DISTANCE 

TABLE  XXXI.                                                 129 

LOGARITHMS  OF  THE  APPARENT  DISTANCE. 

APPARENT  DISTANCE. 

M. 

36* 

37'    J 

38° 

39°    1 

40° 

41-    1 

M. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S . 

Log.  T. 

Log.  S. 

Log.  TJ 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T.  1 

0 

0.7692 

0.8613 

0.7795 

0.8771 

0.7893 

0.8928 

D. 79890.90841 

0.8081 

0.9238 

C. 81690. 9392 

0 

1 

7694 

8615 

7796 

8774 

7895 

8931 

7990 

9086 

8082 

9241 

8171 

9394 

1 

2 

7696 

8618 

7798 

8776 

7897 

8933 

7992 

9089 

8084 

9243 

8172 

9397 

2 

3 

7697 

8621 

7800 

8779 

7898 

8936 

7993 

9091 

8085 

9246 

8174 

9399 

3 

4 

7699 

8623 

7801 

8782 

7900 

8939 

79195 

9094 

8087 

9248 

8175 

9402 

4 

5 

0.7701 

0.8626 

0.7803 

0.8784 

0.7901 

0.8941 

0.7997 

0.9097 

0.8088 

0.9251 

0.8177 

0.9404 

5 

6 

7703 

8629 

7805 

8787 

7903 

8944 

7998 

9099 

8090 

9254 

8178 

9407 

6 

7 

7704 

8631 

7806 

8790 

7905 

8946 

8000 

9102 

8091 

9256 

8180 

9409 

7 

8 

7706 

8634 

7808 

8792 

7906 

8949 

8001 

9104 

8093 

9259 

8181 

9412 

8 

9 

770S 

8637 

7810 

8795 

7908 

8952 

8003 

9107 

8094 

9261 

8182 

9415 

9 

10 

0.7710 

0.8639 

0.7811 

0.8797 

0.7910 

0.8954 

0.8004 

0.9110 

0.8096 

0.9264 

0.8184 

0.9417 

10 

11 

7711 

8642 

7813 

8800 

7911 

8957 

8006 

9112 

8097 

9266 

8185 

9420 

11 
12 

12 

7713 

8644 

7815 

8803 

7913 

8959 

8007 

9115 

8099 

9269 

8187 

9422 

13 

7715 

8647 

7816 

8805 

7914 

8962 

8009 

9117 

8100 

9271 

8188 

9425 

13 

14 
15 

7716 

8650 

7818 

8808 

7916 

8965 

8010 

9120 

8102 

9274 

8190 

9427 

14 

0.7718 

0.8652 

0.7820 

0.8811 

0.7918 

0.8967 

0.8012 

0.9122 

0.8103 

0.9277 

0.8191 

0.9430 

15 

16 

7720 

8655 

7821 

8813 

7919 

8970 

8014 

9125 

8105 

9279 

8193 

9432 

16 

17 

7722 

8658 

7823 

8816 

7921 

8972 

8015 

9128 

8106 

9282 

8194 

9435 

17 

18 

7223 

8660 

7825 

8818 

7922 

8975 

8017 

9130 

8108 

9284 

8195 

9438 

18 

19 

7725 

8663 

7826 

8821 

7924 

8978 

8018 

9133 

8109 

9287 

8197 

9440 

19 

20 

0.7727 

0.8666 

0.7828 

0.8824 

0.7926 

0.8980 

0.8020 

0.9135 

0.8111 

0.9289 

0.8198 

0.9443 

20 

21- 

7728   8668 

7830 

8826 

7927 

8983 

8021 

9138 

8112 

9292 

8200 

9445 

21 

22 

7730 

8671 

7831 

8829 

7929 

8985 

8023 

9140 

8114 

9295 

8201 

9448 

22 

23 

7732 

8674 

7833 

8831 

7930 

8988 

8024 

9143 

8115 

9297 

8203 

9450 

23 

24 

7734 

8676 

7835 

8834 

7932 

8990 

8026 

9146 

8117 

9300 

8204 

9453 

24 

25 

0.7735 

0.8679 

0.7836 

1) .  8837 

0.7934 

0.8993 

0.8027 

0.9148 

0.8118 

0.9302 

0.8206 

0.9455 

25 

26 

7737 

8682 

7838 

8839 

7935 

8996 

8029 

9151 

8120 

9305 

8207 

9458 

26 

27 

7739 

8(i84 

7840 

8842 

7937 

8998 

8031 

9153 

8121 

9307 

8208 

9460 

27 

28 

7740 

8687 

7841 

8845 

7938 

9001 

8032 

9156 

8122 

9310 

8210 

9463 

28 

29 
30 

774-2 

8689 

7843 

8847 

7940 

9003 

8034 

9158 

8124 

9312 

8211 

9466 

29 

0.7744 

0.8692 

0.7844 

0.8850 

0.7942 

0.9006 

0.8035 

0.9161 

0.8125 

0.9315 

0.8213 

0.9468 

30 

31 

7746 

8695 

7846 

8852 

7943 

9009 

8037 

9164 

8127 

9318 

8214 

9471 

31 

32 

7747 

8697 

7848 

8855 

7945 

9011 

8038 

9166 

8128 

9320 

8216 

9473 

32 

33 

7749 

8700 

7849 

8858 

7946 

9014 

8040 

9169 

8130 

9323 

8217 

9476 

33 

34 
35 

7751 

8703 

7851 

8860 

7948 

9016 

8041 

9171 

8131 

9325 

8218 

9478 

34 

0.7752 

0.8705 

0.7853 

0.8863 

0.7949 

0.9019 

0.8043 

0.9174 

0.8133 

0.9328 

0.8220 

0.9481 

''S 

36 

7754 

8708 

-  7854 

8865 

7951 

9022 

8044 

9176 

8134 

9330 

8221 

9483 

ii 

37 

7756 

8711 

7856 

8868 

7953 

9024 

8046 

9179 

8136 

9333 

8223 

9486 

% 

38 

7758 

8713 

7858 

8871 

7954 

9026 

8047 

9182 

8137 

9335 

8224 

9488 

38 

39 

7759 

87  If 

7859 

8873 

7956 

9029 

8049 

9184 

8139 

9338 

8225 

9491 

39 

40 

0.7761 

0.8718 

0.7861 

0.8876 

0.7957 

0.9032 

0.8050 

0.9187 

0.8140 

0.9341 

0.8227 

0.9494 

40 

41 

7763 

87-21 

7863 

8879 

7959 

9035 

8052 

9189 

8142 

9343 

8228 

9496 

41 

42 

7764 

8724 

7864 

8881 

7960 

9037 

8053 

9192 

8143 

9346 

8230 

9499 

42 

43 

7766 

8726 

7866 

8884 

7962 

9040 

8055 

9194 

8145 

9348 

8231 

-9501 

43 

44 

7768 

8729 

7867 

8886 

7964 

9042 

8056 

9197 

8146 

9351 

8233 

9504 

44 

45 

0.7769 

0.8732 

0.7869 

0.8889 

0.7965 

0.9045 

0.8058 

0.9200 

0.8148 

0.9353 

0.8234 

0.9506 

45 

46 

7771 

8734 

7871 

8892 

7967 

9048 

8060 

9202 

8149 

9356 

8235 

9509 

46 

47 

7773 

8737 

7872 

8894 

7968 

9050 

8061 

9205 

8150 

9358 

8237 

9511 

47 

48 

7774 

8740 

7874 

8897 

7970 

9053 

8063 

9207 

8152 

9361 

8238 

9514 

48 

49 

7776 

8742 

7876 

8899 

7972 

9055 

8064 

9210 

8153 

9364 

8240 

9516 

49 
50 

50 

0.7778 

0.8745 

0.7877 

0.8902 

0.7973 

0.9057 

0.8066 

0.9212 

0.8155 

0.9366 

0.8241 

0.9519 

51 

7780 

8747 

7879 

8905 

7975 

9060 

8067 

9215 

8156 

9369 

8242 

9522 

51 

52 

7781 

8750 

7880 

8907 

7976 

9063 

8069 

9218 

8158 

9371 

8244 

9524 

5 

53 

7783 

8753 

7882 

8910 

7978 

9066 

8070 

9220 

8159 

9374 

8245 

9527 

53 

54 

7785 

875  f 

7884 

8912 

7979 

9068 

8072 

9223 

8161 

9376 

8247 

9529 

5; 

55 

0.7786 

0.8758 

0.7885 

0.8915 

0.7981 

0.9071 

0.8073 

0.9225 

0.8162 

0.9379 

0.8248 

0.9532 

55 

56 

7788 

8761 

7887 

8918 

7982 

9073 

8075 

9228 

8164 

9381 

8249 

9534 

56 

57 

779f 

8763 

7889 

8920 

7984 

9076 

8076 

9230 

8165 

9384 

8251 

9537 

57 

58 

7791 

8766 

7890 

8923 

7986 

9079 

8078 

9233 

8167 

9387 

8252 

9539 

58 

59 

7793 

8769 

7892 

8925 

7987 

9081 

8079 

9236 

8168 

9389 

8254 

9542 

59 

60 

7795 

8771 

-7893 

8928 

7989 

9084 

8081 

9238 

8169 

9392 

8255 

9544 

60 

M. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

M 

a 

6* 

37' 

38° 

39° 

40*    1 

4 

I* 

APPARENT  DISTANCE.                                  1 

130                                         TABLK  XXXT. 

LOGARITHMS  OF  THE  APPARENT  DISTANCE. 

APPARENT  DISTANCE. 

1 

M. 

42°     1 

43- 

44" 

45° 

46' 

470 

M. 

Log.  S. 

Log.  T. 

Log.  S 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.T. 

0 

0.8255 

0.9544 

0.8338 

0.9697 

0.8418 

0.9848 

0.8495 

1.0000 

0.8569 

1.0152 

0.8641 

1.0303 

0 

1 

8257 

9547 

8339 

9699 

8419 

9851 

8496 

0003 

8571 

0154 

8642 

0306 

1 

2 

8258 

9549 

8341 

9702 

8420 

9853 

8497 

0005 

8572 

0157 

8644 

0309 

2 

3 

8259 

9552 

8342 

9704 

8422 

9856 

8499 

0008 

8573 

0159 

8645 

0311 

3 

4 

8261 

9555 

8343 

9707 

8423 

9858 

8500 

0010 

8574 

0162 

8646 

0314 

4 

5 

0,8262 

0.9557 

0.8345 

0.9709 

0.8424 

0.9861 

0.8501 

1.0013 

0.8575 

1.0164 

0.8647 

1.0316 

5 

6 

8264 

9560 

8346 

9712 

8426 

9864 

8502 

0015 

8577 

0167 

8648 

0319 

6 

7 

8265 

9562 

8347 

9714 

8427 

9866 

8504 

0018 

8578 

0169 

8650 

0321 

7 

8 

8266 

9565 

8349 

9717 

8428 

9869 

8505 

0020 

8579 

0172 

8651 

0324 

8 

9 

8268 

9567 

8350 

9719 

8429 

9871 

8506 

0023 

8580 

0174 

8652 

0326 

9 

10 

0.8269 

0.9570 

0  8351 

0.9722 

0.8431 

0.9874 

0.8507 

1.0025 

0.8582 

1.0177 

0.8653 

1.0329 

10 

11 

8270 

9572 

8353 

9724 

8432 

9876 

8509 

0028 

8583 

0179 

8654 

0331 

11 

12 

8272 

9575 

8354 

9727 

8433 

9879 

8510 

0030 

8584 

0182 

8655 

0334 

12 

13 

8273 

9577 

8355 

9729 

8435 

9881 

8511 

0033 

8585 

0185 

8657 

0336 

13 

14 

8275 

9580 

8357 

9732 

8436 

9884 

8512 

0035 

8586 

0187 

8658 

0339 

14 

15 

0.8276 

0.9582 

0.8358 

0.9735 

0.8437 

0.9886 

0.8514 

1.0038 

0.8588 

1.0190 

0.8659 

1.0341 

15 

16 

8277 

9585 

8359 

9737 

8439 

9889 

8515 

0040 

8589 

0192 

8660 

0344 

16 

17 

8279 

9588 

8361 

9740 

8440 

9891 

8516 

0043 

8590 

0195 

8661 

0347 

17 

18 

8280 

9590 

8362 

9742 

8441 

9894 

8517 

0045 

8591 

0197 

8662 

0349 

18 

19 

8282 

9593 

8363 

9745 

8442 

9896 

8519 

0048 

8592 

0200 

8663 

0352 

19 

20 

0.8283 

0.9595 

0.8365 

0  9747 

0.8444 

0.9899 

0.8520 

1.0051 

0.8594 

1.0202 

0.8665 

1.0354 

20 

21 

8284 

9598 

8366 

9750 

8445 

990] 

8521 

0053 

8595 

0205 

8666 

0357 

21 

22 

8286 

9600 

8367 

9752 

8446 

9904 

8522 

0056 

8596 

0207 

8667 

0359 

22 

23 

8287 

9603 

8369 

9755 

8448 

9907 

8524 

0058 

8597 

0210 

8668 

0362 

23 

24 

8289 

9605 

8370 

9757 

8449 

9909 

8525 

0061 

8598 

0212 

8669 

0364 

24 

25 

0.8290 

0.9608 

0.8371 

0.9760 

0.8450 

0.9912 

0.8526 

1.0063 

0.8600 

1.0215 

0.8671 

1.0367 

25 

26 

8291 

9610 

8373 

9762 

8451 

9914 

8527 

0066 

8601 

0217 

8672 

0369 

26 

27 

8293 

9613 

8374 

9765 

8453 

9917 

8529 

0068 

8602 

0220 

8673 

0372 

27 

28 

8294 

9615 

8375 

9767 

8454 

9919 

8530 

0071 

8603 

0222 

8674 

0374 

28 

29 

8295 

9618 

8377 

9770 

8455 

9922 

8531 

0073 

8604 

0225 

8675 

0377 

29 
30 

30 

0.8297 

0.9621 

0.8378 

0.9773 

0.8457 

0.9924 

0.8532 

1.0076 

0.8606 

1.0228 

0.8676 

1.0379 

31 

8298 

9623 

8379 

9775 

8458 

9927 

8534 

0078 

8607 

0230 

8677 

0382 

31 

32 

8300 

9626 

8381 

9778 

8459 

9929 

8535 

0081 

8608 

0233 

8679 

0385 

32 

33 

8301 

9628 

8382 

9780 

8460 

9932 

8536 

0083 

8609 

0235 

8680 

0387 

33 

34 
35 

8302 

9631 

8383 

9783 

8462 

9934 

8537 

0086 

8610 

0238 

8681 

0390 

34 

0.8304 

0.9633 

0.8385 

0.9785 

0.8463 

0.9937 

0.8539 

1.0088 

0.8612 

1.0240 

0.8682 

1.0392 

35 

36 

8305 

9636 

8386 

9788 

8464 

9939 

8540 

0091 

8613 

0243 

8683 

0395 

36 

37 

8306 

9638 

8387 

9790 

8466 

9942 

8541 

0093 

8614 

0245 

8684 

0397 

37 

38 

8308 

9641 

8389 

9793 

8467 

9944 

8542 

0096 

8615 

0248 

8686 

0400 

38 

39 

8309 

9643 

8390 

9795 

8468 

9947 

8544 

0099 

8616 

0250 

8687 

0402 

39 
40 

40 

0.8311 

0.9646 

0.8391 

0.9798 

0.8469 

0.9949 

0.8545 

1.0101 

0.8618 

1.0253 

0.8688 

1.0405 

41 

8312 

9648 

8393 

9800 

8471 

9952 

8546 

0104 

8619 

0255 

8689 

0407 

41 

42 

8313 

9651 

8394 

9803 

8472 

9955 

8547 

0106 

8620 

0258 

8690 

0410 

42 

43 

8315 

9653 

8395 

9805 

8473 

9957 

8549 

0109 

8621 

0260 

8691 

0412 

43 

44 

8316 

9656 

8397 

9808 

8475 

9960 

8550 

0111 

8622 

0263 

8692 

0415 

44 

45 

0.8317 

0.9659 

0.8398 

0.9810 

0.8476 

0.9962 

0.8551 

1.0114 

0.8624 

1.0265 

0.8694 

1.0418 

45 

46 

8319 

9661 

8399 

9813 

8477 

9965 

8552 

0116 

8625 

0268 

8695 

0420 

46 

47 

8320 

9664 

8401 

9816 

8478 

9967 

8553 

0119 

8626 

0271 

8696 

0423 

47 

48 

8322 

9666 

8402 

9818 

8480 

9970 

8555 

0121 

8627 

0273 

8697 

0425 

48 

49 

8323 

9669 

8403 

9821 

8481 

9972 

8556 

0124 

8628 

0276 

8698 

0428 

49 

50 

0.8324 

0.9671 

0.8405 

0.9823 

0.8482 

0.9975 

0.8557 

1.0126 

0.8629 

1.0278 

0.8699 

1.0430 

50 

51 

8326 

9674 

8406 

9826 

8483 

9977 

8558 

0129 

8631 

0281 

8700 

0433 

51 

52 

8327 

9676 

8407 

9828 

8485 

9980 

8560 

0131 

8632 

0283 

8702 

0435 

52 

53 

8328 

9679 

8409 

9831 

8486 

9982 

8561 

0134 

8633 

0286 

8703 

0438 

53 

54 
55 

8330 

9681 

8410 

9833 

8487 

9985 

8562 

0136 

8634 

0288 

8704 

0440 

54 

0.8331 

0.9684 

0.8411 

0.9836 

0.8489 

0.9987 

0.8563 

1.0139 

0.8635 

1.0291 

0.8705 

1.0443 

55 

56 

8332 

9686 

8412 

9838 

8490 

9990 

8564 

0142 

8637 

0293 

8706 

0445 

56 

57 

8334 

9689 

8414 

9841 

8491 

9992 

8566 

0144 

8638 

0296 

8707 

0448 

57 

58 

8335 

9691 

8415 

9843 

8492 

9995 

8567 

0147 

8639 

0298 

8708 

0451 

58 

59 

8336 

9694 

8416 

9846 

8494 

9997 

8568 

0149 

8640 

0301 

8710 

0453 

59 

60 

8338 

9697 

8418 

9848 

8495 

1.0000 

8569 

0152 

8641 

0303 

8711 

0456 

60 

M. 

'. '".  s. 

Log.  T. 

Log.  S. 

Loe.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S.  Log.  T. 

M. 

42' 

43- 

44° 

45° 

46" 

47° 

APPARENT  DISTANCE. 

i 

TABLE  XXXI. 

131 

LOGARITHMS  OF  THE  APPARENT  DISTANCE. 

APPARENT  DISTANCE, 

M. 
0 

48' 

49'   _\ 

60' 

51' 

52" 

53" 

M. 

Log.  S.  Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

L..g.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.T. 

0.8711 

1.0456 

0.8778 

1.0608 

0.8843 

1.0762 

0.8905 

1  0916 

0.8965 

1.1072 

0.9023 

1.1229 

0 

1 

8712 

0458 

8779 

0611 

8844 

0764 

8906 

0919 

8966 

1075 

9024 

1231 

1 

2 

8713 

0461 

8780 

0613 

8845 

0767 

8907 

0921 

8967 

1077 

9025 

1234 

2 

3 

8714 

0463 

8781 

0616 

8846 

0770 

8908 

0924 

8968 

1080 

9026 

1237 

3 

4 

8715 

0466 

8782 

0619 

8847 

0772 

89q9 

0927 

8969 

1082 

9027 

1239 

4 

5 

0.8716 

1.0468 

0.8783 

1.0621 

0.8848 

1.0775 

0.8910 

1.0929 

0.8970 

1.1085 

0.9028 

1.1242 

5 

6 

8718 

0471 

8784 

0624 

8849 

0777 

8911 

0932 

8971 

1088 

9029 

1245 

6 

7 

8719 

0473 

87S5 

062ti 

8850 

0780 

8912 

0934 

8972 

1090 

9030 

1247 

7 

8 

8720 

0476 

8787 

0629 

8851 

0782 

8913 

0937 

8973 

1093 

9031 

1250 

8 

9 

8721 

0479 

8788 
0  8789 

0631 

8852 

0785 

8914 

0940 

8974 

1095 

9032 

1253 

9 

10 

0.8722 

10481 

1  .0634 

0.8853 

1.0788 

0.8915 

1.0942 

0.8975 

1.1098 

0.9033 

1.1255 

10 

11 

8723 

0484 

8790 

0636 

8854 

0790 

8916 

0945 

8976 

1101 

9034 

1258 

11 

12 

8724 

0486 

8791 

0639 

8855 

0793 

8917 

0947 

8977 

1103 

9035 

1260 

12 

13 

8725 

0489 

8792 

0642 

8856 

0795 

8918 

0950 

8978 

1106 

9036 

1263 

13 

14 

8727 

0491 

8793 

0644 

8857 

0798 

8619 

0953 

8979 

1108 

9037 

1266 

14 

15 

0.8728 

1.0494 

0.8794 

1.0647 

0.8858 

1.0800 

0.S920 

1.0955 

0.8980 

1.1111 

0.9038 

1.1268 

15 

16 

8729 

0496 

8795 

0649 

8859 

0803 

8921 

0958 

8981 

1114 

9039 

1271 

16 

17 

8730 

0499 

8796 

0652 

8860 

0806 

8922 

0960 

8982 

1116 

9040 

1274 

17 

18 

8731 

0501 

8797 

0654 

8862 

0808 

8923 

0963 

8983 

1119 

9041 

1276 

18 

19 

8732 

0504 

8799 

0657 

8863 

0811 

8924 

0965 

8984 

1121 

9041 

1279 

19 

20 

0.8733 

1.0506 

0.8800 

1.0659 

0.8864 

1.0813 

0.8925 

1.0968 

0.8985 

1.1124 

0,9042 

1.1282 

20 

21 

8734 

0509 

8801 

0662 

8865 

0816 

8926 

0971 

8986 

1127 

9043 

1284 

21 

22 

8736 

0512 

8802 

0665 

8866 

0818 

8927 

0973 

8987 

1129 

9044 

1287 

22 

23 

8737 

0514 

8803 

0667 

8867 

0821 

8928 

0976 

8988 

1132 

9045 

1289 

23 

24 

8738 

0517 

8804 

0670 

8868 

0824 

8929 

0978 

8989 

1135 

9046 

1292 

24 

25 

0.8739 

1.0519 

0.8805 

1.0672 

0.8869 

1.0826 

0.8930 

1.0981 

0.8990 

1.1137 

0.9047 

1.1295 

25 

26 

8740 

0522 

8806 

0675 

8870 

0829 

8931 

0984 

8991 

1140 

9048 

1297 

26 

27 

8741 

0524 

8807 

0677 

8871 

0831 

8932 

0986 

8992 

1142 

9049 

1300 

27 

28 

8742 

0527 

8808 

0680 

8872 

0834 

8933 

0989 

8993 

1145 

9050 

1303 

28 

29 
30~ 

874:^ 

0529 

8809 

0682 

8873 

0836 

8934 

0991 

8994 

1148 

9051 

1305 

29 

0.8745 

1.0532 

0.8810 

1.0685 

0.8874 

1.0839 

0.8935 

1.0994 

0.8995 

1.1150 

0.9052 

1.1308 

30 

31 

8746 

0534 

8812 

0688 

8875 

0842 

8936 

0997 

8996 

1153 

9053 

1311 

31 

32 

8747 

0537 

8813 

0690 

8876 

0844 

8937 

0999 

8997 

1155 

9054 

1313 

32 

33 

8748 

0540 

8814 

0693 

8877 

0847 

8938 

1002 

8998 

1158 

9055 

1316 

33 

34 

8749 

0542 

8815 

0695 

8878 

0849 

8939 

1004 

8999 

1161 

9056 

1318 

34 

35 

0.8750 

1.0545 

0.8816 

1.0698 

0.8879 

1.0852 

0.8940 

1.1007 

0.9000 

1.1163 

0.9056 

1.1321 

35 

36 

8751 

0547 

'^817 

0700 

8880 

0854 

8941 

1010 

9000 

1166 

9057 

1324 

36 

37 

8752 

0550 

8818 

0703 

8881 

0857 

8942 

1012 

9001 

1169 

9058 

1326 

37 

38 

8753 

0552 

8819 

0705 

8882 

0860 

8943 

1015 

9002 

1171 

9059 

1329 

38 

39 

8755 

0555 

8820 

0708 

8883 

0862 

8944 

1017 

9003 

1174 

9060 

1332 

39 

40 

0.8756 

1.0557 

0.8821 

1.0711 

0.8884 

1.0865 

0.8945 

1.1020 

0.9004 

1.1176 

0.9061 

1.1334 

40 

41 

8757 

0560 

8822 

0713 

8885 

0867 

8946 

1022 

9005 

1179 

9062 

1337 

41 

42 

8758 

0562 

8823 

0716 

8887 

0870 

8947 

1025 

9006 

1182 

9063 

1340 

42 

43 

8759 

0565 

8824 

0718 

8888 

0872 

8948 

1028 

9007 

1184 

9064 

1342 

43 

44 
45 

8760 

0568 

8825 

0721 

8889 

0875 

8949 

1030 

9008 

1187 

9065 

1345 

44 

0.8761 

1.0570 

0.8827 

1.0723 

0.8890 

0.0878 

0.8950 

1.1033 

0.9009 

1.1189 

0.9066 

1.1348 

45 

46 

8762 

0573 

8828 

0726 

8891 

0880 

8951 

1035 

9010 

1192 

9067 

1350 

46 

47 

8763 

0575 

8829 

0729 

8892 

0883 

8952 

1038 

9011 

1195 

9068 

1353 

47 

48 

8765 

0578 

8830 

0731 

8893 

0885 

8953 

1041 

9012 

1197 

9069 

1356 

48 

49 
50 

8766 

0580 

8831 

0734 

8894 

0888 

8954 

1043 

9013 

1200 

9069 

1358 

49 

0.8767 

1.0583 

0.8832 

1.0736 

0.8895 

1.0890 

0.8955 

1.1046 

0.9014 

1.1203 

0.9070 

1.1361 

50 

51 

8768 

0585 

8833 

0739 

8896 

0893 

8956 

1048 

9015 

1205 

9071 

1364 

51 

52 

8769 

0588 

8834 

0741 

8897 

0896 

8957 

1051 

9016 

1208 

9072 

1366 

52 

53 

S770 

0591 

8835 

0744 

8898 

0898 

8958 

1054 

9017 

1210 

907» 

1369 

53 

54 

8771 

0593 

8836 

0746 

8899 

0901 

8959 

1056 

9018 

1213 

9074 

1371 

54 

55 

0.8772 

1.0596 

0.8837 

1.0749 

0.8900 

1.0903 

0.8960 

1.1059 

0.9019 

1.1216 

0.9075 

1.1374 

55 

56 

8773 

0598 

8838 

0752 

8901 

0906 

8961 

1061 

9020 

1218 

9076 

1377 

56 

57 

8775 

0601 

8839 

0754 

8902 

0909 

8962 

1064 

9021 

1221 

9077 

1379 

57 

58 

8776 

0603 

8840 

0757 

8903 

0911 

8963 

1067 

9022 

1224 

9078 

1382 

58 

59 

8777 

0606 

8841 

0759 

8904 

0914 

8964 

1069 

9023 

1226 

9079 

1385 

59 

60 

8778 

0608 

8843 

0762 

8905 

0916 

8965 

1072 

9023 

1229 

9080 

1387 

60 

M. 

Log.  S. 

Log  T. 

Log.  8. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  8. 

Log.  T. 

Log.  S. 

Log.T. 

M. 

48- 

49' 

60° 

51* 

52* 

5 

J' 

APPARENT  DISTANCE. 

1 

132 

TABLE  XXXI.                                                          1 

LOGARITHMS  OF  THE  APPARENT  DISTANCE.                 J 

APPARENT  DISTANCE.                                    i 

M. 

54- 

55' 

56°     1 

57°    .     58° 

59° 

M. 

Log.  S. 

Log-T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S.  Log.  T. 

Log.  S. 

Log.  T. 

0 

0.9080 

1.1387 

0.9134 

1.1548 

0.9186 

1.1710 

0.9236 

1.1875 

0.9284 

1.2042 

0.9331 

1.2212 

60 

1 

9080 

1390 

9135 

1550 

9187 

1713 

9237 

1878 

9285 

2045 

9331 

2215 

69 

2 

9081 

1393 

9135 

1553 

9187   1716| 

9238 

1880 

9286 

2048 

9332 

2218 

58 

3 

9082 

1395 

9136 

1556 

91881 

1718 

9238 

1883 

9287 

2051 

9333 

2221 

67 

4 

9083 

1398 

9137 

1558 

9189 

1721 

9239 

1886 

9287 

2053 

9334 

2224 

56 

5 

0.9084 

1.1401 

0.9138 

1.1561 

0.9190 

1.1724 

0.9240 

1.1889 

0.9288 

1.2056 

0.9334 

1  2227 

55 

6 

9085 

1403 

9139 

1564 

9191 

1726 

9241 

1891 

9289 

2059 

9335 

2229 

54 

7 

9086 

1406 

9140 

1567 

9192 

1729 

9242 

1894 

9290 

2062 

9336 

2232 

53 

8 

9087 

1409 

9141 

1569 

9193 

1732 

9242 

1897 

9291 

2065 

9337 

2235 

52 

9 

9088 

1411 

9142 

1572 

9193 

1735 

9243 

1900 

9291 

2067 

9337 

2238 

61 

10 

0.9089 

1.1414 

0.9142 

1.1575 

0.9194 

1.1737 

0.9244 

1.1903 

0.9292 

1.2070 

0.9338 

1.2241 

50 

11 

9090 

1417 

914b 

1577 

9195 

1740 

9245 

1905 

9293 

2073 

9339 

2244 

49 

12 

9091 

1419 

9144 

1580 

9196 

1743 

9246 

1908 

9294 

2076 

9340 

2247 

48 

13 

9091 

1422 

9145 

1583 

9197 

1746 

9247 

1911 

9294 

2079 

9340   2250 

47 

14 

9092 

1425 

9146 

1585 

9198 

1748 

9247 

1914 

9295 

2082 

9341 

2252 

46 

15 

0.9093 

1.1427 

0.9147 

1.1588 

0.9198 

1.1751 

0.9248 

1.1916 

0.9296 

1.2084 

0.9342 

1.2255 

45 

16 

9094 

1430 

9148 

1591 

9199 

1754 

9249 

1919 

9297 

2087 

9343 

2258 

44 

17 

9095 

1433 

9149 

1594 

9200 

1757 

9250 

1922 

9298 

2090 

9343 

2261 

43 

18 

9096 

1435 

9149 

1596 

9201 

1759 

9251 

1925 

9298 

2093 

9344 

2264 

42 

19 

9097 

1438 

9150 

1599 

9202 

1762 

9251 

1928 

9299 

2096 

9345 

2267 

41 

20 

0.9098 

1.1441 

0.9151 

1.1602 

0.9203 

1.1765 

0.9252 

1.1930 

0.9300 

1.2098 

0.9346 

1.2270 

40 

21 

9099 

1443 

9152 

1604 

9204 

1767 

9253 

1933 

9301 

2101 

9346 

3273 

3» 

22 

9100 

1446 

9153 

1607 

9204 

1770 

9254 

1936 

9301 

2104 

9347 

2275 

38 

23 

9101 

1449 

9154 

1610 

9205 

1773 

9255 

1939 

9302 

2107 

9348 

2278 

37 

24 

9101 

1451 

9155 

1612 

9206 

1776 

9255 

1941 

9303 

2110 

9349 

2281 

36 

25 

0.9102 

1.1454 

0.9156 

1.1615 

0.9207 

1.1778 

0.9256 

1.1944 

0.9304 

1.2113 

0.9349 

1.2284 

35 

26 

9103 

1457 

9156 

1618 

9208 

1781 

9257 

1947 

9305 

2115 

9350 

2287 

34 

27 

9104 

1459 

9157 

1621 

9209 

1784 

9258 

1950 

9305 

2118 

9351 

2290 

33 

28 

9105 

1462 

9158 

1623 

9209 

1787 

9259 

1953 

9306 

2121 

9352 

2293 

32 

29 

9106 

1465 

9159 

1626 

9210 

1789 

9259 

1955 

9307 

2124 

9352 

2296 

31 

30 

0.9107 

1.1467 

0.9160 

1.1629 

0.9211 

1.1792 

0.9260 

1.1958 

0.9308 

1.2127 

0.9353 

1.2299 

30 

31 

9108 

1470 

9161 

1631 

9212 

1795 

9261 

1961 

9308 

2130 

9354 

2301 

29 

32 

9109 

1473 

9162 

1634 

9213 

1798 

9262 

1964 

9309 

2132 

9355 

2304 

28 

33 

9110 

1475 

9163 

1637 

9214 

1800 

9263 

1966 

9310 

2135 

9355 

2307 

27 

34 
35 

9110 

1478 

9163 

1639 

9214 

1803 

9264 

1969 

9311 

2138 

9356 

2310 

26 

0.9111 

1.1481 

0.9164 

1.1642 

0.9215 

1.1806 

0.9264 

1.1972 

0.9312 

1.2141 

0.9357 

1.2313 

25 

36 

9112 

1483 

9165 

1645 

9216 

1809 

9265 

1975 

9312 

2144 

9358 

2316 

24 

37 

9113 

1486 

9166 

1648 

9217 

1811 

9266 

1978 

9313 

2147 

9358 

2319 

23 

38 

9114 

1489 

9167 

1650 

:)218 

1814 

9267 

1980 

9314 

2150 

9359 

2322 

22 

39 

9115 

1491 

9168 

1653 

9219 

1817 

9268 

1983 

9315 

2152 

9360 

2325 

21 

40 

0.9116 

1.1494 

0.9169 

1.1656 

0.9219 

1.1820 

0.9268 

1.1986 

0.9315 

1.2155 

0.9361 

1.2327 

20 

41 

9117 

1497 

9169 

1658 

9220 

1822 

9269 

1989 

9316 

2158 

9361 

2330 

19 

42 

9118 

1499 

9170 

1661 

9221 

1825 

9270 

1992 

9317 

2161 

9362 

2333 

18 

43 

9119 

1502 

9171 

1664 

9222 

1828 

9271 

1994 

9318 

2164 

9363 

2336 

17 

44 

9119 

1505 

9172 

1667 

9223 

1831 

9272 

1997 

9318 

2167 

9364 

2339 

16 

45 

0.9120 

1.1507 

0.9173 

1.1669 

0.9224 

1.1833 

0.9272 

1.2000 

0.9319 

1.2169 

0.9364 

1.2342 

15 

46 

9121 

1510 

9174 

1672 

9224 

1836 

9273 

2003 

9320 

.  2172 

9365 

2345 

14 

47 

9122 

1513 

9175 

1675 

9225 

1839 

9274 

2006 

9321 

2175 

9366 

2348 

13 

48 

9123 

1516 

9175 

1677 

9226 

1842 

9275 

2008 

9322 

2178 

9367 

2351 

12 

49 

9124 

1518 

9176 

1680 

9227 

1844 

9275 

2011 

9322 

2181 

9367 

2354 

11 

50 

0.9125 

1.1521 

0.9177 

1.1683 

0.9228 

1.1847 

0.9276 

1.2014 

0.9323 

1.2184 

0.9368 

1.2356 

10 

51 

9126 

1524 

9178 

1686 

9229 

1850 

9277 

2017 

9324 

2187 

9369 

2359 

9 

52 

9127 

1526 

9179 

1688 

9229 

1853 

9278 

2020 

9325 

2189 

9369 

2362 

8 

53 

9127 

1529 

9180 

1691 

9230 

1855 

9279 

2022 

9325 

2192 

9370 

2365 

7 

54 

9128 

1532 

9181 

1694 

9231 

1858 

9279 

2025 

9326 

2195 

9371 

2368 

6 

55 

0.9129 

1.1534 

0.9181 

1.1697 

0.9232 

1.1861 

0.9280 

1.2028 

0.9327 

1.2i98 

0.9372 

1.2371 

5 

56 

9130 

1537 

9182 

1699 

92.33 

1864 

9281 

2031 

9328 

2201 

9372 

2374 

4 

57 

9131 

1540 

9183 

1702 

9233 

1867 

9282 

2034 

9328 

2204 

9373 

2377 

3 

58 

9132 

1542 

9184 

1705 

9-234 

1869 

9283 

2036 

9329 

2207 

9374 

2380 

2 

59 

9133 

1545 

9185 

1707 

9235 

1872 

9283 

2039 

9330 

2209 

937» 

2383 

1 

60 

9134 

1548 

9186 

1710 

9236 

1875 

9284 

2042 

9331 

2212 

9375 

2386 

0 

M. 

Log.  8. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

'og  T. 

Log.  3. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  8.  '  Log.  T. 

M. 

125* 

124° 

123° 

122° 

121° 

120° 

APPARENT  DISTANCE.                                 | 

TABLE  XXXI.                    133 

LOGARITHMS  OF  THE  APPARENT  DISTANCE 

APPARENT  DISTANCE. 

M. 

60°    1 

61* 

62° 

63°    1 

64°     1 

65° 

M. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  8.  Log.  T. 

Log.  S.  1 

Log.  T. 

Log.  S.  1 

Log.  T. 

Log.  S. 

Log.  T. 

0 

3.93751 

L.2386( 

).9418] 

.2562 ( 

). 9459  1 

.27430.9499  J 

1.29280.9537 

1.3118 

3.9573 

1.3313 

(id 

1 

9376 

2389 

9419 

2565 

9460 

2746 

9499 

2931 

9537 

3121 

9573 

3317 

59 

2 

9377 

2391 

9420 

2568 

9461 

2749 

9500 

3935 

9538 

3125 

9574 

3320 

58 

3 

9377 

2394 

9420 

2571 

9461 

2752 

9501 

2938 

9538 

3128 

9575 

3323 

57 

4 

9378 

2397 

9421 

2574 

9462 

2755 

950a 

2941 

9539 

3131 

9575 

3326 

56 

5 

3.9379 

1.2400 

).9422 

1.2577 ( 

3.9463 

1.2759 

3.9502 

1 . 2944 

3.9540 

1.3134 

30'=:6 

1.3330 

55 

6 

9380 

2403 

9422 

2580 

9463 

2762 

9503 

2947 

9540 

3137 

9576 

3333 

54 

7 

9380 

2406 

9423 

2583 

9464 

2765 

9503 

2950 

9541 

3141 

9577 

3336 

53 

8 

9381 

2409 

9424 

2586 

9465 

2768 

9504 

2953 

9542 

3144 

9577 

3340 

52 

9 

9382 

2412 

9424 

2589 

9465 

2771 

9505 

2957 

9542 

3147 

9578 

3343 

61 

10 

0.9383 

1.2415 

0.9425 

1.2592 

0.9466 

1.2774 

0.9505 

1.296U 

0.9543 

1.3150 

0.9579 

1.3346 

50 

11 

9383 

2418 

9426 

2595 

9467 

2777 

9506 

2963 

9543 

3154 

9579 

3350 

49 

12 

9384 

2421 

9427 

2598 

9467 

2780 

9506 

2966 

9544 

3157 

9580 

3353 

48 

13 

9385 

2424 

9427 

2601 

9468 

2783 

9507 

2969 

9545 

3160 

9580 

3356 

47 

14 

9385 

2427 

9428 

2604 

9469 

2786 

9508 

2972 

9545 

3163 

9581 

3360 

46 

15 

0.9386 

1.2429 

0.9429 

1.2607 

0.9469 

1.2789 

0.9508 

1.2975 

0.9546 

1.31660.9582 

1.3363 

45 

16 

9387 

2432 

9429 

2610 

9470 

2792 

9509 

2978 

9546 

3170 

9582 

3366 

44 

17 

9388 

2435 

9430 

2613 

9471 

2795 

9510 

2982 

9547 

3173 

9583 

3370 

43 

18 

9388 

2438 

9431 

2616 

9471 

2798 

9510 

2985 

9548 

3176 

9583 

3373 

42 

19 
20 

9389 

2441 

9431 

2619 

9472 

2801 

9511 

2988 

9548 

3179 

9584 

3376 

41 

0.9390 

1.2444 

0.9432 

1.2622 

0.9473 

1.2804 

0.9512 

1.2991 

0.9549 

1.3183 

0.9584 

1.3380 

40 

21 

9391 

2447 

9433 

2625 

9473 

2808 

9512 

2994 

9549 

3186 

9585 

3383 

39 

22 

9391 

2450 

9433 

2628 

9474 

2811 

9513 

2997 

9550 

3189 

9586 

3386 

38 

23 

9392 

2453 

9434 

2631 

9475 

2814 

9513 

3001 

9551 

3192 

9586 

3390 

37 

24 

9393 

2456 

9435 

2634 

9475 

2817 

9514 

3004 

9551 

3196 

9587 

3393 

36 

25 

0.9393 

1.2459 

0.9436 

1.2637 

0.9476 

1.2820 

0,9515 

1.3007 

0.9552 

1.3199 

0.9587 

1.3396 

35 

26 

9394 

2462 

9436 

2640 

9477 

2823 

9515 

3010 

9552 

3202 

9588 

3400 

34 

27 

9395 

2465 

9437 

2643 

9477 

2826 

9516 

3013 

9553 

3205 

9588 

3403 

33 

28 

9396 

2468 

9438 

2646 

9478 

2829 

9517 

3016 

9554 

3209 

9589 

3406 

32 

29 

9396 

2471 

9438 

2649 

9479 

2832 

9517 

3019 

9554 

3212 

9590 

3410 

31 

30 

0.9397 

1.2474 

0.9439 

1.2652 

0.9479 

1.2835 

0.9518 

1.3023 

0.9555 

1.3215 

0.9590 

1.3413 

30 

31 

9398 

2477 

9440 

2655 

9480 

2838 

9519 

3026 

9555 

3218 

9591 

3416 

29 

32 

9398 

2479 

9440 

2658 

9481 

2841 

9519 

3029 

9556 

3222 

9591 

3420 

28 

33 

9399 

2482 

9441 

2661 

9481 

2844 

9520 

3032 

9557 

3225 

9592 

3423 

27 

34 
35 

9400 

2485 

9442 

2664 

9482 

2848 

9520 

3035 

9557 

3228 

9593 

3426 

26 

0.9401 

1.2488 

0.9442 

1.2667 

0.9483 

1.2851 

0.9521 

1.3038 

0.9558 

1.3231 

0.9593 

1.3430 

25 

36 

9401 

2491 

9443 

2670 

9483 

2854 

9522 

3042 

9558 

3235 

9594 

3433 

24 

37 

9402 

2494 

9444 

2673 

9484 

2857 

9522 

3045 

9559 

3238 

9594 

3436 

23 

38 

9403 

2497 

9444 

2676 

9485 

2860 

9523 

3048 

9560 

3241 

9595 

3440 

22 

39 

9403 

2500 

9445 

2680 

9485 

2863 

9524 

3051 

9560 

3244 

9595 

3443 

21 

40 

0.9404 

1  2503 

0.9446 

1.2683 

0.9486 

1.2866 

0.9524 

1.3054 

0.9561 

1.3248 

0.9596 

1.3447 

20 

41 

9405 

2506 

9447 

2686 

9486 

2869 

9525 

3058 

9561 

3251 

9597 

3450 

19 

42 

9406 

2509 

9447 

2689 

9487 

2872 

9525 

3061 

9562 

3254 

9597 

3453 

18 

43 

9406 

2512 

9448 

2692 

9488 

2875 

9526 

3064 

9563 

3257 

9598 

3457 

17 

44 

9407 

2515 

9448 

2695 

9488 

2879 

9527 

3067 

9563 

3261 

9598 

3460 

16 

45 

0.9408 

1.2518 

0.9449 

1.2698 

0.9489 

1.2882 

0.9527 

1.3070 

0.956-4 

3.3264 

0.9599 

1.3463 

15 

46 

940? 

2521 

9450 

2701 

949C 

2885 

9528 

3073 

9564 

3267 

9599 

3467 

14 

47 

9409 

252-^ 

9451 

270-4 

9490 

2888 

9529 

3077 

9565 

3271 

9600 

3470 

13 

48 

941C 

2527 

9451 

2707 

9491 

2891 

9529 

308C 

956fc 

3274 

9601 

3473 

12 

49 

941C 

)   253C 

9452 

-   271C 

)   9492 

2894 

953C 

3083 

956€ 

3277 

9601 

3477 

11 

50 

0.9411 

1.253c 

!0.945c 

1.271c 

0.9492 

1.2897 

0.953C 

11.3086 

0.9567 

1.3280 

0.9602 

1.3480 

10 

51 

9415 

!   2536 

i   945c 

!   27H 

)   949S 

290C 

9531 

3089 

9567 

3284 

9602 

3484 

9 

52 

941c 

\      253c 

)      945^ 

I   271C 

1   949-5 

[      2903 

9532 

.   3093 

9568 

3287 

9603 

3487 

8 

53 

941c 

s   2545 

!   945^ 

)   2725 

!   9494 

[      2907 

9532 

'   3096 

9569 

3290 

9603 

3490 

7 

54 

941^ 

I   254; 

)   945f 

>   272^ 

)   949^ 

)   291C 

953c 

309S 

9569 

3294 

9604 

3494 

6 

55 

0.941^ 

J1.254J 

50.945f 

51.272^ 

?0.949f 

)1.291c 

0.953-4 

H.3105 

0.957C 

»1.3297 

0.9604 

1.3497 

5 

56 

941^ 

j   255] 

945^ 

'   2731 

949f 

)   291C 

953-4 

[      310t 

957C 

1   330C 

9605 

3501 

4 

57 

941( 

)   255- 

\      945^ 

'   273^ 

I   9497 

'   29U 

953t 

)   3109 

9571 

3303 

9606 

3504 

3 

58 

941' 

r   255' 

•   945J 

5   273'; 

'   949J 

!   2925 

!   953^ 

)   3115 

9572 

!   3307 

9606 

3507 

2 

59 

941' 

I      256( 

)   945t 

>   274C 

)   949J 

!   292.! 

)   953f 

5   311; 

9575 

!   331C 

9607 

3511 

1 

60 

941J 

i      2565 

I      945i 

)   274: 

}   949c 

>   2925 

i   9537 

'      31U 

957c 

!   331c 

9607 

3514 

0 

M. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  3. 

Log.  T. 

Log.  3. 

Log.  T. 

M. 

119° 

118° 

117° 

116° 

115° 

114° 

APPARENT  DISTANCE. 

134                 TABLE  XXXI. 

LOGARITHMS  OF  THE  APPARENT  DISTANCE. 

APPARENT  DISTANCE. 

M. 

66" 

67* 

68° 

69° 

70° 

71° 

M. 
60 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

1  Log.  T. 

0 

0.9607 

1.3514 

0.9640 

1.3721 

0.9672 

1.3936 

0.9702 

1.4158 

0.9730 

1.4389 

0  9757 

1  4630 

1 

9608 

3518 

9641 

3725 

9672 

3940 

9702 

4162 

9730 

4393 

9757 

1634 

59 

2 

9608 

3521 

9641 

3729 

9673 

3943 

9702 

4166 

9731 

4397 

9758 

1638 

58 

3 

9609 

3524 

9642 

3732 

9673 

3947 

9703 

4170 

9731 

4401 

9758 

4643 

57 

4 

9610 

3528 

9642 

3736 

9674 

3950 

9703 

4173 

9732 

4405 

9758 

4647 

56 
55 

5 

0.9610 

1.3531 

0.9643 

1.3739 

0.9674 

1.3954 

0.9704 

1.4177 

0.9732 

1.4409 

0.9759 

1.4651 

6 

9611 

3535 

9643 

3743 

9675 

3958 

9704 

4181 

9733 

4413 

9759 

4655 

54 

7 

9611 

3538 

9644 

3746 

9675 

3961 

9705 

4185 

9733 

4417 

9760 

4659 

53 

8 

9612 

3541 

9645 

3750 

9676 

3965 

9705 

4189 

9734 

4421 

9760 

4663 

52 

9 

9612 

3545 

9645 

3753 

9676 

3969 

9706 

4192 

9734 

4125 

9761 

4667 

51 

10 

0.9613 

1.3548 

0.9646 

1-3757 

0.9677 

1.3972 

0.9706 

1.4196 

0.9734 

1.4429 

0.9761 

1.4671 

50 

11 

9613 

3552 

9646 

3760 

9677 

3976 

9707 

4200 

9735 

4433 

9761 

4676 

49 

12 

9614 

3555 

9647 

3764 

9678 

3980 

9707 

4204 

9735 

4437 

9762 

4680 

48 

13 

9615 

3559 

9647 

3767 

9678 

3983 

9708 

4208 

9736 

4441 

9762 

4684 

47 

14 

9615 

3562 

9648 

3771 

9679 

3987 

9708 

4211 

9736 

4445 

9763 

4688 

46 
45 

15 

0.9616 

1.3565 

0.9648 

1.3774 

0.9679 

1.3991 

0.9709 

1.4215 

0.9737 

1.4449 

0.9763 

1.4692 

16 

9616 

3569 

9649 

3778 

9680 

3994 

9709 

4219 

9737 

4453 

9764 

4696 

44 

17 

9617 

3572 

9649 

3781 

9680 

3998 

9710 

4223 

9738 

4457 

9764 

4700 

43 

18 

9617 

3576 

9650 

3785 

9681 

4002 

9710 

4227 

9738 

4461 

9764 

4705 

42 

19 

9618 

3579 

9650 

3789 

9681 

4005 

9711 

4230 

9739 

4465 

9765 

4709 

41 
40 

20 

0.9618 

1.3583 

0.9651 

1-3792 

0.9682 

1.4009 

0.9711 

1.4234 

0.9739 

1.4469 

0.9765 

1.4713 

21 

9619 

3586 

9651 

3796 

9682 

4013 

9712 

4238 

9739 

4473 

9766 

4717 

39 

22 

9620 

3589 

9652 

3799 

9683 

4016 

9712 

4242 

9740 

4476 

9766 

4721 

38 

23 

9620 

3593 

9652 

3803 

9683 

4020 

9713 

4246 

9740 

4480 

9767 

4725 

37 

24 

9621 

3596 

9653 

3806 

9684 

4024 

9713 

4250 

9741 

4484 

9767 

4730 

36 

25 

0.9621 

1.3600 

0.9654 

1.3810 

0.9684 

1.4028 

0.9714 

1.4253 

0.9741 

1.4488 

0.9767 

1.4734 

35 

26 

9622 

3603 

9654 

3813 

9685 

4031 

9714 

4257 

9742 

4492 

9768 

4738 

34 

27 

9622 

3607 

9655 

3817 

9685 

4035 

9714 

4261 

9742 

4496 

9768 

4742 

33 

28 

9623 

3610 

9655 

3821 

9686 

4039 

9715 

4265 

9743 

4500 

9769 

4746 

32 

29 

9623 

3614 

9656 

3824 

9686 

4042 

9715 

4269 

9743 

4504 

9769 

4751 

31 

;^o 

30 

0.9624 

1.3617 

0.9656 

1.3828 

0.9687 

1.4046 

0.9716 

1.4273 

0.9743 

1.4509 

0.9770 

1.4755 

31 

962'5 

3620 

9657 

3831 

9687 

4050 

9716 

4276 

9744 

4513 

9770 

4759 

29 

32 

9625 

3624 

9657 

3835 

9688 

4053 

9717 

4280 

9744 

4517 

9770 

4763 

28 

33 

9626 

3627 

9658 

3838 

9688 

4057 

9717 

4284 

9745 

4521 

9771 

4767 

27 

34 

9626 

3631 

9658 

3842 

9689 

4061 

9718 

4288 

9745 

4525 

9771 

4772 

26 
25 

35 

0.9627 

1.3634 

0.9659 

1.3846 

0.9689 

1.4065 

0.9718 

1.4292 

0.9746 

1.4529 

0.9772 

1.4776 

36 

9627 

3638 

9659 

3849 

9690 

4068 

9719 

4296 

9746 

4533 

9772 

4780 

24 

37 

9628 

3641 

9660 

3853 

9690 

4072 

9719 

4300 

9747 

4537 

9773 

4784 

23 

38 

9628 

3645 

9660 

3856 

9691 

4076 

9720 

4304 

9747 

1541 

9773 

4788 

22 

39 

9629 

3648 

9661 

3860 

9691 

4079 

9720 

4307 

9747 

4545 

9773 

4793 

21 
20 

40 

0.9629 

1.3652 

0.9661 

1.3864 

0.9692 

1.4083 

0.9721 

1.4311 

0.9748 

1.4549 

0.9774 

1.4797 

41 

9630 

3655 

9662 

3867 

9692 

4087 

9721 

4315 

9748 

4553 

9774 

4801 

19 

42 

9631 

3659 

9662 

3871 

9693 

4091 

9722 

4319 

9749 

4557 

9775 

4805 

18 

43 

9631 

3662 

9663 

3874 

9693 

4094 

9722 

4323 

9749 

4561 

9775 

4810 

17 

44 
45 

9632 

3666 

96631 

3878 

9694 

4098 

9722 

4327 

9750 

4565 

9775 

4814 

16 
15 

0.9632 

1.3669 

0.9664 

1.3882 

0.9694 

1.4102 

0.9723 

1.4331 

0.9750 

1.4569 

0.9776 

1.4818 

46 

9633 

3673 

9664 

3885 

9695 

4106 

9723 

4335 

9751 

4573 

9776 

4822 

14 

47 

9633 

3676 

9665 

3889 

9695 

4109 

9724 

4338 

9751 

4577 

9777 

4827 

13 

48 

9634 

3679 

9665 

3892 

9696 

4113 

9724 

4342 

9751 

4581 

9777 

4831 

12 

49 

9634 

3683 

9666 

3896 

9696 

4117 

9725 

4346 

9762 

4.585 

9778 

4835 

11 
10 

50 

0.9635 

1.3686 

0.9667 

1.3900 

0.9697 

1.4121 

0.9725 

1.4350 

0.9752 

1.4589 

0.9778 

1.4839 

51 

9635 

3690 

9667 

3903 

9697 

4124 

9726 

4354 

9753 

4593 

9778 

4844 

9 

52 

9636 

3693 

9668 

3907 

9698 

4128 

9726 

4358 

9753 

4598 

9779 

4848 

8 

53 

9636 

3697 

9668 

3910 

9698 

4132 

9727 

4362 

9754 

4602 

9779 

4852 

7 

54 

9637 

3700 

9669 

3914 

9699 

4136 

9727 

4366 

9754 

4606 

9780 

4857 

6 
5 

55 

0.9638 

1.3704 

..9669 

1.3918 

0.9699 

1.4139 

0.9728 

1.4370 

0.9755 

1.4610 

0.9780 

1.4861 

56 

9638 

3707 

9670 

3921 

9700 

4143 

9728 

4374 

9755 

4614 

9780 

4865 

4 

57 

9639 

3711 

9670 

3925 

9700 

4147 

9728 

4378 

9755 

4618 

9781 

4869 

3 

58 

9639 

3714 

9671 

3929 

9701 

4151 

9729 

4381 

9756 

4622 

9781 

4874 

2 

59 

9640 

3718 

9671 

3939 

9701 

4154 

9729 

4385 

9756 

4626 

9782 

4878 

1 

60 

9640 

3721 

9672 

3936 

9702 

4158 

9730 

4389 

9757 

4630 

9782 

4882 

0 

M. 

Log.  S. 

Log.  T. 

Log.  8. 

Log.  T. 

Log.  8. 

Log.  T. 

Log.  8. 

Log.  T. 

Log.  8. 

Log.  T. 

Lop.  S. 

Log.  T. 

M. 

US' 

112°    1 

iir      1 

110°         109°    1 

108° 

APPAKENT  DISTANCE.                                  1 

TABLE  XXXI. 

135 

LOGARITHMS  OF  THE  APPARENT  DISTANCE. 

APPARENT  DISTANCE, 

7 

M. 

72"    1 

73° 

74' 

75° 

76° 

7' 

Log.  T. 

M. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

tog.  S. 

0 

C.9782 

1.4882 

0.9806 

1.5147 

0.9828 

1.5425 

0.9849 

1.5719 

0.9869  1.6032 

0.9887 

1.6366 

60 

1 

9782 

4887 

9806 

5151 

9829 

5430 

9850 

5725 

9869 

6038 

9888 

6372 

59 

2 

9783 

4891 

9807 

5156 

9829 

5435 

9850 

5730 

9870 

6043 

9888 

6378 

58 

3 

.9783 

4895 

9807 

5160 

9829 

5439 

9850 

5735 

9870 

6048 

9888 

6384 

57 

4 

9784 

4899 

9807 

5165 

9830 

5444 

9851 

,  5740 

9870 

6054 

9888 

6389 

.'16 

5 

0.9784 

1.4904 

0.9808 

1.5169 

0.9830 

1.5449 

0.9851 

1.5745 

0.9871 

1.6059 

0.9889 

1.6395 

55 

t) 

9785 

4908 

9808 

5174 

9831 

5454 

9851 

5750 

9871 

6065 

9889 

6401 

.••)4 

7 

9785 

4912 

9809 

5178 

9831 

5459 

9852 

5755 

9871 

6070 

9889 

6407 

53 

8 

9785 

4917 

9809 

5183 

9831 

546  > 

9852 

■5760 

9872 

6076 

9890 

6413 

52 

9 

9786 

4921 

9809 

5187 

9832 

546t; 

9852 

5765 

9872 

6081 

9890 

6419 

51 

50 

10 

0.9786 

1.4925 

0.9810 

1.519-2 

0.9832 

1.5473 

0.9853 

1.5770 

0.9872 

1.6086 

0.9890 

1.6424 

11 

9787 

4930 

9810 

5197 

9832 

5478 

9853 

5775 

9872 

6092 

9890 

6430 

49 

12 

9787 

4934 

9811 

5201 

9833 

5483 

9853 

5780 

9873 

6097 

9891 

6436 

-18 

13 

9787 

4938 

9811 

5206 

9833 

5487 

9854 

5786 

9873 

6103 

9891 

6442 

47 

14 

9788 

4943 

9811 

5210 

9833 

5492 

9854 

5791 

9873 

6108 

9891 

6448 

46 
45 

15 

0.9788 

1.4947 

0.9812 

1.5215 

0.9834 

1.5497 

0.9854 

1.5796 

0.9874 

1.6114 

0.9892 

1.6454 

16 

9789 

4951 

9812 

5219 

9834 

5502 

9855 

5801 

9874 

6119 

9892 

6459 

44 

17 

9789 

4H56 

9812 

5224 

9835 

5507 

9855 

5806 

9874 

6125 

9892 

6465 

43 

18 

9789 

4960 

9813 

5229 

9835 

5512 

9855 

5811 

9875 

6130 

9892 

6471 

42 

19 

9790 

4965 

9813 

5233 

9835 

5516 

9856 

5816 

9875 

6136 

9893 

6477 

41 

40 

20 

0.9790 

1.4969 

0.9814 

1.5238 

0.9836 

1.5521 

0.9856 

1.5822 

0.9875 

1.6141 

0.9893 

1.6483 

21 

9791 

4973 

9814 

5242 

9836 

5526 

9856 

5827 

9876 

6147 

9893 

6489 

39 

22 

9791 

4978 

9814 

5247 

9836 

5531 

9857 

5832 

9876 

6152 

9894 

6495 

38 

23 

9791 

4982 

9815 

5252 

9837 

5536 

9857 

5837 

9876 

6158 

9894 

6501 

37 

24 

9792 

4986 

9815 

5256 

9837 

5541 

9857 

5842 

9876 

6163 

9894 

6507 

36 

25 

0.9792 

1.4991 

0.9815 

1.5261 

0.9837 

1.5546 

0.9858 

1.5847 

0.9877 

1.6169 

0.9894 

1.6513 

35 

26 

9793 

4995 

9816 

5265 

9838 

5551 

9858 

5853 

9877 

6174 

9895 

6519 

34 

27 

9793 

5000 

9816 

5270 

9838 

5555 

9858 

5858 

9877 

6180 

9895 

6525 

33 

28 

9793 

5004 

9817 

5275 

9838 

5560 

9859 

5863 

9878 

6185 

9895 

6531 

32 

29 

9794 

5008 

9817 

5279 

9839 

5565 

9859 

5868 

9878 

6191 

9896 

6536 

31 
30 

30 

0.9794 

1.5013 

0.9817 

1.5284 

0.9839 

1.5570 

0.9859 

1.5873 

0.9878 

1.6196 

0.9896 

1.6542 

31 

9795 

5017 

9818 

5289 

9839 

5575 

9860 

5879 

9879 

6202 

9896 

6548 

29 

32 

9795 

5022 

9818 

5293 

9840 

5580 

9860 

5884 

9879 

6208 

9896 

6554 

28 

33 

9795 

5026 

9818 

5298 

9840 

5585 

9860 

5889 

9879 

6213 

9897 

6560 

27 

34 

979- 

5030 

9^19 

5303 

9840 

5590 

9861 

5894 

9880 

6219 

9897 

6566 

26 
25 

35 

0.9796 

1.5035 

0.9819 

1.5307 

0.9841 

1.5595 

0.9861 

1.5900 

0.9880 

1.6224 

0.9897 

1.6572 

36 

9797 

5039 

9820 

5312 

9841 

5600 

9861 

5905 

9880 

6230 

9897 

6578 

24 

37 

9797 

5044 

9820 

5317 

9842 

5605 

9862 

5910 

9880 

6236 

9898 

6584 

23 

38 

9797 

5048 

9820 

5321 

9842 

5610 

9862 

5915 

9881 

6241 

9898 

6591 

22 

39 

40 

9798 

5053 

9821 

5326 

9842 

5614 

9862 

5921 

9881 

6247 

9898 

6597 

21 
20 

0.9798 

1 .5057 

0.9821 

1.5331 

0.9843 

1.5619 

0.9863 

1.5926 

0.9881 

1.6252 

0.9899 

1.6603 

41 

9799 

5061 

9821 

5335 

9843 

5624 

9863 

5931 

9882 

6258 

9899 

6609 

19 

42 

9799 

5066 

9822 

5340 

9843 

5629 

9863 

5936 

9882 

6264 

9899 

6615 

18 

43 

9799 

5070 

9822 

5345 

9844 

5634 

9864 

5942 

9882 

6269 

9899 

6621 

17 

44 

9800 

5075 

9823 

5350 

9844 

5639 

9864 

5947 

9883 

6275 

9900 

6627 

16 
15 

45 

0.9800 

1.5079 

0.9823 

1.5354 

0.9844 

1.5644 

0.9864 

1.5952 

0.9883 

1.6281 

0.9900 

1.6633 

46 

9801 

5084 

9823 

5359 

9845 

5649 

9865 

5958 

9883 

6286 

9900 

6639 

14 

47 

9801 

5088 

9824 

5363 

9845 

5654 

9865 

5963 

9883 

6292 

9901 

6645 

13 

48 

9801 

5092 

9824 

5368 

9845 

5659 

9865 

5968 

9884 

6298 

9901 

6651 

12 

49 

9802 

5097 

9824 

5373 

9846 

5664 

9866 

5973 

9884 

6303 

9901 

6657 

11 
10 

50 

0.9802 

1.5102 

0  9825 

1.5378 

0.9846 

1.5669 

0.9866 

1.5979 

0.9884 

1.6309 

0.9901 

1.6664 

51 

9802 

5106 

9825 

5382 

9846 

5674 

9866 

5984 

9885 

6315 

9902 

6670 

9 

52 

9803 

5111 

9826 

5387 

9847 

5679 

9867 

5989 

9885 

6320 

9902 

6676 

R 

53 

9803 

5115 

9826 

5392 

9847 

5684 

9867 

5995 

9885 

6326 

9902 

6682 

7 

54 

9804 

5120 

9826 

5397 

9847 

5689 

9867 

6000 

9885 

6332 

9902 

6688 

6 
5 

55 

0.9804 

1.5124 

0.9827 

1.5401 

0.9848 

1.5694 

0.9868 

1.6005 

0.9886 

1.6338 

0.9903 

1.6694 

56 

9804 

5129 

9827 

5406 

9848 

5699 

9868 

6011 

9886 

6343 

9903 

6700 

4 

57 

9805 

5133 

9827 

5411 

9848 

5704 

9868 

6016 

9886 

6349 

9903 

6707 

3 

5» 

9805 

5138 

9828 

5416 

9849 

5709 

9868 

6022 

9887 

6355 

9904 

6713 

2 

59 

9806 

5142 

9828 

5420 

9849 

5714 

9869 

6027 

9887 

6361 

9904 

6^19 

1 

60 

9806 

5147 

9828 

5425 

9849 

5719 

9869 

6032 

9887 

6366 

9904 

c;25 

0 

M 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  s. 

Log.  T 

M. 

107' 

106'    1 

105° 

104° 

103*    1 

H 

)2* 

APPARENT  DISTANCE 

1 

126                                          TABLE  XXXi. 

LOGARITHMS  OF  THE  APPARENT  DISTANCE. 

APPARENT  DISTANCE. 

M. 

78° 

79" 

80° 

81° 

82° 

83° 

M. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S.  Log.  T. 

Log.  S. 

Log.  T. 

0 

0.9904 

1.6725 

0.9919 

1.7113 

0.9934 

1.7537 

0.9946 

1.8003 

0.9958  1.8522 

0.9968 

1.9109 

6C 

1 

9904 

6731 

9920 

7120 

9934 

7544 

9946 

8011 

9958 

8531 

9968 

9119 

59 

2 

9905 

6738 

9920 

7127 

9934 

7552 

9947 

8019 

9958 

8540 

9968 

9129 

58 

3 

9905 

6744 

9920 

7134 

9934 

7559 

9947 

8027 

9958 

8550 

9968 

9140 

57 

4 

9905 

6750 

9920 

7141 

9934 

7566 

9947 

8036 

9958 

8559 

9968 

9151 

56 
55 

5 

0.9905 

1.6756 

0.9921 

1.7147 

0,9935 

1.7574 

0.9947 

1.8044 

0.9958 

1.8568 

0.9968 

1.9161 

6 

9906 

6763 

9921 

7154 

9935 

7581 

9947 

8052 

9959 

8577 

9968 

9172 

54 

7 

9906 

6769 

9921 

7161 

9935 

7589 

9948 

8060 

9959 

8587 

9969 

9182 

53 

8 

9906 

6775 

9921 

7168 

9935 

7596 

9948 

8069 

9959 

8596 

9969 

9-193 

52 

9 

9906 

6781 

9922 

7175 

9936 

7604 

9948 

8077 

9959 

8605 

1.9969 

9204 

51 
50 

10 

0.9907 

1.6788 

0.9922 

1.7181 

0.9936 

1.7611 

0.9948 

1.8085 

0.9959 

1.8615 

1 . 9-969 

1.9214 

11 

9907 

6794 

9922 

7188 

9936 

7619 

9948 

8094 

9959 

8624 

9969 

9225 

49 

12 

9907 

6800 

9922 

7195 

9936 

7626 

9949 

8102 

9960 

8633 

9969 

9236 

48 

13 

9907 

6807 

9923 

7202 

9936 

7634 

9949 

8110 

9960 

8643 

9969 

9246 

47 

14 

9908 

6813 

9923 

7209 

9937 

7641 

9949 

8119 

9960 

8652 

9970 

9257 

46 

15 

0.9908 

1.6819 

0.9923 

1.7216 

0.9937 

1.7649 

0.9949 

1.8127 

0.9960 

1.8662 

1.9970 

1.9268 

45 

16 

9908 

6826 

9923 

7223 

9937 

7657 

9949 

8136 

9960 

8671 

9970 

9279 

44 

17 

9908 

6832 

9924 

7230 

9937 

7664 

9950 

8144 

9960 

8681 

9970 

9290 

43 

18 

9909 

6838 

9924 

7236 

9937 

7672 

9950 

8152 

9961 

8690 

9970 

9301 

42 

19 

9909 

6845 

9924 

7243 

9938 

7679 

9950 

8161 

9961 

8700 

9970 

9312 

41 

20 

0.9909 

1.6851 

0.9924 

1.7250 

0.9938 

1.7687 

0.9950 

1.8170 

0.9961 

1.8709 

1.9971 

1.9322 

40 

21 

9910 

6858 

9925 

7257 

9938 

7695 

9950 

8178 

9961 

8719 

9971 

9333 

39 

22 

9910 

6864 

9925 

7264 

9938 

7702 

9951 

8186 

9961 

8728 

9971 

9344 

38 

23 

9910 

687(1 

9925 

7271 

9939 

7710 

9951 

8195 

9962 

8738 

9971 

9355 

37 

24 

9910 

6877 

9925 

7278 

9939 

7718 

9951 

8203 

9962 

8748 

9971 

9367 

36 

25 

0.9911 

1.6883 

0.9925 

1.7285 

0.9939 

1.7725 

0.9951 

1.8212 

0.9962 

1.8757 

1.9971 

1.9378 

35 

26 

9911 

6890 

9926 

7292 

9939 

7733 

9951 

8221 

9962 

8767 

9971 

9389 

34 

27 

9911 

6896 

9926 

7299 

9939 

7741 

9951 

8229 

9962 

8777 

9972 

9400 

33 

28 

9911 

6902 

9926 

7306 

9940 

7748 

9952 

8238 

9962 

8786 

9972 

9411 

32 

29 

9912 

690"\) 

9926 

7313 

9940 

7756 

9952 

8246 

9963 

8796 

9972 

9422 

31 

^- 

30 

0.9912 

1.6915 

0.9927 

1.7320 

0.9940 

1.7764 

0.9952 

1.8255 

0.9963 

1.8806 

1.9972 

1.9433 

30 

31 

9912 

6922 

9927 

7327 

9940 

7772 

9952 

8264 

9963 

8815 

9972 

9445 

29 

32 

9912 

6928 

9927 

7334 

9940 

7779 

9952 

8272 

996^3 

S825 

9972 

9456 

2S 

33 

9913 

6935 

9927 

7342 

9941 

7787 

9953 

8281 

9963 

8835 

9972 

9467 

27 

34 

9913 

6941 

9928 

7349 

9941 

7795 

9953 

8290 

9963 

8845 

9973 

9479 

26 

35 

0.9913 

1  6948 

0.9928 

1.7356 

0.9941 

1.7803 

0.9953 

1.8298 

0.9964 

1.8855 

1.9973 

1.9490 

25 

\ 

36 

9913 

6954 

9928 

7363 

9941 

7811 

9953 

8307 

9964 

8865 

9973 

9501 

24 

37 

9914 

6961 

9928 

7370 

9942 

7819 

9953 

8316 

9964 

8875 

9973 

9513 

23 

38 

9914 

6967 

9929 

7377 

9942 

7826 

9954 

8325 

9964 

8884 

9973 

9524 

22 

39 

9914 

fi974 

9929 

7384 

9942 

7834 

9954 

8333 

9964 

8894 

9973 

9536 

21 

40 

0.9914 

1.6980 

0.9929 

1.7391 

0.9942 

1.7842 

0.9954 

1.8342 

0.9964 

1.8904 

1.9973 

1.9547 

20 

41 

9915 

6987 

9929 

7399 

9942 

7850 

9954 

8351 

9964 

8914 

9974 

9559 

19 

42 

9915 

6994 

9929 

7406 

9943 

7858 

9954 

8360 

9965 

8924 

9974 

9570 

18 

43 

9915 

7oon 

9930 

7413 

9943 

7866 

9954 

8369 

9965 

8934 

9974 

9582 

17 

44 

9915 

7007 

9930 

7420 

9943 

7874 

9955 

8378 

9965 

8944 

9974 

9593 

16 

45 

0.9916 

1.7013 

0.9930 

1.7427 

0.9943 

1.7882 

0.9955 

1.8387 

0.9965 

1.8955 

1.9974 

1.9605 

15 

46 

9916 

7020 

9930 

7435 

9943 

7890 

9955 

8395 

9965 

8965 

9974 

9617 

14 

47 

9916 

7027 

9931 

7442 

9944 

7898 

9955 

8404 

9965 

8975 

9974 

9629 

13 

48 

991  fi 

7033 

9931 

7449 

9944 

7906 

9955 

8413 

9966 

8985 

9975 

9640 

12 

49 

9917 

7040 

9931 

7456 

9944 

7914 

9956 

8422 

9966 

8995 

9975 

9652 

11 

50 

0.9917 

1.7047 

0.9931 

1.7464 

0.9944 

1.7922 

0.9956 

1.8431 

0.9966 

1.9005 

1.9975 

1.9664 

10 

51 

9917 

7053 

9931 

7471 

9944 

7930 

9956 

8440 

9966 

9016 

9975 

9676 

9 

52 

9917 

7060 

9932 

7478 

9945 

7938 

9956 

8449 

9966 

9026 

9975 

9688 

8 

53 

9918 

7066 

9932 

7485 

9945 

7946 

9956 

8458 

9966 

9036 

9975 

9700 

7 

54 

9918 

7073 

9932 

7493 

9945 

7954 

9956 

8467 

9967 

9046 

9975 

9711 

6 
5 

55 

0.9918 

1.7080 

0.9932 

1.7500 

0.9945 

1.7962 

0.9957 

1.8476 

0.9967 

1.9057 

1.9975 

1.9723 

56 

9918 

7087 

9933 

7507 

9945 

7970 

9957 

8485 

9967 

9067 

9976 

9735 

4 

57 

9919 

7093 

9933 

7515 

9946 

7978 

9957 

8495 

9967 

9077 

9976 

9747 

3 

58 

9919 

7100 

9933 

7522 

9946 

7987 

9957 

8504 

9967 

9088 

9976 

9760 

2 

59 

9919 

7107 

9933 

7529 

9946 

7995 

9957 

8513 

9967 

9098 

9976 

9772 

1 

60 

9919 

7113 

9934 

7537 

9946 

8003 

9958 

8522 

9968 

9109 

9976 

9784 

0 

M. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.'T. 

Log.  .S. 

Log.  T. 

Log.  s. 

Log.  T. 

log.  8. 

Log.  T. 

M. 

lor 

100° 

99° 

98° 

97° 

96° 

APPARENT  DISTANCE.                                 j 

.... 

TABLE  XXAi. 

137 

LOGARITHMS  OF  THE  APPARENl  DlSTAi^ClS. 

APPARENT  DISTANCE. 

M. 
0 

84° 

85° 

86° 

87°     1 

88° 

89° 

M. 

Log.  S. 

Log.  T. 

Log.  s. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  b.  1 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

0.9976 

1.9784 

J. 9983; 

2.0580( 

).9989S 

2.15540.9994 

2.2806 

3.9997 

2.4569 

0.9999 

2.7581 

60 

1 

9976 

9796 

9984 

0595 

9989 

1572 

9994 

2830 

9997 

4606 

9999 

7654 

59 

2 

9976 

980S 

9984 

0610 

9990 

1590 

9994 

2855 

9997 

4642 

9999 

7728 

58 

3 

9977 

9820 

9984 

0624 

9990 

1608 

9994 

2879 

9997 

4679 

9999 

7804 

57 

4 

9977 

9833 

9984 

0639 

9990 

1627 

9994 

2904 

9998 

4717 

9999 

7880 

56 

5 

0.9977 

1.9845 

3.9984 

2.0654 

D.9990 

2.1645 

3.9994 

2.2929 

0.9998 

2.4754 

0.9999 

2.7959 

55 

6 

9977 

9857 

9984 

0669 

9990 

1664 

9994 

2954 

9998 

4792 

9999 

8038 

54 

7 

9977 

9870 

9984 

0684 

9990 

1683 

9995 

2979 

9998 

t830 

9999 

8120 

53 

8 

9977 

9882 

9984 

0698 

9990 

1701 

9995 

3004 

9998 

4869 

9999 

8202 

52 

9 

10 

9977 

9895 

9984 

0713 

9990 

1720 

9995 

3029 

9998 

4908 

1.0000 

8287 

51 

0.9977 

1.9907 

0.9985 

2.0728 

0.9990 

2.1739 

0.9995 

2.3055 

0.9998 

2.4947 

1.0000 

2.8373 

50 

11 

9978 

9920 

9985 

0744 

9990 

1758 

9995 

3081 

9998 

4987 

0000 

8460 

49 

12 

9978 

9932 

9985 

0759 

9990 

1777 

9995 

3106 

9998 

5027 

0000 

8550 

48 

13 

9978 

9945 

9985 

0774 

9991 

1796 

9995 

3132 

9998 

5067 

0000 

8641 

47 

14 

9978 

9957 

9985 

0789 

9991 

1815 

9995 

3158 

9998 

5108 

0000 

8735 

46 

15 

0.9978 

1.9970 

0.9985 

2.0804 

0.9991 

2.1835 

0.9995 

2.3185 

0.9998 

2.5149 

1.0000 

2.8830 

45 

16 

9978 

9983 

9985 

0820 

9991 

1854 

9995 

3211 

9998 

5191 

0000 

8928 

44 

17 

9978 

9995 

9985 

0835 

9991 

1874 

9995 

3238 

9998 

5233 

0000 

9028 

43 

18 

9978 

2.0008 

9985 

0850 

9991 

1893 

9995 

3264 

9998 

5275 

0000 

9130 

42 

19 

9979 

0021 

9985 

0866 

9991 

1913 

9995 

3291 

9998 

5318 

0000 

9235 

41 

20 

0.9979 

2.0034 

0.9986 

2.0882 

0.9991 

2.1933 

0.9995 

2.3318 

0.9998 

2.5362 

1.0000 

2.9342 

40 

21 

9979 

0047 

9986 

0897 

9991 

1952 

9995 

3346 

9998 

5405 

0000 

9452 

39 

22 

9979 

0060 

9986 

0913 

9991 

1972 

9995 

3373 

9998 

5449 

0000 

9565 

38 

23 

9979 

0073 

9986 

0929 

9991 

1992 

9995 

3401 

9998 

5494 

0000 

9681 

37 

24 

9979 

0086 

9986 

0944 

9991 

2012 

9996 

3429 

9998 

5539 

0000 

9799 

.36 

25 

0.9979 

2.0099 

0.9986 

2.0960 

0.9991 

2.2033 

0.9996 

2.3456 

0.9998 

2.5584 

1.0000 

2.9922 

35 

26 

9979 

0112 

9986 

0976 

9992 

2053 

9996 

3485 

9998 

5630 

0000 

3.0048 

34 

27 

9980 

0125 

9986 

0992 

9992 

2073 

9996 

3513 

9998 

5677 

0000 

0177 

33 

28 

9980 

0138 

9986 

1008 

9992 

2094 

9996 

3541 

9998 

5724 

0000 

0311 

32 

29 

9980 

0151 

9986 

024 

9992 

2114 

9996 

3570 

9998 

5771 

0000 

0449 

31 

30 

0.9980 

2.0164 

0.9987 

2.1040 

0.9992 

2.2135 

0.9996 

2.3599 

0.9999 

2.5819 

1.0000 

3.0591 

30 

31 

9980 

0178 

9987 

1056 

9992 

2156 

9996 

3628 

9999 

5868 

0000 

0739 

29 

32 

9980 

0191 

9987 

1073 

9992 

2177 

9996 

3657 

9999 

5917 

0000 

0891 

28 

33 

9980 

0204 

9987 

1089 

9992 

2198 

9996 

3687 

9999 

5967 

0000 

1049 

27 

34 

35 

9980 

0218 

9987 

1105 

9992 

2219 

9996 

3717 

9999 

6017 

0000 

1213 

26 
25 

0.9981 

2.0231 

0.9987 

2.1122 

0.9992 

2.2240 

0.9996 

2.3746 

0.9999 

2.6068 

1.0000 

3.1383 

36 

9981 

0244 

9987 

1138 

9992 

2261 

9996 

3777 

9999 

6119 

0000 

1561 

24 

37 

9981 

0258 

9987 

1155 

9992 

2283 

9996 

3807 

9999 

6171 

0000 

1745 

23 

38 

9981 

0271 

9987 

1171 

9992 

2304 

9996 

3837 

9999 

6224 

0000 

1938 

22 

39 

9981 

0285 

9987 

1188 

9993 

2326 

9996 

3868 

9999 

6277 

0000 

2140 

21 

40 

0.9981 

2.0299 

0.9988 

2.1205 

0.9993 

2.2348 

0.9996 

2.3899 

0.9999 

2.6331 

1.0000 

3.2352 

20 

41 

9981 

0312 

9988 

1222 

9993 

2369 

9996 

3930 

9999 

6386 

0000 

2575 

19 

42 

9981 

0326 

9988 

1238 

9993 

2391 

9996 

3962 

9999 

6441 

0000 

2810 

18 

43 

9982 

0340 

9988 

1255 

9993 

2413 

9997 

3993 

9999 

6497 

0000 

3058 

17 

44 

9982 

0354 

9988 

1272 

9993 

2435 

9997 

4025 

9999 

6554 

0000 

3322 

16 

45 

0.9982 

2.0367 

0.9988 

2.1289 

0.9993 

2.2458 

0.9997 

2.4057 

0.9999 

2.6611 

1.0000 

3.3602 

15 

46 

9982 

0381 

9988 

1306 

9993 

2480 

9997 

4089 

9999 

6670 

0000 

3901 

14 

47 

9982 

0395 

9988 

1324 

9993 

2502 

9997 

4122 

9999 

6729 

0000 

4223 

13 

48 

9982 

0409 

998^ 

1341 

9993 

2525 

9997 

4155 

9999 

6789 

0000 

4571 

12 

49 

9982 

0423 

9988 

1358 

9993 

2548 

9997 

4188 

9999 

6850 

0000 

4949 

11 

50 

0.9982 

2.0437 

0.9989 

2.1376 

0.9993 

2.2571 

0.9997 

2.4221 

0.9999 

2.6911 

1.0000 

3.5363 

10 

51 

9982 

0451 

9989 

1393 

9993 

2594 

9997 

4255 

9999 

6974 

0000 

5820 

9 

52 

9983 

0466 

9989 

1411 

9993 

2617 

9997 

4289 

9999 

7037 

0000 

6332 

8 

53 

9983 

048C 

9989 

1425 

9994 

2640 

9997 

4323 

9999 

7101 

0000 

6912 

7 

54 

9983 

0494 

9989 

1446 

9994 

2663 

9997 

4357 

9999 

7167 

0000 

7581 

6 
5 

55 

0.9983 

2.0508 

0.998S 

2.146-^ 

0.9994 

2.2687 

0.9997 

2.4392 

0.9999 

2.7233 

1.0000 

3.8373 

56 

9983 

0523 

998£ 

148[ 

9994 

27lf 

9997 

4427 

9999 

7300 

0000 

9342 

4 

57 

9983 

053'/ 

998£ 

1   149£ 

9994 

2734 

9997 

4462 

9999 

7369 

oooo 

4.0592 

3 

58 

9983 

0555 

998£ 

1   1517 

9994 

275? 

9997 

4497 

9999 

7438 

0000 

2352 

2 

59 

9983 

056( 

;   998C 

>   153^ 

9994 

2782 

9997 

4533 

9999 

7509 

0000 

5363 

1 

60 
M. 

9983 

058( 

)   998C 

>   155^ 

9994 

2806 

9997 

456S 

9999 

7581 

ooon 

0 

Leg.  S. 

Log.  T. 

Log.  S. 

Log.  T 

Log.  S. 

Loe.  T. 

Loj.  S. 

Log.  T. 

Log.  S. 

Log.  T. 

Log.  S.  1  Log.  T. 

M 

95" 

94' 

93° 

92° 

'   91° 

90° 

APPARENT  DISTANCE. 

1 

138 

TARLE  XXXII. 

LOGARITH 

MS  OF  THE  FIRST  i 
a  taken  from  the  Top,  and  al 

VND  SECOND  CORRECTIONS. 

The  First  Correction  it  always  to  b 

so  the  Second,  when  the  Apparent  Distance  ii  greater  than  9fV.I 

2  DEGREES. 

11'  , 

s. 

0' 

r 

2' 

3' 

4' 

5' 

6' 

7' 

8 

9'    10' 

0 

1.0000 

1.0024 

1.0049 

1.0073 

1.0098 

1.0122 

1.0147 

1.0172 

1.0197 

1.0223 

1.0248 

1.0274 

60  1 

1 

0000 

0025 

0049 

0073 

0098 

0123 

0148 

0173 

0198 

0223 

0249 

027,4 

59 

2 

0001 

0025 

0049 

0074 

0098 

0123 

0148 

0173 

0198 

0224 

0249 

0275'  58  1 

3 

0001 

0025 

0050 

0074 

0099 

0124 

0148 

0174 

0199 

0224 

0250 

0275  57  1 

4 

0002 

0026 

0050 

0075 

0099 

0124 

0149 

0174 

0199 

0224 

0250 

0276 

56 

5 

1.0002 

1.0026 

1.0051 

1.0075 

1.0100 

1.0124 

1.0149 

1.0174 

1.0200 

1.0225 

1.0250 

1.0276 

55 

6 

0002 

0027 

0051 

0075 

0100 

0125 

0150 

0175 

0200 

0225 

0251 

0276 

64 

7 

0003 

0027 

0051 

0076 

0100 

0125 

0150 

0175 

0200 

0226 

0251 

0277 

53 

8 

0003 

0027 

0052 

0076 

0101 

0126 

0151 

0176 

0201 

0226 

0252 

0277 

52 

9 

0004 

0028 

0052 

0077 

0101 

0126 

0151 

0176 

0201 

0227 

0252 

0278 

51 
50 

10 

1.0004 

1.0028 

1.0053 

1.0077 

1.0102 

1.0126 

1.0151 

1.0176 

1.0202 

1.0227 

1.0252 

1.0278 

11 

0004 

0029 

0053 

0077 

0102 

0127 

0152 

0177 

0202 

0227 

0253 

0279 

49 

12 

0005 

0029 

0053 

0078 

0103 

0127 

0152 

0177 

0202 

0228 

0253 

0279 

48 

13 

0005 

0029 

0054 

0078 

0103 

0128 

0153 

0178 

0203 

0228 

0253 

0279 

47 

14 

0006 

0030 

0054 

0079 

0103 

0128 

0153 

0178 

0203 

0229 

0254 

0280 

46 

15 

1.0006 

1.0030 

1.0C55 

1.0079 

1.0104 

1.0129 

1  0153 

1.0179 

1.0204 

1.0229 

1.0255 

1.0280 

45 

16 

0006 

0031 

0055 

0080 

0104 

0129 

0154 

0179 

0204 

0230 

0255 

0281 

44 

17 

0007 

0031 

0055 

0080 

0105 

0129 

0154 

0179 

0205 

0230 

0255 

0281 

43 

18 

0007 

0031 

0056 

0080 

0105 

0130 

0155 

0180 

0205 

0230 

0256 

0282 

42 

19 
20 

0008 

0032 

0056 

0081 

0105 

0130 

0155 

0180 

0205 

0231 

0256 

0282 

41 

1.0008 

1.0032 

1.0057 

1.0081 

1.0106 

'.0131 

1.0156 

1.0181 

1.0206 

1.0231 

1.0257 

1.0282 

40 

21 

0008 

0033 

0057 

0082 

0106 

0131 

0156 

0181 

0207 

0232 

0257 

0283 

39 

22 

0009 

0033 

0057 

0082 

0107 

0131 

0156 

0181 

0207 

0232 

0258 

0283 

38 

23 

0009 

0034 

0058 

0082 

0107 

0132 

0157 

0182 

0207 

0233 

0258 

0284 

37 

24 

0010 

0034 

0058 

0083 

0107 

0132 

0157 

0182 

0208 

0233 

0258 

0284 

36 

25 

1.0010 

1.0034 

1.0059 

1.0083 

1 .0108 

1.0133 

1.0158 

1.0183 

1.0208 

1.0233 

1.0259 

1.0285 

35 

26 

0010 

0035 

0059 

0084 

0108 

0133 

0158 

0183 

0208 

0234 

0259 

0285 

34 

27 

0011 

0035 

0060 

0084 

0109 

0134 

0158 

0184 

0209 

0234 

0259 

0285 

33 

28 

0011 

0036 

0060 

0084 

0109 

0134 

0159 

0184 

0209 

0235 

0260 

0286 

32 

29 

0012 

0036 

0060 

0085 

0110 

0134 

0159 

0184 

0210 

0235 

0260 

0286 

31 

30 

1.0012 

1.0036 

1.0061 

1.0085 

1.0110 

1.0135 

1.0160 

1.0185 

1.0210 

1.0235 

1.0261 

1.0287 

30 

31 

0012 

0037 

0061 

0086 

0110 

0135 

0160 

0185 

0211 

0236 

0261 

0287 

29 

32 

0013 

0037 

0062 

0086 

0111 

0136 

0161 

0186 

0211 

0236 

0261 

0288 

28 

33 

0013 

0038 

0062 

0087 

0111 

0136 

0161 

0186 

o".n 

0237 

0262 

0288 

27 

34 

0014 

0038 

0062 

0087 

0112 

0136 

0161 

0187 

0212 

0237 

0262 

0288 

26 

35 

1.0014 

1.0038 

1.0063 

1.0087 

1.0112 

1.0137 

1.0162 

1.0187 

1.0212 

1.0238 

1.0263 

1.0289 

25 

36 

0015 

0039 

0063 

0088 

0112 

0137 

0162 

0187 

0213 

0238 

0263 

0289 

24 

37 

0015 

0039 

0064 

0088 

0113 

0138 

0163 

0188 

0213 

0238 

0264 

0290 

23 

38 

0015 

0040 

0064 

0089 

0113 

0138 

0163 

0188 

0213 

0239 

0264 

0290 

22 

39 

0016 

0040 

0064 

0089 

0114 

0139 

0163 

0189 

0214 

0239 

0264 

0291 

21 

40 

1.0016 

1.0040 

1.0065 

1.0089 

1.0114 

1.0139 

1.0164 

1.0189 

1.0214 

1.0240 

1.0265 

1.0291 

20 

41 

0017 

0041 

0065 

0090 

0114 

0139 

0164 

0189 

0215 

0240 

0266 

0291 

19 

42 

0017 

0041 

0066 

0090 

0115 

0140 

0165 

0190 

0215 

0241 

0266 

0292 

18 

43 

0017 

0042 

0066 

0091 

0115 

0140 

0165 

0190 

0216 

0241 

0267 

0292 

17 

44 

0018 

0042 

0066 

0091 

0116 

0141 

0166 

0191 

0216 

0241 

0267 

029 

16 

45 

1.0018 

1.0042 

1.0067 

1.0091 

1.0116 

1.0141 

1.0166 

1.0191 

1.0216 

1.0242 

1.0267 

1.0293 

15 

46 

0019 

0043 

0067 

0092 

0117 

0141 

0166 

0192 

0217 

0242 

0268 

0294 

14 

47 

0019 

0043 

0068 

0092 

0117 

0142 

0167 

0192 

0217 

0243 

0268 

0294 

13 

48 

0019 

0044 

0068 

0093 

0117 

0142 

0167 

0192 

0218 

0243 

0269 

0294 

12 

49 

0020 

0044 

0068 

0093 

0113 

0143 

0168 

0193 

0218 

0244 

0269 

0295 

11 

50 

1.0020 

1.0044 

1.0069 

1.0093 

1.0118 

1.0143 

1.0168 

1.0193 

1.0219 

1.0244 

1.0270 

1.0295 

10 

51 

0021 

0045 

0069 

0094 

0119 

0143 

0169 

0194 

0219 

0244 

0270 

0296 

9 

52 

0021 

0045 

0070 

0094 

0119 

0144 

0169 

0194 

0219 

0245 

0270 

0296 

8 

53 

0021 

0046 

0070 

0095 

0119 

0144 

0169 

0194 

0220 

0245 

0271 

0297 

7 

54 
55 

0022 

0046 

0071 

0095 

0120 

0145 

0170 

0195 

0220 

0246 

0271 

0297 

6 

1.0022 

1.0046 

1.0071 

1.0096 

1.0120 

1.0145 

1.0170 

1.0195 

1.0221 

1.0246 

1.C272 

1.0297 

5 

56 

0023 

0047 

0071 

0096 

0121 

0146 

0171 

0196 

0221 

0247 

0272 

0298 

4 

57 

0023 

0047 

0072 

0096 

0121 

0146 

0171 

0196 

0221 

0247 

0273 

0298 

3 

58  i 
59' 

0023 

0048 

0072 

0097 

0122 

0146 

0171 

0197 

0222 

0247 

0273 

0299 

2 

0024 

0048 

0073 

0097 

0122 

0147 

0172 

0197 

0222 

0248 

0273 

0299 

1 

60 

0024 

0049 

0073 

0098 

0122 

0147 

0172   0197 

0223 

0248 

0274 

0300 

0 

'   59' 

58' 

57' 

56' 

55' 

54'    53'  1   52' 

51' 

50' 

49' 

48' 

s. 

7  DEGREES. 

the  Botto 

1 

vn, 

en  the  Apparent  Distance  is 

less  than  9tP,  the  Second  Oorrection  is  to  be  tak»n  from 

"          1 

TABLE  XXXII. 

139      1 

LOGARITHMS  OF  THE  FIRST  AND  SECOND  CORRECTIONS. 

The  First  Correction  is  alvaya  to  be  taken  from  the  Top,  and  also  the  Second,  when  tie  Apparent  Distance  is^ 

reaUr  than  »0O  1 

2   DEGREES.                                                                                                  1 

s. 

0 

12' 

13' 

14' 

15' 

16' 

17' 

18' 

19' 

20' 

21' 

22' 

23'            1 

1.0300 

1.0326 

1.0352 

1.0378 

1.0405 

1.0431 

1.0458 

1.04841.0512 

1.0539 

1.0566 

1.0594 

60 

1 

0300 

0326 

0352 

-0378 

0405 

0432 

0458 

0485 

0512 

0539 

0567 

0594 

59 

2 

0300 

0326 

0353 

0379 

0406 

0432 

0459 

0485 

0512 

0540 

0567 

0595 

58 

3 

0301 

0327 

0353 

0379 

0406 

0433 

0459 

0486 

0513 

0540 

0568 

0595 

57 

4 

0301 

0327 

0353 

0380 

0406 

0433 

0460 

0486 

0513 

0541 

0568 

0596 

56 
55 

5 

1.0302 

1.0328 

1.0354 

1.0380 

1.0407 

1.0434 

1.0460 

1.0487 

1.0514 

1.0541 

1.0568 

1.0596 

6 

0302 

0328 

0354 

0381 

0407 

0434 

0461 

0487 

0514 

0541 

0569 

0596 

54 

7 

03C3 

0329 

0355 

0381 

0408 

0434 

0461 

0488 

0515 

0542 

0569 

0597 

53 

8 

0303 

0329 

0355 

0381 

0408 

0435 

0462 

0488 

0515 

0542 

0570 

0597 

52 

9 

0304 

0329 

0356 

0382 

0409 

0435 

0462 

0489 

0516 

0543 

0570 

0598 

51 
50 

10 

1.0304 

1.0330 

1.0356 

1.0382 

1.0409 

1.0436 

1.0462 

1.0489 

1.0516 

1.0543 

1.0571 

1.0598 

11 

0304 

0330 

0356 

0383 

0409 

0436 

0463 

0489 

0517 

0544 

0571 

0599 

49 

12 

0305 

0331 

0357 

0383 

0410 

0437 

0463 

0490 

0517 

0544 

0572 

0599 

48 

13 

0305 

0331 

0358 

0384 

.0410 

0437 

0464 

0490 

0517 

0545 

0572 

0600 

47 

14 

0306 

0332 

0358 

0384 

0410 

0438 

0464 

0491 

0518 

0545 

0573 

0600 

46 

15 

1.0306 

1.0332 

1.0359 

1.0384 

1.0411 

1.0438 

1.0465 

1.0491 

1.0518 

1.0546 

1.0573 

1.0601 

45 

16 

0307 

0333 

0359 

0385 

0411 

0438 

0465 

0492 

0519 

0546 

0573 

0601 

44 

17 

0307 

0333 

0360 

0385 

0412 

0439 

0466 

0492 

0519 

0546 

0574 

0602 

43 

18 

0307 

0333 

0360 

0386 

0412 

0439 

0466 

0493 

0520 

0547 

0574 

0602 

42 

19 

0308 

0334 

0361 

0386 

0413 

0440 

0466 

0493 

0520 

0547 

0575 

0602 

41 
40 

20 

1.0308 

1.0334 

1.0361 

1.0387 

1.0413 

1.0440 

1.0467 

1.0493 

1.0521 

1.0548 

1.0575 

1.0603 

21 

0309 

0335 

0361 

0387 

0414 

0440 

0467 

0494 

0521 

0548 

0576 

0603 

39 

22 

0309 

0335 

0362 

0388 

0414 

0441 

0468 

0494 

0521 

0549 

0576 

0604 

38 

23 

0310 

0336 

0362 

0388 

0414 

0441 

0468 

0495 

0522 

0549 

0577 

0604 

37 

24 

0310 

0336 

0362 

0388 

0415 

0442 

0469 

0495 

0522 

0550 

0577 

0605 

36 

25 

1.0310 

1.0336 

1.0363 

1.0389 

1.0415 

1.0442 

1.0469 

1.0496 

1.0523 

1.0550 

1.0578 

1.0605 

35 

26 

0311 

0337 

0363 

0389 

0416 

0442 

0470 

0496 

0523 

0551 

0578 

0606 

34 

27 

0311 

0337 

0.^63 

0390 

0416 

0443 

0470 

0497 

0524 

0551 

0579 

0606 

33 

28 

0312 

0338 

0364 

0390 

0417 

0443 

0470 

0497 

0524 

0552 

0579 

0607 

32 

29 

0312 

0338 

0364 

0391 

0417 

0444 

0471 

0498 

0525 

0552 

0579 

0607 

31 

30 

1.0313 

1.0339 

1.0365 

1.0391 

1.0418 

1.0444 

1.0471 

1.0498 

1.0525 

1.0552 

1.0580 

1.0608 

30 

31 

0313 

0339 

0365 

0392 

0418 

0445 

0471 

0498 

0526 

0553 

0580 

0608 

29 

32 

0313 

0339 

0366 

0392 

0418 

0445 

'  0472 

0499 

0526 

0553 

0581 

0609 

28 

33 

0314 

0340 

0366 

0392 

0419 

0446 

0472 

0499 

0526 

0554 

0581 

0609 

27 

34 
35 

0314 

0340 

0366 

0393 

0419 

0446 

0472 

0500 

0527 

0554 

0582 

0609 

26 

1.0315 

1.0341 

1.0367 

1.0393 

1.0420 

1.0446 

1.0473 

1.0500 

1.0527 

1.0555 

1.0582 

1.0610 

25 

36 

0315 

0341 

0367 

0394 

0420 

0447 

0474 

0501 

0528 

0555 

0583 

0610 

24 

37 

0316 

0342 

0368 

0394 

0421 

0447 

0474 

0501 

0528 

0556 

0583 

0611 

23 

38 

0316 

0342 

0368 

0395 

0421 

0448 

0475 

0502 

0529 

0556 

0584 

0611 

22 

39 

40 

0317 

0342 

0369 

0395 

0422 

0448 

0475 

0502 

0529 

0557 

0584 

0612 

21 

1.0317 

1.0343 

1.0369 

1.0395 

1.0422 

1.0449 

1.0475 

1.0502 

1.0530 

1.0557 

1.0585 

1.0612 

20 

41 

0318 

0343 

0370 

0396 

0422 

0449 

0476 

0503 

0531 

0557 

0585 

0613 

19 

42 

0318 

0344 

0370 

0396 

0423 

0450 

0476 

0503 

0531 

05  58 

0585 

0613 

18 

43 

0318 

0344 

0370 

0397 

0423 

0450 

0477 

0504 

0531 

0558 

0586 

0614 

17 

44 

0319 

0345 

0371 

0397 

0424 

0450 

0477 

0504 

0532 

0559 

0586 

0614 

16 

45 

1.0319 

1.0345 

1.0371 

1.0398 

1.0424 

1.0451 

1.0478 

1.0505 

1.0532 

1.0559 

1.0587 

1.0615 

15 

46 

0319 

0346 

0372 

0398 

0425 

0451 

0478 

0505 

0532 

0560 

0587 

0615 

14 

47 

0320 

0346 

0372 

0399 

0425 

0452 

0479 

0506 

0533 

0560 

0588 

0615 

13 

48 

0320 

0346 

0373 

0399 

0426 

0452 

0479 

0506 

0533 

0561 

0588 

0616 

12 

49 

0321 

0347 

0373 

0399 

0426 

0453 

0480 

0507 

0534 

0561 

0589 

0616 

11 

50 

1.0321 

1.0347 

1.0374 

1.0400 

1.0426 

1.0453 

1.0480 

1.0507 

1.0534 

1.0562 

1.0589 

1.0617 

10 

51 

0322 

0348 

0374 

0400 

0427 

0454 

0480 

0507 

0535 

0562 

0590 

0617 

9 

52 

0322 

0348 

0374 

0401 

0427 

0454 

0481 

0508 

0535 

0562 

0590 

061S 

8 

53 

0323 

0349 

0375 

0401 

0428 

0454 

0481 

0508 

0536 

0563 

0591 

0618 

7 

54 

0323 

0349 

0375 

0402 

0428 

0455 

0482 

0509 

0536 

0563 

0591 

0619 

6 

55 

1.0323 

1.0349 

1.0376 

1.0402 

1.0429 

1.0455 

1.0482 

1.0509 

1.0536 

1.0564 

1.0591 

1.0619 

5 

56 

0324 

03.50 

0376 

0403 

0429 

0456 

0483 

0510 

0537 

0/64 

0592 

0620 

4 

57 

0324 

0350 

0377 

0403 

0430 

0456 

0483 

0510 

0537 

Of  65 

0592 

0620 

3 

58 

0325 

0351 

0377 

0403 

0430 

0457 

0484 

0511 

0538 

0565 

0593 

0621 

2 

59 

0325 

0351 

0377 

0404 

0430 

0457 

0484 

0511 

0538 

0566 

0593 

0621 

1 

60 

0326 

0352 

0378 

0404 

0431 

0458 

0484 

0512 

0539 

OiS6 

0594 

0621 

0 

47' 

46' 

45' 

44' 

43' 

42'  1       41'  1       40' 

39' 

38 

37' 

36' 

s. 

7  DEGREES. 

■WTi 

en  the  Apparent  I 

istance  is 

less  than  90O,  the  Second  Correction 

s  to  be  taken  from 

the  Botto 

1 

140                                         TABLE  XXXII. 

LOGARITHMS  OF  THE  FIRST  AND  SECOND  CORRECTIONS. 

The  First  Correction  is  alwayg  to  b 

9  taken  from  the  Top,  and  al 
2  DEG] 

so  the  Second,  -vrhen  the  Apparent  Distance  is  greater  than  909. 

lEES. 

s. 

24' 

25' 

26' 

27' 

28' 

29' 

30' 

31' 

32' 

33' 

34' 

35' 

0 

1 

2 
3 

4 

1.0621 
0622 
0622 
0623 
0623 

1.0649 
0650 
0650 
0651 
0651 

1.0678 
0678 
0678 
0679 
0679 

1.0706 
0706 
0707 
0707 
0708 

1.0734 
0735 
0735 
0736 
0736 

1.0763 
0763 
0764 
0764 
0765 

1.0792 
0792 
0793 
0793 
0794 

1.0821 
0821 
0822 
0822 
0823 

1.0850 
0851 
0851 
0852 
0852 

1.0880 
0880 
0881 
0881 
0882 

1.0909 
0910 
0910 
0911 
0911 

1.0939 
0940 
0940 
0941 
0941 

60  1 

59 
5>J 
57 
56 

5 
6 

7 
8 
9 

1.0624 
0624 
0625 
0625 
0626 

1.0652 
0652 
0653 
0653 
0654 

1.0680 
0680 
0681 
0681 
0682 

1.0708 
0709 
0709 
0710 
0710 

1,0737 
0737 
0738 
0738 
0739 

1.0765 
0766 
0766 
0767 
0767 

1.0794 
0795 
0795 
0796 
0796 

1.0823 
0824 
0824 
0825 
0825 

1.0853 
0853 
0854 
0854 
0855 

1.0882 
0883 
0883 
0883 
0884 

1.0912 
0912 
0913 
0913 
0914 

1.0942 
0942 
0943 
0943 
0944 

55 
54 
53 
,52 
51 

10 
11 
12 
13 
14 

1.0626 
0627 
0627 
0628 
0628 

1.0654 
0655 
0655 
0655 
0656 

1.0682 
0683 
0683 
0684 
0684 

1.0711 
0711 
0711 
0712 
0712 

1.0739 
0740 
0740 
0740 
0741 

1.0768 

0768 

0769 

0769 

•0770 

1.0797 
0797 
0798 
0798 
0799 

1.0826 
0826 
0827 
0827 
0828 

1.0855 
0855 
0856 
0856 
0857 

1.0884 

0885 
0885 
0886 
0886 

1.0914 
0915 
0915 
0916 
0916 

1.0944 
0945 
0945 
0946 
0946 

50 
49 
48 
47 
46 

15 
16 
17 
18 
19 

1.0628 
0629 
0629 
0630 
0630 

1.0656 
0657 
0657 
0658 
0658 

1.0685 
0685 
0686 
0686 
0686 

1.0713 
0713 
0714 
0714 
0715 

1.0741 
0742 
0742 
0743 
0743 

1.0770 
0771 
0771 
0772 
0772 

1.0799 
0800 
0800 
0801 
0801 

1.0828 
0829 
0829 
0830 
0830 

1.0857 
0858 
0858 
0859 
0859 

1.0887 
0887 
0888 
0888 
0889 

1.0917 
0917 
0918 
0918 
0919 

1.0947 
0947 
0948 
0948 
0949 

45 
44 
43 
42 
41 

20 
21 

22 
23 
24 

1.0631 
0631 
0632 
0632 
0633 

1.0659 
0659 
0660 
0660 
0661 

1.0687 
0687 
0688 
0688 
0689 

1.0715 
0716 
0716 
0717 
0717 

1.0744 
0744 
0745 
0745 
0746 

1.0773 
0773 
0774 
0774 
0774 

1.0801 
0802 
0802 
0803 
0803 

1.0831 
0831 
0832 
0832 
0833 

1.0860 
0860 
0861 
0861 
0862 

1.0889 
0890 
0890 
0891 
0891 

1.0919 
0920 
0920 
0921 
0921 

1.0949 
0950 
0950 
0951 
0951 

40 
39 
38 
37 
36 

25 
26 

27 
28 
29 

1.0633 
0634 
0634 
0634 
0635 

1.0661 
0662 
0662 
0663 
0663 

1.0689 
0690 
0690 
0691 
0691 

1.0718 
0718 
0719 
0719 
0720 

1.0746 

.0747 

0747 

0748 

0748 

1.0775 
0775 
0776 
0776 
0777 

1.0804 
0804 
0805 
0805 
0806 

1.0833 
0834 
0834 
0834 
0835 

1.0862 
0863 
0863 
0864 
0864 

1.0892 
0893 
0893 
0894 
0894 

1.0922 
0922 
0923 
0923 
0924 

1.0952 
0952 
0953 
0953 
0954 

35 
34 
33 
32 
31 

30 
31 
32 
33 
34 

1.0635 
0636 
0636 
0637 
0637 

1.0663 
0664 
0664 
0665 
0665 

1.0692 
0692 
0693 
0693 
0694 

1.0720 
0721 
0721 
0721 

0722 

1.0749 
0749 
0750 
0750 
0751 

1.0777 
0778 
0778 
0779 
0779 

1.0806 
0807 
0807 
0808 
0808 

1.0835 
0836 
0836 
0837 
0837 

1.0865 
0865 
0866 
0866 
0867 

1.0895 
0895 
0896 
0896 
0897 

1.0924 
0925 
0925 
0926 
0926 

1.0954 
0955 
0955 
0956 
0956 

30 

29 
28 
27 
26 

35 

36 
37 
38 
39 

1.0738 
0638 
0639 
0639 
0640 

1.0666 
0666 
0667 
0667 
0668 

1.0694 
0694 
0695 
0695 
0696 

1.0722 
0723 
0723 
0724 
0724 

1.0751 
0751 
0752 
0752 
0753 

1.0780 
0780 
0781 
0781 
0782 

1.0809 
0809 
0810 
0810 
0811 

1.0838 
0838 
0839 
0839 
0840 

1.0867 
0868 
0868 
0869 
0869 

1.0897 
0898 
0898 
0899 
0899 

1.0927 
0927 
0928 
0928 
0929 

1.0957 
0957 
0958 
0958 
0959 

25 
24 
23 

22 

21 

40 
41 
42 
43 
44 

1.0640 
0641 
0641 
0641 
0642 

1.0668 
0669 
0669 
0670 
0670 

1.0696 
0697 
0697 
0698 
0698 

1.0725 
0725 
0726 
0726 
0727 

1.0753 
0754 
0754 
0755 
0755 

1.0782 
0783 
0783 
0784 
0784 

1.0811 
0812 
0812 
0813 
0813 

1.0840 
0841 
0841 
0842 
0842 

1.0870 
0870 
0871 
0871 
0872 

1.0899 
0900 
0900 
0901 
0901 

1.0929 
0930 
0930 
0931 
0931 

1.0959 
0960 
0960 
0961 
0961 

20 
19 
18 

17 
16 

45 

46 
47 
48 
49 

1.0642 
0643 
0643 
0644 
0644 

1.0670 
0671 
0671 
0672 
0672 

1.0699 
0699 
0700 
0700 
0701 

1.0727 
0728 
0728 
0729 
0729 

1.0756 
0756 
0757 
0757 
0758 

1.0785 
0785 
0786 
0786 
0787 

1.0814 
0814 
0815 
0815 
0816 

1.0843 
0843 
0844 
0844 
0845 

1.0872 
0873 
0873 
0874 
0874 

1.0902 
0902 
0903 
0903 
0904 

1.0932 
0932 
0933 
0933 
0934 

1.0962 
0962 
0963 
0963 
0964 

15 
14 
13 
12 
11 

50 
51 
52 
53 
54 

1.0645 
0645 
0646 
0646 
0647 

1.0673 
0673 
0674 
0674 
0675 

1.0701 
0702 
0702 
0703 
0703 

1.0730 
0730 
0730 
0731 
0731 

1.0758 
0759 
0759 
0760 
0760 

1.0787 
0787 
0788 
0788 
0789 

1.0816 
0816 
0817 
0817 
0818 

1.0845 
0846 
0846 
0847 
0847 

1.0875 
0875 
0876 
0876 
0877 

1.0904 
0905 
0905 
0906 
0906 

1.0934 
0935 
0935 
0936 
0936 

1.0964 
0965 
0965 
0966 
0966 

10 
9 

8 

7 
6 

5 
4 
3 
2 
1 
0 

55 
56 
57 
58 
59 
60 

1.0647 
0648 
0648 
0648 
0649 
0649 

1.0675 
0676 
0676 
0677 
0677 
0678 

1.0703 
0704 
0704 
0705 
0705 
0706 

1.0732 
0732 
0733 
0733 
0734 
0734 

1.0761 
0761 
0762 
0762 
0762 
0763 

1.0789 
0790 
0790 
0791 
0791 
0792 

1.0818 
0819 
0819 
0820 
0820 
0821 

1.0848 
0848 
0849 
0849 
0850 
0850 

1.0877 
0878 
0878 
0879 
0879 
0880 

1.0907 
0907 
0908 
0908 

0«»09 
0909 

1.0937 
0937 
0938 
0938 
0939 
0939 

1.0967 
0967 
0968 
0968 
0969 
(1969 

35'  1   34'    33' 

32'  1   31' 

30'    29' 

28'  1   27' 

26' 

25' 

1   24' 

S. 

7  DBGREES. 

When  the  Apparent  Distance  is  less  than  90O,  the  Second  Correction  is  to  be  taken  from  the  Bottom.          1 

TABl-K  XXXII. 

141 

LOGARITHMS  OF  THE  FIRST  AND  SECOND  CORRECTIONS. 

The  First  Corruction  is  always  to  be  taken  from  the  Top,  and  also  the  Socond,  when 

the  Apparent  Distance  is  griper  than  SO".! 

2   DEGKEES.                                                                                                | 

s. 

36' 

37' 

38' 

39' 

40' 

41' 

42' 

43' 

44' 

45' 

46' 

47' 

60 

0 

1.0969 

1.0999 

1.1030 

1.1061 

1.1091 

1.1123 

1.1154 

1.1186 

1.1217 

1.1249 

1.1282 

1.1314 

1 

0970 

lOOi) 

1030 

1061 

1092 

1123 

1154 

1186 

1218 

1250 

1282 

1315 

59 

2 

0970 

1000 

1031 

1062 

1092 

1124 

1155 

1187 

1218 

1250 

1283 

1315 

58 

3 

0971 

1001 

1031 

1062 

1093 

1124 

1156 

1187 

1219 

1251 

1283 

1316 

57 

4 

0971 

1001 

1032 

1063 

1094 

1125 

1156 

•   1188 

1219 

1252 

1284 

1316 

56 

5 

1.0972 

1.1002 

1.1032 

1.1063 

1.1094 

1.1125 

1.1157 

1.1188 

1.1220 

1.1252 

1.1284 

1.1317 

55 

6 

0972 

1002 

1032 

1064 

1095 

1126 

1157 

1189 

1221 

1253 

1285 

1317 

54 

7 

0973 

1003 

1033 

1064 

1095 

1126 

1158 

1189 

1221 

1253 

1285 

1318 

53 

8 

0973 

1003 

1034 

1065 

1096 

1127 

1158 

1190 

1222 

1254 

1286 

1319 

52 

9 

0974 

1004 

1034 

1065 

1096 

1127 

1159 

1190 

1222 

1254 

1287 

1319 

51 

10 

1.0974 

1.1004 

1.1035 

1.1066 

1.1097 

1.1128 

1.1159 

1.1191 

1.1223 

1,1255 

1.1287 

1.1320 

50 

11 

0975 

1005 

1035 

1066 

1097 

1128 

1160 

1191 

1223 

1255 

1288 

1320 

49 

12 

0975 

1005 

1036 

1067 

1098 

1129 

1160 

1192 

1224 

1256 

1288 

1321 

48 

13 

0976 

1006 

1036 

1067 

1098 

1129 

1161 

1192 

1224 

1256 

1289 

1321 

47 

14 

0976 

1006 

1037 

1068 

1099 

1130 

1161 

1193 

1225 

1257 

1289 

1322 

46 

15 

1.0977 

1.1007 

1,1037 

1.1068 

1.1099 

1.1130 

1.1162 

1.1193 

1.1225 

1.1257 

1.1290 

1.1322 

45 

16 

0977 

1007 

1038 

1069 

1100 

1131 

1162 

1194 

1226 

1258 

1290 

1323 

44 

17 

0978 

1008 

1039 

1069 

1100 

1131 

1163 

1195 

1226 

1259 

1291 

1323 

43 

18 

0978 

1008 

1039 

1070 

1101 

1132 

1163 

1195 

1227 

1259 

1291 

1324 

42 

19 

0979 

1009 

1040 

1070 

1101 

1132 

1164 

1196 

1227 

1260 

1292 

1325 

41 

20 

1.0979 

1.1009 

1.1040 

1.1071 

1.1102 

1.1133 

1.1164 

1.1196 

1.1228 

1.1260 

1.1292 

1.1325 

40 

21 

0980 

1010 

1041 

1071 

1102 

1134 

1165 

1197 

1229 

1261 

1293 

1326 

39 

22 

0980 

1011 

1041 

1072 

1103 

1134 

1165 

1197 

1229 

1261 

1294 

1326 

38 

23 

0981 

1011 

1042 

1072 

1103 

1135 

1166 

1198 

1230 

1262 

1294 

1327 

37 

24 

0981 

1012 

1042 

1073 

1104 

1135 

1167 

1198 

1230 

1262 

1295 

1327 

36 

25 

1.0982 

1.1012 

1.1043 

1.1073 

1.1104 

1.1136 

1.1167 

1.1199 

1.1231 

1.1263 

1.1295 

1.1328 

35 

26 

0982 

1013 

1043 

1074 

1105 

1136 

1168 

1199 

1231 

1264 

1296 

1328 

34 

27 

0983 

1013 

1044 

1074 

1105 

1137 

1168 

1200 

1232 

1264 

1296 

1329 

33 

28 

0983 

1014 

1044 

1075 

1106 

1137 

1169 

1200 

1232 

1265 

1297 

1329 

32 

29 

0984 

1014 

1045 

1075 

1106 

1138 

1169 

1201 

1233 

1265 

1297 

1330 

31 
30 

30 

1.0984 

1.1015 

1.1045 

1.1076 

1.1107 

1.1138 

1.1170 

1.1201 

1.1233 

1.1266 

1.1298 

1.1331 

31 

3985 

1016 

1046 

1076 

1108 

1139 

1170 

1202 

1234 

1266 

1298 

1331 

29 

32 

0985 

1016 

1046 

1077 

1108 

1139 

1171 

1202 

1234 

1267 

1299 

1332 

28 

33 

0986 

1017 

1047 

1078 

1109 

1140 

1171 

1203 

1235 

1267 

1300 

1332 

27 

34 
35 

0986 

1017 

1047 

1078 

1110 

1140 

1172 

1204 

1235 
1.1236 

1268 

1300 

1333 

26 
25 

1.0987 

1.1018 

1.1048 

1.1079 

1.1110 

1.1141 

1.1172 

1.1204 

1.1268 

1.1301 

1.1333 

36 

0987 

1018 

1.048 

1079 

nil 

1141 

1173 

1205 

1237 

1269 

1301 

1334 

24 

37 

0988 

1019 

1049 

1080 

1111 

1142 

1173 

1205 

1237 

1269 

1302 

1334 

23 

38 

0988 

1019 

1049 

1080 

1112 

1142 

1174 

1206 

1238 

1270 

1302 

1335 

22 

39 

0989 

1020 

1050 

1081 

1112 

1143 

1174 

1206 

1238 

1270 

1303 

1335 

21 

40 

1.0989 

1.1020 

1.1050 

1.1081 

1.1112 

1.1143 

1.1175 

1.1207 

>.1239 

1.1271 

1.1303 

1.1336 

20 

41 

0990 

1021 

1051 

1082 

1113 

1144 

1175 

1207 

1239 

1271 

1304 

1337 

19 

42 

0990 

1021 

1051 

1082 

1113 

1145 

1176 

1208 

1240 

1272 

1304 

1337 

18 

43 

0991 

1022 

1052 

1083 

1114 

1145 

1177 

1208 

1240 

1273 

1305 

1338 

17 

44 

0991 

1022 

1052 

1083 

1114 

1146 

1177 

1209 

1241 

1273 

1306 

1338 

16 

45 

1.0992 

1.1023 

1.1053 

1.1084 

1.1115 

1.1146 

1.1178 

1.1209 

1.1241 

1.1274 

1.1306 

1.1339 

15 

46 

0992 

1023 

1053 

1084 

1115 

1147 

1178 

1210 

1242 

1274 

1307 

1339 

14 

47 

0993 

1024 

1054 

1085 

1116 

1147 

1179 

1210 

1242 

1275 

1307 

1340 

13 

48 

0993 

1024 

1054 

1085 

1116 

1148 

1179 

1211 

1243 

1275 

1308 

1340 

12 

49 

0994 

1025 

1055 

1086 

1117 

1148 

1180 

1211 

1243 

1276 

1308 

1341 

11 

10 

50 

1.0994 

1.1025 

1.1055 

1.1086 

1.1117 

1.1149 

1.1180 

1.1212 

1.1244 

).1276 

1.1309 

1    1342 

51 

0995 

1026 

1056 

1087 

1118 

1149 

1181 

1213 

1245 

1277 

1309 

1342 

9 

52 

0995 

1026 

1056 

1087 

1118 

1150 

1181 

1213 

1245 

1277 

1310 

1343 

8 

53 

0996 

1027 

1057 

1088 

1119 

1150 

1182 

1214 

1246 

1278 

1310 

1343 

7 

54 

0996 

1027 

1057 

1088 

1119 

1151 

1182 

1214 

1246 

1278 

1311 

1344 

6 

55 

1.0997 

1.1028 

1.105^ 

1.1089 

1.1120 

1.1151 

1.1183 

1.1215 

1.1247 

1.1279 

>    1311 

1.1344 

5 

56 

0997 

1028 

1058 

1089 

1120 

1152 

1183 

1215 

1247 

1280 

1312 

1345 

4 

57 

0998 

1028 

1059 

1090 

1121 

1152 

1184 

1216 

1248 

1280 

1313 

1345 

3 

58 

0998 

1029 

1060 

1090 

1122 

1153 

1184 

1216 

1248 

1281 

1313 

1346 

2 

59 

0999 

1029 

1060 

1091 

1122 

1153 

1185 

1217 

1249 

1281 

1314 

1346 

1 

fiO 

0999 

1030 

1061 

1091 

1123 

1154 

1186 

1217 

1249 

1282 

1314 

1347 

0 

23' 

1      22' 

21' 

25: 

19' 

18' 

17'  1      16' 

15' 

14' 

1      13' 

1       12' 

s. 

7   DEGREES. 

"vr 

hen  the  Appajent  Distance  ialeas  than  90".  the  Second  Correction 

IS  to  be  taken  from  the  Botb 

i>-n. 

142 

TABLE  XXXIl. 

The^ 

LOGARITHMS  OF  THE  FIRST  AND  SECOND  CORRECTIONS. 

J 

rst  Correction  is  always  to  be  taken  from  the  Top.  and  also  the  Second,  when  the  Apparent  Distance  is  greater  thaa  90°  ■1 

2   DEGREES. 

S. 

48' 

49' 

50' 

51' 

52 

53' 

54' 

55' 

56' 

57' 

68' 

59' 

60 

0 

1.1347 

1.1380 

1.1413 

1.1447 

1.1481 

1.1515 

1.1549 

1.1584 

1.1619 

1.1654 

1.1689 

1.1725 

1 

1348 

1381 

1414 

1447 

1481 

1515 

155» 

1584 

1619 

1654 

1690 

1725 

59 

2 

1348 

1381 

1414 

1448 

1482 

1516 

1550 

1585 

1620 

1655 

1690 

1726 

58 

3 

1349 

1382 

1415 

1449 

1482 

1516 

1551 

1585 

1620 

1655 

1691 

1727 

57 

4 

1349 

1382 

1416 

1449 

1483 

1517 

1551 

1586 

1621 

1656 

1692 

1727 

56 
55 

5 

1.1350 

1.1383 

1.1416 

1.1450 

1.1483 

1.1518 

1.1552 

1.1587 

1.1621 

1.1657 

1.1692 

1.1728 

6 

1350 

1383 

1417 

1450 

1484 

1518 

1552 

1587 

1622 

1657 

1693 

1728 

54 

7 

1351 

1384 

1417 

1451 

1485 

1519 

1553 

1588 

1623 

1658 

1693 

1729 

53 

8 

1351 

1384 

1418 

1451 

1485 

1519 

1554 

1588 

1623 

1658 

1694 

1730 

52 

9 

1352 

1385 

1418 

1452 

1486 

1520 

1554 

1589 

1624 

1659 

1694 

1730 

51 

50 

10 

1.1352 

1.1386 

1.1419 

1.1452 

1.1486 

1.1520 

1.1555 

1.1589 

1.1624 

1.1660 

1.1695 

1.1731 

11 

1353 

1386 

1419 

1453 

1487 

1521 

1555 

1590 

1625 

1660 

1696 

1731 

49 

12 

1354 

1387 

1420 

1454 

1487 

1522 

1556 

1591 

1625 

1661 

1696 

1732 

48 

13 

1354 

1387 

1421 

1454 

1488 

1522 

1556 

1591 

1626 

1661 

1697 

1733 

47 

14 

1355 

1388 

1421 

1455 

1489 

1523 

1557 

1592 

1627 

1662 

1697 

1733 

46 

15 

1.1355 

1.1388 

1.1422 

1.1455 

1.1489 

1.1523 

1.1558 

1.1592 

1.1627 

1.1663 

1.1698 

1.1734 

45 

16 

1356 

1389 

1422 

1456 

1490 

1524 

1558 

1593 

1628 

1663 

1699 

1734 

44 

17 

1356 

1389 

1423 

1456 

1490 

1524 

1559 

1593 

1628 

1664 

1699 

1735 

43 

18 

1357 

1390 

1423 

1457 

1491 

1525 

1559 

1594 

1629 

1664 

1700 

1736 

42 

19 

1357 

1391 

1424 

1458 

1491 

1526 

1560 

1595 

1630 

1665 

1700 

1736 

41 

20 

1.1358 

1.1391 

1.1424 

1.1458 

1.1492 

1.1526 

1.1561 

1.1595 

1.1630 

1.1665 

1.1701 

1.1737 

40 

21 

1359 

1392 

1425 

1459 

1493 

1527 

1561 

1596 

1631 

1666 

1702 

1737 

39 

22 

1359 

1392 

1426 

1459 

1493 

1527 

1562 

1596 

1631 

1667 

1702 

1738 

38 

23 

1360 

1393 

1426 

1460 

1494 

1528 

1562 

1597 

1632 

1667 

1703 

1739 

37 

24 

1360 

1393 

1427 

1460 

1494 

1528 

1563 

1598 

1633 

1668 

1706 

1739 

36 

25 

1.1361 

1.1394 

1.1427 

1.1461 

1.1495 

1.1529 

1.1563 

1.1598 

1.1633 

1.1668 

1.1704 

1.1740 

35 

26 

1361 

1394 

1428 

1461 

1495 

1530 

1564 

1599 

1634 

1669 

1705 

1740 

34 

27 

1362 

1395 

1428 

1462 

1496 

1530 

1565 

1599 

1634 

1670 

1705 

1741 

33 

28 

1362 

1396 

1429 

1463 

1496 

1531 

1565 

1600 

1635 

1670 

170b 

1742 

32 

29 

1363 

1396 

1429 

1463 

1497 

1531 

1566 

1600 

1635 

1671 

1706 

1742 

31 

30 

1.1363 

1.1397 

1.1430 

1.1464 

1.1498 

1.1532 

1.1566 

1.1601 

1.1636 

1.1671 

1.1707 

1.1743 

30 

31 

1364 

1397 

1431 

1464 

1498 

1532 

1567 

1602 

1637 

1672 

1708 

1743 

29 

32 

1365 

1398 

1431 

1465 

1499 

1533 

1567 

1602 

1637 

1673 

1708 

1744 

28 

33 

1365 

1398 

1432 

1465 

1499 

1534 

1568 

1603 

1638 

1673 

1709 

1745 

27 

34 
35 

1366 

1399 

1432 

1466 

1500 

1534 

1569 

1603 

1638 

1674 

1709 

1745 

26 
25 

1.1366 

1.1399 

1.1433 

1.1467 

1.1500 

1.1535 

1.1569 

1.1604 

1.1639 

1.1675 

1.1710 

1.1746 

36 

1367 

1400 

1433 

1467 

1501 

1535 

1570 

1605 

1640 

1675 

1711 

1746 

24 

37 

1367 

1401 

1434 

1468 

1502 

1536 

1570 

1605 

1640 

1676 

1711 

1747 

23 

38 

1368 

1401 

1435 

1468 

1502 

1536 

1571 

1606 

1641 

1676 

1712 

1748 

22 

39 

1368 

1402 

1435 

1469 

1503 

1537 

1571 

1606 

1641 

1677 

1712 

1748 

21 

40 

1.1369 

1.1402 

1.1436 

1.1469 

1.1503 

1.1538 

1.1572 

1.1607 

1.1642 

1.1677 

1.1713 

1.1749 

20 

41 

1370 

1403 

1436 

1470 

1504 

1538 

1573 

1607 

1643 

1678 

1714 

1749 

19 

42 

1370 

1403 

1437 

1470 

1504 

1539 

1573 

1608 

1643 

1678 

1714 

1750 

18 

43 

1371 

1404 

1437 

1471 

1505 

1539 

1574 

1609 

1644 

1679 

1715 

1751 

17 

44 

1371 

1404 

1438 

1472 

1506 

1540 

1574 

1609 

1644 

1680 

1715 

1751 

16 

45 

1.1372 

1.1405 

1.1438 

1.1472 

1.1506 

1.1540 

1.1575 

1.1610 

1.1645 

1.1680 

1.1716 

1.1752 

15 

46 

1372 

1405 

1439 

1473 

1507 

1541 

1576 

1610 

1645 

1681 

1717 

1752 

14 

47 

1373 

1406 

1440 

1473 

1507 

1542 

1576 

1611 

1646 

1681 

1717 

1753 

13 

48 

1373 

1406 

1440 

1474 

1508 

1542 

1577 

1612 

1647 

1682 

1718 

1754 

12 

49 

1374 

1407 

1441 

1474 

1508 

1543 

1577 

1612 

1647 

1683 

1718 

1754 

11 

50 

1.1374 

1.1407 

1.1441 

1.1475 

1.1509 

1.1543 

1.1578 

1.1613 

1.1648 

1.1683 

1.1719 

1.1755 

10 

51 

1375 

1408 

1442 

1476 

1510 

1544 

1578 

1613 

1648 

1684 

1719 

1755 

9 

52 

1376 

1408 

1442 

1476 

1510 

1544 

1579 

1614 

1649 

1684 

1720 

1756 

8 

53 

1376 

1409 

1443 

1477 

1511 

1545 

1580 

1614 

1650 

1685 

1721 

1757 

7 

54 

1377 

1409 

1443 

1477 

1511 

1546 

1580 

1615 

1650 

1686 

1721 

1757 

6 

55 

I   1377 

1.1410 

1.1444 

1.1478 

1.1512 

1.1546 

1.1581 

1.1616 

1.1651 

1.1686 

.17221 

1.1758 

5 

56 

1378 

1411 

1445 

1478 

1512 

1547 

1581 

1616 

1651 

1687 

1722 

1759 

4 

57 

1378 

1411 

1445 

1479 

1513 

1547 

1582 

1617 

1652 

1687 

1723 

1759 

3 

58 

1379 

1412 

1446 

1479 

1514 

1548 

1582 

1617 

1652 

1688 

1724 

1760 

2 

59 

1379 

1412 

1446 

1480 

1514 

1548 

1583 

1618 

1653 

1689 

1724 

1760 

1 

60 

1380 

1413 

1447 

1481 

1515 

1549 

1584 

1619 

1654 

1689 

1725 

1761 

0 

11' 

10' 

9'  1        8'  1 

7' 

6'   1        5'   1 

4'  1 

3' 

2'  1        1' 

0' 

s. 

7   DEGREES. 

^  , 

•w 

tien  the  Apparent  Distance  inle»$  than  90",  the  Second  C 

orrection 

is  to  be  t! 

iken  from  the  Bottc 

)m.                        1 

TABLE  XXXll. 

143   1 

LOGARITHMS  OF  THE  FIRST  AND  SECONE 

CORRECTIONS. 

idO« 

Che  Fiist  Corxeotion  is  always  to  be  taken  from  the  Top.  and  also  the  Second,  whet 

I  the  Apparent  Distance  ih  greater  thai 

3  DEGKEES.                                         1 

S. 

0 

0' 

1' 

2' 

3' 

4' 

5' 

6' 

7' 

8' 

9' 

10' 

11' 

60 

i.i;6i 

1.1797 

1.1834 

1.1871 

1.1908 

1.1946 

1.1984 

1.2022 

1.2061 

1.2099 

1.2139 

1.2178 

1 

1762 

1798 

1835 

1871 

1909 

1946 

1984 

2023 

2061 

2100 

2139 

2179 

59 

2 

1762 

1798 

1835 

1872 

1909 

1947 

1985 

2023 

2062 

2101 

2140 

2180 

58 

3 

1763 

1799 

1836 

1873 

1910 

1948 

1986 

2024 

2062 

2101 

2141 

2180 

57 

4 

1763 

1800 

1836 

1873 

1911 

1948 

1986 

• 

2025 

2063 

2102 

2141 

2181 

56 

5 

1.1764 

1.1800 

1.1837 

1.1874 

1.1911 

1.1949 

1.1987 

1.2025 

1.2064 

1.2103 

1.2142 

1.2182 

55 

6 

1765 

1801 

1838 

1875 

1912 

1950 

1987 

2026 

2064 

2103 

2143 

2182 

54 

7 

1765 

1802 

1838 

1875 

1913 

1950 

1988 

2026 

2065 

2104 

2143 

2i83 

53 

8 

1766 

1802 

1839 

1876 

1913 

1951 

1989 

2027 

2066 

2106 

2144 

2184 

52 

9 

1766 

1803 

1839 

1876 

1914 

1951 

1989 

2028 

2066 

2105 

2145 

2184 

51 

10 

1.1767 

1.1803 

1.1840 

1.1877 

1.1914 

1.1952 

1.1990 

1.2028 

1.2067 

1.2106 

1.2145 

1.2185 

50 

11 

1768 

1804 

1841 

1878 

1915 

1953 

1991 

2029 

2068 

2107 

,    2146 

2186 

49 

12 

1768 

1805 

1841 

1878 

1916 

1953 

1991 

2030 

2068 

2107 

2147 

2186 

48 

13 

1769 

1805 

1842 

1879 

1916 

1954 

1992 

2030 

2069 

2108 

2147 

2187 

47 

14 

1769 

1806 

1843 

1880 

1917 

1955 

1993 

2031 

2070 

2109 

2148 

2188 

46 

15 

1.1770 

1.1806 

1.1843 

1.1880 

1.1918 

1.1955 

1.1994 

1.2032 

1.2070 

1.2109 

1.2149 

1.2188 

45 

16 

1771 

1807 

1844 

1881 

1918 

1956 

1994 

2032 

2071 

2110 

2149 

2189 

44 

17 

1771 

1808 

1844 

1881 

1919 

1956 

1995 

2033 

2072 

2111 

2150 

2190 

43 

18 

1772 

1808 

1845 

1882 

1919 

1957 

1996 

2033 

2072 

2111 

2151 

2190 

42 

19 

1772 

1809 

1846 

1883 

1920 

1958 

1996 

2034 

2073 

2112 

2151 

2191 

41 

20 

1.1773 

1.1809 

1.1846 

1.1883 

1.1921 

1.1959 

1.1997 

1.2035 

1.2073 

1.2113 

1.2152 

1.2192 

40 

21 

1774 

1810 

1847 

1884 

1921 

1960 

1997 

2035 

2074 

2113 

2153 

2192 

?9 

22 

1774 

1811 

1847 

1884 

1922 

1960 

1998 

2036 

2075 

2114 

2153 

2193 

38 

23 

1775 

1811 

1848 

1885 

1923 

1961 

1998 

2037 

2075 

2115 

2154 

2194 

37 

24 

1775 

1812 

1849 

1886 

1923 

1962 

1999 

2037 

2076 

2115 

2155 

2194 

36 

25 

1.1776 

1.1812 

1.1849 

1.1886 

1.1924 

1.1962 

1.2000 

1.2038 

1.2077 

1.2116 

1.2155 

1.2195 

35 

26 

1777 

1813 

1850 

1887 

1924 

1963 

2000 

2039 

2078 

2116 

2156 

2196 

34 

27 

1777 

1814 

1850 

1888 

1925 

1963 

2001 

2039 

2079 

2117 

2157 

2196 

33 

28 

1778 

1814 

1851 

1888 

1926 

1964 

2001 

2040 

2079 

2118 

2157 

2197 

32 

29 

1778 

1815 

1852 

1889 

1926 

1964 

2002 

2041 

2080 

2118 

2158 

2198 

31 
30 

30 

1.1779 

1.1816 

1.1852 

1.1889 

1.1927 

1.1965 

1.2003 

1.2041 

1.2080 

1.2119 

1.2158 

1.2198 

31 

1780 

1816 

1853 

1890 

1928 

1965 

2003 

2042 

2081 

2120 

2159 

2199 

29 

32 

1780 

1817 

1854 

1891 

1928 

1966 

2004 

2042 

2081 

2120 

2160 

2200 

28 

33 

1781 

1817 

1854 

1891 

1929 

1967 

2005 

2043 

2082 

2121 

2161 

2200 

27  1 

34 
35 

1781 

1818 

1855 

1892 

1929 

1967 

2005 

2044 

2083 

2122 

2161 

2201 

26 

1.1782 

1 .1819 

1.1856 

1.1893 

1.1930 

1.1968 

1.2006 

1.2044 

1.2083 

1.2122 

1.2162 

1.2202 

25 

36 

1783 

1819 

1.857 

1893 

1931 

1968 

2007 

2045 

2084 

2123 

2163 

2202 

24 

37 

1783 

1820 

1857 

1894 

1931 

1969 

2007 

2046 

2085 

2124 

2163 

2203 

23 

38 

1784 

1820 

1858 

1894 

1932 

1970 

2008 

2046 

2085 

2124 

2164 

2204 

22 

39 

1785 

1821 

1858 

1895 

1933 

1970 

2009 

2047 

2086 

2125 

2165 

2204 

21 

40 

1.1785 

1.1822 

1.1859 

1.1896 

1.1933 

1.1971 

1.2009 

1.2048 

1.2086 

1.2126 

1.2165 

1.2205 

20 

41 

1786 

1822 

1859 

1896 

1934 

1972 

2010 

2048 

2087 

2126 

2166 

2206 

19 

42 

1786 

1823 

1860 

1897 

1934 

1972 

2010 

2049 

2088 

2127 

2167 

2206 

18 

43 

1787 

1823 

1860 

1898 

1935 

1973 

2011 

2050 

2088 

2128 

2167 

2207 

17 

44 

1788 

1824 

1861 

1898 

1936 

1974 

2012 

2050 

2089 

2128 

2168 

2208 

16 

45 

1.1788 

1.1825 

1.1862 

1.1899 

1.1936 

1.1974 

1.2012 

1.2051 

1.2090 

1.2129 

1.2169 

1.2208 

15 

46 

1789 

1825 

1862 

1899 

1937 

1975 

2013 

2052 

2090 

2130 

2169 

2209 

14 

47 

1789 

1826 

1863 

1900 

1938 

1975 

2014 

2052 

2091 

2130 

2170 

22J0 

13 

48 

1790 

1827 

1863 

1901 

1938 

1976 

2014 

2053 

2092 

2131 

2170 

2210 

12 

49 

1791 

1827 

1864 

1901 

1939 

1977 

2015 

2053 

2092 

2132 

2171 

2211 

11 

50 

1.1791 

1.1828 

1.1865 

1.1902 

1.1939 

1.1977 

1.2016 

1.2054 

1.2093 

1.2132 

1.2172 

1.2212 

10 

51 

1792 

1828 

1865 

1903 

1940 

1978 

2016 

2055 

2094 

2133 

2172 

2212 

9 

52 

53 

'  64 

1792 

1829 

1866 

1903 

1941 

1979 

2017 

2055 

2094 

2134 

2173 

2213 

8 

1793 

1830 

1867 

1904 

1941 

1979 

2017 

2056 

2095 

2134 

2174 

2214 

7 

1794 

1830 

1867 

1904 

1942 

1980 

2018 

2057 

2096 

2135 

2174 

2214 

6 

55 

1.1794 

1.1831 

1.1868 

1.1905 

1.1942 

1.1981 

1.2019 

1.2057 

1.2096 

1.2136 

1.2175 

1.2215 

5 

56 

1795 

1831 

1868 

1906 

1943 

1981 

2019 

2058 

2097 

2136 

2176 

2216 

4 

57 

1795 

1832 

1869 

1906 

1944 

1982 

2020 

2059 

2098 

2137 

2176 

2216 

3 

58 

1796 

1833 

1870 

1907 

1944 

1982 

2021 

2059 

2098 

2137 

2177 

2217 

2 

59 

1797 

1833 

1870 

1908 

1945 

1983 

2021 

2060 

2099 

2138 

2178 

2218 

1 

60 

1797 

1834 

1871 

1908 

1946 

1984 

2022|  2061 

2099 

2139 

2178 

2218 

0 

69' 

58' 

57' 

56' 

55'    54' 

53' 

52- 

51' 

50-  1   49- 

48' 

s. 

6  DEGREES. 

W 

Tien  the  Apparent 

Distance 

8  less  than  90",  the  Second  Correction 

is  to  be  taken  from  the  Bottom. 

10 


14^1  TABLE  XXXIi. 

LOGARITHMS  OF  THE  FIRST  AND  SECOND  CORRECTIONS. 


Th«  First  Correction  is  always  to  be  ta.ken  frorr  the  Top,  and  also  the  Second,  when  the  Apparent  Distance  ia  greater  than  90°. 


S. 


10 
11 
12 
13 
14 


15 
16 
17 
18 
19 


20 
'21 
22 
23 

24 


25 
26 
27 
28 
29 


30 
31 
32 
33 
34 


35 

36 
37 
38 
39 


40 
41 
42 
43 
44 


45 
46 
47 
48 
49 


50 
51 
52 
53 
54 


55 
56 
57 
58 
59 
60 


3  DEGREES. 


1: 


.2218 
2219 
2220 
2220 
2221 


.2222 
2223 
2223 

2224 
2225 


.2225 
2226 
2227 
2227 
2228 


.2229 
2229 
2230 
2231 
2231 


.2232 
2233 
2233 
2234 
2235 


13' 


.2259 
2260 
2260 
2261 
2262 


1, 


2262 
2263 
2264 
2264 
2265 


.2266 
2266 
2267 
2268 
2268 


2269 
2270 

2270 

2271 
2272 


.2235 
2236 
2237 
223 
2238 


.2239 
2239 
2240 
2241 
2241 


.2242 
2243 
2243 
2244 
2245 


.2245 
2246 
2247 
2247 
2248 


.2249 
2249 
2250 
2251 
2251 


.2252 
2253 
2253 
2254 
2255 


.2256 
2256 
2257 
2258 
2258 
2259 


.2272 
2273 
2274 
2274 
2275 


.2276 

2277 
2277 
2278 
2279 


.2279 
2280 
2281 
2281 
2282 


14' 


.2300 
2300 
2301 
2302 
2302 


1 


2303 
2304 
2304 

2305 
2306 


1. 


2307 
2307 
2308 
2309 
2309 


2310 
2311 
2312 
2313 
2313 


.2314 
2315 
2315 
2316 
2317 


1.2317 
2318 
2319 
2320 
2320 


2283 
2283 

2284 
2285 
2285 


1, 


2286 
2287 
2287 
2288 
2289 


.2289 
2290 
2291 
2291 
2292 


2293 
2294 
2294 
2295 
2296 


.2296 
2297 
2298 
2298 
2299 
2300 


ir 


46 


.2321 
2321 
2322 
2322 
2323 


15' 


.2341 
2342 
2342 
2343 
2344 


2344 
2345 
2346 
2346 
2347 


2348 
2348 
2349 
2350 
2350 


.2351 
2352 
2353 
2353 
2354 


.2355 
2355 
2356 
2357 
2357 


1.2358 
2359 
2359 
2360 
2361 


2324 
2324 
2325 
2326 
2326 


1 


2327 
2328 
2328 
2329 
2330 


2331 
2331 
2332 
2333 
2333 


.2334 
2335 
2335 
2336 
2337 


.2337 
2338 
2339 
2339 
2340 
2341 


2362 
2363 
2364 
2364 


16' 


.2382 
2383 
2384 
2384 
2385 


1. 


2386 

2387 
2387 
2388 
2389 


1 


2389 
2390 
2391 
2391 
2392 


2393 
2394 
2394 
2395 
2396 


.2396 
2397 
2398 
2398 
2399 


1.2400 
2401 
2401 
2402 
2403 


1.23621.2403 


1.2365 
2366 
2366 
2367 
2368 


.2368 
2369 
2370 
2371 
2371 


.2372 
2373 
2373 
2374 
2375 


.2375 
2376 
2377 
2378 
2378 


.2379 
2380 
2380 
2381 
2382 
2382 


2404 
2405 
2405 


17 


.2424 

2425 
2426 
2426 

2427 


1, 


2428 
2429 
2429 
2430 
2431 


.2431 
2432 
2433 
2433 
2434 


1, 


2435 
2436 
2436 

2437 
2438 


.2438 
2439 
2440 
2441 
2441 


.2442 
2443 
2443 
2444 
2445 


1.2445 
2446 

2447 
2448 


2406   2448 


1.2407 
2408 
2408 
2409 
2410 


1 


2410 
2411 
2412 
2412 
2413 


.2414 
2415 
2415 
2416 
2417 


2417 
2418 
2419 
2419 
2420 


1.2421 
2422 
2422 
2423 
2424 
2424 


1.2449 
2450 
2450 
2451 
2452 


.2453 
2453 
2454 
2455 
2455 


.2456 
2457 
2458 
2458 
2459 


18' 


2467 
2467 
2468 
2469 
2470 


1 


2470 
2471 

2472 
2472 
2473 


.2474 
2475 
2475 
2476 
2477 


.2477 
2478 
2479 
2480 
2480 


1, 


2481 
2482 
2482 
2483 
2484 


1 


2485 
2485 
2486 
2487 
2487 


1.2488 
2489 
2489 
2490 
2491 


2492 
2492 
2493 
2494 
2494 


19' 


I. 


2510 
2510 
2511 
2512 

2512 


.2513 
2514 
2515 
2515 
2516 


1 


2517 
2517 
2518 
2519 
2520 


.2520 
2521 
2522 
2522 
2523 


,2524 
2525 
2525 
2526 
2527 


.2527 
2528 
2529 
2530 
2530 


1.2531 
2532 
2533 
2533 
2534 


1.2535 
2535 
2536 
2537 
2538 


1.24951.2538 


2496 
2497 
2497 
2498 


1, 


2460 
2460 
2461 

2462 
2462 


45' 


44' 


43' 


1.2463 
2464 
2465 
2465 
2466 
2467 
42'  I 


2499 
2499 
2500 
2501 
2502 


2502 
2503 
2504 
2504 
2505 


1.2506 
2507 
2507 
2508 
2509 
2610 


2539 
2540 
2540 
2541 


20' 


1, 


2553 
2553 

2554 
2555 
2556 


2556 
2557 
2558 
2559 
2559 


.2560 
2561 
2561 
2562 
2563 


.2564 
2564 
2565 
2566 
2566 


.2567 
2568 
2569 
2569 
2570 


1 


2571 
2572 
2572 
2573 
2574 


1.2574 
2575 
2576 

2577 
2577 


1.2578 
2579: 
2580 
2580 
2581 


21' 


.2596 
2597 
2598 
2599 
2599 


2600 
2601 
2601 
2602 
2603 


2604 
2604 
2605 
2606 
2607 


.2607 
2608 
2609 
2610 
2610 


.2611 
2612 
2612 
2613 
2614 


.2615 
2615 
2616 
2617 
2618 


1.2618 
2619 
2620 
2621 
2621 


.2542 
2543 
2543 
2544 
2545 


2545 
2546 

2547 
2548 
2548 


1.2549 
2550 
2551 
2551 
2552 
2553 


1.2582 
2583 
2583 
2584 
2585 


2585 
2586 
2587 
2588 
2588 


1 


2589 
2590 
2591 
2591 
2592 


1.2593 
2593 
2594 
2595 
2596 
2596 


1.2622 
2623 
2624 
2624 
2625 


1.2626 
2626 
2627 
2628 
2629 


22' 


2640 
2641 
2642 
2643 
2643 


.2644 
2645 
2646 
2646 
2647 


.2648 
2649 
2649 
2650 
2651 


1, 


2652 
2652 
2653 
2654 
2655 


1, 


2655 
2656 
2657 
2657 
2658 


1. 


2659 
2660 
2660 
2661 
2662 


.2663 
2663 
2664 
2665 
2666 


1.2666 
2667 
2668 
2669 
2669 


.2629 
2630 
2631 
2632 
2632 


.2633 
2634 
2635 
2635 
2636 


1.2637 
2638 
2638 
2639 
2640 
2640 


1.2670 
2671 
2672 
2672 
2673 


23' 


.2685 
2686 
2687 
2688 
2688 


1, 


2689 
2689 
2690 
2691 
2692 


2692 
2693 
2694 
2695 
2695 


2696 
2697 
2698 
2698 
2699 


.2700 
2701 
2701 
2702 
2703 


.2704 
2704 
2705 
2706 
2707 


1.2707 
2708 
2709 
2710 
2710 


1.2711 
2712 
2713 
2713 
2714 


.2674 
2675 
2675 
2676 
2677 


.2678 
2678 
2679 
2680 
2681 


41'  I   40'    39'  1  38' 


1.2681 
2682 
2683 
2684 
2684 
2685 


1.2715 
2716 
2716 

2717 
2718 


.2719 
2719 
2720 
2721 

2722 


2722 
2723 
2724 
2725 
2725 


37' 


.2726 
2727 
2728 
2729 
2729 
2730 
36' 


6  DEGREES. 


60 
59 
58 
67 
56 


55 
54 
53 
52 
51 


50 
49 
48 
47 
46 


45 
44 
43 
42 
41 


40 
39 
38 
37 
36 


35 

34 
S3 
32 
31 


30 
29 

28 
27 
26 


25 

24 
23 
22 
21 


20 
19 
18 
17 
16 


15 
14 
13 
12 
11 


10 
9 
8 

7 
6 


5 
4 
3 
2 
1 
_0^ 

s. 


When  the  Apparent  Distance  is  lets  than  90°,  the  Second  Correction  is  to  be  taken  from  the  Bottom. 


TABLE  XXXII.                                                   145 

LOGARITHMS  OF  THE  FIRST  AND  SECOND  CORRECTIONS. 

Tha  Fint  Correction  is  always  to  be  taken  from  the  Top,  and  also  the  Second,  when  the  Apparent  Distance  it  greater  thaa  90°. 

3   DEGREES. 

S. 
0 

24' 

25' 

26'         27' 

28' 

29' 

30' 

31' 

32' 

33' 

34' 

35' 

60 

1.2730 

1.2775 

1.2821 

1.2868 

1.2915 

1.2962 

1.3010 

1.3059 

1.3108 

1.3158 

1.3208 

1.3259 

1 

2731 

2776 

2822 

2869 

2916 

2963 

3011 

3060 

3109 

3158 

3209 

3259 

59 

2 

7232 

2777 

2823 

2869 

2916 

2964 

3012 

3060 

3110 

3159 

3209 

3260 

58 

3 

2732 

2778 

2824 

2870 

2917 

2965 

3013 

3061 

3110 

3160 

3210 

3261 

57 

4 
5 

^33 

2779 

2825 

2871 

2918 

2965 

3014 

3062 

3111 

3161 

3211 

3262 

56 

1.2734 

1.2779 

1.2825 

1.2872 

1.2919 

1.2966 

1.3014 

1.3063 

1.3112 

1.3162 

1.3212 

1.3263 

55 

6 

2735 

2780 

2826 

2873 

2920 

2967 

3015 

3064 

3113 

3163 

3213 

3264 

54 

7 

2735 

2781 

2827 

2873 

2920 

2968 

3016 

3065 

3114 

3163 

3214 

3265 

53 

8 

2736 

2782 

2828 

2874 

2921 

2969 

3017 

3065 

3114 

3164 

3214 

3265 

52 

9 

2737 

2782 

2828 

2875 

2922 

2969 

3018 

3066 

3115 

3165 

3215 

3266 

51 

10 

1.2738 

1.2783 

1.2829 

1.2876 

1.2923 

1.2970 

1.3018 

1.3067 

1.3116 

1.3166 

1.3216 

1.3267 

50 

11 

2738 

2784 

2830 

2876 

2924 

2971 

3019 

3068 

3117 

3167 

3217 

3268 

49 

12 

2739 

2785 

2831 

2877 

2924 

2972 

3020 

3069 

3118 

3168 

3218 

3269 

48 

13 

2740 

2785 

2831 

2878 

2925 

2973 

3021 

3069 

3119 

3168 

3219 

3270 

47 

14 
15 

2741 

2786 

2832 

2879 

2926 

2973 

3022 

3070 

3119 

3169 

3220 

3270 

46 

1.2741 

1.2787 

1.2833 

1.2880 

1.2927 

1.2974 

1.3022 

1.3071 

1.3120 

1.3170 

1.3220 

1.3271 

45 

16 

2742 

2788 

2834 

2880 

2927 

2975 

3023 

3072 

3121 

3171 

3221 

3272 

44 

17 

2743 

2788 

2835 

2881 

2928 

2976 

3024 

3073 

3122 

3172 

3222 

3273 

43 

18 

2744 

2789 

2835 

2882 

2929 

2977 

3025 

3073 

3123 

3173 

3223 

3274 

42 

19 

2744 

2790 

2836 

2883 

2930 

2977 

3026 

3074 

3124 

3173 

3224 

3275 

41 
40 

20 

1.2745 

1.2791 

1.2837 

1.2883 

1.2931 

1.2978 

1.3026 

1.3075 

1.3124 

2.3174 

1.3225 

1.3276 

21 

2746 

2792 

2838 

2884 

2931 

2979 

3027 

3076 

3125 

3175 

3225 

3276 

39 

22 

2747 

2792 

2838 

2885 

2932 

29S0 

3028 

3077 

3126 

3176 

3226 

3277 

38 

23 

2747 

2793 

2839 

2886 

»933 

2981 

3029 

3078 

3127 

3177 

3227 

3278 

37 

24 

2748 

2794 

2840 

2887 

2934 

2981 

3030 

3078 

3128 

3178 

3228 

3279 

36 

25 

1.2749 

1.2795 

1.2841 

1.2887 

1.2935 

1.2982 

1.3030 

1.3079 

1.3129 

1.3178 

1.3229 

1.3280 

35 

26 

2750 

2795 

2841 

2888 

2935 

2983 

3031 

3080 

3129 

3179 

3230 

3281 

34 

27 

2750 

2796 

2842 

2889 

2936 

2984 

3032 

3081 

3130 

3180 

3231 

3282 

33 

28 

2751 

2797 

2843 

2890 

2937 

2985 

3033 

3082 

3131 

3181 

3231 

3282 

32 

29 

2752 

2798 

2844 

2891 

2938 

2985 

3034 

3082 

3132 

3182 

3232 

3283 

31 

30 

1.2753 

1.2798 

1.2845 

1.2891 

1.2939 

1.2986 

1.3034 

1.3083 

1.3132 

1.3183 

1.3233 

1.3284 

30 

31 

2753 

2799 

2845 

2892 

2939 

2987 

3035 

3084 

3133 

3183 

3234 

3285 

29 

32 

2754 

2800 

2846 

2893 

2940 

2988 

3036 

3085 

3134 

3184 

3235 

3286 

28 

33 

2755 

2801 

2847 

2894 

2941 

2989 

3037 

3086 

3135 

3185 

3236 

3287 

27 

34 

2756 

2801 

2848 

2894 

2942 

2989 

3038 

3087 

3136 

3186 

3236 

3288 

26 

35 

1.2756 

1.2802 

1.2848 

1.2895 

1.2942 

1.2990 

1.3039 

1.3087 

1.3137 

1.3187 

1.3237 

1.3288 

25 

36 

2757 

2803 

2849 

2896 

2943 

2991 

3039 

3088 

3138 

3188 

3238 

3289 

S4 

37 

2758 

2804 

2850 

2897 

2944 

2992 

3040 

3089 

3138 

3188 

3239 

3290 

23 

38 

2759 

2805 

2851 

2898 

2945 

2993 

3041 

3090 

3139 

3189 

3240 

3291 

22 

39 

40 

2760 

2805 

2852 

2898 

2946 

2993 

3042 

3091 

3140 

3190 

3241 

3292 

21 

1.27fi0 

1,2806 

1.2852 

1.2899 

1.2946 

1.2994 

1.3043 

1.3091 

1.3141 

1.3191 

1.3242 

1.3293 

20 

41 

2761 

2807 

2853 

2900 

2947 

2995 

3043 

3092 

3142 

3192 

3242 

3294 

19 

42 

2762 

2808 

2854 

2901 

2948 

2996 

3044 

3093 

3143 

3193 

3243 

3294 

18 

43 

2763 

2808 

2855 

2901 

2949'     2997 

3045'     3094'     3143 

3193 

3244 

3295 

17 

44 

2763 

2809 

2855 

2902 

2950,     2;|Q7 

3046 

3095 

3144,     3194 

3245 

3296 

16 

l.-) 

1.2764 

1.2810 

1.2856 

1.2903 

1.2950 

1.2998 

1.3047 

1.3096 

1.3145 

1.3195 

1.3246 

1.3297 

15 

46 

2765 

2811 

2857 

2904 

2951 

2999 

3047 

3096 

3146 

3196 

3247 

3298 

14 

47 

2766 

2811 

2858 

2905 

2952 

3000 

3048 

3097 

3147 

3197 

3247 

3299 

13 

48 

2766 

2812 

2859 

2905 

2953 

3001 

3049 

3098 

3148 

3198 

3248 

3200 

12 

49 

2767 

2813 

2859 

2906 

2954 

3001 

3050 

3099 

3148 

3198 

3249 

3200 

11 

50 

1.2768 

1.2814 

1.2860 

1.2907 

1.2954 

1.3002 

1.3051 

1.3100 

1.3149 

1.3199 

1.3250 

1.3301 

10 

51 

2769 

2815 

2861 

2908 

2955 

3003 

3052 

3101 

3150 

3200 

3251 

3302 

9 

52 

2769 

2815 

2862 

2909 

2956 

3004 

3052 

3101 

3151 

3201 

3252 

3303 

8 

53 

2770 

2816 

2862 

2909 

2957 

3005 

3053 

3102 

3152 

3202 

3253 

3304 

7 

54 

2771 

2817 

2863 

2910 

2958 

3005 

3054 

3103 

.1153 

3203 

3253 

3305 

6 

55 

1.2772 

1.2818 

1.2864 

1.2911 

1.2958 

1.3006 

1.3055 

1.3104 

1.3153 

1.3204 

1.3254 

1.3306 

5 

56 

2772 

2818 

2865 

2912 

2959 

3007 

3056 

;no5 

3154 

3204 

3255 

3306 

4 

57 

2773 

2819 

2866 

2912 

2960 

3008 

3056 

3105 

3155 

3205 

3256 

3307 

3 

58 

2774 

2820 

2866 

2913 

2961 

3009 

3057 

3106 

3156 

,   3206 

3257 

33f8 

2 

59 

2775 

2821 

2867 

2914 

2962 

3009 

3058 

3107 

3157 

3207 

3258 

3309 

1 

60 

2775 

2821 

2868 

2915 

2962 

3010 

3059 

3108 

3158 

3208 

3259 

3310 

0 

35" 

34' 

33' 

32'  1       31'        30' 

29'  1       28' 

27' 

26' 

25     1       24' 

S. 

6  DfiG 

REES. 

Wl 

len  the  Apparent  Distance  is  lets  than  90°,  the  Second  Correction  U  to  be  taken  from  the  Bottom.                        1 

146 

TABLE  XXXII. 

LOGARITHMS  OF  THE  FIRST  AND  SECOND  CORRECTIONS. 

The  Fin'  Correction  is  always  to  b 

e  taken  from  the  Top,  and  also  the  Second,  -when  the  Apparent  Distance  is  greater  than  90° 

3  DEGREES. 

' 

S. 
0 

36' 

37' 

38' 

39' 

40' 

41' 

42' 

43' 

44' 

45' 

46' 

47' 

60 

1  3310 

1.3362 

1.3415 

1.3468 

1.3522 

1.3576 

1.3632 

1.3688 

1.3745 

1.3802 

1.3860 

1.3919 

1 

3311 

3363 

3415 

3469 

3523 

3577 

3633 

3689 

3746 

3803 

3861 

3920 

59 

• 

2 

3312 

3364 

3416 

3470 

3524 

3578 

3634 

3690 

3746 

3804 

3862 

3921 

58 

3 

3313 

3365 

3417 

3471 

3525 

3579 

3635 

3691 

3747 

3805 

3863 

3922 

57 

4 

3313 

3365 

3418 

3471 

3525 

3580 

3635 

3692 

3748 

3806 

3864 

3023 

56 

5 

1.3314 

1.3366 

1.3419 

1.3472 

1.3526 

1.3581 

1.3636 

1.3693 

1.3749 

1.3807 

1.3865 

1.3924 

55 

6 

3315 

3367 

3420 

3473 

3527 

3582 

3637 

3694 

3750 

3808 

3866 

3925 

54 

7 

3316 

3368 

3421 

3474 

3528 

3583 

3638 

3695 

3751 

3809 

3867 

3926 

53 

8 

3317 

3369 

3422 

3475 

3529 

3584 

3639 

3695 

3752 

3810 

3868 

3927 

52 

9 

3318 

3370 

3423 

3476 

3530 

3585 

3640 

3696 

3753 

3811 

3869 

3928 

51 

10 

1.3319 

1.3371 

1.3423 

1.3477 

1.3531 

1.3586 

1.3641 

1.3697 

1.3754 

1.3812 

1.3870 

1.3929 

50 

11 

3319 

3372 

3424 

3478 

3532 

3587 

3642 

3698 

3755 

3813 

3871 

3930 

49 

12 

3320 

3372 

3425 

3479 

3533 

3587 

3643 

3699 

3756 

3814 

3872 

3931 

48 

13 

3321 

3373 

3426 

3480 

3534 

3588 

3644 

3700 

3757 

3815 

3873 

3932 

47 

14 

15 

3322 

3374 

3427 

3480 

3535 

3589 

3645 

3701 

3758 

3816 

3874 

3933 

46 

1.3323 

1.3375 

1.3428 

1.3481 

1.3535 

1.3590 

1.3646 

1.3702 

1.3759 

1.3817 

1.3875 

1.3934 

45 

16 

3324 

3376 

3429 

3482 

3536 

3591 

3647 

3703 

3760 

3818 

3876 

3935 

44 

17 

3325 

3377 

3430 

3483 

3537 

3592 

3648 

3704 

3761 

3819 

3877 

3936 

43 

18 

3325 

3378 

3431 

3484 

3538 

3593 

3649 

3705 

3762 

3819 

3878 

3937 

42 

19 

3326 

3379 

3431 

3485 

3539 

3594 

3649 

3706 

3763 

3820 

3879 

3938 

41 

40 

20 

1.3327 

1.3379 

1.3432 

1.3486 

1.3540 

1.3595 

1.3650 

1.3707 

1.3764 

2.3821 

1.3880 

1.3939 

21 

3328 

3380 

3433 

3487 

3541 

3596 

3651 

3708 

3765 

3822 

3881 

3940 

39 

22 

3329 

3381 

3434 

3488 

3542 

3597 

3652 

3709 

3766 

3823 

3882 

3941 

38 

23 

3330 

3382 

3435 

3488 

3543 

3598 

3653 

3709 

3767 

3824 

3883 

3942 

37 

24 

3331 

3383 

3436 

3489 

3544 

3598 

3654 

3710 

3768 

3825 

3884 

3943 

36 

25 

1.3332 

1.3384 

1.3437 

1.3490 

1.3545 

1.3599 

1.3655 

1.3711 

1.3768 

1.3826 

1.3885 

1.3944 

35 

26 

3332 

3385 

3438 

3491 

3545 

3600 

3656 

3712 

3769 

3827 

3886 

3945 

34 

27 

3333 

3386 

3438 

3492 

3546 

3601 

3657 

3713 

3770 

3828 

3887 

3946 

33 

28 

3334 

3386 

3439 

3493 

3547 

3602 

3658 

3714 

3771 

3829 

3888 

3947 

32 

29 
30 

3335 

3387 

3440 

3494 

3548 

3603 

3659 

3715 

3772 

3830 

3889 

3948 

31 

1.3336 

1.3388 

1.3441 

1.3495 

1.3549 

1.3604 

1.3660 

1.3716 

1.3773 

1.3831 

1.3890 

1.3949 

30 

31 

3337 

3389 

3442 

3496 

3550 

3605 

3661 

3717 

3774 

3832 

3891 

3950 

29 

32 

3338 

3390 

3443 

3497 

3551 

3606 

3662 

3718 

3775 

3833 

3892 

3951 

28 

33 

3338 

3391 

3444 

3498 

3552 

3607 

3663 

3719 

3776 

3834 

3893 

3952 

27 

34 

333S 

3392 

3445 

3499 

3553 

3608 

3663 

3720 

3777 

3835 

3894 

3953 

26 

35 

1.3340 

1.339a 

1.3446 

1.3500 

1.3554 

1.3609 

1.3664 

1.3721 

1.3778 

1.3836 

1.3895 

1.3954 

25 

36 

3341 

3393 

3446 

3501 

3555 

3610 

3665 

3722 

3779 

3837 

3896 

3955 

24 

37 

3342 

3394 

3447 

3502 

3555 

3610 

3666 

3723 

3780 

3838 

3897 

3956 

23 

38 

3343 

3395 

3448 

3503 

3556 

3611 

3667 

3724 

3781 

3839 

3898 

3957 

22 

39 

3344 

3396 

3449 

3504 

3557 

3612 

3668 

3725 

3782 

3840 

3899 

3958 

21 

40 

1.3345 

1.3397 

1.3450 

1.3505 

1.3558 

1.3613 

1.3669 

1.3726 

1.3783 

1.3841 

1.3900 

1.3959 

20 

41 

3345 

3398 

3451 

3506 

3559 

3614 

3670 

3727 

3784 

3842 

3901 

3960 

19 

■ 

42 

3346 

3399 

3452 

3506 

3560 

3615 

3671 

3727 

3785 

3843 

3902 

3961 

18 

43 

3347 

3400 

3453 

3507 

3561 

3616 

3672 

3728 

3786 

3844 

3903 

3962 

17 

44 

3348 

3400 

3454 

3508 

3562 

3617 

3673 

3729 

3787 

3845 

3904 

3963 

16 
15 

45 

1.3349 

1.3401 

1.3454 

1.3509 

1.3563 

1.3618 

1.3674 

1.3730 

1.3788 

1.3846 

1.3905 

1.3964 

46 

3350 

3402 

3455 

3510 

3564 

3619 

3675 

3731 

3789 

3847 

3906 

3965 

14 

47 

3361 

3M? 

34.fi(i 

35J 1 

2.W^      3620 

3676 

3732 

3790 

3848 

3907 

3966 

13 

48 

3351 

3404   3457 

3512 

3565 

3621 

3677 

3733 

3791 

3849 

3908 

3967 

12 

49 

3352 

3405 

3458 

3513 

3566 

3622 

3677 

3734 

3792 

3850 

3909 

3968 

11 

50 

1.3353 

1.3406 

1.3459 

1.3513 

1.3567 

1.3623 

1.3678 

1.3735 

1.3793 

1.3851 

1.3910 

1.3969 

10 

51 

3354 

3407 

3460 

3514 

3568 

3623 

3679 

3736 

3793 

3852 

3911 

3970 

9 

52 

3355 

3408 

3461 

3515 

3569 

3624 

3680 

3737 

3794 

3853 

3912 

3971 

8 

53 

3356 

3408 

3462 

3516 

3570 

3625 

3681 

3738 

3795 

3854 

3913 

3972 

7 

54 
55 

3357 

3409 

3463 

3516 

3571 

3626 

3682 

3739 

3796 

3855 

3914 

3973 

6 

1,3358 

1.3410 

1.3463 

1.3517 

1.3572 

1.3627 

1.3683 

2,3740 

1.3797 

1.3856 

1.3915 

1.3974 

5 

56 

3358 

3411 

3464 

3518 

3573 

3628 

3684 

3741 

3798 

3856 

3916 

3975 

4 

57 

3359 

3412 

3465 

3519 

3574 

3629 

3685 

3742 

3799 

3857 

3917 

3976 

3 

58 

3360 

3413 

3466 

3520 

3575 

3630 

3686 

3743 

3800 

3858 

3918 

3977 

2 

59 

3361 

3414 

3467 

3521 

3576 

3631 

3687 

3744 

3801 

3859 

3919 

39V8 

1 

60 

3362 

3415 

3468 

3522 

3576 

3632 

3688 

3745 

3802 

3860 

3919 

3979 

0 

23' 

22' 

21' 

20' 

19' 

IS'    17'  I   16'  1   15'  1  41'  i  13' 

12' 

s. 

6  DEGREES. 

■m 

an  the  Apparent  I 

istance  ie 

less  than  90°,  the  Second  Correction  is  to  be  taken  from  the  Botto 

1 

TABLE  XXXII.                                                  147      1 

LOGARITHMS  OF  THE  FIRST  AND  SECOND  CORRECTIONS. 

1  90°. 

rhe  First  Correction  ia  attoays  to  be  taken  from  the  Top,  and  also  the  Second,  when  the  Apparent  Distance  la  greater  thai 

3   DEGREES.                                                                                                  1 

S. 
0 

48' 

49' 

50' 

51' 

52' 

53' 

54' 

55- 

56' 

57' 

58' 

59' 

1.3979 

1.4040 

1.4102 

1.4164 

1.4228 

1.4292 

1.4357 

1.4424 

1.4491 

1.4559 

1.4629 

1.4699 

60 

1 

3980 

4041 

4103 

4165 

4229 

4293 

4358 

4425 

4492 

4560 

4630 

4701 

59 

2 

3981 

4042 

4104 

4166 

4230 

4294 

4359 

4426 

4493 

4562 

4631 

4702 

68 

3 

3982 

4043 

4105 

4167 

4231 

4295 

4361 

4427 

4494 

4563 

4632 

4703 

57 

4 

3983 

4044 

4106 

4168 

4232 

4296 

4362 

4428 

4495 

4564 

4633 

4704 

56 

5 

1.3984 

1.4045 

1.4107 

1    4169 

1.4233 

1.4297 

1.4363 

1.4429 

1.4497 

1.4565 

1.4635 

1.4705 

55 

6 

3985 

4046 

4108 

4171 

4234 

4298 

4364 

4430 

4498 

4566 

4636 

4707 

54 

3986 

4047 

4109 

4172 

4235 

4300 

4365 

4431 

4499 

4567 

4637 

4708 

53 

8 

3987 

4048 

4110 

4173 

4236 

4301 

4366 

4433 

4500 

4569 

4638 

4709 

52 

9 

3988 

4049 

4111 

4174 

4237 

4302 

4367 

4434 

4501 

4570 

4639 

4710 

51 

10 

1.3989 

1.4050 

1.4112 

1.4175 

1.4238 

1.4303 

1.4368 

1.4435 

1.4502 

1.4571 

1.4640 

1.4711 

50 

11 

3990 

4051 

4113 

4176 

4239 

4304 

4369 

4436 

4503 

4572 

4642 

4712 

49 

12 

3991 

4052 

4114 

4177 

4240 

4305 

4370 

4437 

4504 

4573 

4643 

4714 

48 

13 

3992 

4053 

4115 

4178 

4241 

4306 

4372 

4438 

4506 

4574 

4644 

4715 

47 

14 

3993 

4054 

4116 

4179 

4243 

4307 

4373 

4439 

4507 

4575 

4645 

4716 

46 

15 

1.3995 

1.4055 

1.4117 

1.4180 

1.4244 

1.4308 

1.4374 

1.4440 

1.4508 

1.4577 

1.4646 

1.4717 

45 

16 

3996 

4056 

4118 

4181 

4245 

4309 

4375 

4441 

4509 

4578 

4648 

4718 

44 

17 

3997 

4058 

4119 

4182 

4246 

4310 

4376 

4443 

4510 

4579 

4649 

4720 

43 

18 

3998 

4059 

4120 

4183 

4247 

4311 

4377 

4444 

4511 

4580 

4650 

4721 

42 

19 

3999 

4060 

4121 

4184 

4248 

4313 

4378 

4445 

4512 

4581 

4651 

4722 

41 

20 

1.4000 

1.4061 

1.4122 

1.4185 

1.4249 

1.4314 

1.4379 

1.4446 

1.4514 

2.4582 

1.4652 

1.4723 

40 

21 

4001 

4062 

4124 

4186 

4250 

4315 

4380 

4447 

4515 

4584 

4653 

4724 

39 

22 

4002 

4063 

4125 

4187 

4251 

4316 

4381 

4448 

4516 

4585 

4655 

4726 

!}8 

23 

4003 

4064 

4126 

4188 

4252 

4317 

4383 

4449 

4517 

4586 

4656 

4727 

37 

24 

4004 

4065 

4127 

4189 

4253 

4318 

4384 

4450 

4518 

4587 

4657 

4728 

36 

25 

1.4005 

1.4066 

1.4128 

1.4191 

1.4254 

1.4319 

1.4385 

1.4452 

1.4519 

1.4588 

1.4658 

1.4729 

35 

26 

4006 

4067 

4129 

4192 

4255 

4320 

4386 

4453 

4520 

4589 

4659 

"4730 

34 

27 

4007 

4068 

4130 

4193 

4256 

4321 

4387 

4454 

4522 

4590 

4660 

4732 

33 

28 

4008 

4069 

4131 

4194 

4258 

4322 

4388 

4455 

4523 

4592 

4662 

47R3 

32 

29 

4009 

4070 

4132 

4195 

4259 

4323 

4389 

4456 

4524 

4593 

4663 

4734 

31 

30 

1 .4010 

1.4071 

1.4133 

1.4196 

1.4260 

1.4325 

1.4390 

1.4457 

1.4525 

1.4594 

1.4664 

1.4735 

30 

31 

4011 

4072 

4134 

4197 

4261 

4326 

4391 

4458 

4526 

4595 

4665 

4736 

29 

32 

4012 

4073 

4135 

4198 

4262 

4327 

4393 

4459 

4527 

4596 

4666 

4737 

28 

33 

4013 

4074 

4136 

4199 

4263 

4328 

4394 

4460 

4528 

4597 

4668 

4739 

27 

34 

4014 

4075 

4137 

4200 

4264 

4329 

4395 

4462 

4530 

4599 

4669 

4740 

26 

35 

1.4015 

1.4076 

1.4138 

1.4201 

1.4265 

1.4330 

1.4396 

1.4463 

1.4531 

1.4600 

1.4670 

1.47A1. 

25 

36 

4016 

4077 

4139 

4202 

4266 

4331 

4397 

4464 

4532 

4601 

4671 

4742 

24 

37 

4017 

4078 

4140 

4203 

4267 

4332 

4398 

4465 

4533 

4602 

4672 

4744 

23 

38 

4018 

4079 

4141 

4204 

4268 

4333 

4399 

4466 

4534 

4603 

4673 

4745 

22 

39 

4019 

4080 

4142 

4205 

4269 

4334 

4400 

4467 

4535 

4604 

4675 

4746 

21 

40 

1.4020 

1.4081 

1.4143 

1.4206 

1.4270 

1.4335 

1.4401 

1.4468 

1.4536 

1.4606 

1.4676 

1.4747 

20 

41 

4021 

4082 

4144 

4207 

4271 

4336 

4402 

4469 

4538 

4607 

4677 

4748 

19 

42 

4022 

4083 

4145 

4209 

4273 

4338 

4404 

4471 

4539 

4608 

4678 

4750 

18 

43 

4023 

4084 

4146 

4210 

4274 

4339 

4405 

4472 

4540 

4609 

4679 

4751 

17 

44 

4024 

4085 

4147 

4211 

4275 

4340 

4406 

4473 

4541 

4610 

4680 

4752 

16 
15 

45 

1.4025 

1.408b 

1.4149 

1.4212 

1.4276 

1.4341 

1.4407 

1.4474 

1.4542 

1.4611 

1.4682 

1.4753 

46 

4026 

4087 

4150 

4213 

4277 

4342 

4408 

4475 

4543 

4612 

4683 

4754 

14 

47 

4027 

4088 

4151 

4214 

4278 

4343 

4409 

4476 

4544 

4614 

4684 

4756 

13 

48 

4028 

4089 

4152 

4215 

4279 

4344 

4410 

4477 

4546 

4615 

4685 

4757 

12 

49 

4U29 

4090 

4153 

4216 

4280 

4345 

4411 

4479 

4547 

4616 

4686 

4758 

11 

50 

1.403(. 

1  .4'J91 

1.4154 

1.4217 

1.4281 

1.4346 

1.4412 

1.4480 

1.4548 

1,4617 

1.4688 

1.4759 

10 

51 

4031 

4092 

4155 

4218 

4282 

4347 

4414 

4481 

4549 

4618 

4689 

4760 

9 

52 

403ii 

4093 

4156 

4219 

4283 

4349 

4415 

4482 

4550 

4619 

4690 

4762 

8 

53 

4033 

4095 

4157 

4220 

4284 

4350 

4416 

4483 

4551 

4621 

4691 

4763 

7 

54 

55 

403^ 

409h 

4158 

4221 

4285 

4351 

4417 

4484 

4552 

4622 

4692 

4764 

6 

1.403c 

1.4097 

1.4159 

1.4222 

1.4287 

1.4352 

1.4418 

1.4485 

1.4554 

1.4623 

1.4693 

1.4765 

5 

n6 

403(. 

4098 

4160 

4223 

4288 

4353 

4419 

4486 

4555 

4624 

4695 

4766 

4 

57 

4037 

4099 

4161 

4224 

4289 

4354 

442C 

4488 

!      4556 

4625 

4696 

4768 

3 

58 

403i^ 

i      410C 

416-2 

4226 

4290 

4355 

4421 

448S 

4557 

4626 

4697 

4769 

2 

59 

403ir 

4101 

4163 

4227 

4291 

4356 

4422 

449C 

4558 

4628 

4698 

4770 

1 

60 

404C 

)      4102 

4164 

4228 

4292 

4357 

4424 

4491 

4559 

4629 

4699 

4771 

0 

u' 

10' 

9' 

8'  1         7'           6' 

5' 

1         4'          3'          2            1' 

0' 

S. 

6  DEGREES. 

"Whea  the  Apparent  Distance  Is  less  than  90°,  the  Second  Correction  is  to  be  taken  from  the  Bottom. 

148 

TABLE  XXXII. 
LOGARITHMS  OF  THE  FIRST  AND  SECOND  CORRECTIONS. 

) 

The  Pint  Correction  is  always  to  be  taken  from  the  Top,  and  also  the  Second,  when  the  Apparent  Distance  is  greater  than  90" . 

4  DEGREES. 

s. 

0' 

1' 

2' 

3' 

4' 

5' 

6' 

7' 

8' 

9' 

10' 

11' 

60 

0 

1.4771 

1.4844 

1.4918 

1.4994 

1.5071 

1.5149 

1.5229 

1.5310 

1.5393 

1.5477 

1.5563 

1.5651 

1 

4772 

4845 

4920 

4995 

5072 

5150 

5230 

5311 

5394 

5478 

5564 

5652 

59 

2 

4774 

4847 

4921 

4997 

5073 

5152 

5231 

5313 

5395 

5480 

5566 

5654 

58 

3 

4775 

4848 

4922 

4998 

5075 

5153 

5233 

5314 

5397 

5481 

5567 

5655 

57 

4 

4776 

4849 

4923 

4999 

5076 

5154 

5234 

5315 

5398 

5483 

5569 

5657 

56 
55 

5 

1.4777 

1.4850 

1.4925 

1.5000 

1.5077 

1.5156 

1.5235 

1.5317 

1.5400 

1.5484 

1.5570 

1.5658 

' 

6 

4778 

4852 

4926 

5002 

5079 

5157 

5237 

5318 

5401 

5486 

5572 

5660 

54 

7 

4780 

4853 

4927 

5003 

5080 

5158 

5238 

5320 

5402 

5487 

5573 

5661 

63 

8 

4781 

4854 

4928 

5004 

5081 

5160 

5240 

5321 

5404 

5488 

5575 

5663 

52 

9 

4782 

4855 

4930 

5005 

5082 

5161 

5241 

5322 

5405 

5490 

5576 

5664 

51 

10 

1.4783 

1.4856 

1.4931 

1.5007 

1.5084 

1.5162 

1.5242 

1.5324 

1.5407 

1.5491 

1.5578 

1.5666 

50 

11 

4785 

4858 

4932 

5008 

5085 

5164 

5244 

5325 

5408 

5493 

5579 

5667 

49 

12 

4786 

4859 

4933 

5009 

5086 

5165 

5245 

5326 

5409 

5494 

5580 

5669 

48 

13 

4787 

4860 

4935 

5011 

5088 

5166 

5246 

5328 

5411 

5496 

5582 

5670 

47 

14 

4788 

4861 

4936 

5012 

5089 

5168 

5248 

5329 

5412 

5497 

5583 

5671 

46 

15 

1.4789 

1.4863 

1.4937 

1.5013 

1.5090 

1.5169 

1.5249 

1.5331 

1.5414 

1.5498 

1.5585 

1.5673 

45 

1 

16 

4791 

4864 

4938 

5014 

5092 

5170 

5250 

5332 

5415 

5500 

5586 

5674 

44 

17 

4792 

4865 

4940 

5016 

5093 

5172 

5252 

5333 

5416 

5501 

5588 

5676 

43 

18 

4793 

4866 

4941 

5017 

5094 

5173 

5253 

5335 

5418 

5503 

5589 

5677 

42 

19 

4794 

4868 

4942 

5018 

5095 

5174 

5254 

5336 

5419 

5504 

5591 

5679 

41 

20 

1.4795 

1.4869 

1.4943 

1.5019 

1.5097 

1.5175 

1.5256 

1.5337 

1.5421 

1.5506 

1.5592 

1.5680 

40 

21 

4797 

4870 

4945 

5021 

5098 

5177 

5257 

5339 

5422 

5507 

5594 

5682 

39 

22 

4798 

4871 

4946 

5022 

5099 

5178 

5258 

5340 

5423 

5508 

5595 

5683 

38 

23 

4799 

4873 

4947 

5023 

5101 

5179 

5260 

5341 

5425 

5510 

5596 

5685 

37 

24 

4800 

4874 

4949 

5025 

5102 

5181 

5261 

5343 

5426 

5511 

5598 

5686 

36 

25 

1.4801 

1.4875 

1.4950 

1.5026 

1.5103 

1.5182 

1.5262 

1.5344 

1.5428 

1.5513 

1.5599 

1.5688 

35 

26 

4803 

4876 

4951 

5027 

5105 

5183 

5264 

5346 

5429 

5514 

5601 

5689 

34 

27 

4804 

4877 

4952 

5028 

5106 

5185 

5265 

5347 

5430 

5516 

5602 

5691 

33 

28 

4805 

4879 

4954 

5030 

5107 

5186 

5266 

5348 

5432 

5517 

5604 

5692 

32 

29 

4806 

4880 

4955 

5031 

5108 

5187 

5268 

5350 

5433 

5518 

5605 

5694 

31 

30 

1.4808 

1.4881 

1.4956 

1.5032 

1.5110 

1.5189 

1.5269 

1.5351 

1.5435 

1.5520 

1.5607 

1.5695 

30 

31 

4809 

4882 

4957 

5034 

5111 

5190 

5271 

5353 

5436 

5521 

5608 

5697 

29 

32 

4810 

4884 

4959 

5035 

5112 

5191 

5272 

5354 

5437 

5522 

5610 

5698 

28 

33 

4811 

4885 

4960 

5036 

5114 

5193 

5273 

5355 

5439 

5524 

5611 

5700 

27 

34 

4812 

4886 

4961 

5037 

5115 

5194 

5275 

5357 

5440 

5526 

5613 

5701 

26 

35 

1.4814 

1.4887 

1.4962 

1.5039 

1.5116 

1.5195 

1.5276 

1.5358 

1.5442 

1.5527 

1.5614 

1.5703 

25 

36 

4815 

4889 

4964 

5040 

5118 

5197 

5277 

5359 

5443 

5528 

5615 

5704 

24 

37 

4816 

4890 

4965 

5041 

5119 

5198 

5279 

5361 

5445 

5530 

5617 

5706 

23 

38 

4817 

4891 

4966 

5043 

5120 

5199 

5280 

5362 

5446 

5531 

5618 

5707 

22 

39 

4819 

4892 

4967 

5044 

5122 

5200 

5281 

5364 

5447 

5533 

5620 

5709 

21 

40 

1.4820 

1.4894 

1.4969 

1.5045 

1.5123 

1.5202 

1.5283 

1.5365 

1.5449 

1.5534 

1.5621 

1.5710 

20 

41 

4821 

4895 

4970 

5046 

5124 

5203 

5284 

5366 

5450 

5536 

5623 

5712 

19 

42 

4822 

4896 

4971 

5048 

5125 

5205 

5285 

5368 

5452 

5537 

5624 

5713 

18 

43 

4823 

4897 

4972 

5049 

5127 

5206 

5287 

5369 

5453 

5538 

5626 

5715 

17 

44 

4825 

4899 

4974 

5050 

5128 

5207 

5288 

5370 

5454 

5540 

5627 

5716 

16 

45 

1.4826 

1.4900 

1.4975 

1.5051 

1.5129 

1.5209 

1.5290 

1.5372 

1.5456 

1.5541 

1.5629 

1.5718 

15 

46 

4827 

4901 

4976 

5053 

5131 

5210 

5291 

5373 

5457 

5543 

5630 

5719 

14 

47 

4828 

4902 

4977 

5054 

5132 

5211 

5292 

5375 

5459 

5544 

5632 

5721 

13 

48 

4830 

4903 

4979 

5055 

5133 

5213 

5294 

5376 

5460 

5546 

5633 

5722 

12 

49 

4831 

4905 

4980 

5057 

5135 

5214 

5295 

5377 

5461 

5547 

5635 

5724 

11 

50 

1.4832 

1.4906 

1.4981 

1.5058 

1.5136 

1.5215 

1.5296 

1.5379 

1.5463 

1.5549 

1.5636 

1.5725 

10 

51 

4833 

4907 

4983 

5059 

5137 

5217 

5298 

5380 

5464 

5550 

5637 

5727 

9 

52 

4834 

4908 

4984 

5061 

5139 

5218 

5299 

5382 

5466 

5551 

5639 

5728 

8 

53 

4836 

4910 

4985 

5062 

5140 

5219 

5300 

5383 

5467 

5553 

5640 

5730 

7 

54 

4837 

4911 

4986 

5063 

5141 

5221 

5302 

5384 

5469 

5554 

5642 

5731 

6 

55 

1.4838 

1.4912 

1.4988 

1.5064 

1.5143 

1.5222 

1.5303 

1.5386 

1.5470 

1.5556 

1.5643 

1.5733 

5 

56 

4339 

4913 

4989 

5066 

5144 

5223 

5305 

5387 

5471 

5557 

5645 

5734 

4 

57 

4841 

4915 

4990 

5067 

5145 

5225 

5306 

5389 

5473 

5559 

5646 

5736 

3 

58 

4842 

4916 

4991 

5068 

5146 

5226 

5307 

5390 

5474 

5560 

5648 

5737 

2 

59 

4843 

4917 

4992 

5070 

5148 

5227 

5309 

5391 

5476 

5562 

5649 

5739 

1 

60 

4844 

4918  4994 

5071 

5149 

5229   5310/  5393 

5477   5563 

5651 

5740 

0 

59' 

58'  1   57'    56'    55'    54'    53'    52'    51'  |   50' 

49' 

48' 

s. 

S  DEGREES. 

Wl 

len  the  Apparent  Distance  \»leti  than  90",  the  Second  Correction  is  to  be  taken  from  the  Botto 

-          1 

TABLE  XXXll.                                                  149 

LOGARITHMS  OF  THE  FIRST  AND  SECOND  CORRECTIONS. 

1  k^  First  Correotion  is  always  to  be  taken  from  the  Top,  and  also  the  Second,  when  the  Apparent  Distance  is  greater  than  90°  1 

4  DE0KEE3.                                                                                                1 

12' 

13' 

14' 

15' 

16'         17' 

18' 

19' 

20' 

21' 

22' 

23' 

60 

1.5740 

1.58321.5925 

1.6021 

1.6118,1.6218 

1.6320 

1.6425 

1.6532 

1.6642 

1.6755 

1.6871 

1 

5742 

5833 

5927 

6022 

6120^ 

6220' 

6322 

6427 

6534 

6644 

6757 

6873 

59 

.> 

5743 

5835 

5928 

6024 

6121 

6221      6324| 

6428 

6536 

6646 

6759 

6875 

58 

3 

5745 

5836 

5930 

6025 

0123 

6223 

6325 

6430 

6538 

6648 

6761 

6877 

57 

4 

5746 

5838 

5931 

6027 

6125 

6225 

6827 

6432 

6539 

6650 

6763 

6879 

56 

5 

1.5748 

1.5839 

1.5933 

1.6029 

1.6126 

1.6226 

1.6329 

1.6434 

1.6541 

1.6651 

1.6764 

1.6881 

55 

t) 

5749 

5841 

5935 

6030 

6128 

6228 

6331 

6435 

6543 

6653 

6766 

6882 

54 

1 

5751 

5843 

5936 

6032 

6130 

6230 

6332 

6437 

6545 

6655 

6768 

6884 

53 

8 

5752 

5844 

5938 

6033 

6131 

6232 

6334 

6439 

6547 

6657 

6770 

6886 

52 

9 

5754 

5846 

5939 

6035 

6133 

6233 

6336 

6441 

6548 

6659 

6772 

6888 

51 

10 

1.5755 

1.5847 

1.5941 

1.6037 

1.6135 

1.6235 

1.6338 

1.6443 

1.6550 

1.6661 

1.6774 

1.6890 

50 

11 

5757 

5849 

5942 

6038 

6136 

6237 

6339 

6444 

6552 

6663 

6776 

6892 

49 

12 

5758 

5850 

5944 

6040 

6138 

6238 

6341 

6446 

6554 

6664 

6778 

6894 

48 

13 

5760 

5852 

5946 

6042 

6140 

6240 

6343 

6448 

6556 

6666 

6780 

6896 

47 

14 

5761 

5853 

5947 

6043 

6141 

6242 

6344 

6450 

6558 

6668 

6782 

6898 

46 

15 

1.5763 

1.5855 

1.5949 

1.6045 

1.6143 

1.6243 

1.6346 

1.6451 

1.6559 

1.6670 

1.6784 

1.6900 

45 

16 

5765 

5856 

5950 

6046 

6145 

6245 

6348 

6453 

6561 

6672 

6785 

6902 

44 

17 

5766 

5858 

5952 

6048 

6146 

6247 

6350 

6455 

6563 

6674 

6787 

6904 

43 

18 

5768 

5860 

5954 

6050 

6148 

6248 

6351 

6457 

6565 

6676 

6789 

6906 

42 

19 

5769 

5861 

5955 

6051 

6150 

6250 

6353 

6459 

6567 

6677 

6791 

6908 

41 

20 

1.5771 

1.5863 

1.5957 

1.6053 

1.6151 

1.6252 

1.6355 

1.6460 

1.6568 

1.6679 

1.6793 

1.6910 

40 

■n 

5772 

5864 

5958 

6055 

6153 

6254 

6357 

6462 

6570 

6681 

6795 

6912 

39 

i-Z 

5774 

5866 

5960 

6056 

6155 

6255 

6358 

6464 

6572 

6683 

6797 

6914 

38 

23 

5775 

5867 

596r 

6058 

6156 

6257 

6360 

6466 

6574 

6685 

6799 

6916 

37 

U 

25 

5777 

5869 

5963 

6059 

6158 

6259 

6362 

6467 

6576 

6687 

6801 

6918 

36 

1.5778 

1.5870 

1.5965 

1.6061 

1.6160 

1.6260 

1.6364 

1.6469 

1.6578 

1.6689 

1.6803 

1.6920 

35 

26 

5780 

5872 

5966 

6063 

6161 

6262 

6365 

647V     8579 

6691 

6805 

6922 

34 

27 

5781 

5874 

5968 

6064 

6163 

6264 

6367 

6472il 

6581 

6692 

6807 

6924 

33 

28 

5783 

5875 

5969 

6066 

6165 

6265 

6369      6475 

6583 

6694 

6809 

6926 

32 

29 

5784 

5877 

5971 

6067 

6166 

6267 

6371,     6476 

6585 

6696 

6810 

6928 

31 

30 

1.5786 

1.5878 

1.5973 

1.6069 

1.6168 

1.6269 

1.6372 

1.6478 

1.6587 

1.6698 

1.6812 

1.6930 

30 

31 

5787 

5880 

5974 

6071 

6169 

6271 

6374 

6480 

6589 

6700 

6814 

6932 

29 

32 

5789 

5881 

5976 

6072 

6171 

6272 

6376 

6482 

6590 

6702 

6816 

6934 

28 

33 

5790 

5883 

5977 

6074 

6173 

6274 

6377 

6484 

6592 

6704 

6818 

6936 

27 

34 

5792 

5884 

5979 

6076 

6174 

6276 

6379 

6485 

6594 

6706 

6820 

6938 

26 

35 

1.5793 

1.5886 

1.5981 

1.6077 

1.6176 

1.6277 

1.6381 

1.6487 

1.6596 

1.6708 

1.6822 

1.6940 

25 

36 

5795 

5888 

5982 

6079 

6178 

6279 

6383 

6489 

6598 

6709 

6824 

6942 

24 

37 

5796 

5889 

5984 

6081 

6179 

6281 

6384 

6491 

6600 

6711 

6826 

6944 

23 

38 

5798 

5891 

5985 

6082 

6181 

6282 

6386 

6492 

6601 

6713 

6828 

6946 

22 

39 

5800 

5892 

5987 

6084 

6183 

6284 

6388 

6494 

6603 

6715 

6830 

6948 

21 

10 

1.5801 

1.5894 

1.5989 

1.6085 

1.6185 

1.6286 

1.6390 

1.6496 

1.6605 

1.6717 

1.6832 

1.6950 

20 

11 

5803 

5895 

5990 

6087 

6186 

6288 

6391 

6498 

6607 

6719 

6834 

6952 

19 

42 

5804 

5897 

5992 

6089 

6188 

6289 

6393 

6500 

6609 

6721 

6836 

6954 

18 

13 

5806 

5898 

5993 

6090 

6190 

6291 

6395 

6501 

6611 

6723 

6838 

6956 

17 

14 

5807 

5900 

5995 

6092 

6191 

6293 

6397 

6503 

6612 

6725 

6840 

6958 

16 

.45 

1.5809 

1.6902 

1.5997 

1.6094 

1.6193 

1.6294 

1.6398 

1.6505 

1.6614 

1.6726 

1.6841 

1.696*0 

15 

46 

5810 

5903 

5998 

6095 

6195 

6296 

6400 

6507 

6616 

6728 

6843 

6962 

14 

47 

5812 

5905 

6000 

6097 

6196 

6298 

6402 

6509 

6618 

6730 

6845 

6964 

13 

48 

5813 

5906 

6001 

6099 

6198 

6300 

6404 

6510 

6620 

6732 

6847 

6966 

12 

49 

5815 

5908 

6003 

6100 

6200 

6301 

6406 

6512 

6622 

6734 

6849 

6968 

11 

50 

1.5? 16 

1.5909 

1.6005 

1.6102 

1.6201 

1.6303 

1.6407 

1.6514 

1.6624 

1.6736 

1.6851 

1.6970 

10 

51 

5818 

5911 

6006 

6103 

6203 

6305 

6409 

6516 

6625 

6738 

6853'     6972 

9 

52 

5819 

5913 

6008 

6105 

6205 

6306 

6411 

6518 

6627 

6740 

6855 

6974 

8 

53 

5821 

5914 

6009 

6107 

6206 

6308 

6413 

6519 

6629 

6742 

HH.'iT 

6976 

7 

54 

5823 

5916 

6011 

6108 

6208 

6310 

6414 

6521 

6631 

6743 

6859 

6978 

6 



55 

1.5824 

1.5917 

1.6013 

1.6110 

1.6210 

1.6312 

1.6416 

1.6523 

1.6633 

1.6745 

1.68611    6980 

5 

56 

5826 

5919 

6014 

6112 

6211 

6313 

6418 

6525 

6635 

6747 

6863      6982 

4 

57 

5827 

5920 

6016 

6113 

6213 

6315 

6420 

6527 

6637 

6749 

6865      6984 

3 

58 

5829 

5922 

6017 

6115 

6215 

6317 

6421 

6529 

6638 

6751 

6867,     6986 

2 

59 

5830 

5924 

6019 

6117 

6216 

6319 

6423 

6530 

6640 

6753 

6869 

6988 

1 

60 

5832 

5925 

6021 

6118 

6218 

6320 

6425 

6532 

6642 

6755 

6871 

6990 

0 

47' 

46'  1      45' 

44'  1      43'         42'         41' 

1      40'  1      39' 

38' 

37' 

36' 

S. 

- 

6   DEGREES. 

When  the  Apparent  Distance  ialess  than  90°,  the  Second  Correction  is  to  be  taken  from  the  Bottom. 

150 

TABLE  XXXII. 
LOGARITHMS  OF  THE  FIRST  AND  SECOND  CORRECTIONS. 

Tt»  First  Correction  i»  aitoays  to  be  taken  from  the  Top,  and  also  the  Second,  when  the  Apparent  Distance  itgrcattr  than  90O.| 

4  DEGREES.                                       1 

S. 
0 

24' 

25' 

26' 

27' 

28' 

29' 

30' 

31' 

32' 

33' 

34' 

35' 

1.6990 

1.7112 

1.7238 

1.7368 

1.7501 

1.7639 

1.7782 

1.7929 

1.8081 

1.8239 

1.8403 

1.8573 

60 

1 

6992 

7114 

7240 

7370 

7503 

7641 

7784 

7931 

8084 

8242 

8406 

8576 

59 

2 

6994 

7116 

7242 

7372 

7506 

7644 

7786 

7934 

8O186 

8244 

8409 

8579 

58 

3 

6996 

7118 

7244 

7374 

7508 

7646 

r789 

7936 

8089 

8247 

8411 

8582 

57 

4 

6998 

7120 

7246 

7376 

7510 

7648 

7791 

7939 

8091 

8250 

8414 

8583 

56 

5 

1.7000 

1.7122 

1.7249 

1.7379 

1.7513 

1.7651 

1.7794 

1.7941 

1.8094 

1.8253 

1.8417 

1.8588 

55 

6 

7002 

7124 

7251 

7381 

7515 

7653 

7796 

7944 

8097 

8255 

8420 

8591 

64 

7 

7004 

7127 

2253 

7383 

7517 

7655 

7798 

7946 

8099 

8258 

8423 

8594 

53 

8 

7006 

7129 

7255 

7385 

7519 

7658 

7801 

7949 

8102 

8261 

8425 

8597 

52 

9 

7008 

7131 

7257 

7387 

7522 

7660 

7803 

7951 

8104 

8263 

8428 

8599 

51 

10 

1.7010 

1.7133 

1.7259 

1.7390 

1.7524 

1.7663 

1.7806 

1.7954 

1 .8107 

1.8266 

1.8431 

1.8602 

50 

11 

7012 

7135 

7261 

7392 

7526 

7665 

7808 

7956 

8110 

8269 

8434 

8605 

49 

12 

7014 

7137 

7264 

7394 

7528 

7667 

7811 

7959 

8112 

8271 

8437 

8608 

48 

13 

7016 

7139 

7266 

7396 

7531 

7670 

7813 

7961 

8115 

8274 

8439 

8611 

47 

14 
15 

7018 

7141 

7268 

7398 

7533 

7672 

7815 

7964 

8117 

8277 

8442 

8614 

46 

1.7020 

1.7143 

1.7270 

1.7401 

1.7535 

1.7674 

1.7818 

1.7966 

1.8120 

1.8279 

1.8445 

1.8617 

45 

16 

7022 

7145 

7272 

7403 

7538 

7677 

7820 

7969 

8123 

8282 

8448 

8620 

44 

17 

7024 

7147 

7274 

7405 

7540 

7679 

7823 

7971 

8125 

8285 

8451 

8623 

43 

18 

7026 

7149 

7276 

7407 

7542 

7681 

7825 

7974 

8128 

8288 

8453 

8626 

42 

19 

7028 

7152 

7279 

7409 

7544 

7684 

7828 

7976 

8131 

8290 

8456 

8629 

41 
40 

20 

1.7030 

1.7154 

1.7281 

1.7412 

1.7547 

1.7686 

1.7830 

1.7979 

1.8133 

1.8293 

1.8459 

1.8632 

21 

7032 

7156 

7283 

7414 

7549 

7688 

7832 

7981 

8136 

8296 

8462 

8635 

39 

22 

7034 

7158 

7285 

7416 

7551 

7691 

7835 

7984 

8138 

8298 

8465 

8637 

38 

23 

7036 

7160 

7287 

7418 

7554 

7693 

7837 

7987 

8141 

8301 

8467 

8640 

37 

24 

7038 

7162 

7289 

7421 

7556 

7696 

7840 

7989 

8144 

8304 

8470 

8643 

36 

25 

1.7040 

1.7164 

1.7291 

1.7423 

1.7558 

1.7698 

1.7842 

1.7992 

1.8146 

1.8307 

1.8473 

1.8646 

35 

26 

7042 

7166 

7294 

7425 

7560 

7700 

7845 

7994 

8149 

8309 

8476 

8649 

34 

27 

7044 

7168 

7296 

7427 

7563 

7703 

7847 

7997 

8152 

8312 

8479 

8652 

33 

28 

7046 

7170 

7298 

7429 

7565 

7705 

7850 

7999 

8154 

8315 

8482 

8655 

32 

29 
30 

7048 

7172 

7300 

7432 

7567 

7707 

7852 

8002 

8157 

8318 

8484 

8658 

31 

1.7050 

1.7175 

1.7302 

1.7434 

1.7570 

1.7710 

1.7855 

1.8004 

1.8159 

1.8320 

1  8487 

1.8661 

30 

31 

7052 

7177 

7304 

7436 

7572 

7712 

7857 

8007 

8162 

8323 

8490 

8664 

29 

32 

7055 

7179 

7307 

7438 

7574 

7714 

7859 

8009 

8165 

8326 

8493 

8667 

28 

33 

7057 

7181 

7309 

7441 

7576 

7717 

7862 

8012 

8167 

8328 

8496 

8670 

27 

34 
35 

7059 

7183 

7311 

7443 

7579 

7719 

7864 

8014 

8170 

8331 

8499 

8673 

26 

1.7061 

1.7185 

1.7313 

1.7445 

1.7581 

1.7722 

1.7867 

1.8017 

1.8173 

1.8334 

1.8502 

1.8676 

25 

36 

7063 

7187 

7315 

7447 

7583 

7724 

7869 

8020 

8175 

8337 

8504 

8679 

24 

37 

7065 

7189 

7317 

7450 

7586 

7726 

7872 

8022 

8178 

8339 

8507 

8682 

23 

38 

7067 

7191 

7320 

7452 

7588 

7729 

7874 

8025 

8181 

8342 

8510 

8685 

22 

39 

7069 

7193 

7322 

7454 

7590 

7731 

7877 

8027 

8183 

8345 

8513 

8688 

21 

40 

1.7071 

1.7196 

1.7324 

1.7456 

1.7593 

1.7734 

1.7879 

1.8030 

1.8186 

1.8348 

1.8516 

1.8691 

20 

41 

7073 

7198 

7326 

7458 

7595 

7736 

7882 

8032 

8188 

8350 

8519 

8694 

19 

42 

7075 

7200 

7328 

7461 

7597 

7738 

7884 

8035 

8191 

8353 

8522 

8697 

18 

43 

7077 

7202 

7330 

7463 

7600 

7741 

7887 

8037 

8194 

8356 

8524 

8700 

17 

44 

7079 

7204 

7333 

7465 

7602 

7743 

7889 

8040 

8196 

8359 

8527 

8703 

16 
15 

45 

1.7081 

1.7206 

1.7335 

1.7467 

1.7604 

1.7745 

1.7891 

1.8043 

1.8199 

1.8361 

1.8530 

1.8706 

46 

7083 

7208 

7337 

7470 

7607 

7748 

7894 

8045 

8202 

8364 

8533 

8709 

14 

47 

7085 

7210 

7339 

7472 

7609 

7750 

7896 

8048 

8204 

8367 

8536 

8712 

13 

48 

7087 

7212 

7341 

4774 

7611 

7753 

7899 

8050 

8207 

8370 

8539 

8715 

12 

49 

7089 

7215 

7344 

7476 

7613 

7755 

7901 

8053 

8210 

8372 

8542 

8718 

11 

50 

1.7091 

1.7217 

1.7346 

1.7479 

1.7616 

1.7758 

1.7904 

1.8055 

1.8212 

1.8375 

1.8544 

1.8721 

10 

51 

7093 

7219 

7348 

7481 

7618 

7760 

7906 

8058 

8215 

8378 

8547 

8724 

9 

52 

7096 

7221 

7350 

7483 

7620 

7762 

7909 

8061 

8218 

8381 

8550 

8727 

8 

53 

7098 

7223 

7352 

7485 

7623 

7765 

7911 

8063 

8220 

8384 

8553 

8730 

7 

54 

7100 

7225 

7354 

7488 

7625 

7767 

7914 

8066 

8223 

8386 

8556 

8733 

6 
5 

55 

1.7102 

1.7227 

1.7357 

1.7490 

1.7627 

1.7769 

1.7916 

1.8068 

1.8226 

1.8389 

1.8559 

1.8736 

56 

7104 

7229 

7359 

7492 

7630 

7772 

7919 

8071 

8228 

8392 

8562 

8739 

4 

57 

7106 

7232 

7361 

7494 

7632 

7774 

7921 

8073 

8231 

8395 

8565 

8742 

3 

58 

7108 

7234 

6363 

7497 

7634 

7777 

7924 

8076 

8234 

8397 

8568 

8745 

2 

59 

7110 

7236 

7365 

7499 

7637 

7779 

7926 

8079 

8236 

8400 

8570 

8748 

1 

60 

1  7112 

7238 

7368 

7501 

7639 

7782 

7929 

8081 

8239 

8403 

8573 

8751 

0 

35 

1   34' 

33' 

32'  1   31' 

30' 

29' 

28'    27'    26' 

25'    24' 

S. 

5  DEGREES. 

1  ^^ 

Wl 

hen  the  Apparent  Distance  is  less  thai 

1  9llO,  the 

Second  C 

orrection  ii  to  be  taken  from  the  Bottom.          1 

TABLE  XXXll. 

151 

LOGARITHMS  OF  THE  FIRST  AND  SECOND  CORRECTIONS. 

Th«  Firit  OoRMtion  is  always  to  be  taken  from  ihe  Top,  and  also  the  Second,  when  the  Apparent  Distance  ii  greater  than  90"  -1 

4  DEGKEES.                                      1 

S. 
0 

36' 

37' 

38' 

39' 

40' 

41' 

42' 

43' 

44' 

45' 

46' 

47' 

60 

1.8751 

1.8935 

1.9128 

1.9331 

1.9542 

1.9765 

2.0000 

2.0248 

2.0512 

2.0792 

2.1091 

2.1413 

1 

8754 

8939 

9132 

9334 

9546 

9769 

0004 

0252 

0516 

0797 

1097 

1419 

59 

2 

8757 

8942 

9135 

9337 

9550 

9773 

0008 

0257 

0521 

0801 

1102 

1424 

58 

3 

8760 

8945 

9138 

9341 

9553 

9777 

0012 

0261 

0525 

0806 

1107 

1430 

57 

4 

8763 

8948 

9142 

9344 

9557 

9780 

0016 

0265 

0530 

0811 

1112 

1436 

56 

5 

1.8766 

1.8951 

1.9145 

1.9348 

1.9561 

1.9784 

2.00^0 

2.0270 

2.0534 

2.0816 

2.1117 

2.1441 

55 

6 

8769 

8954 

9148 

9351 

9564 

9788 

0024 

0274 

0539 

0821 

1123 

1447 

54 

7 

8772 

8958 

9152 

9355 

9568 

9792 

0028 

0278 

0543 

0826 

1128 

1452 

53 

8 

8775 

8961 

9155 

9358 

9571 

9796 

0032 

0282 

0548 

0831 

1133 

1458 

52 

9 
10 

8778 

8964 

9158 

9362 

9575 

9800 

0036 

0287 

0552 

0835 

1138 

1464 

51 

1.8781 

1.8967 

1.9162 

1.9365 

1.9579 

1.9803 

2.0040 

2.0291 

2.0557 

2.0840 

2.1143 

2.1469 

50 

11 

8784 

8970 

9165 

9369 

9582 

9807 

0044 

0295 

0562 

0845 

1149 

1475 

49 

12 

8787 

8973 

9168 

9372 

9586 

9811 

0049 

0300 

0566 

0850 

1154 

1481 

48 

13 

8790 

8977 

9172 

9376 

9590 

9815 

0053 

0304 

0571 

0855 

1159 

1486 

47 

14 

8793 

8980 

9175 

9379 

9593 

9819 

0057 

0308 

0575 

0860 

1164 

1492 

46 

15 

1.8796 

1.8983 

1.9178 

1.9383 

1.9597 

1.9823 

2.0061 

2.0313 

2.0580 

2.0865 

2.1170 

2.1498 

45 

16 

8799 

8986 

9181 

9386 

9601 

9827 

0065 

0317 

0585 

0870 

1175 

1503 

44 

17 

8802 

8989 

9185 

939.0 

9604 

9830 

0069 

0321 

0589 

0875 

1180 

1509 

43 

18 

8805 

8992 

9188 

9393 

9608 

9834 

0073 

0326 

0594 

0880 

1186 

1515 

42 

19 

8808 

8996 

9191 

9397 

9612 

9838 

0077 

0330 

0598 

0884 

1191 

1520 

41 

20 

1.8811 

1.8999 

1.9195 

1.9400 

1.9615 

1.9842 

2.0081 

2.0334 

2.0603 

2.0889 

2.1196 

Sf.l526 

40 

21 

8814 

9002 

9198 

9404 

9619 

9846 

0085 

0339 

0608 

0894 

1201 

1532 

39 

22 

8817 

9005 

9201 

9407 

9623 

9850 

0089 

0343 

0612 

0899 

1207 

1538 

38 

23 

8821 

9008 

9205 

9411 

9626 

9854 

0093 

0347 

0617 

0904 

1212 

1543 

37 

24 

8824 

9012 

9208 

9414 

9630 

9858 

0098 

0352 

0621 

0909 

1217 

1549 

36 
35 

25 

1.8827 

1.9015 

1.9212 

1.9418 

1.9634 

1.9861 

2.0102 

2.0356 

2.0626 

2.0914 

2.1223 

2.1555 

26 

8830 

9018 

9215 

9421 

9638 

9865 

0106 

0360 

0631 

0919 

1228 

1561 

34 

27 

8833 

9021 

9218 

9425 

9641 

9869;  0110 

0365 

0635 

0924 

1233 

1566 

33 

28 

8836 

9024 

9222 

9428 

9645 

9873 

01141 

0369 

0640 

0929 

1239 

1572 

32 

29 

8839 

9028 

9225 

9432 

9649 

9877 

0118 

0374 

0645 

0934 

1244 

1578 

31 

30 

1.8842 

1.9031 

1.9228 

1.9435 

1.9652 

1.9881 

2.0122 

2.0378 

2.0649 

2.0939 

2.1249 

2.1584 

30 

31 

8845 

9034 

9232 

9439 

9656 

9885 

0126 

0382 

0654 

0944 

1255 

1589 

29 

32 

8848 

9037 

9235 

9442 

9660 

9889 

0131 

0387 

0659 

0949 

1260 

1595 

28 

33 

8851 

9041 

9238 

9446 

9664 

9893 

0135 

0391 

0663 

0954 

1266 

1601 

27 

34 
35 

8854 

9044 

9242 

9449 

9667 

9897 

0139 

0395 

0668 

0959 

1271 

1607 

26 
25 

1.8857 

1.9047 

1.9245 

1.9453 

1.9671 

1.9901 

2.0143 

2.0400 

2.0673 

2.0964 

2.1276 

2.1613 

36 

8861 

9050 

9249 

9456 

9675 

9905 

0147 

0404 

0678 

0969 

1282 

1619 

24 

37 

8864 

9053 

9252 

9460 

9678 

9908 

0151 

0409 

0682 

0974 

1287 

1624 

23 

38 

8867 

9057 

9255 

9464 

9682 

9912 

0156 

0413 

0687 

0979 

1292 

1630 

22 

39 

8870 

9060 

9259 

9467 

9686 

9916 

0160 

0418 

0692 

0984 

1298 

1636 

21 

40 

1.8873 

1.9063 

1.9262 

1.9471 

1.9690 

1.9920 

2.0164 

2.0422 

2.0696 

2.0989 

2.1303 

2.1642 

20 

41 

8876 

9066 

9266 

9474 

9693 

9924 

0168 

0426 

0701 

0994 

1309 

1648 

19 

42 

8879 

9070 

9269 

9478 

9697 

9928 

0172 

0431 

0706 

0999 

1314 

1654 

18 

43 

8882 

9073 

9272 

9481 

9701 

9932 

0176 

0435 

0711 

1004 

1320 

1660 

17 

44 

8885 

9076 

9276 

9485 

9705 

9936 

0181 

0440 

0715 

1009 

1325 

1665 

16 
15 

45 

1.8888 

1.9079 

1.9279 

1.9488 

1.9708 

1.9940 

2.0185 

2.0444 

2.0720 

2.1015 

2.1331 

2.1671 

46 

8892 

9083 

9283 

9492 

9712 

9944 

0189 

0449 

0725 

1020 

1336 

1677 

14 

47 

8895 

9086 

9286 

9496 

9716 

9948 

0193 

0453 

0730 

1025 

1342 

1683 

13 

48 

8898 

9089 

9289 

9499 

9720 

9952 

0197 

0458 

0734 

1030 

1347 

1689 

12 

49 

8901 

9092 

9293 

9503 

9723 

9956 

0202 

0462 

0739 

1035 

1352 

1695 

11 

50 

1.8904 

1.9096 

1.9296 

1.9506 

1.9727 

1.9960 

2.0206 

2.0467 

2.0744 

2.1040 

2.1358 

2.1701 

10 

51 

8907 

9099 

9300 

9510 

9731 

9964 

0210 

0471 

0749 

1045 

1363 

1707 

9 

52 

8910 

9102 

9303 

9514 

9735 

9968 

0214 

0475 

0753 

1050 

1369 

1713 

8 

53 

8913 

9106 

9306 

9517 

9739 

9972 

0219 

0480 

0758 

1055 

1374 

1719 

7 

54 

8917 

9109 

9310 

9521 

9742 

9976 

0223 

0484 

0763 

1061 

13«0 

1725 

6 
5 

55 

1.8920 

1.9112 

1.9313 

1.9524 

1.9746 

1.9980 

2.0227 

2.0489 

2.0768 

2.1066 

2.13vti 

2.1731 

56 

8923 

9115 

9317 

9528 

9750 

9984 

0231 

0493 

0773 

1071 

13  ill 

1737 

4 

57 

8926 

9119 

9320 

9532 

9754 

9988 

0235 

0498 

0777 

1076 

1397 

1743 

3 

58 

8929 

9122 

9324 

9535 

9758 

9992 

0240 

0502 

0782 

1081 

1402 

1749 

2 

59 

8932 

9125 

9327 

9539 

9761 

9996 

0244 

0507 

0787 

1086 

1408 

1755 

1 

60 

8935 

9128 

9331   9542 

9765 

2.0000 

0248 

0512 

0792 

1091 

1413 

1761 

0 

23' 

22'  1   21'    20' 

19' 

18' 

17' 

16' 

15' 

14' 

13' 

12' 

S. 

5   DEGREES. 

Wl 

lien  the  Apparent  Distance  is  lets  than  90",  the  Second  Correction  is  to  be  taken  from  the  Botto 

»          1 

J  52                 TABLE  XXXII.                        \ 

LOGARITHMS  OF  THE  FIRST  AND  SI 

XOND 

ond,  whe 

CORRECTIONS.            | 

Ih*  Fint  Correction  it  alieays  to  be  taken  from  the  Top,  and  also  the  Sec 

a  the  Apparent  Distance  is  greater  than  OOO.f 

4  DEGREES.                                     \ 

S. 
0 

48' 

49' 

50' 

51' 

52' 

53' 

54' 

55' 

56' 

57' 

58' 

69' 

2.1761 

2.2139 

2.2553 

2.3010 

2.3522 

2.4102 

2.4771 

2.5563 

2.6532 

2.7782 

2.9542 

3.2553 

60 

1 

1767 

2145 

2560 

3018 

3531 

4112 

4783 

5578 

6550 

7806 

9579 

2626 

59 

2 

1773 

2152 

2567 

3026 

3540 

4122 

4795 

5592 

6568 

7830 

9615 

2700 

58 

3 

1779 

2159 

2574 

3034 

3549 

4133 

4808 

5607 

6587 

7855 

9652 

2775 

57 

4 

1785 

2165 

2582 

3043 

3558 

4143 

4820 

5621 

6605 

7879 

9690 

2852 

56 

5 

2.1791 

2.2172 

2.2589 

2.3051 

2.3567 

2.4154 

2.4832 

2.5636 

2.6624 

2.7904 

2.9727 

3.2931 

55 

6 

1797 

2178 

2596 

3059 

3576 

4164 

4844 

5651 

6642 

7929 

9765 

3010 

54 

7 

1803 

2185 

2604 

3067 

3586 

4175 

4856 

5666 

6661 

7954 

9803 

3091 

53 

8 

1809 

2192 

2611 

3075 

3595 

4185 

4869 

5680 

6679 

7979 

9842 

3174 

52 

9 

181ti 

2198 

2618 

3083 

3604 

4196 

4881 

5695 

6698 

8004 

9881 

3259 

51 

50 

10 

2.1822 

2.2205 

2.2626 

2.3091 

2.3613 

2.4206 

2.4894 

2.5710 

2.6717 

2.8030 

2.9920 

3.3345 

11 

1828 

2212 

2633 

3100 

3623 

4217 

4906 

5725 

6736 

8055 

9960 

3432 

49 

12 

1834 

22.18 

2640 

3108 

3632 

4228 

4918 

5740 

6755 

8081 

3.0000 

3522 

48 

13 

1840 

2225 

2648 

3116 

3641 

4238 

4931 

5755 

6774 

8107 

0040 

3613 

47 

14 

1846 

2232 

2655 

8124 

3650 

4249 

4943 

5771 

6793 

8133 

0081 

3707 

46 

15 

2.1852 

2.2239 

2.2663 

2.3133 

2.3660 

2.4260 

2.4956 

2.5786 

2.6812 

2.8159 

3.0122 

3.3802 

45 

16 

1859 

2245 

2670 

3141 

3669 
^3678 

4270 

4969 

5801 

6832 

8186 

0164 

3900 

44 

17 

1865 

2252 

2678 

3149 

4281 

4981 

5816 

6851 

8212 

0206 

4000 

43 

18 

1871 

2259 

2685 

3158 

3688 

4292 

4994 

5832 

6871 

8239 

0248 

4102 

42 

19 

1877 

2266 

2692 

3166 

3697 

4303 

5007 

5847 

6890 

8266 

0291 

4206 

41 
40 

20 

2.1883 

2.2272 

2.2700 

2.3174 

2.3707 

2.4314 

2.5019 

2.5863 

2.6910 

2.8293 

3.0334 

3.4314 

21 

1889 

2279 

2707 

3183 

3716 

4325 

5032 

5878 

6930 

8320 

0378 

4424 

39 

22 

1896 

2286 

2715 

3191 

3726 

4335 

5045 

5894 

6950 

8348 

0422 

4536 

38 

23 

1902 

2293 

2722 

3199 

3735 

4346 

5058 

5909 

6970 

8375 

0467 

4652 

37 

24 

1908 

2300 

2730 

3208 

3745 

4357 

5071 

5925 

6990 

8403 

0512 

4771 

36 
35 

25 

2.1914 

2.2307 

2.2738 

2.3216 

2.3754 

2.4368 

2.5084 

2.5941 

2.7010 

2.8431 

3.0557 

3.4894 

26 

1921 

2313 

2745 

3225 

3764 

4379 

5097 

5957 

7030 

8459 

0603 

5019 

34 

27 

1927 

2320 

2753 

3233 

3773 

4390 

5110 

5973 

7050 

8487 

0649 

5149 

33 

28 

1933 

2327 

2760 

3242 

378o 

4401 

5123 

5989 

7071 

8516 

0696 

5283 

32 

29 

1939 

2334 

2768 

3250 

3792 

4412 

5136 

6005 

7091 

8544 

0744 

5421 

31 

30 

2.1946 

2. 2341 

2.2775 

2.3259 

2.3802 

2.4424 

2.5149 

2.6021 

2.7112 

2.8573 

3.0792 

3.5563 

30 

31 

1952 

2348 

2783 

3267 

3812 

4435 

5162 

6037 

7133 

8602 

0840 

5710 

29 

32 

1958 

2355 

2791 

3276 

3821 

4446 

5175 

6053 

7154 

8632 

C889 

5863 

28 

33 

1965 

2362 

2798 

3284 

3831 

4457 

5189 

6069 

7175 

8661 

0939 

6021 

27 

34 

1971 

2368 

2806 

3293 

3841 

4468 

5202 

6085 

7196 

8691 

0989 

6185 

26 

25 

35 

2.1977 

2.2375 

2.2814 

2.3301 

2.3851 

2.4480 

2.5215 

2.6102 

2.7217 

2.8721 

3.1040 

3.6355 

36 

1984 

2382 

2821 

3310 

3860 

4491 

5229 

6118 

7238 

8751 

1091 

6532 

24 

37 

1990 

2389 

2829 

3319 

3870 

4502 

5242 

6135 

7259 

8781 

1143 

6717 

23 

38 

1996 

2396 

2837 

3327 

3880 

4514 

5256 

6151 

7281 

8811 

1196 

6910 

22 

39 

2003 

2403 

2845 

3336 

3890 

4525 

5269 

6168 

7302 

8842 

1249 

7112 

21 

40 

2.2009 

2.2410 

2.2852 

2.3345 

2.3900 

2.4536 

2.5283 

2.6185 

2.7324 

2.8873 

3.1303 

3.7324 

20 

41 

2016 

2417 

2860 

3353 

3910 

4548 

5296 

6201 

7346 

8904 

1358 

7547 

19 

42 

2022 

2424 

2868 

3362 

3919 

4559 

5310 

6218 

7368 

8935 

1413 

7782 

18 

43 

2028 

2431 

2876 

3371 

3929 

4571 

5324 

6235 

7390 

8967 

1469 

8030 

17 

44 

2035 

2438 

2883 

3379 

3939 

4582 

5337 

6252 

7412 

8999 

1526 

8293 

16 
15 

45 

2.2041 

2.2445 

2.2891 

2.3388 

2.3949 

2.4594 

2.5351 

2.6269 

2.7434 

2.9031 

3.1584 

3.8573 

46 

2048 

2453 

2899 

3397 

3959 

4606 

5365 

6286 

7456 

9063 

1642 

8873 

14 

47 

2054 

2460 

2907 

3406 

3969 

4617 

5379 

6303 

7479 

9096 

1701 

9195 

13 

48 

2061 

2467 

2915 

3415 

3979 

4629 

5393 

6320 

7501 

9128 

1761 

9542 

12 

49 

2067 

2474 

2923 

3423 

3989 

4640 

5407 

6338 

7524 

9162 

1822 

9920 

11 

50 

2.2073 

2.2481 

2.2931 

2.3432 

2 . 4000 

2.4652 

2.5421 

2.6355 

2.7547 

2.9195 

3.1883 

4.0334 

10 

51 

2080 

2488 

2939 

3441 

4010 

4664 

5435 

6372 

7570 

9228 

1946 

0792 

9 

52 

3086 

2495 

2946 

3450 

4020 

4676 

5449 

6390 

7593 

9262 

2009 

1303 

8 

53 

2093 

2502 

2954 

3459 

4030 

4688 

5463 

6407 

7616 

9296 

2073 

1883 

7 

54 

2099 

2510 

2962 

3468 

4040 

4699 

5477 

6425 

7639 

9331 

2139 

2553 

6 

55 

2.2106 

2.2517 

2.2970 

2.3477 

2 . 4050 

2.4711 

2.5491 

2.6443 

2.7663 

2.9365 

3.2205 

4.3345 

5 

56 

2113 

2524 

2978 

3486 

4061 

4723 

5506 

6460 

7686 

9400 

2272 

4314 

4  ; 

57 

2119 

2531 

2986 

3495 

4071 

4735 

5520 

6478 

7710 

9435 

2341 

5563 

3 

58 

2126 

2538 

2994 

3504 

4081 

4747 

5534 

6496 

7734 

9471 

2410 

7324 

2 

59 

2132 

2545 

3002 

3513 

4091 

4759 

5549 

6514 

7757 

9506 

2481 

5.0334 

1 

60 

2139 

2553 

3010 

3522 

4102 

4771 

5563 

6532 

7782 

9542 

2553 

0 

11'    1^ 

9' 

8"     7'  1    6' 

5' 

4' 

3'  1   2' 

1'     0' 

s. 

5  DEGREES. 

1 
1 

. 

When  the  Apparent  Distance  is  leas  than  90°,  the  Second  Correction  is  to  be  taken  from  the  Bottom.          1 

TABLE. 

153      1 

ANGLE  OF  AZIMUTH  AND  CORRESPONDING  CHANGE  OF  ALTITUDE  IN  ONE  MINCJTE 

OF  TIME. 

Enter  this  Table  with  the  Latitude  in,  at  the  side,  and  opposite  to  which,  in  the  body  of  the  Table,  find  the 
approximate  Azimuth  or  Sun's  Angle  from  the  Meridian  in  Degrees  at  the  time  of  the  observation.     Then  *l 
the  Top  will  be  found  the  Sun's  change  of  altitude  in  1  minute  of  time. 

This  Table  is  useful  to  verify  a  set  of  Altitudes  for  Chronometer,  taken  when  the  Sun  is  not  on  the  Prime 
Vertical,  and  for  other  purposes  when  precision  is  required. 

Lai. 

CHANQK    OP    ALTITUDE    IN    1    MUfUTB. 

/ 

/           / 

/ 

t 

/ 

r 

/ 

t 

1 

/ 

/ 

/ 

1 

1 

.> 

4 

5 

6 

7 

? 

9 

10 

11 

12 

13 

14 

15 

0 

,1 

O 

0 

0 

4 

0 

8 

0 

12 

o 
15 

o 

19 

o 
24 

o 
28 

o 
32 

o 
37 

o 
42 

o 
47 

o 
53 

o 
60 

o 
69 

o 

87 

i 

0 

4 

8 

12 

15 

19 

24 

28 

32 

37 

42 

47 

53 

60 

69 

87 

4 

0 

4 

8 

12 

15 

20 

24 

28 

32 

37 

42 

47 

53 

60 

69 

6 

0 

4 

8 

12 

16 

20 

24 

28 

32 

37 

42 

48 

54 

61 

70 

8 

0 

4 

8 

12 

16 

20 

24 

28 

33 

37 

42 

48 

54 

61 

71 

10 

0 

4 

8 

12 

16 

20 

24 

28 

33 

38 

43 

48 

54 

62 

71 

11 

0 

4 

8 

12 

16 

20 

24 

28 

33 

38 

43 

48 

55 

62 

72 

12 

0 

4 

8 

12 

16 

20 

24   . 

28 

33 

38 

43 

49 

55 

62 

73 

13 

0 

4 

8 

12 

16 

20 

24 

29 

33 

38 

43 

49 

55 

63 

73 

14 

0 

4 

8 

12 

16 

20 

24 

29 

33 

38 

43 

49 

56 

63 

74 

15 

0 

4 

8 

12 

16 

20 

24 

29 

34 

38 

44 

49 

56 

64 

75 

16 

0 

4 

8 

12 

16 

20 

25 

29 

34 

39 

44 

50 

56 

64 

76 

17 

0 

4 

8 

12 

16 

20 

25 

29 

34 

39 

44 

50 

57 

65 

77 

"18 

0 

4 

8 

12 

16 

21 

25 

29 

34 

39 

44 

50 

57 

66 

79 

19 

0 

4 

8 

12 

16 

21 

25 

30 

34 

39 

45 

51 

58 

66 

81 

20 

0 

4 

8 

12 

16 

21 

25 

30 

35 

40 

45 

51 

58 

67 

83 

21 

0 

4 

8 

12 

17 

21 

25 

30 

35 

40 

46 

52 

59 

68 

89 

22 

0 

4 

8 

12 

17 

21 

26 

30 

35 

40 

46 

52 

60 

69 

23 

0 

4 

8 

13 

17 

21 

26 

30 

35 

41 

46 

53 

60 

70 

24 

0 

4 

8 

13 

17 

21 

26 

31 

36 

41 

47 

53 

61 

72 

25 

0 

4 

8 

13 

17 

22 

26 

31 

36 

41 

47 

54 

62 

73 

26 

0 

4 

9 

13 

17 

22 

26 

31 

36 

42 

48 

55 

63 

75 

27 

0 

4 

9 

13 

17 

22 

27 

32 

37 

42 

48 

55 

64 

77 

28 

0 

4 

9 

13 

18 

22 

27 

32 

37 

43 

49 

56 

65 

79 

29 

0 

4 

9 

13 

18 

22 

27 

32 

37 

43 

50 

57 

66 

82 

30 

0 

4 

9 

13 

18 

23 

27 

33 

38 

44 

50 

58 

67 

31 

0 

4 

9 

13 

18 

23 

28 

33 

38 

44 

51 

f59 

69 

32 

0 

5 

9 

14 

18 

23 

28 

33 

39 

45 

52 

60 

71 

33 

0 

5 

9 

14 

19 

23 

28 

34 

39 

46 

53 

61 

73 

34 

0 

5 

9 

14 

19 

24 

29 

34 

40 

46 

54 

62 

75 

35 

0 

3 

9 

14 

19 

24 

29 

35 

41 

47 

54 

64 

78 

36 

0 

5 

9 

14 

19 

24 

30 

35 

41 

48 

55 

65 

81 

37 

0 

5 

10 

14 

19 

25 

30 

36 

42 

49 

57 

67 

38 

0 

5 

10 

15 

20 

25 

30 

36 

43 

49 

58 

69 

39 

0 

5 

10 

15 

20 

25 

31 

37 

43 

51 

59 

71 

40 

0 

5 

10 

15 

20 

26 

31 

38 

44 

52 

60 

73 

41 

0 

5 

10 

15 

21 

26 

32 

38 

45 

53 

62 

76 

42 

0 

5 

10 

16 

21 

27 

33 

39 

46 

54 

64 

81 

43 

0 

5 

10 

16 

21 

27 

33 

40 

47 

55 

66 

44 

0 

5 

11 

16 

22 

28 

34 

40 

48 

57 

68 

45 

0 

5 

11 

16 

22 

28 

34 

41 

49 

58 

71 

46 

0 

5 

11 

17 

23 

29 

35 

42 

50 

60 

74 

47 

0 

6 

11 

17 

23 

29 

36 

43 

51 

62 

78 

48 

0 

6 

11 

17 

23 

30 

37 

44 

53 

64 

85 

49 

0 

6 

12 

18 

24 

31 

38 

45 

54 

66 

50 

0 

6 

12 

18 

25 

31 
32 

38 

47 

56 

69 

51 

0 

6 

12 

19 

25 

39 

48 

58 

72 

52 

0 

6 

12 

19 

26 

33 

41 

49 

60 

77 

53 

0 

6 

13 

19 

26 

34 

42 

51 

62 

85 

54 

0 

7 

13 

20 

27 

35 

43 

53 

65 

55 

0 

7 

13 

20 

28 

36 

44 

54 

68 

56 

0 

7 

14 

21 

28 

37 

46 

57 

73 

57 

0 

7 

14 

22 

29 

38 

47 

59 

78 

58 

0 

7 

15 

22 

30 

40 

49 

62 

59 

0 

■7 

15 

23 

31 

40 

51 

65 

60 
61 

0 
0 

8 

8 

15 

24 

32 

42 

53 

69 

16 

24 

33 

43 

56 

74 

62 

0 

8 

16 

25 

35 

45 

58 

84 

63 

0 

8 

17 

26 

36 

47 

62 

64 

0 

9 

18 

27 

37 

49 

66 

65 

0 

9 

18 

28 

39 

52 

70 

66 

0 

9 

19 

29 

41 

55 

80 

1 

X) 


154                TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  20o. 

. 

Alt. 

APPARENT  ALTITUDE  OF  THE  SUN,  OR  A  STAB. 

3>'s 
App 
Alt. 

0 

6» 

70 

S* 

90 

10«> 

11° 

12» 

14° 

16° 
1    II 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

o 

1    It 

t    n 

/  // 

/  II 

1    II 

/  n 

/  II 

1    II 

/  // 

/  // 

/  II 

1    II 

/  II 

/  II 

/  // 

6  1  38 

1  42 

1  46 

I  55 

2  7 

2  19 

2  34 

3  9 

3  43 

4  17 

4  51 

5  25 

5   59 

6  32 

H 

7  1  46 

1  37 

1  40 

1  46 

1  53 

2  3 

2  12 

2  36 

3  1 

3  29 

3  57 

4  24 

4  50 

5  16 

7 

8 

1  55 

1  43 

1  36 

1  40 

1  44 

1  49 

1  56 

2  14 

2  35 

2  56 

3  17 

3  39 

4  0 

4  21 

4  42 

8 

9 

2  8 

1  51 

1  40 

1  36 

1  39 

1  42 

1  45 

1  57 

2  12 

2  29 

2  47 

3  5 

3  23 

3  41 

3  58 

9 

10 

2  23 

2  0 

1  46 

1  40 

1  36 

1  37 

1  39 

1  46 

1  56 

2  10 

2  24 

2  38 

2  53 

3  8 

2  44 

3  23 

2  56 

3  37 

10 

11 

2  38 

2  11 

1  54 

1  45 

1  38 

1  37 

1  37 

1  40 

1  46 

1  56 

2  8 

2  20 

2  32 

3  7 

11 

12 

2  53 

2  23 

2  3 

1  51 

1  41 

1  37 

1  35 

1  37 

1  41 

1  47 

1  56 

2  6 

2  16 

2  26 

2  35 

2  44 

12 

13 

3  9 

2  35 

2  13 

1  57 

1  46 

1  40 

1  37 

1  35 

1  37 

1  41 

1  48 

1  56 

2  4 

2  12 

2  19 

2  26 

13 

14 

3  25 

2  47 

2  23 

2  3 

1  52 

1  44 

1  39 

1  33 

1  34 

1  37 

1  42 

1  48 

1  54 

2  0 

2  5 

2  11 

14 

15 

3  41 

3  0 

2  34 

2  11 

1  58 

1  49 

1  42 

1  35 

1  33 

1  35 

1  38 

1  41 

1  45 

1  50 

1  54 

1  59 

15 

16 

3  58 

3  13 

2  45 

2  20 

2  4 

1  54 

1  46 

1  36 

1  32 

1  33 

1  34 

1  36 

1  38 

1  42 

1  46 

1  50 

16 

17 

4  15 

3  26 

2  56 

2  29 

2  10 

1  59 

1  50 

1  38 

1  33 

1  31 

1  32 

1  33 

1  34 

1  36 

1  39 

1  42 

17 

18 

4  32 

3  40 

3  7 

2  38 

2  17 

2  4 

1  54 

1  40 

1  34 

1  30 

1  30 

1  30 

1  31 

1  32 

1  34 

1  36 

18 

19 

4  49 

3  53 

3  18 

2  47 

2  24 

2  9 

1  58 

1  43 

1  35 

1  31 

1  29 

1  29 

1  29 

1  30 

1  32 

1  33 

19 

20 

5  5 

4  6 

3  28 

2  56 

2  31 

2  15 

2  2 

1  46 

1  37 

1  31 
1  32 

1  28 

1  28 

1  28 

1  29 

1  30 

1  30 
1  27 

20 
21 

21 

5  21 

4  19 

3  39 

3  4 

2  38 

2  20 

2  6 

1  49 

1  39 

1  29 

1  27 

1  27 

1  27 

1  27 

22 

5  36 

4  32 

3  49 

3  12 

2  46 

2  26 

2  11 

1  53 

1  40 

1  33 

1  29 

1  26 

1  25 

1  25 

1  25 

1  25 

22 

23 

5  51 

4  44 

3  59 

3  20 

2  53 

2  32 

2  16 

1  57 

1  42 

1  34 

1  29 

1  26 

1  25 

1  24 

1  24 

1  23 

23 

24 

6  5 

4  56 

4  9 

3  28 

3  0 

2  38 

2  22 

2  0 

1  43 

1  35 

1  30 

1  26 

1  24 

1  24 

1  23 

1  22 

24 

25 

6  19 

5  7 

4  18 

3  36 

3  7 

2  44 

2  26 

2  3 

1  45 

1  36 

1  30 

1  26 

1  24 

1  23 

1  21 

1  20 

2b 

26 

6  32 

5  18 

4  27 

3  44 

3  14 

2  49 

2  31 

2  6 

1  47 

1  37 

1  31 

1  27 

1  25 

1  23 

1  21 

1  19 

26 

27 

6  45 

5  29 

4  35 

3  52 

3  20 

2  54 

2  35 

2  8 

1  49 

1  38 

1  32 

1  28 

1  25 

1  23 

1  21 

1  19 

27  1 

28 

5  39 

4  42 

3  59 

3  26 

2  59 

2  38 

2  11 

1  50 

1  39 

1  33 

1  28 

1  25 

1  23 

1  21 

1  19 

28 

29 

4  49 

4  6 

3  32 

3  4 

2  41 

2  13 

1  52 

1  40 

1  33 

1  28 

1  25 

1  23 

1  21 

1  19 

29 

30 

4  12 

3  37 

3  8 

2  45 

2  15 

1  54 

1  41 

1  34 

1  28 

1  25 

1  23 

1  21 

1  19 

30 

31 

3  42 

3  12 

2  49 

2  16 

1  56 

1  42 

1  34 

1  28 

1  25 

1  22 

1  20 

1  18 

31 

32 

3  16 

2  52 

2  18 

1  58 

1  43 

1  34 

1  28 

1  24 

1  21 

1  19 

1  18 

32 

33 

2  55 

2  20 

1  59 

1  43 

1  33 

1  27 

1  24 

1  21 

1  19 

1  17 

33 

34 

2  21 

1  59 

1  43 

1  33 

1  26 

1  23 

1  20 

1  18 

1  16 

34 

35 

2  22 

1  59 

1  43 

1  32 

1  25 

1  22 

1  19 

1  17 

1  15 

35 

36 

1  59 

1  42 

1  31 

1  24 

1  20 

1  17 

1  15 

1  14 

36 

37 

1  59 

1  42 

1  30 

1  23 

1  19 

1  16 

1  14 

1  13 

37 

38 

1  41 

1  29 

1  22 

1  18 

1  15 

1  13 

1  12 

38 

39 

1  41 

1  28 

1  21 

1  17 

1  13 

1  11 

1  11 

39 

40 

1  27 

1  20 

1  15 

1  12 

1  10 

1  10 

40 

41 

1  26 

1  18 

1  13 

1  10 

1  9 

1  8 

41 

42 

1  17 

1  11 

1  8 

1  7 

1  7 

42 

43 

1  16 

1  10 

1  6 

1  5 

1  5 

43 

44 

/ 

1  9 

1  4 

1  3 

1  3 

44 

46 

48 

1  7 

1  2 

1  0 

1  0 

46 
48 

0  59 

0  56 

0  56 

50 

) 

0  52 

0  50 

50 

5^ 

0  45 

52 

54 

54 

56 

66 

58 

• 

58 

60 

60 

62 

62 

64 

64 

66 

66 

68 

68 

70 

72 

70 

72 

74 

74 

76 

'  76 
78 

78 

80 

80 

82 

82 

84 

84 

86 

1 

86 

6° 

70 

8«» 

90  1  10<» 

11° 

12° 

140 

16°^ 

18° 

20° 

22° 

24° 

26° 

28° 

1  30° 

^H. 

5-8 

App, 
Alt, 


6 
7 
8 
9 
10 


11 
12 
13 
14 

15 


16 
17 

18 
19 
20 


21 
22 
23 
24 
25 


26 
27 
28 
29 
30 


31 
32 
33 
34 
35 


36 
37 
38 
39 

40 


41 
42 
43 
44 
46 


48 
50 
52 
54 
56 


58 
60 
62 
64 
66 


68 
70 
72 
74 
76 


78 
80 
82 
84 
86 


TABLE  XXXIII. 
THIRD  CORRECTION,  TO  APPARENT  DISTANCE  20°. 


APPARENT    ALTITUDE    OF    TUB    SUN,    OR    STAR. 


12= 


34^'  360  380  42©  450  5Q0 


16 

52 

32 

16 

3 


53 
44 
37 
33 
30 


27 
24 
22 
21 
19 


17 
17 
17 
17 

18 


2  38 
2  21 

2  7 


1  56 
1  46 
1  39 
1  34 
1  30 


1  26 
1  23 
1  -21 
1  20 


13 
12 
11 
10 
9 


0  56 
0  52 
0  48 
0  44 


32' 


2  13 


59 
48 
40 
34 
29 


1  25 
1  22 
1  20 
1  18 


1  18  1  16 


1  16 
1  15 
1  15 
1  16 
1  17 


17  1  16 

17  1  16 

1^1  15 

l?'l  14 

14  1  13 


1  12 
1  11 
1  10 
1  10 
1  9 


0  58 
0  54 
0  49 
0  43 
0  38 


14 
13 
13 
14 
15 


1  51 

1  41 
1  34 

1  28 


1  23 
1  20 
1  18 
1  16 
1  14 


1  15 
1  14 
1  13 
1  13 
1  12 


1  11 

1  10 
1  9 

1  9 

1  8 


0  59 
0  55 
0  50 
0  45 
0  40 


0  35 


34^ 


12 
11 
10 
11 
12 


1  26 


1  12 
1  12 
1  12 
1  11 
1  11 


1  10 
1  9 
1  8 
1 
1  6 


0  59 
0  56 
0  51 
0  46 
0  42 


0  38 
0  34 


36°  I  38*= 


21 
18 
15 
12 
9 


0  58 
0  55 
0  51 
0  47 
0  44 


0  40 
0  36 
0  33 
0  30 


1  8 
1  4 


1  1 
1  0 
0  57 
0  58 

0  59 


0  59 
0  59 
1 
1 
1 


0  50 
0  50 
0  50 


1  0 
0  59 
0  59 
0  59 
0  58 


0  56 
0  54 
0  51 

0  48 
0  45 


42= 


0  42 
0  39 
0  36 
0  33 
0  30 


0  27 


46° 


0  51 
0  51 
0  52 
0  53 
0  53 


0  54 
0  54 
0  55 
0  55 
0  55 


0  55 
0  55 
0  55 
0  55 
0  54 


0 

0  51 
0  49 
0  47 
0  45 


54= 


58®  62"  66°  70°  74°  78°  82°  i,6° 


0  42 
0  43 
0  43 
0  44 


0  45 
0  46 
0  47 
0  47 
0  48 


0  48 
0  48 
0  48 
0  48 
0  48 


53  0 
0 
0 


43 
41 
38 
35 
32 


0  29 
0  27 
0  25 


50° 


49 
48 
47 
45 
44 


r    ff 


It 


0  36 
0  37 
0  38 
0  39 
0  39 


0  39 
0  40 
0  40 
0  40 
0  41 


42 
41 
39 
37 
35 


0  32 
0  30 
0  27 
0  25 
0  23 


54° 


43 
43 

43 
43 

42 


0  32 


0  32 
0  33 
0  33 
0  34 
0  35 


0  29 
0  30 


0  40 
0  39 
0  38 
0  37 
0  36 


0  34 
0  32 
0  29 
0  27 
0  25 


0  23 
0  21 


58° 


0  37 
0  38 
0  39 
0  40 
0  40 


0  38 
0  36 
0  35 
0  35 
0  34 


0  32 
0  31 

0  29 
0  27 
0  26 


0  24 
0  23 
0  22 
0  21 


0  31 
0  33 
0  35 
0  36 
0  35 


0  33 
0  32 
0  32 
0  31 


0  25 
0  27 
0  29 
0  30 
0  31 


0  24 
0  25 
0  27 


0  34  0  31 


0  30 

0  29 
0  28 
0  27 
0  26 


62° 


0  25 
0  24 
0  23 
0  22 
0  21 


66° 


0  29 
0  29 
0  29 
0  29 


0  28 
0  27 
0  27 
0  26 
0  25 

0  24 
0  23 
0  22 
0  21 
C  20 


0  27 
0  26 
0  26 
0  27 
0  27 


0  26 
0  26 
0  25 
0  24 
0  24 


0  23 
0  22 
0  21 
0  21 
0  20 


70= 


74° 


0  22 


0  23 
0  23 
0  24 
0  25 
0  25 


0  25 
0  24 
0  23 

0  22 
0  22 


0  21 
0  22 

0  22 
0  23 


0  21 
0  21 
0  21 


78° 


23 
22 
21 
21 
10 


0  20 

0  20 


82° 


155 


3) 

App 
A.t. 
o 

6 
7 
8 
9 
10 


0  21 


11 

12 
13 
14 
15 

16 
17 
18 
19 

20 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

31 

32 
33 
34 
35 


36 
37 
38 
39 
40 


41 
42 
44 
45 
46 

48 
50 
52 
54 
56 


0  21 

0  20 
0  20 
0  20 
0  19 


58 
60 
62 
64 
66 


68 
70 
72 
74 
76 


78 
80 
82 
84 
86 


86° 


156                TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  24''. 

App.. 
Alt. 

APPARENT  ALTITUDE  OF  THE  SUN,  OR  A  STAR. 

D's 

App. 
Alt. 

0 

6° 

70 

8» 

9° 

10* 

11° 

120  140 

16° 

1    II 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

o 

r    It 

f    II 

/  // 

/  n 

1   n 

t  II 

1    II 

1    n 

1    II 

/  II 

/  // 

/  II 

/  II 

1    II 

/  II 

6 

1  28 

1  31 

1  35 

1  42 

1  52 

2  3 

2  16 

2  46 

3  16 

3  47 

4  19 

4  50 

5   20 

5  50 

6  20 

6  50 

6 

7 

1  35 

1  27 

1  30 

1  34 

1  39 

1  46 

1  54 

2  15 

2  38 

3  3 

3  29 

3  55 

4  20 

4  46 

5  10 

5  34 

7 

8 

1  45 

1  32 

1  26 

1  28 

1  30 

1  35 

1  41 

1  58 

2  17 

2  37 

2  58 

3  18 

3  39 

4  1 

4  20 

4  39 

8 

9 

1  56 

1  39 

1  30 

1  25 

1  26 

1  29 

1  34 

1  44 

1  59 

2  15 

2  31 

2  48 

3  6 

3  24 

3  40 

3  56 

9 

10 

2  8 

1  48 

1  36 

1  29 

1  25 

1  26 

1  28 

1  35 

1  45 

1  57 

2  13 

2  27 

2  43 

2  58 

3  12 
2  49 

3  26 

10 

11 

2  21 

1  58 

1  43 

1  34 

1  28 

1  24 

1  26 

1  30 

1  36 

1  46 

1  58 

2  11 

2  24 

2  37 

3  0 

H 

12 

2  36 

2  9 

1  52 

1  41 

1  33 

1  27 

1  24 

1  26 

1  30 

1  37 

1  47 

1  58 

2  9 

2  20 

2  29 

2  38 

12 

13 

2  51 

2  20 

2  1 

1  48 

1  38 

1  31 

1  27 

1  24 

1  27 

1  32 

1  40 

1  48 

1  57 

2  6 

2  14 

2  22 

13 

14 

3  6 

2  31 

2  10 

1  55 

1  43 

1  35 

1  30 

1  23 

1  25 

1  28 

1  33 

1  40 

1  48 

1  55 

2  2 

2  10 

14 

15 

3  21 

2  42 

2  20 

2  2 

1  50 

1  39 

1  33 

1  24 

1  23 

1  22 

1  25 

1  24 

1  34 

1  40 

1  46 

1  52 

1  59 

15 

16 

3  36 

2  54 

2  30 

2  9 

1  56 

1  44 

1  36 

1  26 

1  23 

1  25 

1  29 

1  33 

1  38 

1  44 

1  50 

16 

17 

3  51 

3  6 

2  40 

2  17 

2  S 

1  49 

1  39 

1  28 

1  23 

1  21 

1  23 

1  26 

1  29 

1  34 

1  39 

1  43 

17 

18 

4  6 

3  18 

2  49 

2  25 

2  8 

1  54 

1  43 

1  31 

1  24 

1  20 

1  21 

1  23 

1  26 

1  30 

1  34 

1  37 

18 

19 

4  21 

3  30 

2  59 

2  33 

2  14 

1  59 

1  47 

1  33 

1  25 

1  21 

1  20 

1  22 

1  24 

1  27 

1  30 

1  32 

19 

20 

4  35 

3  42 

3  9 

2  41 

2  21 

2  6 

1  52 

1  36 

1  27 

1  22 
1  23 

1  19 

1  20 

1  22 

1  24 

1  26 

1  28 
1  25 

20 

21 

4  50 

3  54 

3  19 

2  50 

2  28 

2  11 

1  56 

1  39 

1  29 

1  20 

1  19 

1  20 

1  21 

1  23 

21 

22 

5  4 

4  6 

3  28 

2  58 

2  35 

2  17 

2  1 

1  42 

1  31 

1  24 

1  20 

1  18 

1  19 

1  19 

1  20 

1  22 

2£ 

23 

5  19 

4  18 

3  38 

3  6 

2  43 

2  23 

2  6 

1  46 

)  33 

1  25 

1  21 

1  18 

1  18 

1  18 

1  18 

1  19 

23 

24 

5  33 

4  29 

3  48 

3  14 

2  51 

2  29 

2"  12 

1  50 

1  36 

1  27 

1  22 

1  19 

1  17 

1  17 

1  17 

1  17 

24 

25 

5  47 

4  41 

3  57 

3  22 

2  58 

2  35 

2  17 

1  53 

1  38 

1  28 
1  30 

1  23 

1  20 

1  18 

1  16 

1  16 

1  16 

25 

26 

6  1 

4  52 

4  6 

3  30 

3  4 

2  41 

2  22 

1  57 

"l  41 

1  24 

1  20 

1  18 

1  16 

1  15 

1  15 

26 

27 

6  14 

5  4 

4  15 

3  38 

3  10 

2  47 

2  27 

2  0 

1  43 

1  32 

1  25 

1  21 

1  18 

1  15 

1  14 

1  13 

27 

28 

6  27 

5  15 

4  23 

3  45 

3  16 

2  53 

2  32 

2  4 

1  46 

1  34 

1  27 

1  21 

1  18 

1  15 

1  13 

1  12 

28 

29 

6  38 

5  26 

4  32 

3  53 

3  22 

2  58 

2  38 

2  8 

1  49 

1  36 

1  28 

1  22 

1  18 

1  15 

1  13 

1  11 

29 

30 

6  50 

5  36 

4  41 

4  0 

3  28 

3  3 

2  44 

2  12 

1  52 

1  38 

1  29 

1  23 

1  19 

1  15 

1  13 

1  11 

30 
31 

31 

7  0 

5  45 

4  50 

4  7 

3  34 

3  8 

2  49 

2  16 

1  55 

1  40 

1  30 

1  24 

1  19 

1  15 

1  13 

1  11 

32 

5  53 

4  58 

4  14 

3  40 

3  13 

2  54 

2  19 

1  57 

1  41 

1  31 

1  24 

1  19 

1  15 

1  13 

1  11 

32 

33 

5  5 

4  20 

3  46 

3  18 

2  58 

2  22 

1  59 

1  42 

1  31 

1  24 

1  19 

1  15 

1  13 

1  11 

33 

34 

4  25 

3  51  3  22 

3  1 

2  24 

2  1 

1  43 

1  32 

1  25 

1  20 

1  15 

1  13 

1  11 

34 

35 

3  56,3  26 

3  3 

2  26 

2  2 

1  45 

1  33 

1  25 

1  20 

1  15 

1  13 

1  11 

35 

36 

3  30 

3  5 

2  28 

2  4 

1  46 

1  34 

1  25 

1  20 

1  15 

1  12 

1  10 

36 

37 

3  7 

2  30 

2  6 

1  47 

1  35 

1  25 

1  20 

1  15 

1  12 

1  10 

37 

38 

2  32 

2  7 

1  48 

1  35 

1  25 

1  20 

1  15 

1  12 

1  10 

38 

39 

2  34 

2  8 

1  49 

1  35 

1  25 

1  19 

1  15 

1  12 

1  10 

39 

40 

2  9 

1  50 

1  35 

1  25 

1  19 

1  15 

1  11 

1  9 

40 

41 

2  10 

1  60 

1  35 

1  25 

1  19 

1  15 

1  11 

1  8 

41 

42 

1  51 

1  36 

1  25 

1  19 

1  14 

1  10 

1  7 

42 

43 

1  52 

1  36 

1  25 

1  18 

1  13 

1  9 

1  6 

43 

44 

1  36 

1  25 

1  18 

1  13 

1  8 

1  5 

44 

46 
48 



1  36 

1  25 

1  17 

1  12 

1  7 

1  3 

46 

* 

1  25 

1  17 

1  10 

1  5 

1  1 

48 

50 

1  17 

1  8 

1  4 

0  59 

50 

52 

1  7 

1  3 

0  58 

52 

54 

1  2 

0  57 

54 

56 

0  56 

56 

58 

58 

60 

60 

62 

62 

64 

64 

66 

66 

68 

68 

70 

1 

70 

72 

I 

72 

74 

, 

74 

76 

76 
78 

78 

80 

80 

82 

82 

84 

84 

86 

86 

6<» 

70 

8» 

90 

in» 

110 

12° 

140 

16« 

18° 

20° 

22" 

24° 

26° 

28° 

30° 

1 

TABLE  XXXlll. 

157  1 

1 

THIRD  CORREOTION.  TO  APPARENT  DISTANCE  24° 

App. 

\ 

APPARENT  ALTITUDK  OF  THK  SUN,  OR  STAR. 

App 

Alt. 

'32« 

34° 

360 

38«» 

420 

46°  50° 

54° 

58° 

62° 

66" 

70" 

74° 

78" 

82° 

*6° 

Alt. 

o 
6 

/ 

tf 

1 

// 

t 

n 

t 

// 

/  n 

1    It 

1    1' 

1    n 

/  >> 

t    II 

1    II 

1    II 

t    n 

/  // 

/  // 

/  // 

o 
6 

7 
8 

4 

58 

7 
8 

9 

4 

12 

9 

10 

3 

39 

3 

51 

10 

11 

3 

11 

3 

21 

3 

30 

11 

12 

2 

48 

2 

56 

3 

5 

3 

12 

12 

13 

2 

30 

2 

37 

2 

44 

2 

49 

13 

14 

2 

16 

2 

22 

2 

27 

2 

32 

14 

15 

2 

4 

2 

9 

2 

14 

2 

18 

15 

16 

16 

54 

59 

2 

3 

2 

6 

2  11 

17 

46 

50 

53 

56 

2  0 

17 

18 

40 

43 

45 

47 

1  51 

18 

19 

35 

37 

39 

41 

1  43 

19 

20 

30 

32 

33 

34 

1  36 

1  38 

20 

21 

26 

27 

28 

29 

1  30 

1  31 

21 

22 

22 

23 

24 

24 

1  25 

1  25 

22 

23 

20 

20 

21 

21 

1  21 

1  21 

23 

24 

18 

18 

19 

19 

1  18 

1  17 

1  15 

24 

25 
26 

16 

16 

17 

17 

1  16 

1  14 

1  11 

25 

14 

14 

14 

14 

1  13 

1  11 

1  8 

26 

27 

13 

13 

12 

12 

1   1 

1  9 

1  6 

27 

28 

12 

12 

11 

10 

1  9 

1  7 

1  4 

1   1 

28 

29 

11 

U 

10 

9 

1  8 

1  5 

1  2 

0  59 

29 

30 

11 

10 

9 

8 

1  7 

1  4 

1   0 

0  57 

30 

31 

10 

9 

8 

8 

1  6 

1  2 

0  58 

0  55 

31 

32 

9 

9 

8 

7 

1  5 

1   1 

0  57 

0  54 

0  51 

82 

33 

9 

8 

7 

6 

1  4 

1  1 

0  57 

0  53 

0  50 

33 

34 

9 

7 

6 

5 

1  3 

1  0 

0  57 

0  53 

0  49 

34 

35 

9 

7 

6 

5 

1  2 

1  0 

0  56 

0  52 

0  48 

\ 

35 
36 

36 

8 

7 

6 

4 

1  2 

1   0 

0  56 

0  51 

0  47 

0  44 

37 

8 

6 

5 

3 

1  1 

0  58 

0  55 

0  51 

0  46 

0  43 

37 

38 

8 

6 

5 

3 

1  0 

0  57 

0  54 

0  50 

0  46 

0  43 

38 

39 

8 

6 

4 

2 

0  59 

0  56 

0  52 

0  48 

0  45 

0  42 

39 

40 

7 

5 

4 

2 

0  59 

0  55 

0  51 

0  47 

0  44 

0  41 

0  39 

40 
41 

41 

6 

4 

3 

1 

0  58 

0  54 

0  50 

0  47 

0  44 

0  41 

0  38 

42 

5 

4 

3 

1 

0  57 

0  54 

0  50 

0  47 

0  44 

0  41 

0  38 

42 

43 

4 

3 

2 

0 

0  56 

0  53 

0  50 

0  47 

0  43 

0  40 

0  37 

0  34 

43 

44 

3 

2 

1 

0 

59 

0  56 

0  53 

0  50 

0  47 

0  43 

0  40 

0  37 

0  34 

44 

46 

1 

0 

0 

59 

0 

58 

0  55 

0  52 

0  49 

0  46 

0  43 

0  40 

0  37 

0  34 

0  32 

46 
48 

48 

0 

59 

0 

59 

0 

58 

0 

57 

0  54 

0  51 

0  49 

0  46 

0  43 

0  40 

0  37 

0  34 

0  32 

50 

0 

57 

0 

57 

0 

56 

0 

55 

0  53 

0  50 

0  48 

0  45 

0  43 

0  40 

0  37 

0  34 

0  32 

0  30 

50 

52 

0 

55 

0 

54 

0 

53 

0 

52 

0  51 

0  49 

0  47 

0  45 

0  43 

0  40 

0  37 

0  34 

0  32 

0  30 

52 

54 

0 

54 

0 

52 

0 

51 

0 

50 

0  49 

0  47 

0  46 

0  44 

0  42 

0  39 

0  37 

0  34 

0  32 

0  29 

0  27 

54 

56 

0 

53 

0 

51 

0 

49 

0 

48 

0  47 

0  45 

0  44 

0  43 

0  41 

0  38 

0  36 

0  34 

0  31 

0  29 

0  27 

56 

58 

0 

52 

0 

49 

0 

47 

0 

46 

0  45 

0  44 

0  43 

0  42 

0  40 

0  37 

0  35 

0  33 

0  31 

0  29 

0  27 

0  26 

58 

60 

0 

47 

0 

45 

0 

44 

0  43 

0  42 

0  41 

0  40 

0  38 

0  36 

0  34 

0  32 

0  30 

0  28 

0  27 

0  26 

60 

62 

0 

43 

0 

43 

0  41 

0  40 

0  39 

0  38 

0  37 

0  35 

0  33 

0  31 

0  29 

0  28 

0  27 

0  26 

62 

64 

0 

42 

0  39 

0  38 

0  38 

0  37 

0  36 

0  34 

0  32 

0  30 

0  29 

0  28 

0  27 

0  26 

64 

66 

68 

0  38 

0  37 

0  37 

0  36 

0  35 

0  33 

0  31 

0  29 

0  28 

0  27 

0  26 

0  25 

66 

0  37 

0  35 

0  35 

0  34 

0  34 

0  33 

0  31 

0  29 

0  28 

0  27 

0  26 

0  25 

68 

70 

0  34 

0  34 

0  33 

0  33 

0  32 

0  30 

0  28 

0  27 

0  26 

0  25 

0  25 

70 

72 

0  33 

0  33 

0  32 

0  32 

0  31 

0  29 

0  28 

0  26 

0  25 

0  24 

0  25 

72 

74 

0  32 

0  31 

0  31 

0  30 

0  29 

0  28 

0  26 

0  25 

0  24 

74 

76 

0  31 

0  30 

0  30 

0  29 

0  28 

0  27 

0  25 

0  24 

0  24 

76 

78 

0  29 

0  29 

0  29 

0  28 

0  27 

0  25 

0  24 

78 

80 

0  28 

0  28 

0  28 

0  27 

0  26 

0  25 

0  24 

80 

82 

0  27 

0  27 

0  26 

0  25 

0  24 

82 

84 

0  26 

0  26 

0  25 

0  25 

0  24 

84 

86 

0  26 

0  25 

0  25 

86 

32" 

34« 

1  36*» 

38" 

42" 

46" 

50« 

54" 

58" 

62" 

66"  70" 1 

74" 

78" 

82° 

86° 

_J 

158 

TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE 

28«». 

App. 

APPARENT 

ALTITUDE  OF  THE  SUN,  OR  A  STAR. 

App. 

Alt. 
0 

Alt. 

6° 

7°       S"   1 

9° 

10° 

11°  1 

12° 

14° 

16° 

1    It 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

o 

r  // 

r    n 

/  II 

/  // 

/ 

II 

/ 

II 

1    II 

/  n 

/  // 

/  // 

1    II 

t 

II 

1    II 

1 

II 

1 

II 

6 

1  20 

1  23 

1  27 

1  33 

40 

49 

2  00 

2  28 

2  56 

3  24 

3  53 

4  21 

4 

48 

5  15 

5 

42 

6 

9 

6 

7 

1  25 

1  20 

1  23 

1  27 

32 

38 

1  45 

2  5 

2  26 

2  49 

3  13 

3  36 

3 

58 

4  20 

4 

43 

5 

6 

7 

8 

1  32 

1  24 

1  20 

1  22 

25 

29 

1  35 

1  50 

2  7 

2  26 

2  46 

3  4 

3 

23 

3  42 

4 

1 

4 

20 

8 

9 

1  41 

1  29 

1  23 

1  20 

22 

24 

1  28 

1  39 

1  52 

2  7 

2  22 

2  37 

2 

53 

3  9 

3 

25 

3 

41 

9 

10 

1  53 

1  37 

1  28 

1  23 

20 

— 

21 
20 

1  23 

1  30 

1  39 

1  52 
1  41 

2  5 

2  18 

2 

31 

2  44 

2 

58 

3 

11 

10 

11 

2  6 

1  46 

1  34 

1  27 

23 

1  21 

1  24 

I  31 

1  52 

2  4 

2 

15 

2  26 

2 

37 

2 

48 

11 

12 

2  19 

1  56 

1  41 

1  32 

1 

26 

22 

1  19 

1  21 

1  26 

1  33 

1  42 

1  52 

2 

1 

2  10 

2 

20 

2 

30 

■  12 

13 

2  32 

2  6 

1  49 

1  38 

30 

25 

1  21 

1  20 

1  23 

1  28 

1  34 

1  42 

49 

1  57 

2 

6 

2 

15 

13 

14 

2  46 

2  17 

1  58 

1  44 

34 

28 

1  23 

1  19 

1  21 

1  24 

1  28 

1  34 

40 

1  47 

55 

2 

3 

14 

15 

3  00 

2  28 

2  7 

1  51 

39 

32 

1  25 

1  20 

1  19 

1  21 

1  24 

1  28 

33 

1  39 

45 

1 

52 

15 
16 

16 

3  14 

2  39 

2  16 

1  58 

45 

36 

1  28 

1  21 

1  18 

1  19 

1  21 

1  24 

28 

1  33 

38 

44 

17 

3  28 

2  51 

2  25 

2  5 

51 

41 

1  32 

1  23 

1  19 

1  18 

1  19 

1  21 

24 

1  28 

33 

38 

17 

18 

3  41 

3  2 

2  35 

2  13 

58 

46 

1  36 

1  25 

1  20 

1  17 

1  18 

1  19 

21 

1  24 

28 

33 

18 

19 

3  55 

3  13 

2  45 

2  21 

2 

5 

52 

1  41 

1  27 

1  21 

1  18 

1  16 

1  17 

18 

1  21 

24 

28 

19 

20 

4  9 

3  24 

2  55 

2  29 

2 

11 

57 

1  46 

1  30 

1  23 

1  18 
1  19 

1  16 

1  15 

— 

16 
15 

1  18 

21 

24 

20 

21 

4  23 

3  35 

3  4 

2  37 

2 

17 

2 

3 

1  51 

1  33 

1  25 

1  16 

1  14 

1  16 

18 

20 

21 

22 

4  36 

3  46 

3  13 

2  45 

2 

24 

2 

9 

1  56 

1  36 

1  27 

1  20 

1  16 

1  13 

14 

1  15 

16 

17 

22 

23 

4  49 

3  57 

3  22 

2  53 

2 

31 

2 

14 

2  1 

1  40 

1  29 

1  22 

1  17 

1  13 

13 

1  13 

14 

15 

23 

24 

5  2 

4  8 

3  31 

3  0 

2 

37 

2 

20 

2  6 

1  43 

1  31 

1  24 

1  18 

1  14 

12 

1  12 

12 

13 

24 

25 

5  16 

4  19 

3  40 

3  8 

2 

43 

2 

26 

2  11 

1  47 

1  34 

1  26 

1  28 

1  19 

1  15 

13 

1  11 

11 

12 

25 
26 

26 

5  29 

4  30 

3  49 

3  15 

2 

50 

2 

32 

2  16 

1  51 

1  36 

1  20 

1  15 

13 

1  11 

11 

11 

27 

5  42 

4  41 

3  58 

3  23 

2 

57 

2 

38 

2  21 

1  55 

1  39 

1  30 

1  21 

1  16 

13 

1  11 

10 

10 

27 

28 

5  55 

4  52 

4  7 

3  30 

3 

4 

2 

44 

2  26 

1  59 

1  42 

1  32 

1  22 

1  17 

14 

1  11 

10 

10 

28 

29 

6  7 

5  3 

4  16 

3  38 

3 

11 

2 

50 

2  31 

2  3 

1  45 

1  34 

1  24 

1  18 

14 

1  12 

10 

10 

29 

30 

6  19 

5  13 

4  25 

3  45 

3 

18 

2 

bb 

2  36 

2  7 

1  47 

1  36 

1  26 

1  19 

15 

1  12 

10 

9 

30 
31 

31 

6  31 

5  23 

4  34 

3  52 

3 

25 

3 

1 

2  41 

2  10 

1  50 

1  38 

1  27 

1  20 

15 

1  12 

10 

9 

32 

6  4^ 

5  32 

4  43 

3  59 

3 

31 

3 

7 

2  46 

2  13 

1  53 

1  40 

1  29 

1  21 

16 

1  12 

10 

9 

32 

33 

6  53 

5  41 

4  51 

4  6 

3 

37 

3 

12 

2  51 

2  17 

1  56 

1  42 

1  31 

1  22 

16 

1  12 

10 

9 

33 

34 

7  4 

5  50 

4  58 

4  13 

3 

43 

3 

17 

2  55 

2  20 

1  58 

1  44 

1  32 

1  23 

17 

1  12 

10 

9 

34 

35 

7  15 

5  59 

5  5 

4  20 

3 

48 

3 

21 

2  59 

2  23 

2  00 

1  46 

1  33 

1  23 
1  24 

17 

1  13 

10 

8 

35 

36 

6  8 

5  11 

4  26 

3 

53 

3 

25 

3  3 

2  26 

2  3 

1  47 

1  34 

18 

1  13 

10 

8 

36 

37 

5  17 

4  32 

3 

58 

3 

29 

3  7 

2  29 

2  5 

1  49 

1  35 

1  25 

18 

1  13 

10 

8 

37 

38 

4  38 

4 

2 

3 

33 

3  10 

2  32 

2  7 

1  51 

1  36 

1  26 

19 

1  14 

10 

8 

38 

39 

4 

6 

3 

37 

3  12 

2  34 

2  9 

1  52 

1  37 

1  27 

19 

1  14 

11 

8 

39 

40 

3 

41 

3  15 

2  37 

2  11 

1  53 

1  38 

1  27 

20 

1  15 

11 

8 

40 

41 

3  17 

2  40 

2  13 

1  54 

1  39 

1  28 

20 

1  15 

11 

8 

41 

42 

i 

2  42 

2  )5 

1  55 

1  40 

1  29 

21 

1  15 

10 

7 

44 

43 

2  44 

2  17 

1  06 

1  40 

1  29 

21 

1  15 

10 

7 

43 

44 

2  18 

1  57 

1  41 

1  30 

21 

1  15 

10 

7 

44 

46 
48 

2  19 

1  59 

1  42 

1  30 
1  31 

22 

1  15 

10 

7 

46 

2  0 

1  43 

22 

1  15 

10 

6 

48 

50 

1  44 

1  32 

23 

1  15 

10 

6 

50 

52 

1  33 

24 

1  15 

9 

5 

52 

54 

25 

1  15 

9 

5 

54 

56 

1  15 

9 

4 

56 

58 

1 

9 

3 

58 

60 

3 

60 

62 

62 

64 

64 

66 

— 

— 

— 

66 

68 

68 

70 

70 

72 

72 

74 

74  1 

76 

1 

76 
78 

78 

80 

80 

82 

82 

84 

84 

1  86 

26° 

86 

L_ 

6" 

70   go  ■  go 

100 

1|0 

12° 

140 

16" 

18° 

20° 

22°  24° 

28°) 

30° 

1 

TABLE  XXXlll. 

159 

J)'s 

App. 
Alt. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE 

28°. 

APPARENT  ALTITUDE  OF  THE  SUN,  OR  STAR. 

App 

Alt. 

o 

32° 

34^ 

36° 

38° 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

70° 

74° 

78° 

82° 

86° 

o 

f 

// 

1 

tt 

/  // 

/  It 

/  n 

1    II 

1    n 

/  // 

/  n 

/  // 

/  // 

t 

II 

1    II 

1    It 

1    II 

6 

6  37 

7 

4 

6 

7 
8 

5  28 

5 

49 

6 

8 

7 

4  40 

4 

57 

5 

11 

8 

9 

3  58 

4 

13 

4 

26 

4  38 

9 

10 

3  25 

3 

38 

3 

50 

4  2 

\ 

10 

11 

3  0 

3 

12 

3 

23 

3  33 

11 

12 

2  40 

2 

50 

2 

59 

3  7 

3  22 

12 

13 

2  24 

2 

33 

2 

41 

2  48 

3  0 

;  13 1 

14 

2  11 

2 

18 

2 

25 

2  31 

2  42 

14 

15 

1  59 

2 

6 

2 

12 

2  17 

2  27 

15 
16 

16 

1  50 

56 

2 

1 

2  6 

2  14 

2  21 

17 

1  43 

48 

52 

1  56 

2  3 

2  9 

17 

18 

1  37 

41 

45 

1  48 

1  54 

1  59 

18 

19 

1  31 

35 

38 

1  41 

1  46 

1  50 

19 

20 

1  26 

29 

32 

1  34 

1  38 

1  42 

1  45 

20 

21 

1  22 

25 

27 

1  29 

1  32 

1  36 

1  38 

21 

22 

1  19 

21 

23 

1  25 

1  28 

1  30 

1  32 

22 

23 

1  17 

18 

20 

1  22 

1  24 

1  26 

1  27 

23 

24 

1  15 

16 

17 

1  18 

1  20 

1  22 

1  23 

1  24 

24 

25 

1  13 

14 

14 

1  15 

1  16 

1  18 

1  19 

1  19 



25 

26 

1  11 

12 

12 

1  13 

1  13 

1  14 

1  15 

1  15 

26 

27 

1  10 

11 

11 

1  11 

1  11 

1  11 

1  12 

1  12 

27 

28 

1  10 

10 

10 

1  10 

1  10 

1  9 

1  9 

1  9 

1  9 

28 

29 

1  10 

10 

10 

1  9 

1  9 

1  8 

1   7 

1  6 

1  6 

29 

30 

1  9 

9 

9 

1  8 

1  8 

1  7 

1   6 

1  4 

1  3 

30 
31 

31 

1  8 

8 

7 

1  7 

1  6 

1  5 

1  4 

1  2 

1   1 

32 

1  8 

7 

6 

1  6 

1  5 

1  4 

1  3 

1   1 

1   0 

0  59 

32 

33 

1  7 

6 

5 

1  5 

1  4 

1  3 

1  2 

1  0 

0  58 

0  56 

33 

34 

1  7 

5 

4 

1  4 

1   3 

1  2 

1   1 

0  59 

0  57 

0  54 

34 

35 

1  7 

5 

4 

1  3 

1  2 

1  1 

1  0 

0  58 

0  55 

0  53 

35 
36 

36 

1  6 

5 

1 

4 

1  3 

1   1 

1  0 

0  58 

0  56 

0  54 

0  52 

0  51 

37 

1  6 

4 

3 

1  2 

1   0 

0  59 

0  57 

0  55 

0  53 

0  51 

0  50 

37 

38 

1  6 

4 

3 

1  1 

0  59 

0  58 

0  56 

0  54 

0  52 

0  50 

0  49 

38 

39 

1   6 

4 

2 

1   0 

0  59 

0  57 

0  55 

0  53 

0  51 

0  49 

0  47 

39 

40 

1  6 

4 

2 

1  0 

0  58 

0  57 

0  55 

0  52 

0  50 

0  48 

0  46 

0  44 

40 
41 

41 

1  6 

4 

2 

1  0 

0  58 

0  56 

0  54 

0  51 

0  49 

0  47 

0  45 

0  43 

42 

1  5 

4 

2 

0  59 

0  57 

0  55 

0  53 

0  50 

0  48 

0  46 

0  44 

0  42 

42 

43 

1  5 

3 

1 

0  59 

0  57 

0  55 

0  53 

0  50 

0  48 

0  46 

0  44 

0  42 

0 

41 

43 

44 

1  5 

3 

1 

0  59 

0  56 

0  54 

0  52 

0  50 

0  47 

0  45 

0  43 

0  41 

0 

40 

44 

46 

48 

1  4 

2 

0 

0  58 

0  55 

0  53 

0  51 

0  49 

0  47 

0  44 

0  42 

0  40 

0 

39 

46 
48 

1  3 

1 

0 

59 

0  57 

0  54 

0  52 

0  50 

0  48 

0  46 

0  43 

0  41 

0  39 

0 

38 

0  37 

50 

1  3 

1 

0 

58 

0  56 

0  53 

0  51 

0  49 

0  47 

0  45 

0  42 

0  40 

0  38 

0 

37 

0  36 

50 

52 

1  2 

0 

0 

57 

0  55 

0  52 

0  50 

0  48 

0  46 

0  44 

0  42 

0  40 

0  38 

0 

36 

0  35 

0  34 

52 

54 

1  2 

0 

59 

0 

56 

0  54 

0  51 

0  49 

0  47 

0  45 

0  43 

0  41 

0  39 

0  37 

0 

35 

0  34 

0  33 

54 

56 

1   1 

0 

58 

0 

55 

0  53 

0  50 

0  48 

0  46 

0  44 

0  42 

0  40 

0  38 

0  36 

0 

35 

0  34 

0  33 

0  32 

56 

58 

1  0 

0 

57 

0 

54 

0  52 

0  49 

0  47 

0  45 

0  43 

0  41 

0  39 

0  37 

0  36 

0 

35 

0  34 

0  32 

0  31 

58 

60 

0  58 

0 

55 

0 

53 

0  51 

0  48 

0  46 

0  44 

0  42 

0  40 

0  38 

0  37 

0  36 

0 

35 

0  34 

0  32 

0  31 

60 

2 

0  56 

0 

54 

0 

52 

0  50 

0  47 

0  45 

0  43 

0  41 

0  39 

0  3S 

0  37 

0  36 

0 

35 

0  34 

0  32 

0  31 

62 

r,4 

0 

52 

0 

50 

0  49 

0  46 

0  44 

0  42 

0  40 

0  38 

0  37 

0  36 

0  35 

0 

34 

0  33 

0  32 

0  30 

64 

66 

68 

0 

48 

0  48 

0  45 

0  43 

0  41 

0  39 

0  38 

0  37 

0  36 

0  35 

0 

34 

0  33 

0  31 

0  29 

66 
68 

0  46 

0  43 

0  41 

0  40 

0  38 

0  37 

0  36 

0  35 

0  34 

0 

33 

0  32 

0  30 

0  28 

70 

0  42 

0  40 

0  39 

0  38 

0  37 

0  36 

0  35 

0  34 

0 

33 

0  31 

0  29 

70 

72 

0  41 

0  39 

0  38 

0  37 

0  36 

0  35 

0  34 

0  33 

0 

32 

0  30 

0  28 

72 

74 

0  39 

0  37 

0  36 

0  35 

0  34 

0  33 

0  32 

0 

30 

0  28 

74 

76 

0  38 

0  36 

0  35 

0  34 

0  34 

0  33 

0  31 

0 

29 

0  27 

76 

78 

0  36 

0  34 

0  34 

0  33 

0  32 

0  30 

0 

28 

78 

80 

0  35 

0  34 

0  33  0  32 

0  31 

0  30 

0 

28 

80 

82 

0  33 

0  32  0  31 

0  30 

0  29 

82 

84 

0  32 

0  32 

0  31 

0  30 

0  29 

84 

86 

0  31 

0  30 

0  29 

86 

32° 

34" 

36® 

38° 

42° 

46°  50° 

54° 

58° 

62° 

66° 

70° 

74° 

78°  82° 

86° 

.. 

11 


160        .         TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  82<». 

APPARENT  ALTITUDE  OF  THE  SUN,  OR  A  STAR. 

App. 
Alt. 

0 

Alt. 

6« 

70 

8° 

90 

10° 

11° 

12° 

14° 

16° 

18° 

20°  1  22°  1 

24° 

26° 

28° 

30° 

f    II 

o 

1    tr 

t   ti 

t    n 

/  // 

f    n 

/  // 

/  // 

/  // 

/  11 

/  n 

/  II 

/  II 

/  II 

/  II 

/  // 

6 

1  18 

1  21 

1  25 

1  30 

I  37 

1  47 

1  59 

2  23 

2  48 

3  13 

3  39 

4  5 

4  30 

4  55 

5  20 

5 

45 

6 

7 

1  23 

1  18 

1  21 

1  24 

1  28 

1  33 

1  42 

2  0 

2  18 

2  37 

2  58 

3  20 

3  42 

4  4 

4  25 

4 

46 

7 

8 

1  30 

1  22 

1  18 

1  20 

1  22 

1  25 

1  29 

1  42 

1  57 

2  14 

2  32 

2  50 

3  8 

3  26 

3  44 

4 

2 

8 

9 

1  38 

1  27 

1  20 

1  18 

1  19 

1  21 

1  23 

1  31 

1  44 

1  58 

2  12 

2  26 

2  41 

2  56 

3  11 

3 

26 

9 

10 

1  47 

1  33 

1  23 

1  20 

1  18 

1  19 

1  20 

1  25 

1  34 

1  45 

1  57 

2  9 

2  21 

2  34 

2  46 

2 

59 

10 

11 

1  57 

1  41 

1  28 

1  23 

1  19 

1  17 

1  18 

1  21 

1  27 

1  36 

1  46 

1  56 

2  6 

2  17 

2  28 

2 

39 

11 

12 

2  9 

1  50 

1  34 

1  27 

1  22 

1  19 

1  17 

1  19 

1  23 

1  29 

1  37 

1  46 

1  55 

2  4 

2  13 

2 

23 

12 

13 

2  21 

1  59 

1  41 

1  32 

1  26 

1  21 

1  18 

1  17 

1  20 

1  24 

1  30 

1  37 

1  45 

1  53 

2  1 

2 

9 

13 

14 

2  34 

2  8 

1  50 

1  38 

1  30 

1  24 

1  20 

1  16 

1  18 

1  21 

1  25 

1  30 

1  36 

1  43 

1  51 

58 

14 

15 

2  47 

2  18 

1  59 

1  45 

1  35 

1  28 

1  22 

1  17 

1  16 

1  18 

1  21 

1  25 

1  30 

1  35 

1  42 

49 

15 

16 

2  59 

2  28 

2  7 

1  52 

1  41 

1  32 

1  25 

1  19 

1  15 

1  16 

1  18 

1  21 

1  25 

1  29 

1  35 

41 

16 

17 

3  12 

2  38 

2  16 

1  59 

1  47 

1  36 

1  28 

1  21 

1  16 

1  15 

1  16 

1  18 

1  21 

1  25 

1  30 

35 

17 

18 

3  25 

2  48 

2  25 

2  7 

1  52 

1  41 

1  32 

1  23 

1  17 

1  14 

1  15 

1  17 

1  19 

1  22 

1  25 

29 

18 

19 

3  38 

2  58 

2  34 

2  14 

1  58 

1  46 

1  36 

1  25 

1  18 

1  15 

1  14 

1  15 

1  17 

1  19 

1  22 

25 

19 

20 

3  50 

3  9 

2  43 

2  21 

2  4 

1  51 

1  40 

1  27 

1  20 

1  16 

1  13 

1  14 

1  15 

1  17 

1  19 

21 

20 

21 

4  3 

3  19 

2  52 

2  28 

2  10 

1  56 

1  45 

1  30 

1  22 

1  17 

1  14 

1  13 

1  14 

1  15 

1  16 

18 

21 

22 

4  15 

3  30 

3  0 

2  35 

2  17 

2  2 

1  50 

1  33 

1  24 

1  18 

1  14 

1  11 

1  12 

1  13 

1  14 

16 

22 

23 

4  28 

3  40 

3  9 

2  42 

2  24 

2  7 

1  55 

1  36 

1  26 

1  19 

1  15 

1  12 

1  11 

1  12 

1  13 

14 

23 

24 

4  40 

3  51 

3  17 

2  50 

2  30 

2  13 

I  59 

1  39 

1  28 

1  21 

1  16 

1  12 

1  10 

1  11 

1  11 

12 

24 

25 

4  52 

4  1 

3  26 

2  57 

2  36 

2  18 

2  4 

1  42 

1  30 

1  22 

1  17 

1  13 

1  11 

1  10 

1  10 

10 

25 

26 

5  4 

4  12 

3  34 

3  5 

2  43 

2  24 

2  8 

1  46 

1  32 

1  24 

1  18 

1  13 

1  11 

1  9 

1  9 

9 

26 

27 

5  16 

4  22 

3  43 

3  12 

2  50 

2  30 

2  13 

1  50 

1  34 

1  26 

1  19 

1  14 

1  11 

1  9 

1  8 

8 

27 

28 

5  28 

4  33 

3  52 

3  20 

2  57 

2  35 

2  17 

1  53 

1  37 

1  27 

1  20 

1  15 

1  11 

1  9 

1  7 

8 

28 

29 

5  41 

4  44 

4  1 

3  28 

3  3 

2  41 

2  21 

1  57 

1  40 

1  29 

1  21 

1  16 

1  12 

1  10 

1  8 

7 

29 

30 

5  53 

4  54 

4  10 

3  35 

3  9 
3  15 

2  46 

2  26 

2  0 

1  43 

1  31 

1  23 

1  17 

1  13 

1  10 

1  8 

6 

30 

31 

6  5 

5  4 

4  19 

3  42 

2  52 

2  31 

2  4 

1  46 

1  33 

1  24 

1  18 

1  13 

1  10 

1  8 

6 

31 

32 

6  17 

5  14 

4  27 

3  49 

3  21 

2  57 

2  36 

2  8 

1  49 

1  36 

1  26 

1  19 

1  14 

1  11 

1  9 

7 

32' 

33 

6  29 

5  23 

4  35 

3  56 

3  27 

3  2 

2  41 

2  12 

1  52 

1  38 

1  27 

1  20 

1  15 

1  11 

1  9 

7 

33 

34 

6  40 

5  32 

4  43 

4  3 

3  32 

3  7 

2  46 

2  15 

1  55 

1  40 

1  29 

1  21 

1  16 

1  12 

1  9 

7 

34 

35 

6  50 

5  40 

4  50 

4  9 

3  38 

3  12 

2  50 

2  19 

1  58 

1  43 

1  31 

1  22 

1  17 

1  13 

1  9 

7 

35 

36 

6  59 

5  48 

4  57 

4  15 

3  43 

3  16 

2  54 

2  22 

2  1 

1  45 

1  32 

1  23 

1  18 

1  13 

1  10 

7 

36 

37 

7  7 

5  56 

5  4 

4  21 

3  49 

3  21 

2  59 

2  25 

2  4 

1  47 

1  34 

1  24 

1  19 

1  14 

1  10 

7 

37 

38 

7  15 

6  3 

5  10 

4  29 

3  54 

3  25 

3  3 

2  28 

2  6 

1  49 

1  35 

1  25 

1  19 

1  14 

1  10 

7 

38 

39 

7  22 

6  10 

5  16 

4  33 

3  59 

3  30 

3  7 

2  31 

2  8 

1  51 

1  36 

1  26 

1  20 

1  15 

1  10 

7 

39 

40 

6  17 

5  21 

4  38 

4  4 

3  34 

3  11 

2  34 

2  10 

1  52 

1  38 

1  27 

1  20 

1  15 

1  11 

1  12 

8 

40 

; 

41 

5  26 

4  43 

4  8 

3  38 

3  15 

2  36 

2  13 

1  54 

1  39 

1  28 

1  21 

1  16 

8 

41 

42 

4  47 

4  12 

3  42 

3  18 

2  39 

2  16 

1  56 

1  41 

1  29 

1  22 

1  16 

1  12 

8 

42 

43 

4  16 

3  46 

3  21 

2  42 

2  18 

1  58 

1  42 

1  30 

1  22 

1  16 

1  12 

8 

43 

44 

3  50 

3  24 

2  45 

2  20 

2  0 

1  43 

1  31 

1  23 

1  17 

1  12 

8 

44 

46 
48 

3  27 

2  50 

2  23 

2  2 

1  45 

1  32 

1  24 

1  17 

1  12 

8 

46 

2  54 

2  26 

2  4 

1  47 

1  34 

1  25 

1  18 

1  12 

8 

48 

50 

2  29 

2  6 

1  49 

1  36 

1  26 

1  19 

1  13 

8 

50 

52 

2  8 

1  51 

1  38 

1  28 

1  19 

1  13 

8 

52 

54 

1  53 

1  39 

1  29 

1  20 

1  14 

8 

54 

56 

1  40 

1  30 

1  21 

1  14 

8 

56 

58 

1  30 

1  21 

1  14 

8 

58 

60 

1  21 

1  14 

8 

60 

S2 

1  14 

8 

62 

64 

8 

64 

66 

66 

68 

68 

70 

70 

72 

72 

74 

74 

76 

76 

78 

78 

80 

80 

82 

82 

84 

84 

86 

21 

86 

«<» 

70 

8«» 

90 

10« 

11° 

12°  I  14° 

16" 

18° 

20° 

22° 

24° 

26° 

_28° 

3 

TABLE  XXXIll. 

161  1 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  32°. 

D's 

App. 
Alt. 

APPARENT  ALTITUDE  OF  THE  SUN,  DR  STAR. 

App 

32° 

34° 

36° 

38° 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

70° 

74°  '  78° 

82°  1  8b' 

Alt. 

o 

1     ti 

/ 

n 

1 

tt 

1    tt 

1    tt 

f    tt 

/  // 

/  tt 

t    It 

/  // 

/  // 

/  ft 

1 

// 

/  It 

1     II     1     II          0  1 

6 

6  10 

6 

33 

6 

55 

7  15 

el 

7 

5  7 

5 

26 

5 

44 

6  2 

71 

8 

4  20 

4 

37 

4 

52 

5  7 

5   35 

8 

9 

3  41 

3 

56 

4 

10 

4  24 

4  50 

9 

10 

3  12 

3 

25 

3 

38 

3  50 

4  12 

10 

11 

2  51 

3 

2 

3 

13 

3  23 

3  42 

11 

12 

2  33 

2 

43 

2 

51 

3  00 

3  17 

3  33 

12 

13 

2  18 

2 

26 

2 

34 

2  42 

2  56 

3  9 

13 

14 

2  5 

2 

12 

2 

19 

2  27 

2  39 

2  50 

14 

15 

1  55 

2 

2 

2 

8 

2  14 

2  25 

2  35 

15 

16 

1  47 

53 

58 

2  3 

2  13 

2  22 

2  30 

16 

17 

1  40 

45 

50 

1  54 

2  2 

2  11 

2  18 

17 

18 

1  34 

38 

42 

1  46 

1  53 

2  0 

2  7 

18 

19 

1  "29 

33 

36 

1  39 

1  45 

1  51 

1  57 

19 

20 

1  25 

28 

31 

1  33 

1  38 

1  43 

1  49 

1  54 

20 

21 

1  21 

24 

26 

1  28 

1  32 

1  37 

1  42 

1  46 

21 

22 

1  18 

20 

22 

1  24 

1  27 

1  31 

1  35 

1  39 

22 

23 

1  15 

17 

19 

1  20 

1  23 

1  27 

1  30 

1  34 

23 

24 

1  13 

14 

16 

1  17 

1  20 

1  23 

1  26 

1  29 

1  32 

24 

25 

1  11 

12 

13 

1  15 

1  17 

1  19 

1  21 

1  24 

1  26 

25 

26 

1   9 

10 

11 

1  12 

1  14 

1  16 

1  17 

1  19 

1  21 

26 

27 

1   8 

9 

9 

1  10 

1  12 

1  13 

1  14 

1  16 

1  17 

27 

28 

1   8 

8 

8 

1  9 

1  10 

1  11 

1  12 

1  13 

1  14 

1  15 

28 

29 

1   7 

7 

7 

1   7 

1  8 

1   9 

]   9 

1  10 

1  11 

1  11 

29 

30 

1   6 

6 

6 

1   6 

1   6 

1   7 

1  7 

1  7 

1  8 

1  8 

30 

31 

1   6 

6 

6 

1  5 

1  5 

1   5 

1   5 

1   5 

1  5 

1  5 

31 

32 

1   6 

A 

5 

5 

1   4 

1   4 

1   4 

1  4 

1   4 

1   3 

1  3 

1  3 

32 

33 

1   5 

4 

4 

1   3 

1   3 

1   2 

1   2 

1  2 

1   1 

1   1 

1   1 

33 

34 

1   5 

4 

3 

1   2 

1   2 

1   1 

1   0 

1  0 

0  59 

0  59 

0  59 

34 

35 

1   5 

3 

3 

1  2 

1   1 

1  0 

0  59 

0  58 

0  57 

0  57 

0  57 

35 
36 

36 

1   5 

3 

2 

1   1 

1   1 

1  0 

0  58 

0  57 

0  56 

0  56 

0  55 

0  54 

37 

1   5 

3 

1 

1  0 

1  0 

0  59 

0  57 

0  56 

0  55 

0  55 

0  54 

0  53 

37 

38 

1   5 

3 

1 

1  0 

0  59 

0  58 

0  56 

0  55 

0  54 

0  54 

0  53 

0  52 

38 

39 

1   5 

3 

1 

0  59 

0  58 

0  57 

0  56 

0  54 

0  53 

0  52 

0  51 

0  50 

39 

40 

1   5 

2 

0 

0  59 

0  58 

0  56 

0  55 

0  53 

0  52 

0  51 

0  50 

0  49 

0 

48 

40 

41 

1   5 

2 

0 

0  59 

0  58 

0  56 

0  54 

0  52 

0  51 

0  50 

0  49 

0  48 

0 

47 

41 

42 

1   5 

2 

0 

0  59 

0  57 

0  55 

0  53 

0  51 

0  50 

0  49 

0  48 

0  47 

0 

47 

42 

43 

1  5 

2 

0 

0  58 

0  56 

0  54 

0  52 

0  51 

0  49 

0  48 

0  47 

0  47 

0 

46 

0  45 

43 

44 

1   5 

2 

0 

0  58 

0  55 

0  53 

0  51 

0  50 

0  49 

0  48 

0  47 

0  46 

0 

45 

0  44 

44 

46 

1   5 

2 

0 

0  58 

0  55 

0  52 

0  51 

0  50 

0  48 

0  47 

0  46 

0  45 

0 

44 

0  43 

46 
48 

48 

1   5 

2 

0 

59 

0  57 

0  55 

0  52 

0  50 

0  49 

0  47 

0  46 

0  45 

0  44 

0 

43 

0  42 

0  41 

50 

1   0 

2 

0 

59 

0  57 

0  54 

0  51 

0  49 

0  48 

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0  46 

0  44 

0  43 

0 

42 

0  41 

0  40 

50 

52 

1   4 

1 

0 

58 

0  56 

0  53 

0  51 

0  49 

0  47 

0  46 

0  45 

0  43 

0  42 

0 

41 

0  40 

0  39 

0  38 

52 

54 

1   4 

1 

0 

58 

0  56 

0  53 

0  50 

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0  45 

0  44 

0  42 

0  41 

0 

40 

0  39 

0  38 

0  37 

54 

56 

1   4 

1 

0 

58 

0  56 

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0  49 

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0  45 

0  44 

0  42 

0  41 

0  40 

0 

39 

0  38 

0  37 

0  36 

56 

58 

58 

1   4 

1 

0 

b% 

0  56 

0  52 

0  49 

0  47 

0  45 

0  43 

0  41 

0  40 

0  39 

0 

38 

0  37 

0  36 

0  35 

60 

1   4 

0 

0 

57 

0  55 

0  51 

0  48 

0  46 

0  44 

0  42 

0  40 

0  39 

0  38 

0 

37 

0  36 

0  35 

0  35 

60 

62 

1   3 

0 

59 

0 

56 

0  54 

0  51 

0  48 

0  45 

0  43 

0  41 

0  39 

0  38 

0  37 

0 

36 

0  35 

0  34 

0  34 

62 

64 

1   3 

0 

59 

0 

56 

0  54 

0  50 

0  47 

0  45 

0  43 

0  41 

0  38 

0  38 

0  37 

0 

36 

0  35 

0  34 

0  33 

64 

66 
68 

1   3 

0 

59 

0 

56 

0  54 

0  50 

0  47 

0  44 

0  42 

0  40 

0  38 

0  37 

0  36 

0 

35 

0  34 

0  33 

66 

0 

59 

0 

55 

0  53 

0  48 

0  46 

0  44 

0  42 

0  40 

0  38 

0  37 

0  36 

0 

35 

0  34 

0  33 

68 

70 

0 

55 

0  52 

0  48 

0  45 

0  43 

0  41 

0  39 

0  37 

0  36 

0  35 

0 

34 

0  33 

70 

72 

0  52 

0  47 

0  44 

0  42 

0  40 

0  38 

0  37 

0  36 

0  35 

0 

33 

0  32 

72 

74 

47 

0  44 

0  42 

0  40 

0  38 

0  36 

0  35 

0  34 

0 

32 

74  1 

76 

47 

0  43 

0  41 

0  39 

0  38 

0  36 

0  35 

0  34 

0 

32 

M 

78 

0  43 

0  41 

0  39 

0  37 

0  35 

0  34 

0  33 

78 

80 

0  43 

0  41 

0  39 

0  37 

0  35 

0  34 

0  33 

80 

82 

0  40 

0  38 

0  36 

0  34 

0  33 

82 

84 

0  39 

0  38 

0  36 

0  34 

0  33 

84 

86 

0  37 

0  35 

0  34 

86 

32* 

34° 

36° 

38° 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

70° 

74°  i 

78°  82° 

86° 

1C2                                          TART<F.  XXXIIT. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  36° 

App,' 

APPARENT  ALTITUDE  OF  THE  SUN,  OB  A  STAR, 

1)'. 

App. 
Alt 
0 

Alt. 

6« 

70 

8«> 

90 

10° 

11° 

12° 

14° 

16° 
/  ti 

18° 

20° 

22° 

24°  1 

26° 

28° 

30° 

o 

/  tt 

/  // 

/  fr 

t    n 

/  // 

/  M 

/  tt 

r    n 

/  // 

/  It 

1    II 

1 

II 

1    II 

/ 

// 

/ 

// 

6 

1  17 

1  19 

1  22 

1  27 

1  33 

1  42 

1  52 

2  13 

2  34 

2  56 

3  19 

3  43 

4 

7 

4  31 

4 

55 

5 

18 

6 

7 

1  20 

1  17 

1  19 

1  22 

1  26 

1  31 

1  37 

1  52 

2  10 

2  28 

2  48 

3  8 

3 

27 

3  46 

4 

6 

4 

25 

7 

8 

1  25 

1  20 

1  17 

1  19 

1  21 

1  23 

1  27 

1  39 

1  53 

2  8 

2  24 

2  40 

2 

57 

3  14 

3 

30 

3 

46 

8 

9 

1  32 

1  24 

1  19 

1  17 

1  18 

1  19 

1  21 

1  29 

1  40 

1  52 

2  5 

2  19 

2 

33 

2  47 

3 

2 

3 

16 

9 

10 

1  42 

1  30 

1  23 

1  19 

1  16 

1  17 

1  18 

1  23 

1  31 

1  40 

1  51. 

1  42 

fe  2 

2 

14 

2  27 

2 

40 

2 

52 

10 

11 

1  52 

1  37 

1  28 

1  22 

1  18 

I  16 

1  17 

1  19 

1  25 

1  33 

1  51 

2 

1 

2  12 

2 

23 

2 

33 

11 

12 

2  3 

1  45 

1  34 

1  26 

1  20 

1  17 

1  15 

1  17 

1  21 

1  27 

1  34 

1  41 

50 

1  59 

2 

8 

2 

17 

12 

13 

2  14 

1  53 

1  40 

1  30 

1  23 

1  19 

1  16 

1  15 

1  18 

1  23 

1  28 

1  34 

41 

1  49 

57 

2 

5 

13 

1 

14 

2  25 

2  1 

1  47 

1  35 

1  26 

1  21 

1  18 

1  14 

1  16 

1  19 

1  24 

1  29 

35 

1  41 

49 

55 

14 

15 

2  36 

2  10 

1  54 

1  41 

1  30 

1  25 

1  21 

1  16 

1  15 

1  17 

1  21 
1  18 

1  25 

30 

1  35 

41 

46 

15 
16 

16 

2  48 

2  20 

2  2 

1  47 

1  35 

1  29 

1  24 

1  18 

1  13 

1  15 

1  21 

25 

1  29 

34 

39 

17 

3  0 

2  30 

2  10 

1  53 

1  40 

1  33 

1  28 

1  20 

1  15 

1  14 

1  16 

1  18 

21 

1  24 

28 

33 

17 

18 

3  12 

2  40 

2  18 

2  0 

1  46 

1  38 

1  32 

1  22 

1  16 

1  13 

1  15 

1  16 

18 

1  20 

23 

27 

18 

19 

3  24 

2  49 

2  27 

2  7 

I  51 

1  43 

1  36 

1  25 

1  18 

1  15 

1  14 

1  15 

16 

1  18 

20 

23 

19 

t 

20 

3  35 

2  59 

2  35 

2  14 

1  57 

1  48 

1  40 

1  28 

1  21 

1  16 
1  17 

1  12 

1  13 

14 

13 

1  16 

18 

— 

20 
18 

20 
21 

! 

1 

21 

3  46 

3  9 

2  43 

2  21 

2  3 

1  53 

1  44 

1  31 

1  23 

1  13 

1  12 

1  14 

16 

22 

3  57 

3  18 

2  61 

2  28 

2  9 

1  58 

1  48 

1  34 

1  25 

1  18 

1  14 

1  11 

12 

1  13 

14 

15 

22 

23 

4  9 

3  28 

2  59 

2  35 

2  16 

2  3 

1  52 

1  36 

1  26 

1  19 

1  14 

1  11 

10 

1  11 

12 

13 

23 

24 

4  20 

3  37 

3  7 

2  42 

2  22 

2  8 

1  56 

1  39 

1  28 

1  20 

1  15 

1  11 

9 

1  9 

10 

11 

24 

25 

4  32 

3  47 

3  15 

2  49 

2  28 

2  13 

2  0 

1  42 

1  30 

1  22 

1  15 

1  11 

9 

1  8 

8 

9 

25 

26 

4  43 

3  56 

3  23 

2  56 

2  34 

2  18 

2  4 

1  45 

1  32 

1  23 

1  16 

1  12 

9 

1  7 

7 

7 

26 

27 

4  55 

4  6 

3  31 

3  3 

2  40 

2  23 

2  9 

1  48 

1  35 

1  25 

1  17 

1  12 

9 

1  7 

6 

6 

27 

28 

5  6 

4  15 

3  39 

3  10 

2  46 

2  28 

2  13 

1  52 

1  38 

1  27 

1  19 

1  13 

9 

1  7 

6 

6 

28 

29 

5  17 

4  25 

3  47 

3  17 

2  52 

2  34 

2  18 

1  56 

1  40 

1  29 

1  20 

1  13 

9 

1  7 

6 

5 

29 

30 

5  28 

4  34 

3  54 

3  24 

2  58 

2  39 

2  23 

2  0 

1  43 

1  31 

1  21 

1  14 

10 

1  8 

6 

5 

30 
31 

31 

5  39 

4  43 

4  2 

3  31 

3  4 

2  44 

2  28 

2  4 

1  46 

1  33 

1  23 

1  16 

11 

1  8 

6 

5 

32 

5  49 

4  52 

4  10 

3  37 

3  10 

2  49 

2  33 

2  7 

1  49 

1  35 

1  25 

1  17 

12 

1  9 

7 

5 

32 

33 

5  59 

5  0 

4  18 

3  44 

3  16 

2  54 

2  37 

2  10 

1  51 

1  37 

1  27 

1  19 

14 

1  10 

7 

5 

33 

34 

6  9 

5  8 

4  25 

3  50 

3  22 

2  59 

2  41 

2  13 

1  53 

1  39 

1  29 

1  21 

15 

1  11 

8 

6 

34 

35 

6  19 

5  16 

4  32 

3  56 

3  28 

3  4 

2  46 

2  16 

1  56 

1  41 

1  30 

1  22 

16 

1  11 

8 

6 

35 

36 

6  28 

5  24 

4  38 

4  2 

3  33 

3  9 

2  50 

2  19 

1  59 

1  43 

1  32 

1  23 

17 

1  12 

9 

6 

36 

37 

6  38 

5  32 

4  45 

4  8 

3  39 

3  14 

2  54 

2  22 

2   1 

1  45 

1  33 

1  24 

18 

1  13 

9 

6 

37 

38 

6  47 

5  40 

4  52 

4  14 

3  44 

3  18 

2  58 

2  25 

2  4 

1  47 

1  35 

1  26 

19 

1  14 

10 

6 

38 

39 

6  57 

5  48 

4  59 

4  20 

3  49 

3  23 

3  2 

2  28 

2  G 

1  49 

1  36 

1  27 

20 

1  14 

10 

7 

39 

40 

7  6 

5  56 

5  5 

4  25 

3  54 

3  27 

3  6 

2  31 

2  8 

1  51 

1  38 

1  28 

21 

1  15 

11 

7 

40 

41 

7  16 

6  4 

5  12 

4  31 

3  59 

3  31 

3  10 

2  33 

2  11 

1  53 

1  40 

1  30 

22 

1  15 

11 

8 

41 

42 

7  25 

6  12 

5  18 

4  36 

4  3 

3  35 

3  13 

2  36 

2  14 

1  55 

1  42 

1  31 

22 

1  16 

11 

8 

42 

' 

43 

7  33 

6  19 

5  24 

4  41 

4  8 

3  39 

3  17 

2  39 

2  16 

1  57 

1  43 

1  32 

23 

1  16 

11 

8 

43 

44 

6  26 

5  30 

4  46 

4  12 

3  43 

3  20 

2  42 

2  18 

1  59 

1  45 

1  33 

24 

1  17 

12 

9 

44 

' 

46 
48 

5  41 

4  55 

4  20 

3  50 

3  26 

2  47 

2  22 

2  2 

1  47 

1  35 
1  37 

25 

1  18 

13 

9 

46 

i 

4  27 

3  57 

3  32 

2  52 

2  26 

2  5 

1  49 

27 

1  20 

14 

10 

48 

50 

3  38 

2  57 

2  30 

2  8 

1  51 

1  39 

29 

1  21 

15 

10 

50 

52 

3  1 

2  33 

2  11 

1  53 

1  41 

31 

1  22 

16 

11 

52 

54 

2  36 

2  13 

1  55 

1  43 

32 

1  23 

16 

11 

54 

56 

2  15 

1  57 

1  44 

33 

1  24 

17 

11 

56 

1 

1  59 

1  45 
1  46 

34 
35 
36 

1  25 
1  26 
1  26 
1  26 

18 
18 
18 
19 
'9 

12 
12 
12 
12 
13 

58 
60 
62 
64 
66 

TABLE  P.  EFFECT  OF  SUN'S  VA 

E 

e 

•. 
90 

Add  the  Numbers  above  th 

Knet  to  2rd  Correction,  sub 

tract  the  others. 

)'«  S 

App  - 
Alt.  5 

un's  Apparent  Altitu( 

1 

13 

i 

68 
70 

72 

'10  20  3 
1 

J  40 

506 

U7080 

n    1 

f      It      « 

5  0^ 

1  3  5 

7 

74 

10  1 
20  4 
30  6 
40  9 
60 
60 
70 
80 

0  2^  4 

5 

76 

3  1  1 
5  3  I 

8  5  3 

7  5 

7 

.a 

'o_ 

2 

4 
5 
6 

4 

2  : 
0 
2 

4  : 
6  < 

1  2 
0  1 

J  2  1 
I  3  2 

I 

0 

28° 

78 
80 
82 
84 
86 

; 

110 

12° 

14° 

I60 

18° 

20° 

22° 

24° 

26° 

30° 

TABLE  XXXIII. 

163 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE 

360. 

App. 
Alt. 

APPARENT  ALTITUDE  OF  THE  SUN, 

OR  STAR. 

App 

32«» 

34° 

360 

38° 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

70° 

74° 

78°  1  82° 

86° 

Alt. 

0 

1 

// 

f    tf 

f 

// 

>    ff 

/  n 

'  n 

f     rr 

r     It 

1    n 

/  // 

1 

II 

/ 

n 

t 

II 

1 

II     r     II 

1    II 

o 

6 

5 

40 

6  1 

6 

22 

6  43 

7  24 

'  6| 

7 

4 

43 

5  1 

5 

19 

5  36 

6  11 

A 

8 

4 

1 

4  16 

4 

31 

4  46 

5  16 

5   45 

8 

9 

3 

29 

3  42 

3 

55 

4  8 

4  33 

4  58 

9 

10 
11 

3 
2 

4 
43 

3  16 

3 

27 

3  38 

3  59 

4  20 

% 

10 

2  54 

3 

4 

3  13 

3  32 

3  50 

11 

12 

2 

27 

2  36 

2 

45 

2  53 

3  10 

3  25 

3  40 

12 

13 

2 

13 

2  21 

2 

29 

2  37 

2  51 

3  4 

3  16 

13 

14 

2 

2 

2  9 

2 

16 

2  23 

2  36 

2  47 

2  57 

14 

15 

1 

53 

1  59 

2 

5 

2  11 

2  23 

2  33 

2  42 

15 
16 

16 

45 

1  50 

56 

2  1 

2  12 

2  21 

2  29 

2  36 

17 

38 

1  42 

47 

1  53 

2  2 

2  10 

2  17 

2  24 

17 

18 

32 

1  36 

40 

1  45 

1  53 

2  1 

2  7 

2  13 

18 

19 

27 

1  30 

34 

1  38 

1  45 

1  52 

1  58 

2  3 

19 

20 

23 

1  26 

29 

1  33 

1  38 

1  44 

1  49 

1  54 

1  58 

20 

21 

20 

1  22 

25 

1  28 

1  33 

1  38 

1  43 

1  47 

1  51 

21 

22 

17 

1  18 

20 

1  23 

1  28 

1  33 

1  37 

1  41 

1  45 

22 

23 

14 

1  15 

17 

1  19 

1  24 

1  28 

1  32 

1  36 

1  39 

23 

24 

11 

1  12 

14 

1  16 

1  20 

1  23 

1  27 

1  31 

1  34 

1  37 

24 

25 
26 

9 

1  10 

11 

1  13 

1  16 

1  19 

1  22 

1  26 

1  29 

I  31 

25 
26 

8 

1  8 

9 

1  11 

1  13 

1  16 

1  18 

1  21 

1  24 

1  26 

27 

7 

1  7 

8 

1  9 

1  11 

1  13 

1  15 

1  17 

1  20 

1  22 

27 

28 

6 

1  6 

7 

1  8 

1  9 

1  11 

1  12 

1  14 

1  16 

1  18 

20 

28 

29 

6 

1  6 

6 

1  7 

1  8 

1  9 

1  10 

1  11 

1  13 

1  14 

16 

29 

30 

5 

1  5 

5 

1  6 

1  7 

1  7 

1  8 

1  9 

1  10 

1  11 

13 

30 
31 

31 

5 

1  5 

5 

1  5 

1  6 

1  6 

1  6 

1  7 

1  8 

1  9 

10 

32 

4 

1  4 

5 

1  5 

1  5 

1  5 

1  5 

1  5 

1  6 

1  7 

8 

1 

9 

32 

33 

4 

1  4 

4 

1  4 

1  4 

1  4 

1  4 

1  4 

1  4 

1  5 

5 

1 

6 

33 

34 

4 

1  3 

3 

1  3 

1  3 

1  3 

1  3 

1  3 

1  3 

1  3 

3 

1 

3 

34 

35 

4 

1  3 

3 

1  3 

1  2 

1  1 

1   1 

1  1 

1   1 

1   1 

1 

1 

1 

35 
36 

36 

4 

1  3 

2 

1  2 

1  1 

1   0 

1   0 

I  0 

1  0 

1  0 

1 

0 

1 

0 

1 

0 

37 

4 

I  3 

2 

1   1 

0  59 

0  59 

0  59 

0  59 

0  59 

0  59 

0 

59 

0 

59 

0 

58 

37 

38 

4 

1  3 

1  0 

0  58 

0  58 

0  58 

0  58 

0  58 

0  58 

0 

58 

0 

58 

0 

57 

38 

39 

5 

1  3 

1  0 

0  58 

0  58 

0  58 

0  58 

0  57 

0  57 

0 

57 

0 

56 

0 

56 

39 

40 

5 

1  3 

1  0 

0  58 

0  57 

0  57 

0  57 

0  57 

0  56 

0 

56 

0 

55 

0 

54 

0 

53 

40 

41 

6 

1  3 

0  59 

0  57 

0  56 

0  56 

0  56 

0  56 

0  55 

0 

54 

0 

53 

0 

52 

0 

52 

41 

42 

6 

1  3 

0  59 

0  57 

0  56 

0  55 

0  55 

0  55 

0  54 

0 

53 

0 

52 

0 

51 

0 

51 

42 

43 

6 

1  3 

0  59 

0  56 

0  55 

0  54 

0  54 

0  54 

0  53 

0 

52 

0 

51 

0 

50 

0 

50 

0  49 

43 

44 

6 

1  3 

0  59 

0  56 

0  54 

0  53 

0  5S 

0  53 

0  52 

0 

51 

0 

50 

0 

49 

0 

49 

0  48 

44 

46 

6 

1  3 

0  59 

0  56 

0  54 

0  53 

0  52 

0  51 

0  50 

0 

49 

0 

48 

0 

48 

0 

47 

0  47 

46 

48 

48 

7 

1  3 

0  59 

0  56 

0  54 

0  52 

0  51 

0  49 

0  48 

0 

47 

0 

46 

0 

46 

0 

45 

0  45 

0  45 

oO 

7 

1  3 

0  59 

0  56 

0  53 

0  51 

0  50 

0  48 

0  47 

0 

46 

0 

45 

0 

45 

0 

44 

0  44 

0  44 

50 

52 

7 

1  3 

0  59 

0  55 

0  52 

0  50 

0  49 

0  48 

0  47 

0 

46 

0 

45 

0 

44 

0 

43 

0  42 

0  42 

52 

54 

7 

1  3 

0  59 

0  55 

0  52 

0  50 

0  48 

0  47 

0  46 

0 

45 

0 

44 

0 

43 

0 

42 

0  41 

0  41 

54 

56 

7 

1  3 

0 

0  58 

0  55 

0  52 

0  49 

0  48 

0  47 

0  46 

0 

45 

0 

44 

0 

43 

0 

42 

041 

0  40 

56 

58 

7 

1  3 

0 

0  58 

0  55 

0  52 

0  49 

0  47 

0  46 

0  45 

0 

44 

0 

43 

0 

42 

0 

41 

0  40 

0  39 

58 

60 

7 

1  3 

0 

0  58 

0  55 

0  51 

0  48 

0  46 

0  45 

0  44 

0 

43 

0 

42 

0 

41 

0 

40 

0  39 

0  38 

60 

62 

7 

1  3 

0 

0  58 

0  54 

0  51 

0  48 

0  46 

0  44 

0  43 

0 

42 

0 

41 

0 

40 

0 

39 

0  38 

62 

64 

7 

1  3 

0 

0  58 

0  54 

0  51 

0  48 

0  46 

0  44 

0  43 

0 

42 

0 

40 

0 

39 

0 

38 

0  37 

64 

66 

8 

1  3 

0 

0  57 

0  54 

0  50 

0  47 

0  45 

0  43 

0  42 

^ 

41 

0 

39 

0 

38 

0 

37 

66 
68 

68 

8 

1  3 

0 

0  57 

0  54 

0  50 

0  47 

0  45 

0  43 

0  42 

0 

40 

0 

39 

0 

38 

0 

37 

70 

8 

1  3 

0 

0  57 

0  53 

0  50 

0  47 

0  44 

0  42 

0  41 

0 

40 

0 

39 

0 

38 

70 

72 

1  3 

0 

0  57 

0  53 

0  50 

0  46 

0  43 

0  41 

0  40 

0 

39 

0 

38 

72 

74 

0 

0  57 

0  52 

0  49 

0  46 

0  43 

0  41 

0  40 

0 

39 

0 

38 

74  1 

76 

0  57 

0  52 

0  48 

0  45 

0  43 

0  41 

0  39 

0 

38 

0 

37 

76 

78 

78 

0  51 

0  48 

0  45 

0  42 

0  40 

0  39 

0 

37 

80 

0  51 

0  47 

0  44 

0  42 

0  40 

0  39 

0 

37 

80 

82 

0  47 

0  44 

0  41 

0  40 

0  38 

1 

82 

84 

0  47 

0  44 

0  41 

0  39 

0  38 

84 

86 

0  44 

0  41 

0  39 

86 

32'' 

34° 

36° 

38° 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

70°  1 

74°  1 

78°  1 

82° 

86° 

t          — . 

164                                          TABLE  XXXUI. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  40° 

App. 
Alt. 

APPARENT  ALTITUDE  OF  THE  SUN,  OB  A  STAR. 

App. 

Alt. 
0 

fe« 

70 

8» 

90 

10° 

11° 

12° 

14° 

16° 

/  II 

18° 

20° 

22° 

24°  I  26° 

28° 

30°  1 

o 

/  n 

t    tf 

t    n 

t    n 

/  It 

/  // 

1    II 

1    II 

1    II 

1    II 

1    II 

/  // 

1    II 

1 

II 

/ 

n 

6 

1  16 

1  18 

1  21 

1  25 

1  31 

1  39 

1  47 

2  5 

2  26 

2  48 

3  10 

3  32 

3  54 

4  16 

4 

38 

4 

59 

6 

7 

1  19 

1  16 

1  18 

1  21 

1  24 

1  28 

1  34 

1  48 

2  4 

2  22 

2  40 

2  58 

3  16 

3  34 

3 

62 

4 

10 

7 

8 

1  24 

1  19 

1  16 

1  18 

1  20 

1  22 

1  26 

1  36 

1  50 

2  4 

2  18 

2  33 

2  48 

3  4 

3 

20 

3 

36 

8 

9 

1  31 

1  23 

1  19 

1  16 

1  18 

1  19 

1  21 

1  27 

1  38 

1  49 

2  1 

2  13 

2  25 

2  38 

2 

52 

3 

5 

9 

10 

1  40 

1  29 

1  23 

1  19 

1  16 

1  17 

1  18 

1  21 

1  29 

1  38 

1  48 

1  58 

2  9 

2  20 

2 

32 

2 

44 

10 

11 

1  50 

1  36 

1  28 

1  22 

1  18 

1  15 

1  16 

1  18 

1  23 

1  31 

1  39 

1  48 

1  57 

2  7 

2 

17 

2 

27 

11 

12 

2  1 

1  44 

1  34 

1  26 

1  20  1  17| 

1  15 

1  17 

1  20 

1  26 

1  33 

1  40 

1  48 

1  57 

2 

5 

2 

13 

12 

13 

2  11 

1  52 

1  40 

1  30 

1  23 

1  19 

1  16 

1  16 

1  18 

1  22 

1  28 

1  34 

1  41 

1  48 

55 

2 

2 

13 

14 

2  21 

2  0 

1  46 

1  34 

1  26 

1  21 

1  17 

1  15 

1  17 

1  19 

1  23 

1  28 

1  34 

1  40 

46 

53 

14 

15 

2  31 

2  8 

1  52 

1  39 

1  30 

1  23 

1  19 

1  16 

1  15 

1  17 

1  20 

1  23 

1  27 

1  32 

38 

44 

15 

16 

2  41 

2  16 

1  58 

1  44 

1  34 

1  26 

1  21 

1  17 

1  14 

1  15 

1  17 

1  19 

1  22 

1  26 

31 

37 

16 

17 

2  52 

2  24 

2  4 

1  49 

1  38 

1  30 

1  24 

1  19 

1  15 

1  14 

1  15 

1  17 

1  19 

1  22 

26 

31 

17 

18 

3  3 

2  32 

2  11 

1  54 

1  43 

1  34 

1  28 

1  21 

1  16 

1  13 

1  14 

1  15 

1  17 

1  19 

22 

26 

18 

19 

3  14 

2  41 

2  18 

2  0 

1  48 

1  39 

1  32 

1  23 

1  17 

1  14 

1  13 

1  14 

1  15 

1  17 

19 

22 

19 

20 

3  25 

2  50 

2  25 

2  6 

1  53 

1  43 

1  36 

1  25 

1  19 

1  15 

1  12 

1  12 

1  13 

1  15 

16 

19 

20 

21 

3  36 

2  59 

2  32 

2  12 

1  58 

1  47 

1  39 

1  27 

1  20 

1  16 

1  13 

1  11 

1  12 

1  13 

14 

16 

21 

22 

3  47 

3  8 

2  40 

2  18 

2  4 

1  52 

1  43 

1  30 

1  22 

1  17 

1  13 

1  11 

1  11 

1  12 

13 

14 

22 

23 

3  58 

3  17 

2  48 

2  25 

2  10 

1  57 

1  47 

1  33 

1  24 

1  18 

1  14 

1  12 

1  10 

1  10 

11 

12 

23 

24 

4  9 

3  26 

2  56 

2  32 

2  15 

2  2 

1  51 

1  37 

1  26 

1  19 

1  15 

1  12 

1  9 

1  9 

9 

10 

24 

25 

4  20 

3  35 

3  4 

2  39 

2  21 

2  7 

1  56 

1  40 

1  28 

1  21 

1  16 

1  13 

1  10 

1  8 

8 

9 

25 

26 

4  30 

3  44 

3  12 

2  45 

2  27 

2  12 

2  0 

1  43 

1  30 

1  22 

1  17 

1  13 

1  10 

1  8 

8 

9 

26 

27 

4  41 

3  53 

3  20 

2  52 

2  33 

2  17 

2  4 

1  47 

1  33 

1  24 

1  18 

1  14 

1  11 

1  8 

7 

8 

27 

28 

4  51 

4  2 

3  28 

2  59 

2  39 

2  23 

2  8 

1  50 

1  35 

1  25 

1  19 

1  14 

1  11 

1  8 

7 

28 

29 

5  1 

4  11 

3  36 

3  6 

2  45 

2  28 

2  12 

1  53 

1  38 

1  27 

1  20 

1  15 

1  12 

1  9 

7 

7 

29 

30 

5  12 

4  20 

3  44 

3  13 

2  50 
2  56 

2  33 

2  17 

1  56 

1  40 

1  29 

1  21 

1  15 

1  12 

1  9 

7 

e 

30 

31 

5  23 

4  29 

3  52 

3  2C 

2  38 

2  21 

2  0 

1  43 

1  30 

1  22 

1  16 

1  12 

1  9 

7 

6 

31 

32 

5  33 

4  3? 

3  59 

3  27 

3  1 

2  43 

2  26 

2  3 

1  45 

1  32 

1  23 

1  17 

1  13 

1  10 

7 

6 

32 

33 

5  43 

4  46 

4  6 

3  33 

3  7 

2  48 

2  30 

2  6 

1  47 

1  34 

1  24 

1  18 

1  14 

1  10 

8 

6 

33 

34 

5  52 

4  54 

t4  13 

3  39 

3  13 

2  53 

2  34 

2  9 

1  49 

1  36 

1  26 

1  19 

1  15 

1  11 

8 

6 

34 

35 

6  1 

5  2 

4  20 

3  4£ 

.  3  19 

2  58 

2  38 

2  12 

1  51 

1  38 

1  27 

1  20 

1  15 

1  11 

8 

6 

35 

36 

6  10 

5  IC 

4  26 

3  51 

3  24 

3  2 

2  42 

2  15 

1  54 

1  40 

1  29 

1  22 

1  16 

1  12 

8 

6 

36 

37 

6  18 

5  17 

4  32 

3  57 

3  29 

3  7 

2  46 

2  18 

1  57 

1  42 

1  31 

1  23 

1  17 

1  12 

9 

7 

37 

38 

6  26 

5  24 

4  38 

4  3 

3  33 

3  11 

2  50 

2  21 

2    n 

1  44 

1  33 

1  25 

1  18 

1  13 

9 

7 

38 

, 

39 

6  34 

5  31 

4  44 

4  g 

1  3  38 

3  15 

2  54 

2  24 

2    2 

1  46 

1  35 

1  26 

1  19 

1  14 

10 

7 

39 

40 

6  42 

5  38 

4  50 

4  13 

3  42 
t  3  47 

3  19 

2  58 

2  27 

2    5 

1  48 

1  37 

1  28 

1  20 

1  14 

10 

7 

40 

41 

6  50 

5  4S 

4  56 

4  18 

3  24 

3  2 

2  30 

2  8 

1  51 

1  39 

1  29 

1  21 

1  15 

11 

8 

41 

42 

6  58 

5  52 

5  2 

4  24 

\  3  51 

3  28 

3  6 

2  33 

2  10 

1  53 

1  41 

1  30 

1  22 

1  16 

11 

8 

42 

43 

7  7 

5  5S 

5  8 

4  29 

3  56 

3  32 

3  10 

2  36 

2  13 

1  55 

1  43 

1  32 

1  23 

1  17 

12 

9 

43 

44 

7  16 

6  6 

5  14 

4  34 

\  4  0 

3  36 

3  13 

2  39 

2  15 

1  57 

1  44 

1  33 

1  24 

1  18 

13 

9 

44 

46 

7  33 

6  21 

5  26 

4  44 

i  4  9 

3  44 

3  20 

2  44 

2  19 

2  1 

1  47 

1  35 
1  37 

1  27 

1  20 

14 

10 

46 

48 

7  50 

6  Zt 

>  5  38 

4  54 

\  4  18 

3  51 

3  27 

2  49 

2  23 

2  5 

1  50 

1  29 

1  22 

15 

11 

48 

50 

5  50 

5  l 

\  4  27 

3  58 

3  33 

2  54 

2  27 

2  8 

1  52 

1  39 

1  31 

1  23 

17 

12 

50 

52 

4  36 

4  5 

3  39 

2  59 

2  31 

2  11 

1  54 

1  42 

1  32 

1  24 

18 

13 

52 

54 

3  45 

3  4 

2  35 

2  14 

1  56 

1  44 

1  34 

1  26 

19 

14 

54 

56 

3  9 

2  39 

2  17 

1  58 

1  46 

1  36 

1  28 

20 

14 

56 

2  43 

2  19 
2  21 

2  0 
2  2 
2  4 

1  48 
1  49 
1  50 
1  51 

1  37 
1  38 
1  39 
1  40 
1  40 

1  29 
1  30 
1  30 
1  31 
1  31 

— 

21 
22 
22 
23 
24 

24 
24 

15 
15 
16 
16 
17 

68 
60 
62 
64 
66 

TABLE  P  EFFECT  OF  STJN'B  Pi 

e 
le. 

Add  tht  Numbers  above  th 

lines  to  3rd  Correr.tion,  sub 

tract  the  others. 

>'8s 

App  _ 
Alt.  6 

Bn'»  Apparent  Altitnc 

10  20  3 

J  40 

50  6 

0170  80 

90 

1  31 

17 
17 
17 

68 
70 
72 
74 

5    0 

10  I 

1  2  4 
0  i  3 

If 

6 
4 

6 

/  tt      ft 

n 

20  4 
30  6 
40  8 
50 
60 
70 
80 
90 

3  1  1 

532 
7  5  4 
9  7  5 

9  7 

8 

2 
'  0 
2 
4 
5 
6 
7 

3 
1 
1 

2  " 

4  ; 

5  ' 

6  ' 
6 

\ 

i   3 

r  0  0 
J  2  2 
» 3 

0 

76 

78 
80 

82 
84 
86 

11» 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

r>0 

30° 

2o 

TABLE  XXXlll. 

165 

THIRD  CORRECTION.  TO  APPARENT  DISTANCE  40°. 

A  pp. 
All. 

APPARENT  ALTITUDE  OF  THE  SUN, 

OR  STAR. 

3>'s 

App 

Alt. 

32° 

34° 

36° 

38° 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

70° 

74° 

78° 

82»  ,  86° 

o 

/  n 

/  ft 

>    II 

1 

n 

1    II 

/  ir 

1    II 

/    n 

1    II 

/  II 

/ 

// 

/ 

II 

1 

II 

/  It 

1    n 

/  II 

0 

6 

5   19 

5  39 

5   59 

6 

19 

6  57 

7  33 

1 

6 

7 

4  27 

4  44 

5  1 

5 

18 

5  51 

6  20 

7 

8 

3  51 

4  6 

4  20 

4 

34 

5  1 

6  26 

5  50 

8 

9 

3  20 

3  34 

3  46 

3 

58 

4  22 

4  44 

5  5 

9 

10 

2  56 

3  8 

3  19 

3 

30 

3  50 

4   9 

4  27 

* 

10 

11 

2  37 

2  47 

2  57 

2 

6 

3  25 

3  42 

3  58 

11 

12 

2  22 

2  30 

2  39 

2 

48 

3  5 

3  20 

3  33 

3  46 

12 

13 

2  10 

2  17 

2  25 

2 

32 

2  47 

3   1 

3  13 

3  25 

13 

14 

2  0 

2   6 

2  12 

2 

18 

2  32 

2  44 

2  55 

3  4 

14 

15 

16 

1  50 

1  56 

2  1 

2 

7 

2  19 

2  30 

2  40 

2  48 

15 

16 

1  42 

1  47 

1  52 

58 

2  8 

2  18 

2  27 

2  35 

2  42 

17 

1  36 

1  40 

1  45 

50 

1  59 

2  8 

2  16 

2  23 

2  30 

17 

18 

1  31 

1  34 

1  38 

43 

1  51 

1  59 

2  6 

2  12 

2  19 

18 

19 

1  26 

1  29 

1  33 

36 

1  44 

1  51 

1  58 

2  3 

2  9 

19 

20 

1  22 

1  24 

1  27 

30 

1  37 

1  44 

1  50 

1  55 

2  0 

2  5 

20 

21 

1  18 

1  20 

1  23 

26 

1  32 

1  38 

1  44 

1  49 

1  53 

1  57 

21 

22 

1  15 

1  17 

1  19 

22 

1  28 

1  33 

1  38 

1  43 

1  47 

1  50 

22 

23 

1  13 

1  14 

1  16 

19 

1  24 

1  29 

1  33 

1  38 

1  42 

1  45 

23 

24 

1  11 

1  12 

1  14 

16 

1  21 

1  25 

1  29 

1  33 

1  37 

1  40 

43 

24 

25 
26 

1  lU 

1  11 

1  12 

14 

1  18 

1  21 

1  25 

1  29 

1  32 

1  35 

37 

25 

1  9 

1  10 

1  11 

12 

1  15 

1  18 

1  21 

1  25 

1  28 

1  30 

32 

26 

27 

1   8 

1  9 

1   9 

10 

1  13 

1  15 

1  18 

1  21 

1  24 

1  26 

27 

27 

28 

1   7 

1   8 

1   8 

9 

1  11 

1  13 

1  16 

1  18 

1  20 

1  22 

23 

24 

28 

29 

1   7 

1   7 

1  7 

8 

1   9 

1  11 

1  13 

1  15 

1  16 

1  18 

19 

20 

29 

30 

1   6 

1   6 

1   6 

7 

1   8 

1   9 

1  11 

1  12 

1  13 

1  15 

16 

17 

30 
31 

31 

1   6 

1   6 

1  6 

7 

1   7 

1   8 

1   9 

1  10 

1  11 

1  13 

14 

15 

32 

1   6 

1   6 

1   6 

6 

1   6 

1   6 

1   7 

1   8 

1   9 

1  10 

11 

12 

13 

32 

33 

1   5 

1   5 

1   5 

5 

1   5 

1   5 

1   6 

1   6 

1   7 

1  8 

9 

10 

10 

33 

34 

1   5 

1  4 

1   4 

4 

1   4 

1   4 

1  5 

1  5 

1   6 

1  7 

7 

8 

8 

34 

35 

1   5 

1  4 

1  4 

-- 

4 

1   4 

1  4 

1   4 

1  4 

1   4 

1   5 

5 

6 

6 

35 
36 

36 

1   5 

1   4 

1   3 

3 

1  3 

1   3 

1   3 

1   3 

1   3 

1   4 

4 

4 

4 

1  4 

37 

1   5 

1   4 

1   3 

2 

1   2 

1   2 

1   2 

1   1 

1   1 

1   2 

2 

2 

2 

1  2 

37 

38 

1   5 

1   4 

1   2 

1 

1   1 

1   1 

1   1 

1  0 

1   0 

1  0 

0 

1 

1 

1  1 

38 

39 

1   5 

1   4 

1   2 

1 

1   0 

1   0 

1   0 

0  59 

Q  59 

0  59 

0 

59 

0 

59 

0 

59 

0  59 

39 

40 

1   5 

1   4 

1   2 

1 

1  0 

0  59 

0  59 

0  58 

0  58 

0  57 

0 

57 

0 

57 

0 

57 

0  57 

0  57 

40 
41 

41 

1  6 

1  4 

1   2 

1 

0  59 

0  58 

0  58 

0  57 

0  57 

0  56 

0 

56 

0 

56 

0 

56 

0  56 

0  56 

42 

1   6 

1  4 

1   2 

0 

0  58 

0  57 

0  57 

0  56 

0  56 

0  55 

0 

55 

0 

55 

0 

55 

0  55 

0  55 

42 

43 

1   6 

1   4 

1   2 

0 

0  58 

0  57 

0  56 

0  55 

0  55 

0  54 

0 

54 

0 

54 

0 

54 

0  54 

0  54 

0  54 

43 

44 

1   6 

1   4 

1   2 

0 

0  58 

0  56 

0  55 

0  54 

0  54 

0  53 

0 

53 

0 

53 

0 

53 

0  53 

0  53 

0  53 

44 

46 

1   7 

1   4 

1   2 

0 

0  58 

0  56 

0  54 

0  53 

0  53 

0  52 

0 

52 

0 

51 

0 

51 

0  51 

0  51 

0  51 

0  4:' 

46 
48 

48 

1   8 

1   5 

1   2 

0 

0  58 

0  55 

0  53 

0  52 

0  52 

0  51 

0 

51 

0 

50 

0 

49 

0  49 

0  4y 

50 

1   8 

1   5 

1   2 

0 

0  57 

0  54 

0  52 

0  51 

0  51 

0  50 

0 

49 

0 

48 

0 

48 

0  48 

0  48 

C  48 

50 

52 

1   9 

1   5 

1   2 

0 

0  57 

0  54 

0  52 

0  50 

0  50 

0  49 

0 

48 

0 

47 

0 

47 

0  46 

0  46 

0  46 

52 

54 

1   9 

1   5 

1   2 

0 

0  57 

0  54 

0  51 

0  49 

0  49 

0  48 

0 

47 

0 

46 

0 

46 

0  45 

0  45 

0  45 

54 

56 

1  10 

1   6 

1   3 

0 

0  56 

0  53 

0  51 

0  49 

0  48 

0  47 

0 

46 

0 

45 

0 

45 

0  44 

0  44 

0  44 

56 

58 

1  10 

1   6 

1   3 

0 

0  56 

0  53 

0  50 

0  48 

0  47 

0  46 

0 

45 

0 

45 

0 

44 

0  43 

0  43 

58 

60 

1  10 

1   7 

1   4 

0  56 

0  52 

0  50 

0  48 

0  47 

0  45 

0 

44 

0 

44 

0 

43 

0  42 

0  42 

60 

62 

1  11 

1   7 

1  4 

0  56 

0  52 

0  50 

0  48 

0  46 

0  45 

0 

44 

0 

43 

0 

42 

U  42    1 

62 

64 

1  11 

1   7 

1  4 

0  56 

0  52 

0  49 

0  47 

0  45 

0  44 

0 

43 

0 

42 

0 

41 

0  41 

64 

66 
68 

1  12 

1  7 

1  4 

0  56 

0  52 

0  49 

0  47 

0  45 

3  43 

0 

42 

0 

42 

0 

41 

66 
68 

1  12 

I  '8 

1   4 

0  56 

0  52 

0  49 

0  47 

0  45 

0  43 

0 

42 

0 

42 

0 

41 

70 

1  12 

1  8 

1   4 

0  55 

0  51 

0  48 

0  46 

0  44 

0  43 

0 

42 

0 

42 

70 

72 

1  13 

1  8 

1   4 

0  55 

0  51 

0  48 

0  46 

0  44 

0  43 

0 

42 

0 

41 

72  1 

74 

1  13 

1   8 

1   4 

0  55 

0  51 

0  48 

0  46 

0  44 

0  43 

0 

42 

74 

76 

1   8 

1   4 

0  55 

0  51 

0  48 

0  46 

0  44 

0  42 

0 

41 

76 
78 

78 

1  4 

0  55 

0  51 

0  48 

0  46 

0  43 

0  42 

80 

0  55 

0  51 

0  48 

0  46 

0  43 

0  41 

80 

82 

0  55 

0  51 

0  48 

0  46 

0  43 

82 

84 

0  55 

0  51 

0  48 

0  46 

0  43 

84 

86 

0  51 

0  48 

0  45 

1 

86 

32° 

34° 

36° 

38° 

42° 

46° 

50° 

54° 

58° 

62°  1 

66°  1 

70°  1 

74°  1  78° 1 

82° 

86° 

166                                         TABLE  XXXllI. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  U° 

• 

App. 
Alt. 

APPARENT  ALTITUDE  OF  THE  SUN,  OR  A  STAR. 

1>'B 

App. 
Alt. 

6° 

70 

8« 

9° 

10° 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

o 

t    ft 

t    tf 

/  // 

1    tl 

/  ft 

1     tl 

/  II 

/  II 

/  // 

/  // 

/  II 

1    If 

/  tl 

/ 

// 

1 

// 

0 

6 

1  16 

1  18 

1  21 

1  25 

1  31 

1  37 

1  45 

2  3 

2  23 

2  44 

3  5 

3  25 

3  45 

4  5 

4 

25 

4 

44 

6 

7 

1  20 

1  16 

1  18 

1  20 

1  24 

1  28 

1  33 

1  46 

2  1 

2  17 

2  34 

2  51 

3  8 

3  25 

3 

42 

3 

59 

7 

8 

1  25 

1  19 

1  16 

1  17 

1  19 

1  22 

1  25 

1  35 

1  47 

2  0 

2  14 

2  29 

2  43 

2  58 

3 

12 

3 

27 

8 

9 

1  31 

1  23 

1  18 

1  15 

1  16 

1  18 

1  21 

1  27 

1  36 

1  47 

1  59 

2  12 

2  24 

2  36 

2 

48 

3 

0 

9 

10 

1  39 

1  28 

1  21 

1  17 

1  15 

1  16 

1  18 

1  22 

1  29 

1  38 
1  31 

1  48 

1  58 

2  8 

2  18 

2 

29 

2 

39 

10 

11 

1  48 

1  34 

1  25 

1  20 

1  17 

1  15 

1  16 

1  19 

1  24 

1  39 

1  47 

1  56 

2  5 

2 

14 

2 

24 

11 

12 

1  58 

1  41 

1  30 

1  23 

1  19 

1  16 

1  15 

1  17 

1  20 

1  25 

1  32 

1  38 

1  46 

1  54 

2 

2 

2 

11 

12 

13 

2  8 

1  48 

1  35 

1  27 

1  22 

1  18 

1  16 

1  15 

1  17 

1  21 

1  26 

1  32 

1  38 

1  45 

52 

59 

13 

14 

2  18 

1  56 

1  41 

1  31 

1  25 

1  20 

1  17 

1  14 

1  15 

1  18 

1  22 

1  27 

1  32 

1  38 

44 

49 

14 

15 
16 

2  28 

2  4 

1  47 

1  36 

1  29 

1  23 

1  19 

1  15 

1  14 

1  16 

1  19 

1  23 

1  27 

1  32 

37 

42 

15 
16 

2  38 

2  12 

1  53 

1  41 

1  33 

1  26 

1  21 

1  17 

1  14 

1  15 

1  17 

1  20 

1  23 

1  27 

32 

36 

17 

2  48 

2  20 

ii  0 

1  47 

1  37 

1  30 

1  24 

1  19 

1  15 

1  15 

1  16 

1  18 

1  20 

1  23 

26 

30 

17 

18 

2  58 

2  28 

2  8 

1  53 

1  42 

1  34 

1  27 

1  20 

1  16 

1  14 

1  15 

1  16 

1  18 

1  20 

22 

25 

18 

19 

3  8 

2  37 

2  15 

1  59 

1  47 

1  38 

1  30 

1  22 

1  17 

1  14 

1  14 

1  15 

1  16 

1  17 

19 

22 

19 

20 

3  18 

2  45 

2  22 

2  5 

1  52 

1  42 

1  34 

1  25 

1  19 

1  15 
1  17 

1  13 

1  14 

1  14 

1  15 

17 

19 

20 

21 

3  29 

2  54 

2  30 

2  12 

1  57 

1  46 

1  37 

1  27 

1  21 

1  14 

1  12 

1  13 

1  14 

15 

17 

21 

22 

3  39 

3  2 

2  37 

2  18 

2  3 

1  51 

1  41 

1  30 

1  23 

1  18 

1  14 

1  11 

1  12 

1  13 

14 

16 

22 

23 

3  49 

3  11 

2  45 

2  24 

2  8 

1  55 

1  45 

1  33 

1  25 

1  19 

1  15 

1  12 

1  11 

1  12 

13 

14 

23 

24 

4  0 

3  19 

2  52 

2  31 

2  14 

2  0 

I  49 

1  36 

1  27 

1  20 

1  16 

1  12 

1  10 

1  10 

11 

13 

24 

25 

4  10 

3  28 

2  59 

2  37 

2  20 

2  5 

1  53 

1  39 

1  29 

1  21 

1  22 

1  17 

1  13 

1  10 

1  9 

10 

11 

25 

26 

4  20 

3  36 

3  6 

2  43 

2  25 

2  10 

1  57 

1  42 

1  31 

1  17 

1  13 

1  10 

1  8 

9 

9 

26 

27 

4  30 

3  45 

3  13 

2  49 

2  31 

2  15 

2  1 

1  45 

1  32 

1  23 

1  18 

1  14 

1  11 

1  9 

8 

8 

27 

28 

4  39 

3  53 

3  20 

2  55 

2  36 

2  20 

2  5 

1  47 

1  34 

1  25 

1  19 

1  15 

1  12 

1  9 

7 

7 

28 

29 

4  48 

4  1 

3  27 

3  1 

2  41 

2  24 

2  9 

1  49 

1  36 

1  27 

1  20 

1  15 

1  12 

1  9 

7 

6 

29 

30 

4  57 

4  9 

3  34 

3  7 

2  46 

2  29 

2  14 

1  52 

1  38 

1  28 

1  21 

1  16 

1  13 

1  9 

7 

6 

30 

31 

5  7 

4  17 

3  41 

3  13 

2  51 

2  34 

2  19 

1  55 

1  40 

1  30 

1  22 

1  17 

1  13 

1  10 

8 

6 

31 

32 

5  16 

4  25 

3  48 

3  19 

2  56 

2  38 

2  23 

1  58 

1  42 

1  31 

1  23 

1  18 

1  14 

1  10 

8 

6 

32 

33 

5  25 

4  33 

3  54 

3  25 

3  1 

2  43 

2  27 

2  1 

1  44 

1  33 

1  24 

1  19 

1  15 

1  11 

9 

7 

33 

34 

5  34 

4  40 

4  1 

3  30' 3  6 

2  47 

2  31 

2  4 

1  47 

1  35 

1  26 

1  20 

1  15 

1  11 

9 

7 

34 

35 

5  43 

4  48 

4  8 

3  3«i 

3  11 

2  52 

2  35 

2  7 

1  50 

1  37 

1  27 

1  21 

1  16 

1  12 

9 

7 

35 

36 

5  51 

4  55 

4  14 

3  42 

3  15 

2  56 

2  39 

2  11 

1  53 

1  39 

1  28 

1  22 

1  17 

1  13 

10 

7 

36 

37 

6  0 

15  3 

4  21 

3  47 

3  20 

3  0 

2  43 

2  15 

1  56 

1  41 

1  30 

1  23 

1  17 

1  13 

10 

8 

37 

38 

6  g 

5  10 

4  27 

3  52 

3  24 

3  4 

2  47 

2  18 

1  58 

1  43 

1  32 

1  24 

1  18 

1  14 

11 

8 

38 

39 

6  18 

5  18 

4  33 

3  58 

3  29 

3  8 

2  51 

2  21 

2  1 

1  45 

1  33 

1  25 

1  19 

1  14 

11 

8 

39 

40 

6  27 

5  25 

4  39 

4  3 

3  33 

3  12 

2  54 

2  24 

2  3 

1  46 

1  35 

1  26 

1  20 

1  15 

11 

8 

40 

41 

6  36 

.5  32 

4  45 

4  8 

3  38 

3  16 

2  58 

2  27 

2  6 

1  48 

1  37 

1  27 

1  21 

1  16 

12 

9 

41 

42 

6  U 

.  5  39 

4  51 

4  13 

3  42 

3  20 

3   1 

2  30 

2  8 

1  50 

1  39 

1  29 

1  22 

1  16 

12 

9 

42 

43 

6  5c 

t  5  46 

4  57 

4  18 

3  47 

3  24 

3  4 

2  33 

2  10 

1  52 

1  40 

1  30 

1  23 

1  17 

13 

9 

43 

44 

7  ( 

)  5  53 

5  5 

4  23 

3  51 

3  28 

3  7 

2  35 

2  12 

1  54 

1  42 

1  32 

1  24 

1  18 

13 

10 

44 

46 

7  U 

I  6  6 

5  14 

4  33 

4  0 

3  35 

3  14 

2  40 

2  17 

1  58 

1  45 

1  35 
1  37 

1  26 

1  20 

14 

10 

46 

18 

7  21 

'  6  IS 

5  25 

4  43 

4  9 

3  43 

3  21 

2  45 

2  21 

2  2 

1  48 

1  28 

1  21 

15 

11 

48 

50 

7  4( 

)  6  29 

5  35 

4  52 

!  4  18 

3  50 

3  27 

2  50 

2  25 

2  6 

1  52 

1  40 

1  31 

1  23 

16 

11 

50 

52 

7  55 

5  6  4C 

1  5  45 

5  1 

4  26 

3  57 

3  33 

2  55 

2  29 

2  10 

1  56 

1  43 

1  33 

1  25 

18 

12 

52 

54 

5  55 

5  £ 

)  4  34 

4  4 

3  39 

3  0 

2  33 

2  14 

1  59 

1  46 

1  35 

1  26 

19 

13 

64 

56  1 

• 

4  42 

4  10 

3  45 

3  5 

2  37 

2  17 

2  2 

1  49 

1  37 

1  39 

1  40 
1  42 
1  43 
1  44 

1  27 

20 

14 

56 

58 
60 
62 
64 
66 

1 

' 

3  50 

3  10 

2  41 
2  44 
2  47 

2  20 
2  22 
2  24 
2  26 

2  4 
2  5 
2  6 
2  7 
2  8 

1  51 
1  52 
1  53 
1  54 
1  55 

1  29 
1  30 
1  31 
1  32 
1  33 

1* 

21 
22 
23 

24 
25 

26 

27 

15 
16 
17 

18 
19 

TABLB  P.  EFFECT  OF  SUN'b  TA 

lH 

« 

«. 

3  14 

Add  the  Numbers  above  th 

lines  to  3rd  Correction,  sul 

tract  the  others. 

J  8  S 

App- 
Alt  5 

u  n's  Appare  nt  Altitnd 

1  56 

1  45 
1  45 

1  34 
1  35 

20 
21 

68 
70 

lU 

•20  3 

3  40 

50  6 

0|70|80 

90 

5  0 

10  1 
on  •! 

1 
0 
3 

5 

2  4 

1  a 
1  0 

3  a 

5 

4 

2 

'  0 

6 

5 
3  ^ 

1  i 

II  It 

I 
i   2 

1 

1  36 

29 
30 

22 
22 
23 

72 
74 
76 

78 

30  5 

40  7 
60  g 
60 
70 
,80 

7 
8 

5  4 

7  5 

8  7 
8 

2 
4 

5 
6 

7 

1  ( 

3  1 

4  ; 

6  ■) 

6 

)  0  1 
>  1  1 

>  2  a 

1  3 

1 

28'' 

80 

82 
84 
86 

11° 

12° 

14° 

16° 

18° 

20° 

22® 

24° 

26° 

30° 

TABLE  XXXIII. 

167 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  44o. 

App. 
Alt. 

APPARENT  ALTITUDE  OF  THE  SUN, 

OR  STAR. 

>'8 

App 

Alt. 

32« 

34° 

36«> 

38° 

42° 

46°  1  50° 

54° 

58° 

62° 

66° 

70° 

74° 

78° 

82° 

86" 

o 

>    It 

/  // 

/  // 

r 

rr 

/  f> 

/  ') 

/  // 

1    ft 

f    n 

/  // 

1 

// 

/ 

n 

/ 

II 

1 

ff 

1    II 

/  // 

o 

6 

5     3 

5  22 

5  41 

5 

59 

6  36 

7  10 

7  40 

6 

7 

4  15 

4  31 

4  47 

5 

2 

5  33 

6  1 

6  29 

7 

8 

3  40 

3  53 

4  6 

4 

20 

4  46 

5  11 

5  35 

5  58 

R 

9 

3  12 

3  24 

3  35 

3 

47 

4  10 

4  31 

4  51 

5  10 

9 

10 

2  50 

3  0 

3  10 

3 

20 

3  39 

3  58 

4  17 

4  34 

» 

10 

11 

2  33 

2  42 

2  52 

3 

0 

3  17 

3  33 

3  48 

4  3 

11 

12 

2  19 

2  27 

2  36 

2 

44 

2  59 

3  13 

3  26 

3  39 

3  51 

12 

13 

2  6 

2  13 

2  21 

2 

29 

2  43 

2  56 

3  9 

3  20 

3  29 

13 

14 

1  55 

2  2 

2  9 

2 

16 

2  29 

2  41 

2  53 

3  2 

3  10 

14 

15 

I  47 

1  53 

1  59 

2 

5 

2  17 

2  28 

2  38 

2  47 

2  54 

15 

16 

16 

1  40 

1  45 

1  50 

56 

2  7 

2  17 

2  26 

2  34 

2  41 

2  47 

17 

1  34 

1  38 

1  43 

48 

1  58 

2  7 

2  15 

2  22 

2  29 

2  35 

17 

18 

1  29 

1  33 

1  37 

42 

1  51 

1  59 

2  6 

2  12 

2  18 

2  24 

18 

19 

1  25 

1  28 

1  32 

36 

1  44 

1  52 

1  59 

2  4 

2  9 

2  14 

19 

20 

1  22 

1  25 

1  28 

31 

1  38 

1  46 

1  52 

1  57 

2  1 

2  6 

2 

11 

20 
21 

21 

1  19 

1  22 

1  25 

27 

1  33 

1  40 

1  46 

1  51 

1  55 

1  59 

2 

2 

22 

1  17 

1  19 

1  22 

24 

1  29 

1  35 

1  40 

1  45 

1  49 

1  53 

55 

22 

23 

1  15 

1  17 

1  19 

21 

1  25 

1  30 

1  35 

1  40 

1  44 

1  47 

49 

23 

24 

1  14 

1  15 

1  16 

18 

1  22 

1  26 

1  30 

1  35 

1  39 

1  42 

44 

46 

24 

25 

26 

1  12 

1  13 

1  14 

16 

1  19 

1  22 

1  26 

1  30 

1  34 

1  37 

39 

40 

25 

1  10 

1  11 

1  12J 

14 

1  16 

1  19 

1  22 

1  26 

1  30 

1  32 

34 

38 

26 

27 

1  9 

1  10 

1  11 

12 

1  14 

1  16 

1  19 

1  23 

1  26 

1  28 

30 

31 

27 

28 

1  8 

1  9 

1  10 

11 

1  12 

1  14 

1  17 

1  20 

1  22 

1  24 

26 

27 

28 

28 

29 

1  7 

1  8 

1  8 

9 

1  10 

1  12 

1  15 

1  17 

1  19 

1  21 

22 

23 

25 

29 

30 

1   6 

1   7 

1   7 

8 

1  9 

1  10 

1  12 

1  14 

1  16 

1  18 

19 

20 

22 

30 
31 

31 

1   6 

1   6 

1  6 

7 

1  8 

1   8 

1  10 

1  12 

1  14 

1  15 

17 

18 

19 

32 

1  5 

1   6 

1   6 

6 

1   7 

1  7 

1  8 

1  10 

1  12 

1  13 

14 

15 

16 

17 

32 

33 

1  5 

1  5 

1   5 

5 

1   6 

1   6 

1  7 

1   8 

1  9 

1  10 

11 

12 

13 

14 

33 

34 

1   5 

1  4 

1  4 

4 

1   5 

1   5 

1   6 

1   6 

1  7 

1   8 

9 

10 

11 

12 

34 

35 

1  5 

1  4 

1  4 

4 

1  4 

1   4 

1   5 

1  5 

1   5 

1   6 

7 

8 

9 

10 

35 

36 

36 

1  5 

1  4 

1   3 

3 

1  3 

1   ? 

1  4 

1  4 

1  4 

1   5 

5 

6 

7 

8 

1   9 

37 

1  6 

1  4 

1  3 

2 

1   2 

1   2 

1   3 

1  3 

1   3 

1  4 

4 

5 

5 

6 

1  7 

37 

38 

1   6 

1  4 

1   2 

1 

1   1 

1   1 

1   2 

1   2 

1   2 

1   3 

3 

4 

4 

4 

1  5 

38 

39 

1   6 

1  4 

1   2 

1 

1   0 

1   0 

1   1 

1   1 

1   1 

1   2 

2 

3 

3 

3 

1   4 

39 

40 

1   6 

1  4 

1  2 

1 

1  0 

1   0 

1   1 

1   1 

1   1 

1   1 

1 

1 

1 

1 

1   2 

1   3 

40 

41 

1  7 

1   5 

1   3 

1 

1  0 

1   0 

1  0 

1  0 

1   0 

1  0 

1 

0 

1 

0 

1 

0 

1 

0 

1  0 

1   1 

41 

42 

1  7 

1  5 

1   3 

1 

0  59 

0  59 

0  59 

0  59 

0  59 

0  59 

0 

59 

0 

59 

0 

59 

0 

59 

0  59 

0  59 

42 

43 

1  7 

1   5 

1   3 

1 

0  59 

0  59 

0  58 

0  58 

0  58 

0  58 

0 

58 

0 

58 

0 

58 

0 

58 

0  58 

0  58 

43 

44 

1  7 

1   5 

1   3 

1 

0  59 

0  58 

0  57 

0  57 

0  57 

0  57 

0 

57 

0 

57 

0 

57 

0 

57 

0  57 

0  57 

44 

46 

1  7 

1  5 

1   3 

1 

0  59 

0  57 

0  56 

0  56 

0  56 

0  56 

0 

55 

0 

55 

0 

55 

0 

55 

0  55 

0  55 

46 
48 

48 

1  8 

1   6 

1  4 

2 

0  59 

0  57 

0  55 

0  55 

0  55 

0  54 

0 

54 

0 

54 

0 

53 

0 

53 

0  53 

0  53 

50 

1   8 

1   6 

1  4 

2 

0  59 

0  57 

0  55 

0  54 

0  54 

0  53 

0 

53 

0 

53 

0 

52 

0 

52 

0  52 

0  52 

50 

52 

1   9 

1   6 

1  4 

2 

0  59 

0  56 

0  54 

0  53 

0  53 

0  52 

0 

52 

0 

51 

0 

51 

0 

51 

0  50 

0  61 

52 

54 

1  10 

1  7 

1  4 

2 

0  59 

0  56 

0  54 

0  53 

0  52 

0  51 

0 

51 

0 

50 

0 

50 

0 

49 

0  49 

54 

56 

1  10 

1  7 

1  5 

2 

0  59 

0  56 

0  54 

0  52 

0  51 

0  50 

0 

50 

0 

49 

0 

49 

0 

48 

0  47 

56 

58 

1  11 

1  8 

1  5 

3 

0  59 

0  56 

0  53 

0  51 

0  50 

0  49 

0 

49 

0 

48 

0 

48 

0 

47 

58 

60 

1  11 

1  8 

1  5 

3 

0  59 

0  56 

0  53 

0  51 

0  50 

0  49 

0 

48 

0 

47 

0 

47 

0 

46 

60 

62 

1  12 

1  9 

1   6 

3 

0  59 

0  56 

0  53 

0  51 

0  49 

0  48 

0 

47 

0 

47 

0 

46 

62 

64 

1  13 

1   9 

1   6 

3 

0  59 

0  56 

0  53 

0  51 

0  49 

0  48 

0 

47 

0 

46 

0 

45 

64 

6fi 

1  14 

1  10 

1   7 

4 

0  59 

0  56 

0  53 

0  51 

0  49 

0  48 

0 

47 

0 

46 

66 

68 

68 

1  15 

1  11 

1  7 

4 

0  59 

0  56 

0  53 

0  51 

0  49 

0  47 

0 

46 

0 

45 

70 

1  16 

1  11 

1  7 

4 

0  59 

0  55 

0  53 

0  51 

0  49 

0  47 

0 

46 

70 

72 

1  16 

1  12 

1  8 

4 

0  59 

0  55 

0  52 

0  50 

0  48 

0  46 

0 

45 

72 

74 

1  16 

1  12 

1  8 

4 

0  59 

0  55 

0  52 

0  50 

0  48 

0  46 

74 

76 

1  17 

1  12 

1  8 

5 

0  59 

0  55 

0  52 

0  49 

0  47 

0  46 

76 

78 

78 

1  17 

1  12 

1  8 

5 

0  59 

0  55 

0  52 

0  49 

0  47 

80 

1  12 

1  8 

5 

0  59 

0  55 

0  52 

0  49 

0  47 

80 

82 

1  8 

5 

0  59 

0   55 

0  52 

0  49 

82 

84 

5 

0  59 

0  55 

0  52 

0  49 

84 

86 

0  59 

0  55 

0  52 

86 

32" 

34" 

36" 

3>" 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

70°  1 

74°  1  78° 1 

82"  86° 1 

\ 


168                                          TARI.K  XXXIH. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  48*». 

•'"                   APPARENT  ALTITUDE  OF  THE  StTN,  OK  A  STAR. 

App. 

A.pp. 
Alt. 

Alt.  6" 

70 

8» 

9° 

10° 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

o      1    n 

t    n 

/  tf 

t    If 

/  If 

r     ff 

/  ff 

f    It 

1    If 

/  ft 

/    If 

f    II 

/  If 

/  // 

f    If 

f    ft 

0 

%     1  16 

1  17 

1  19 

1  23 

1  29 

1  36 

1  43 

2  1 

2  20 

2  39 

2  58 

3  16 

3  35 

3  54 

4  13 

4  32 

6 

7  1  19 

1  16 

1  17 

1  19 

1  23 

1  28 

1  33 

1.  46 

2  0 

2  16 

2  32 

2  47 

3  2 

3  18 

3  34 

3  50 

7 

8  1  24 

]  19 

1  16 

1  17 

1  19 

1  22 

1  26 

1  35 

1  47 

1  59 

2  12 

2  25 

2  39 

2  53 

3  7 

3  21 

8 

9  1  30 

1  23 

1  18 

1  16 

1  17 

1  19 

1  21 

1  28 

1  37 

1  47 

1  58 

2  9 

2  20 

2  32 

2  44 

2  55 

9 

10  1  37 

1  27 

1  21 

1  18 

1  16 

1  17 

1  18 

1  23 

1  30 

1  38 

1  47 

1  56 

2  6 

2  16 

2  26 

2  36 

10 

11  1  45 

1  33 

1  25 

1  21 

1  18 

1  16 

1  17 

1  20 

1  25 

1  32 

1  39 

1  47 

1  55 

2  4 

2  13 

2  22 

11 

12  1  53 

1  39 

1  30 

1  24 

1  21 

1  18 

1  16 

1  19 

1  22 

1  27 

1  33 

1  40 

1  47 

1  54 

2  2 

2  10 

12 
13 

13  2  2 

1  46 

1  36 

1  28 

1  24 

1  20 

1  18 

1  17 

1  19 

1  23 

1  28 

1  34 

1  40 

1  46 

1  53 

2  0 

14  2  11 

1  54 

1  42 

1  33 

1  27 

1  23 

1  20 

1  16 

1  17 

1  20 

1  24 

1  29 

1  34 

1  39 

1  45 

1  51 

14 

15  2  20 

2  1 

1  48 

1  37 

1  42 

1  30 

1  26 

1  22 

1  17 

1  16 

1  18 

1  21 

1  24 

1  29 

1  33 

1  38 

1  43 

15 

16  2  30 

2  9 

1  54 

1  34 

1  29 

1  24 

1  18 

1  16 

1  17 

1  18 

1  20 

1  24 

1  28 

1  32 

1  37 

16 

17  2  40 

2  17 

2  0 

1  47 

1  38 

1  32 

1  27 

1  20 

1  17 

1  16 

1  17 

1  18 

1  21 

1  25 

1  28 

1  32 

17 

18  2  50 

2  25 

2  7 

1  52 

1  42 

1  35 

1  30 

1  22 

1  18 

1  15 

1  16 

1  17 

1  19 

1  22 

1  25 

1  28 

18 

19  3  0 

2  32 

2  14 

1  58 

1  46 

1  39 

1  33 

1  24 

1  19 

1  16 

1  15 

1  16 

1  17 

1  19 

1  22 

1  24 

19 

20  3  9 

2  40 

2  20 
2  26 

2  3 

1  51 

1  43 

1  36 

1  27 
1  30 

1  21 

1  17 

1  14 

1  15 

1  16 

1  17 
1  16 

1  19 

1  21 

20 

21  3  18 

2  48 

2  9 

1  56 

1  47 

1  40 

1  23 

1  18 

1  15 

1  14 

1  15 

1  17 

1  19 

21 

22  3  27 

2  56 

2  33 

2  15 

2  2 

1  52 

1  43 

1  32 

1  24 

1  19 

1  16 

1  13 

1  14 

1  15 

1  16 

1  18 

22 

23  3  37 

3  3 

2  40 

2  21 

2  7 

1  56 

1  46 

1  35 

1  26 

1  20 

1  16 

1  14 

1  13 

1  14 

1  15 

1  16 

23 

24  3  46 

3  11 

2  47 

2  26 

2  12 

2  0 

1  50 

1  37 

1  27 

1  21 

1  17 

1  14 

1  12 

1  13 

1  13 

1  14 

24 

25  3  56 

3  19 

2  54 

2  32 

2  17 

2  5 

1  54 

1  40 

1  29 

1  22 
1  24 

1  18 

1  15 

1  13 

1  12 

1  12 

1  13 

25 
26 

26  4  5 

3  27 

3  1 

2  38 

2  22 

2  9 

1  58 

1  42 

1  31 

1  19 

1  16 

1  13 

1  11 

1  11 

1  12 

27  4  15 

3  34 

3  8 

2  44 

2  27 

2  14 

2  2 

1  44 

1  33 

1  25 

1  20 

1  16 

1  13 

1  11 

1  10 

1  11 

27 

28  4  24 

3  42 

3  15 

2  50 

2  32 

2  18 

2  6 

1  47 

1  35 

1  27 

1  21 

1  17 

1  14 

1  12 

1  10 

1  10 

28 

29  4  33 

3  50 

3  21 

2  56 

2  37 

2  23 

2  10 

1  50 

1  37 

1  28 

1  22 

1  18 

1  15 

1  12 

1  10 

1  9 

29 

30  4  42 

3  58 

3  28 

3  2 

2  42 

2  27 

2  13 

1  53 

1  40 

1  30 

1  23 

1  19 

1  15 

1  12 

1  '0 

1   9 

30 
31 

31  4  51 

4  6 

3  35 

3  8 

2  47 

2  31 

2  17 

1  57 

1  42 

1  32 

1  25 

1  20 

1    16 

1  13 

1  11 

1  9 

32  5  0 

4  13 

3  42 

3  14 

2  52 

2  35 

2  20 

2  0 

1  44 

1  33 

1  26 

1  21 

1  16 

1  .3 

1  n 

1  9 

32 

33  5  9 

4  21 

3  49 

3  20 

2  57 

2  39 

2  23 

2  3 

1  46 

1  35 

1  27 

1  22 

1  17 

1  14 

1  12 

1  10 

33 

34  5  18 

4  28 

3  55 

3  25 

3  2 

2  44 

2  27 

2  6 

1  49 

1  37 

1  28 

1  23 

1  18 

1  14 

1  12 

1  10 

34 

35  5  27 

4  36 

4   1 

3  31 

3  7 

2  48 

2  31 
2  35 

2  9 

1  52 

1  39 

1  30 

1  24 
1  25 

1  19 

1  15 

1  12 

1  10 

35 

36  5  35 

4  43 

4  8 

3  37 

3  12 

2  52 

2  12 

1  54 

1  41 

1  31 

1  19 

1  15 

1  12 

1  10 

36 

37  5  44 

4  5(1 

4  14 

3  42 

3  17 

2  57 

2  39 

2  16 

1  56 

1  43 

1  33 

1  26 

1  20 

1  16 

1   13 

1  11 

37 

38  5  52 

4  57 

4  20 

3  47 

3  22 

3   1 

2  43 

2  19 

1  59 

1  45 

1  34 

1  27 

1  21 

1  17 

1  14 

1  11 

38 

39  6  0 

5  4 

4  26 

3  53 

3  26 

3  5 

2  47 

2  22 

2  2 

1  47 

1  35 

1  28 

1  22 

1  17 

1  14 

1  11 

39 

40  6  8 

5  11 

4  32 

3  58 

3  30 

3  10 

2  51 

2  25 

2  5 

1  49 

1  37 

1  29 

1  23 

1  18 

1  15 

1  12 

40 

41  6  16 

5  18 

4  38 

4  3 

3  35 

3  14 

2  55 

2  28 

2  7 

1  51 

1  39 

1  31 

1  24 

1  19 

1  16 

1  13 

41 

42  6  24 

5  24 

4  44 

4  8 

3  40 

3  18 

2  58 

2  31 

2  10 

1  53 

1  41 

1  33 

1  26 

1  20 

1  16 

1  13 

42 

43  6  32 

5  31 

4  50 

4  13 

3  44 

3  22 

3  2 

2  33 

2  12 

1  55 

1  43 

1  34 

1  27 

1  21 

1  17 

1  14 

43 

44  6  39 

5  37 

4  55 

4  1? 

3  48 

3  26 

3  5 

2  36 

2  14 

1  57 

1  45 

1  36 

1  28 

1  22 

1  18 

1  15 

44 

46  6  53 

5  49 

5  5 

4  2? 

3  56 

3  34 

3  12 

2  41 

2  18 

2  1 

1  48 

1  38 

1  30 

1  23 

1  18 

1  15 

46 
48 

48  7  7 

6  1 

5  15 

4  37 

4  4 

3  41 

3  18 

2  46 

2  22 

2  5 

1  51 

1  40 

1  31 

1  24 

1  19 

1  16 

50  7  21 

6  13 

5  25 

4  M 

)  4  12 

3  47 

3  2A 

2  51 

2  26 

2  8 

1  53 

1  42 

1  33 

1  25 

1  20 

1  16 

50 

52  7  34 

6  2'1 

\  5  34 

4  5^ 

I  4  20 

3  53 

3  3n 

2  56 

2  30 

2  12 

1  56 

1  44 

1  35 

1  27 

1  22 

1  17 

52 

54  7  47 

6  3£ 

>  5  43 

5  ] 

4  27 

3  59 

3  36 

3   1 

2  34 

2  15 

1  59 

1  46 

1  37 

1  29 

1  23 

1  19 

54 

56  8  C 

»  6  M 

)  5  51 

5  I 

I  4  34 

4  5 

3  41 

3  6 

2  38 

2  18 

2  2 

1  49 

1  39 

1  31 

1  25 

1  20 

56 

58 

5  59 

5   11 

5  4  40 
4  46 

4  11 
4  16 

3  U 
3  5C 

3  54 

)  3  10 

I  3  13 

I  3  15 

3  17 

2  42 
2  45 
2  47 
2  49 
2  51 

2  21 
2  23 
2  25 
2  27 
2  29 

2  4 
2  6 
2  8 
2  10 
2  11 

1  51 
1  53 
1  54 
1  56 
1  57 

1  41 

1  42 
1  43 
1  45 
1  46 

1  32 
1  33 
1  34 
1  35 
1  36 

1  26 
1  27 
1  28 
1  28 
1  29 

1  30 

1  30 

1  21 
1  21 
1  22 
1  22 
1  23 

58 
60 
62 
64 
66 

TABLE  P.  EFFECT  OF  SUN's  PAE 

Add  the  Numbers  above  the 
lines to^rd  Corrertion, sub- 
tract the  others. 

f   "  Sun's  Apparent  Altitude. 
App    .. 

2  31 

2  12 
2  13 

1  58 
1  59 

!  47 
1  48 

1  37 
1  38 

1  24 
1  24 

68 
70 

Alt.  5  10 

•20  3(l4f 

50 

60  7 

O80 

[90 

tl        1 

It      f       »t 





ff 

ff 

2  0 

1  49 

1  39 

1  31 

1  24 

72 

5  0  1 

2  3  4 

5 

1  50 

1  40 

1  32 

1  25 

74 

10  1  1 
20  3  3 
30  5  5 
40  7  6 
50  9  8 
60    9 

1  2  3 

1  0  1 
3  2  1 
543 

6  5  4 
8  6  5 

4 
2 
0 
2 

3 
4 

5 

3  J 
1  V 

1  i 

2  \ 

3  : 

r  1 

0 

1  41 

1  33 

1  25 

76 

78 
80 
82 
84 

1  33 

1  26 
1  26 

70 
80 

9(1 

9  7  fi 

8  7 

7 

5 

6 

4 

. 

86 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  48°. 

App. 
Alt. 

APPARENT  ALTITUDE  OF  THE  SUN, 

OB  STAR. 

32* 

34° 

36° 

38° 

42° 

46° 

50° 

64° 

58° 

62° 

66° 

70° 

74° 

78° 

82° 

86° 

0 

t    n 

/  // 

/  n 

r 

>r 

/    n 

/  It 

t    n 

;  ti 

/  // 

/  ti 

/ 

// 

/ 

// 

t 

// 

/ 

// 

/ 

ti 

/  // 

6 

4  51 

5  10 

5   28 

5 

46 

6  18 

6  49 

7  19 

7  47 

7 

4  6 

4  21 

4  36 

4 

51 

5  19 

5  45 

6  11 

6  35 

7 

8 

3  34 

3  iS 

4  1 

4 

14 

4  38 

5  1 

5  22 

5  42 

6  1 

8 

9 

3  7 

3  19 

3  30 

3 

41 

4  3 

4  24 

4  43 

5  0 

5  17 

9 

10 

2  47 

2  57 

2  40 

3  7 

3 

17 

3  36 

3  54 

4  11 

4  26 

4  40 

10 

11 

2  31 

2  49 

2 

57 

3  14 

3  30 

3  44 

3  57 

4  10 

11 

•12 

2  17 

2  25 

2  33 

2 

40 

2  55 

3  9 

3  22 

3  34 

3  45 

3  55 

12 

13 

2  6 

2  13 

2  20 

2 

27 

2  40 

2  52 

3  4 

3  15 

3  25 

3  32 

13 

14 

1  57 

2  4 

2  10 

2 

16 

2  27 

2  38 

2  49 

2  59 

3  8 

3  15 

14 

15 

1  49 

1  55 

2  1 

2 

6 

2  16 

2  26 

2  35 

2  44 

2  53 

3  0 

15 
16 

16 

1  42 

1  47 

1  52 

57 

2  7 

2  15 

2  23 

2  32 

2  40 

2  46 

2 

52 

17 

1  36 

1  41 

1  45 

50 

1  59 

2  6 

2  14 

2  22 

2  29 

2  34 

2 

40 

17 

18 

1  31 

1  35 

1  39 

43 

1  51 

1  59 

2  6 

2  13 

2  19 

2  24 

2 

29 

18 

19 

1  27 

1  31 

1  34 

38 

1  45 

1  52 

1  58 

2  4 

2  10 

2  15 

2 

19 

19 

20 

1  24 

1  27 

1  30 

33 

1  39 

1  45 

1  51 

1  57 

2  2 

2  7 

2 

11 

2 

15 

__ 

20 

21 

1  22 

1  24 

1  27 

29 

1  34 

1  40 

1  45 

1  51 

1  56 

2  0 

2 

4 

2 

7 

21 

22 

1  20 

1  22 

1  24 

26 

1  30 

1  35 

1  40 

1  45 

1  50 

1  54 

57 

59 

22 

23 

1  18 

1  19 

1  21 

23 

1  27 

1  31 

1  36 

1  40 

1  45 

1  49 

51 

53 

23 

24 

1  16 

1  17 

1  19 

21 

1  25 

1  28 

1  32 

1  36 

1  40 

1  44 

46 

48 

50 

^ 

24 

25 

26 

1  14 

1  15 

1  16 

18 

1  22 

1  25 

1  29 

1  32 

1  36 

1  39 
1  34 

41 

43 

45 

25 

1  12 

1  13 

1  14 

16 

1  19 

1  23 

1  26 

1  29 

1  32 

1 

36 

38 

40 

26 

27 

1  11 

1  12 

1  13 

14 

1  17 

1  20 

1  23 

1  26 

1  28 

1  30 

32 

34 

36 

27 

28 

1  10 

1  11 

1  12 

13 

1  15 

1  18 

1  20 

1  23 

1  25 

1  27 

28 

30 

32 

34 

28 

29 

1  9 

1  10 

1  11 

12 

1  14 

1  16 

1  18 

1  20 

1  22 

1  24 

25 

27 

28 

30 

29  1 

30 

1  9 

1  10 

1  10 

11 

1  12 

1  14 

1  16 

1  18 

1  19 

1  21 

22 

24 

25 

26 

30 

31 

1  9 

1  9 

1  9 

10 

1  11 

1  12 

1  14 

1  16 

1  17 

1  19 

20 

21 

22 

23 

31 

32 

1  8 

1  8 

1  8 

9 

1  10 

1  11 

1  13 

1  14 

1  15 

1  17 

18 

19 

19 

20 

21 

32 

33 

1  8 

1  7 

1  7 

8 

1  9 

1  10 

1  11 

1  12 

1  13 

1  15 

16 

17 

17 

17 

18 

33 

34 

1  8 

1  6 

1  6 

7 

1  8 

1  9 

1  10 

1  11 

1  12 

1  13 

14 

14 

15 

15 

J 

16 

34 

35 

1  8 

1  6 

1  5 

G 

1  7 

1  8 

1  9 

1  9 

1  10 

1  11 

12 

12 

13 

13 

14 

13 

35 
36 

36 

1  8 

1  6 

1  5 

5 

1  5 

1   6 

1  7 

1  7 

1  8 

1  9 

10 

10 

11 

11 

12 

37 

1  9 

1  7 

1  5 

4 

1  4 

1   5 

1  6 

1  6 

1  7 

1  7 

8 

8 

9 

9 

10 

•  11 

37 

38 

1   9 

1  7 

1  5 

3 

1  3 

1   4 

1  5 

1  5 

1  6 

1  6 

7 

7 

8 

8 

8 

!   9 

38 

39 

1   9 

1  7 

1  5 

3 

1  3 

1   3 

1  4 

1  4 

1  5 

1  5 

6 

6 

6 

7 

7 

J  7 

39 

40 

1   9 

1  7 

1  5 

3 

1  2 

1   2 

1  3 

1  3 

1  4 

1   4 

5 

5 

5 

6 

6 

1  6 
1  t 

40 
41 

41 

1  10 

1  8 

1  5 

3 

1   1 

1   1 

1  2 

1  2 

1  3 

1  3 

4 

4 

4 

5 

5 

42 

1  1-0 

1  8 

1  5 

3 

1   1 

1   1 

1   1 

1  2 

1  2 

1  2 

3 

3 

3 

4 

4 

1  4 

42 

43 

1  11 

1  8 

1  6 

4 

1   1 

1   0 

1  0 

1   1 

1   1 

1   1 

2 

2 

2 

3 

3 

1  3 

43 

44 

1  12 

1  9 

1   6 

4 

1   1 

1  0 

1  0 

1  0 

1   0 

1  0 

1 

1 

1 

1 

1 

1  1 

44 

46 

1  12 

1  9 

1  6 

4 

1   1 

0  59 

0  59 

0  59 

0  59 

0  59 

0 

59 

0 

59 

0 

59 

0 

59 

0 

59 

0  59 

46_ 
48 

48 

1  13 

1  10 

1  7 

4 

1  1 

0  59 

0  58 

0  58 

0  58 

0  58 

0 

57 

0 

57 

0 

57 

0 

57 

0 

57 

0  67 

50 

1  13 

1  10 

1  7 

5 

1   1 

0  59 

0  57 

0  57 

0  57 

0  57 

0 

56 

0 

56 

0 

56 

0 

56 

0 

56 

50 

52 

1  14 

1  11 

1  8 

5 

1   1 

0  59 

0  57 

0  56 

0  56 

0  56 

0 

55 

0 

55 

0 

54 

0 

54 

0 

54 

52 

54 

1  15 

1  11 

1  8 

6 

1  2 

0  59 

0  57 

0  56 

0  55 

0  55 

0 

54 

0 

54 

0 

53 

0 

53 

54 

56 

1  15 

1  11 

1  8 

6 

1   2 

0  59 

0  57 

0  55 

0  54 

0  54 

0 

53 

0 

53 

0 

52 

0 

52 

56 

58 

1  16 

1  12 

1  9 

6 

1  2 

0  59 

0  57 

0  55 

0  54 

0  53 

0 

52 

0 

52 

0 

51 

.  68  1 

60 

1  16 

1  12 

1  9 

6 

1  2 

0  59 

0  57 

0  55 

0  53 

0  52 

0 

52 

0 

51 

0 

50 

60 

62 

1  17 

1  13 

1  10 

7 

1  2 

0  59 

0  57 

0  55 

0  53 

0  52 

0 

51 

0 

51 

62 

64 

1  17 

1  13 

1  10 

7 

1  2 

0  59 

0  57 

0  55 

0  53 

0  52 

0 

51 

0 

50 

64 

66 

68 

1  18 

1  14 

1  10 

7 

1  3 

0  59 

0  57 

0  54 

0  52 

0  51 

0 

50 

66 

1  18 

1  14 

1  10 

7 

1  3 

0  59 

0  56 

0  54 

0  52 

0  51 

0 

50 

68 

70 

1  19 

1  15 

1  11 

8 

1  3 

0  59 

0  56 

0  54 

0  52 

0  51 

70 

72 

1  19 

1  15 

1  11 

8 

1  3 

0  59 

0  56 

0  54 

0  52 

0  50 

72 

74 

1  20 

1  15 

1  11 

8 

1  3 

0  59 

0  56 

0  53 

0  51 

74 

76 

1  20 

1  16 

1  12 

8 

1  3 

0  59 

0  56 

0  53 

0  51 

76 

78 

1  21 

1  16 

1  12 

9 

1   4 

0  59 

0  56 

0  53 

78 

80 

1  21 

1  16 

1  12 

9 

1   4 

0  59 

0  56 

0  53 

80 

82 

1  21 

1  16 

1  12 

9 

1   4 

0  59 

0  56 

82 

84 

1  16 

1  12 

9 

1   -1 

0  59 

0  56 

84 

86 

1  12 

9 

1   -1 

0  59 

86 

32^ 

34° 

36° 

38° 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

70° 

74° 

78° 

82° 

86° 

170                 TABLE  XXXIII. 

1 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  62='. 

9 

Fs" 

APPARENT  ALTITUDE  OF  THE  SUN,  OR  STAR. 

D's 

App 

Alt. 

App. 

Alt. 

6» 

70 

30 

90 

lO* 

11» 

12° 

140 

16° 

18° 

20° 

22° 

24° 

26°  1 

2B°  1 

30° 

o 

t    It 

/  // 

/  // 

t    n 

/  fi 

1    II 

/  // 

/  n 

/  II 

/  // 

1    II 

1    II 

1 

// 

1 

// 

1 

If 

/ 

// 

0 

6 

1  18 

1  19 

1  21 

1  24 

1  30 

1  37 

1  44 

2  0 

2  17 

2  34 

2  51 

3  10 

3 

28 

3 

47 

4 

6 

4 

24 

6 

7 

1  21 

1  18 

1  19 

1  21 

1  24 

1  29 

1  34 

1  46 

2  0 

2  14 

2  28 

2  42 

2 

57 

3 

12 

3 

27 

3 

43 

7 

8 

1  25 

1  21 

1  18 

1  19 

1  21 

1  24 

1  27 

1  36 

1  47 

1  58 

2  11 

2  23 

2 

36 

2 

50 

3 

3 

3 

16 

8 

9 

1  30 

1  24 

1  20 

1  18 

1  19 

1  21 

1  23 

1  29 

1  37 

1  47 

1  57 

2  8 

2 

19 

2 

31 

2 

42 

2 

53 

9 

10 

1  37 

1  28 

1  23 

1  20 

1  18 

1  19 

1  21 

1  25 

1  30 

1  38 

1  46 

1  56 

2 

6 

2 

16 

2 

26 

2 

36 

10 

11 

1  45 

1  34 

1  28 

1  23 

1  20 

1  18 

1  19 

1  22 

1  26 

1  32 

1  39 

1  47 

5Q 

2 

4 

2 

13 

2 

22 

11 

12 

1  54 

1  41 

1  33 

1  27 

1  22 

1  20 

1  18 

1  20 

1  23 

1  27 

1  33 

1  40 

47 

54 

2 

2 

2 

10  12  1 

13 

2  2 

1  48 

1  38 

1  31 

1  25 

1  22 

1  19 

1  19 

1  21 

1  24 

1  29 

1  35 

41 

47 

54 

2 

1 

13  1 

14 

2  11 

1  55 

1  44 

1  35 

1  28 

1  24 

1  21 

1  18 

1  19 

1  22 

1  26 

1  30 

35 

41 

47 

52 

14  " 

15 

2  19 

2  2 

1  50 

1  39 

1  32 

1  27 

1  23 

1  19 

1  18 

1  20 

1  23 

1  26 

30 

35 

40 

44 

15 

16 

16 

2  28 

2  9 

1  55 

1  44 

1  35 

1  30 

1  25 

1  20 

1  17 

1  18 

1  20 

1  23 

26 

30 

1 

34 

38 

17 

2  37 

2  16 

2  0 

1  48 

1  39 

1  33 

1  27 

1  21 

1  18 

1  17 

1  18 

1  20 

23 

26 

30 

33 

17 

18 

2  46 

2  23 

2  6 

1  53 

1  43 

1  36 

1  30 

1  23 

1  19 

1  16 

1  17 

1  18 

20 

23 

■1 

26 

29 

18 

19 

2  56 

2  30 

2  12 

1  59 

1  48 

1  40 

1  33 

1  25 

1  20 

1  17 

1  16 

1  17 

18 

20 

^ 

23 

26 

19 

20 

3  5 

2  37 

2  18 

2  4 

1  52 

1  44 

1  37 

1  27 

1  22 

1  18 

1  15 

1  16 

17 

18 

20 

23 

20 

21 

3  14 

2  44 

2  24 

2  9 

1  57 

1  48 

1  40 

1  29 

1  23 

1  19 

1  16 

1  16 

16 

17 

18 

20 

21 

22 

3  23 

2  52 

2  31 

2  15 

2  1 

1  52 

1  44 

,1  32 

1  25 

1  20 

1  16 

1  15 

15 

16 

17 

18 

22 

23 

3  32 

2  59 

2  38 

2  20 

2  6 

1  56 

1  47 

1  34 

1  26 

1  21 

1  17 

1  15 

14 

15 

16 

17 

23 

24 

3  41 

3  7 

'2  44 

2  26 

2  11 

2  0 

1  51 

1  37 

1  28 

1  22 

1  18 

1  15 

14 

14 

16 

16 

24 

25 
26 

3  50 

3  14 

2  51 

2  31 

2  16 

2  4 

1  54 

1  40 

1  30 

1  23 

1  19 

1  16 

14 

13 

14 

15 

25 

3  59 

3  22 

2  58 

2  37 

2  21 

2  8 

1  58 

1  42 

1  32 

1  25 

1  20 

1  16 

14 

. 

13 

13 

14 

26 

27 

4  8 

3  30 

3  5 

2  42 

2  26 

2  12 

2  2 

1  45 

1  33 

1  26 

1  21 

1  17 

15 

14 

13 

13 

27 

28 

4  17 

3  38 

3  12 

2  48 

2  31 

2  16 

2  6 

1  48 

1  35 

1  28 

1  22 

1  18 

15 

14 

13 

13 

28 

29 

4  26 

3  45 

3  19 

2  53 

2  36 

2  21 

2  10 

1  51 

1  37 

1  29 

1  23 

1  19 

16 

14 

13 

12  29  1 

30 
31 

4  34 

3  53 

3  25 

2  59 

2  41 

2  25 

2  13 

1  54 

1  39 

1  31 

1  24 

1  19 

16 

14 

13 

12  30  1 

4  43 

4  0 

3  32 

3  5 

2  45 

2  29 

2  17 

1  57 

1  41 

1  32 

1  25 

1  20 

17 

15 

13 

12 

31 

32 

4  52 

4  3 

3  38 

3  10 

2  50 

2  34 

2  20 

1  59 

1  43 

1  34 

1  27 

1  21 

17 

15 

13 

12 

32 

33 

5  0 

4  15 

3  44 

3  16 

2  55 

2  38 

2  24 

2  2 

1  45 

1  36 

1  29 

1  23 

18 

15 

13 

12 

33 

34 

5  9 

4  22 

3  50 

3  21 

2  59 

2  42 

2  27 

2  5 

1  48 

1  38 

1  30 

1  24 

19 

16 

14 

12 

34 

35 

5  17 

4  29 

3  56 

3  27 

3  4 

2  46 

2  31 

2  7 

1  51 

1  40 

1  32 

1  25 

20 

17 

14 

12 

35 
36 

36 

5  26 

4  36 

4  2 

3  32 

3  9 

2  50 

2  34 

2  10 

1  53 

1  42 

1  33 

1  26 

21 

17 

14 

12 

37 

5  34 

4  42 

4  8 

3  37 

3  14 

2  54 

2  38 

2  13 

1  56 

1  44 

1  34 

1  27 

22 

18 

15 

13 

37 

38 

5  42 

4  49 

4  13 

3  42 

3  18 

2  58 

2  42 

2  16 

1  58 

1  46 

1  36 

1  28 

22 

18 

15 

13 

38 

39 

5  50 

4  56 

4  19 

3  47 

3  23 

3  2 

2  46 

2  19 

2  1 

1  48 

1  38 

1  30 

23 

18 

15 

13 

39 

40 

5  58 

5  3 

4  24 

3  52 

3  27 

3  6 

2  49 

2  22 

2  3 

1  50 

1  39 

1  31 

25 

19 

16 

14 

40 
41 

41 

6  6 

5  9 

4  30 

3  57 

3  32 

3  10 

2  53 

2  25 

2  6 

1  52 

1  41 

1  32 

26 

20 

16 

14 

42 

6  14 

5  15 

*  35 

4  2 

3  36 

3  14 

2  56 

2  28 

2  8 

1  54 

1  42 

1  34 

27 

21 

17 

15 

42 

43 

6  21 

5  21 

4  41 

4  7 

3  40 

3  18 

3  C 

2  31 

2  11 

1  56 

1  44 

1  35 

28 

22 

18 

15 

43 

44 

6  28 

5  27 

4  46 

4  12 

3  44 

3  22 

3  3 

2  34 

2  13 

1  58 

1  45 

1  37 

29 

23 

19 

16 

44 

46 

6  42 

5  39 

4  56 

4  21 

3  52 

3  29 

3  IC 

2  39 

2  18 

2  1 

1  48 

1  39 

31 

24 

20 

17 

46 
48 

48 

6  55 

5  51 

5  6 

4  30 

3  59 

3  36 

3  16 

2  44 

2  22 

2  5 

1  51 

1  41 

33 

26 

21 

18 

50 

7  8 

6  2 

5  16 

4  38 

4  7 

3  43 

3  23 

2  49 

2  26 

2  8 

1  54 

1  43 

35 

27 

22 

19 

50 

52 

7  21 

6  13 

5  25 

4  46 

4  15 

3  50 

3  2S 

2  54 

2  30 

2  11 

1  57 

1  45 

36 

29 

24 

20 

52 

54 

7  33 

6  23 

5  34 

4  53 

■4  22 

3  56 

3  3S 

2  59 

2  34 

2  14 

2  0 

1  48 

38 

31 

25 

21 

54 

56 

7  44 

6  33 

5  43 

4  59 

4  29 

4  2 

3  4C 

3  4 

2  38 

2  17 

2  2 

1  50 

40 

32 

26 

22 

56 
58 

58 

7  53 

6  42 

5  50 

5  6 

4  35 

4  7 

3  45 

3  8 

2  42 

2  20 

2  5 

1  53 

42 

33 

27 

23 

60 

8  2 

6  49 

5  56 

5  12 

4  40 

4  12 

3  5C 

3  12 

2  46 

2  23 

2  7 

1  55 

44 

35 

29 

24 

60 

62 

6  2 

5  14 

4  45 

4  16 

3  54 

3  15 

2  49 

2  26 

2  9 

1  57 

46 

36 

30 

25 

62 

64 

4  50 

4  20 

3  58 

3  18 

2  51 

2  28 

2  11 

1  59 

48 

37 

31 

26 

64 

66 

4  1 

3  20 

2  53 

2  30 

2  13 

2  0 

49 

39 

32 

26 

66 

68 

3  22 

2  54 

2  32 

2  15 

2  1 

50 

40 

33 

27 

68 

70 

2  55 

2  33 

2  16 

2  2 

51 

41 

34 

28 

70 

72 

2  34 

2  17 

2  3 

52 

42 

34 

28 

72 

74 

2  18 

2  4 

53 

43 

35 

29 

74 

76 

2  5 

54 

44 

36 

29 

76 

78 

1 

55 

44 

36 

30 

78 

80 

45 

37 

30 

80 

82 

38 

30 

82 

84 

31 

84 

86 

86 

6" 

70 

8° 

9" 

10° 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

TABLE  XXXllI. 

171 

THIRD  CORRECTION.  TO  APPARENT  DISTANCE  52°. 



D's 

APPARENT   ALTITUDE    OF   THE    SUN. 

OR    STAR. 

•  V 

App. 

Alt. 

App 
Alt. 

32° 

340 

36° 

38° 1  42° 

46° 

50° 

54^     58° 

62° 

66° 

70° 

74° 

78° 

82° 

86° 

o 

r    n 

/    n 

t    II 

/ 

/' 

/ 

// 

/    II 

/    II 

/    // 

/    n 

r    II 

1 

// 

/ 

// 

f    // 

/    // 

/    // 

1   ft 

■> 

6 

4  43 

5      1 

5   18 

5 

34 

6 

6 

6  36 

7     4 

7   29 

7  53 

6 

7 

3   59 

4  14 

4  29 

4 

43 

5 

9 

5  34 

5   58 

6  20 

6  42 

7 

8 

3  30 

3  43 

3  55 

4 

8 

4 

30 

4  52 

5   13 

5  32 

5  50 

6     6 

8 

9 

3     4 

3   15 

3  26 

3 

37 

3 

58 

4   17 

4  36 

4  51 

5     5 

5   18 

9 

10 

2  45 

2  54 
2  38 

3     4 

3 

14 

3 

32 

3  48 

4     4 

4  20 

4  33 
4     6 

'4  45 

10 
11 

11 

2  30 

2  47 

2 

55 

3 

11 

3  26 

3  40 

3   54 

4  10 

12 

2   17 

2  25 

2  32 

2 

40 

2 

54 

3     7 

3   20 

3  32 

3  43 

3  52 

4 

1 

12 

13 

2     7 

2   13 

2  20 

2 

26 

2 

39 

2  51 

3     3 

3   14 

3  24 

3  32 

3 

38 

13 

14 

1   58 

2     3 

2     9 

2 

14 

2 

26 

2  37 

2  48 

2  58 

3     7 

3   14 

3 

20 

14 

15 

1    49 

1   54 

1   59 

2 

4 
56 

2 

15 

2   26 

2  35 

2  44 

2  52 

2  59 

3 

5 

15 

16 

1   42 

1   47 

1   51 

2 

7 

2   16 

2  24 

2  32 

2  40 

2  46 

2 

52 

2 

57 

16 

17 

1   37 

1   41 

1    45 

50 

2 

0 

2     8 

2   15 

2  22 

2  29 

2  35 

2 

40 

2 

44 

17 

18 

1    32 

1   36 

1    40 

45 

53 

2     0 

2     7 

2   13 

2   19 

2  25 

2 

30 

2 

33 

18 

19 

1   29 

1   32 

1   36 

40 

47 

1   53 

2     0 

2     6 

2   11 

2   10 

2 

21 

2 

24 

19 

20 

1   26 

1   29 

1   32 

35 

— 

41 
37 

1   47 

1   53 
1   47 

1   59 

2     4 

2     9 

2 

13 

2 

16 

2   19 

20 

21 

1   23 

1   26 

1   28 

31 

1   42 

1   53 

1   58 

2     2 

2 

6 

2 

9 

2  11 

21 

22 

1   21 

1   23 

1   25 

28 

33 

1   37 

1   42 

1   47 

1   52 

1   56 

59 

2 

2 

2     4 

22 

23 

1    19 

1   21 

1   23 

25 

29 

1   33 

1   38 

1   42 

1   47 

1   51 

54 

56 

1  58 

23 

24 

1   17 

I    19 

1   21 

23 

26 

1   30 

1   34 

1   38 

1   42 

1   46 

49 

51 

1   53 

1   55 

24 

25 

1    16 

1    17 

1   19 

20 

23 
21 

1   27 

1   30 

1   34 

1   37 

1   41 

44 

46 

1   48 

1   49 

25 

26 

1    15 

1    16 

1   17 

18 

1   24 

1   27 

1   30 

1   33 

1   36 

39 

41 

1   43 

1   44 

26 

27 

1    14 

1    15 

1    16 

17 

19 

1   22 

1   24 

1   27 

1   30 

1   32 

35 

37 

1   39 

1   40 

27 

28 

1    13 

1    14 

1    15 

16 

17 

1   20 

1   22 

1   24 

1   27 

1   29 

31 

33 

1   35 

1   36 

1   37 

28 

29 

1    12 

1    13 

1    14 

15 

16 

1    18 

1   20 

1   22 

1   24 

1   26 

28 

30 

1   31 

1   32 

1   33 

29 

30 

1    12 

1    12 

1    13 

13 

14 

1    16 

1    18 

1   20 

1   22 

1   24 

25 

27 
24 

1   28 

1   29 

1   30 

30 

31 

1    11 

1    11 

1    12 

12 

13 

1    15 

1   16 

1    18 

1   20 

1   22 

23 

1   25 

1   2« 

1   27 

31 

32 

1    11 

1    11 

1    11 

11 

12 

1    14 

1   15 

1    16 

1    18 

1   20 

21 

22 

1   23 

1   23 

1   24 

1   25 

32 

33 

1    11 

1    10 

1    10 

10 

11 

1   13 

1   14 

1    15 

1    17 

1    18 

19 

20 

1   21 

1   21 

1   22 

1   22 

33 

34 

1    11 

1    10 

1    10 

10 

11 

1    12 

1    13 

1   14 

1    16 

1    17 

17 

18 

1    19 

1    19 

1   20 

1   20 

34 

35 

1    11 

1    10 

1    10 

10 

10 

1    11 

1   12 

1   13 

1   14 

1   15 

15 

16 

1   17 

1    17 

1    18 

1   18 

35 

36 

1    11 

1    10 

1     9 

9 

9 

1   10 

1    11 

1   11 

1   12 

1   13 

13 

14 

1    15 

1    15 

1    16 

1   16 

3^ 

37 

1    11 

1    10 

1     9 

9 

9 

1     9 

1   10 

1   10 

1    11 

1    11 

12 

12 

1    13 

1   13 

1    14 

1   14 

37 

38 

1    11 

1    10 

1      9 

8 

8 

1     9 

1      9 

1     9 

1   10 

1   10 

11 

11 

1    11 

1    11 

1    12 

1   12 

38 

39 

1    11 

1    10 

1      9 

8 

8 

1      8 

1      8 

1     8 

1     9 

1     9 

10 

10 

1    10 

1    10 

1    10 

1   10 

39 

40 

1    12 

1    10 

1     9 

8 

7 

1     7 

1     7 

1      7 

1     8 

1     8 

9 

9 

1     9 

1     9 

1     9 

1      9 

40 
41 

41 

1    12 

1  11 

1      9 

8 

7 

1     7 

1     7 

1     7 

1      7 

1     7 

8 

8 

1     8 

1      8 

1     8 

1     8 

42 

1    13 

1  11 

1      » 

8 

6 

1      6 

1     6 

1      6 

1     6 

1     6 

7 

7 

1      7 

1     7 

1      7 

1      7 

42 

43 

1    13 

1  11 

1      9 

8 

6 

1     6 

1     6 

1     6 

1     6 

1     6 

6 

6 

1      6 

1     6 

1     6 

1     6 

43 

44 

1    14 

1  11 

1     9 

8 

6 

1     5 

1     5 

1     5 

1     5 

1     5 

5 

5 

1     5 

1     5 

1     5 

1     5 

44 

46 

1    14 

1    12 

1    10 

9 

6 

1      4 

1     4 
1     3 

1     4 

1     4 

1     4 

4 

3 

1     3 

1     3 

1     3 

46 

48 

1    15 

1    13 

1    11 

9 

6 

1     4 

1     3 

1     3 

1     2 

1 

2 

1 

1      1 

1      1 

1      1 

48 

50 

1    16 

1   14 

1    11 

9 

6 

1     4 

1      2 

1     2 

1     2 

1      1  1 

1 

0 

1     0 

1     0 

50 

52 

1   17 

1    15 

1    12 

9 

6 

1     4 

1     2 

1      1 

1     1 

1     0 

1 

0 

0 

59 

0  58 

52 

54 

1    18 

1    15 

1    12 

9 

6 

1     4 

1      2 

1      1 

1     0 

0  59 

0 

59 

0 

58 

0  57 

54 

56 

1    18 

1    15 

1   12 

10 

6 

1     4 

1      2 

1     0 

0  59 

0  58 

0 

58 

0 

57 

0  56 

56 

58 
60 
62 

1   19 

1   20 
1   21 

1    16 
1    16 
1    17 

1    13 

1    13 
1    13 

10 
10 

10 

6 

7 
7 

1     4 
1     4 

1      4 

1     2 
1     2 
1      1 

1     0 
1     0 

0  59 

0  59 

0  58 
0  58 

0  58 
0  57 
0  56 

0 
0 
0 

57 
56 
55 

0 
0 

56 
55 

TABLK  P.  EFFECT  OF  SHN's  PAS 

AtU  the  Numiers  above  the 

64 

1    22 

1    18 

1    14 

11 

7 

1     4 

1      1 

0  59 

0  57 

0  56 

u 

54 

lines  to  3rd  Ccrrection,  sub- 

66 

1    22 

1    18 

1    14 

11 

7 

1      4 

I      1 

0  59 

0  57 

0  55 
0  54 

tract  the  others. 

)8 

App 
Alt. 

Sun's  Apparent  Altitude  | 

68 

1   22 

1    18 

1    14 
1    14 

1 1 

7 

1     3 
1      3 

1     0 
1     0 

0  58 
0  58 

0  56 
0  56 

70 

1   23 

1    18 

11 

7 

5  10-2 

3  30 

40  5 

0  60 

70  5 

3090 

72 

1    23 

1    19 

1    15 

11 

7 

1     3 

1      0 

0  57 

0  55 

tr     n     II 

/' 

it      / 

n 

// 

" 

74 

1    24 

1    19 

1    15 

11 

7 

1     3 

1      0 

0   57 

5 

0    1    2 

3 

4    4 

76 

1    24 

1    19 

1    15 

12 

7 

1     3 

1      0 

0  56 

10 
20 

r  1  \_ 
331 

2 
0 

3   -i 
1    0 

4 

3 
1 

78 

1    24 

1    19 

1    15 

12 

7 

1      3 

1     0 

30 

5  4  3 

"a 

r  0 

0 

80 

1    24 

1    19 

1    15 

12 

7 

1     3 

1      0 

40 

7   6   5 

4 

3  2 

1 

1 

B   0 

82 

1   25 

1    20 

1    16 

12 

7 

1      3 

50 

B   8  6 

5 

4  3 

3 

0 

2 

84 

1    25 

1    20 

1    16 

12 

7 

1      3 

60 
70 
80 

90 

9  7 

6 

5  4 

4 

3 

86 

1   25 

1    21 

1    16 

12 

7 

ei 

V 
8 

6  ti 

7  6 

7 

5 

32° 

34° 

36° 

oqo 

42° 

46° 

50° 

54° 

58° 

62° 

aao 

70°   1 

HM^ 

'-' 

172                 TABLE  XXXIII. 

1 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  56°.               1 

J's 

APPARENT  ALTITUDE  OF  THE 

SUN, 

OR  STAR. 

:D's| 

App. 
Alt. 

App 

6° 

70 

8° 

Q*' 

100 

11° 

12° 

14° 

16° 

18°  1 

20° 

22° 

24° 

26° 

28° 

30° 

Alt. 

o 

/  // 

r  // 

f    ff. 

/  ff 

/  // 

/  ff 

r     ff 

r     rr 

1    ft 

/ 

// 

t 

n 

/  // 

/ 

// 

/  // 

/  ff 

/  // 

0 

6 

1  20 

1  22 

1  25 

1  29 

1  35 

1  41 

1  48 

2  2 

2  18 

2 

35 

2 

52 

3  10 

3 

27 

3  45 

4  3 

4  20 

6 

7 

1  23 

1  20 

1  22 

1  24 

1  27 

1  32 

1  37 

1  48 

2  1 

2 

15 

2 

29 

2  43 

2 

58 

3  12 

3  27 

3  42 

7 

8 

1  28 

1  23 

1  20 

1  21 

1  23 

1  26 

1  29 

1  38 

1  48 

2 

0 

2 

12 

2  23 

2 

35 

2  48 

3  1 

3  14 

8 

9 

1  34 

1  27 

1  22 

1  20 

1  21 

1  23 

1  25 

1  31 

1  39 

48 

58 

2  8 

2 

18 

2  29 

2  40 

2  50 

9 

10 

1  40 

1  31 

1  25 

1  22 

1  20 

1  21 

1  22 

1  26 

1  32 

39 

48 

1  56 

2 

5 

2  15 

2  24 

2  33 

10 

11 

1  47 

1  30 

1  29 

1  25 

1  22 

1  20 

1  21 

1  23 

1  27 

33 

4!^ 

1  47 

55 

2  4 

2  12 

2  20 

11 

12 

1  54 

1  42 

1  33 

1  28 

1  24 

1  21 

1  20 

1  21 

1  24 

28 

34 

1  40 

47 

1  55 

2  2 

2  9 

12 

13 

2  2 

1  48 

1  38 

1  31 

1  26 

1  23 

1  21 

1  20 

1  22 

25 

30 

1  35 

41 

1  47 

1  54 

2  0 

13 

14 

2  10 

1  54 

1  43 

1  35 

1  29 

1  25 

1  22 

1  19 

1  20 

23 

27 

1  31 

36 

1  41 

1  47 

1  52 

14 

15 

2  18 

2  1 

1  48 

1  39 

1  33 

1  28 

1  24 

1  21 

1  19 

21 

24 

1  27 

32 

1  36 

1  41 

1  46 

15 
16 

16 

2  27 

2  8 

1  53 

1  43 

1  36 

1  31 

1  26 

1  22 

1  19 

19 

21 

1  24 

28 

1  32 

1  36 

1  40 

17 

2  35 

2  15 

1  59 

1  47 

1  40 

1  34 

1  29 

1  23 

1  20 

18 

19 

1  22 

25 

1  28 

1  32 

1  35 

17 

18 

2  44 

2  22 

2  4 

1  52 

1  43 

1  37 

1  31 

1  25 

1  20 

17 

18 

1  20 

22 

1  25 

1  28 

1  31 

18 

19 

2  53 

2  29 

2  10 

1  57 

1  47 

1  40 

1  34 

1  26 

1  21 

18 

17 

1  19 

20 

1  23 

1  25 

1  28 

19 

20 

3  2 

2  36 

2  16 

2  2 

1  51 

1  44 

1  37 

1  28 

1  22 

19 

17 

1  18 

19 

1  21 

1  23 

1  25 

20 

21 

3  11 

2  44 

2  22 

2  8 

1  55 

1  47 

1  40 

1  30 

1  24 

20 

18 

1  17 

18 

1  19 

1  21 

1  23 

21 

22 

3  20 

2  51 

2  29 

2  13 

2  0 

1  51 

1  43 

1  32 

1  25 

21 

18 

1  16 

17 

1  18 

1  19 

1  21 

22 

23 

3  29 

2  58 

2  35 

2  18 

2  5 

1  55 

1  46 

1  35 

1  27 

22 

19 

1  17 

16 

1  17 

1  18 

1  19 

23 

24 

3  38 

3  5 

2  42 

2  23 

2  9 

1  59 

1  50 

1  37 

1  29 

24 

20 

1  17 

16 

1  16 

1  17 

1  18 

24 

25 

26 

3  47 

3  13 

2  49 

2  29 

2  14 

2  3 

1  53 

1  39 

1  31 

25 

27 

21 

1  18 

16 

1  16 

1  16 

1  17 

25 
26 

3  55 

3  20 

2  55 

2  34 

2  19 

2  7 

1  57 

1  42 

1  33 

22 

1  19 

17 

1  16 

1  16 

1  16 

27 

4  4 

3  27 

3  1 

2  39 

2  24 

2  12 

2  1 

1  45 

1  35] 

28 

23 

1  19 

17 

1  16 

1  16 

1  16 

27 

28 

4  12 

3  34 

3  8 

2  45 

2  29 

2  16 

2  5 

1  48 

1  37 

30 

24 

1  20 

18 

1  16 

1  15 

1  16 

28 

29 

4  21 

3  41 

3  14 

2  50 

2  33 

2  20 

2  8 

1  51 

1  39 

31 

25 

1  21 

18 

1  16 

1  15 

1  15 

29 

30 

4  29 

3  48 

3  20 

2  55 

2  38 

2  24 

2  12 

1  54 

1  41 

33 

26 

1  21 

18 

1  16 

1  15 

1  15 

30 
31 

31 

4  38 

3  55 

3  26 

3  0 

2  43 

2  28 

2  16 

1  57 

1  44 

34 

28 

1  22 

18 

1  16 

1  16 

1  15 

32 

4  46 

4  2 

3  32 

3  6 

2  48 

2  32 

2  19 

2  0 

1  46 

36 

29 

1  23 

19 

1  17 

1  16 

1  15 

32 

33 

4  54 

4  9 

3  39 

3  11 

2  53 

2  36 

2  23 

2  3 

1  49 

38 

31 

1  25 

20 

1  17 

1  16 

1  15 

33 

34 

5  2 

4  16 

3  46 

3  16 

2  57 

2  40 

2  26 

2  6 

1  51 

40 

32 

1  26 

21 

1  18 

1  16 

1  15 

34 

35 

5  10 

4  23 

3  51 

3  22 

3  2 

2  44 

2  30 

2  9 

1  53 

42 

34 

1  27 

22 

1  18 

1  16 

1  15 

35 
36 

36 

5  18 

4  30 

3  57 

3  27 

3  6 

2  48 

2  33 

2  12 

1  55 

44 

35 

1  28 

23 

1  19 

1  17 

1  16 

37 

5  26 

4  37 

4  3 

3  32 

3  10 

2  52 

2  37 

2  15 

1  58 

46 

37 

1  29 

24 

1  20 

1  18 

1  16 

37 

38 

5  33 

4  43 

4  8 

3  37 

3  14 

2  56 

2  41 

2  17 

2  0 

48 

38 

1  30 

25 

1  21 

1  18 

1  16 

38 

39 

5  41 

4  50 

4  14 

3  42 

3  19 

3  0 

2  45 

2  20 

2  2 

50 

39 

1  31 

25 

1  21 

1  18 

1  16 

39 

40 
41 

5  48 

4  56 

4  19 

3  47 

3  23 

3  4 

2  48 

2  23 

2  4 

51 

40 

1  32 

26 

1  22 

1  19 

!  16 

40 

5  55 

5  2 

4  25 

3  52 

3  28 

3  8 

2  51 

2  25 

2  6 

53 

42 

1  33 

27 

1  23 

1  20 

1  17 

41 

42 

6  2 

5  8 

4  30 

3  57 

3  32 

3  11 

2  54 

2  28 

2  9 

55 

43 

1  34 

28 

1  24 

1  20 

1  17 

42 

43 

6  9 

5  14 

4  35 

4  2 

3  36 

3  15 

2  58 

2  31 

2  12 

57 

44 

1  35 

29 

1  25 

1  21 

1  17 

43 

44 

6  16 

5  20 

4  40 

4  7 

3  40 

3  19 

3  1 

2  34 

2  14 

59 

46 

1  37 

31 

1  26 

1  22 

1  18 

44 

46 

6  29 

5  32 

4  50 

4  16 

3  48 

3  26 

3  8 

2  40 

2  18 

2 

2 

49 

1  40 

33 

1  28 

1  23 

1  19 

46 

48 

48 

6  42 

5  43 

4  59 

4  24 

3  56 

3  33 

3  14 

2  45 

2  22 

2 

6 

52 

1  43 

36 

1  30 

1  25 

1  20 

50 

6  54 

5  54 

5  8 

4  32 

4  3 

3  40 

3  19 

2  50 

2  26 

2 

9 

55 

1  45 

38 

1  32 

1  26 

1  21 

50 

52 

7  6 

6  4 

5  17 

4  39 

4  10 

3  46 

3  24 

2  55 

2  30 

2 

12 

58 

1  48 

40 

1  33 

1  27 

1  22 

52 

54 

7  18 

6  14 

5  25 

4  46 

4  16 

3  52 

3  29 

2  59 

2  34 

2 

15 

2 

0 

1  50 

42 

1  35 

1  29 

1  24 

54 

56 

7  29 

6  24 

5  33 

4  53 

4  22 

3  57 

3  34 

3  3 

2  37 

2 

19 

2 

3 

1  52 

43 

1  36 

1  30 

1  25 

56 

58 

7  40 

6  33 

5  41 

5  0 

4  28 

4  2 

3  39 

3  7 

2  41 

2 

22 

2 

6 

1  54 

45 

1  37 

1  31 

1  26 

58 

60 

7  50 

6  41 

5  48 

5  7 

4  34 

4  7 

3  43 

3  11 

2  44 

2 

25 

2 

8 

1  56 

47 

1  39 

1  32 

1  27 

60 

62 

7  58 

6  48 

5  55 

5  13 

4  40 

4  12 

3  48 

3  15 

2  47 

2 

28 

2 

11 

1  58 

48 

1  40 

1  33 

1  28 

62 

64 

8  6 

6  55 

6  1 

5  19 

4  45 

4  17 

3  52 

3  18 

2  50 

2 

30 

2 

13 

8  0 

50 

1  41 

1  34 

1  29 

64 

66 

68 

6  7 

5  24 

4  50 

4  21 

3  56 

3  20 

2  53 

2 

32 

2 

15 

2  2 

51 

1  42 

1  35 

1  29 

66 

4  55 

4  25 

4  0 

3  22 

2  55 

2 

34 

2 

17 

2  4 

52 

1  43 

1  36 

1  30 

68 

70 

4  4 

3  24 

2  57 

2 

36 

2 

18 

2  5 

53 

1  44 

1  37 

1  31 

70 

72 

3  26 

2  59 

2 

37 

2 

19 

2  6 

54 

1  45 

1  38 

1  32 

72 

74 

3  1 

2 

38 

2 

20 

2  7 

55 

1  46 

1  39 

1  32 

74 

76 

2 

39 

2 

21 

2  8 

56 

1  47 

1  39 

1  33 

76 

78 

2 

22 

2  8 

57 

1  48 

1  40 

1  33 

78 

80 

2  9 

58 

1  48 

1  40 

1  34 

80 

82 

58 

1  48 

1  40 

1  34 

82 

84 

1  49 

1  41 

1  34 

84 

86 

22° 

1  41 

1  34 

86 

6" 

7» 

8° 

9** 

10" 

11° 

12° 

14° 

16° 

18° 

20° 

24° 

26° 

28° 

30° 

TABLE  XXXIII. 

I7S  1 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  66<». 

D'B 

A  pp. 

Alt. 

APPARENT  AhTlTVDK    OF 

THE  SUN, 

OR  STAR.                    ' 

App. 

32° 

340 

36° 

38° 

42° 

46°  1 

50° 

54° 

58° 

62° 

66° 

70° 

74° 

78° 

82° 

86° 

Alt. 

o 

/  ff 

/  ff 

/  /r 

f     tr 

1 

II 

1 

II 

1    II 

/  /' 

/ 

II 

/  // 

/ 

II 

1 

// 

/  n 

/  // 

/  // 

/  // 

0 

6 

4  37 

4  54 

5  10 

5  26 

5 

56 

6 

25 

6  52 

7  15 

7 

37 

7  58 

6| 

7 

3  57 

4  11 

4  25 

4  38 

5 

3 

5 

29 

5  52 

6  12 

6 

31 

6  48 

7 

8 

3  26 

3  38 

3  51 

4  3 

4 

26 

4 

47 

5  5 

5  23 

5 

40 

5  55 

6 

8 

8 

9 

3   1 

3  12 

3  23 

3  33 

3 

53 

4 

12 

4  30 

4  46 

5 

0 

5  13 

5 

25 

9 

10 
11 

2  43 

2  53 

3  2 

3  11 

3 
3 

28 
9 

3 

45 

4   1 

4  15 

4 

27 

4  39 

4 

50 

10 

11 

2  29 

2  37 

2  45 

2  53 

3 

24 

3  38 

3  50 

4 

1 

4  12 

4 

21 

12 

2  16 

2  23 

2  30 

2  38 

2 

52 

3 

6 

3  18 

3  28 

3 

38 

3  47 

3 

56 

4 

4 

12 

13 

2  6 

2  12 

2  18 

2  25 

2 

37 

2 

50 

3  1 

3  10 

3 

19 

3  28 

3 

36 

3 

42 

13 

14 

1  57 

2  3 

2  8 

2  14 

2 

25 

2 

36 

2  47 

2  56 

3 

4 

3  12 

3 

19 

3 

24 

14 

15 

1  50 

1  55 

1  59 

2  5 

2 

15 

2 

25 

2  35 

2  44 

2 

51 

2  58 

3 

4 

3 

10 

15 

16 

1  44 

1  48 

1  53 

1  58 

2 

7 

2 

16 

2  25 

2  33 

2 

39 

2  45 

2 

51 

2 

57 

3   2 

16 

17 

1  39 

1  43 

1  48 

1  52 

2 

0 

2 

8 

2  16 

2  24 

2 

30 

2  35 

2 

40 

2 

45 

2  49 

17 

18 

1  35 

1  39 

1  43 

1  47 

54 

2 

1 

2  8 

2  15 

2 

21 

2  26 

2 

31 

2 

35 

2  38 

18 

19 

1  31 

1  35 

1  38 

1  42 

48 

55 

2  1 

2  7 

2 

13 

2  18 

2 

23 

2 

27 

2  30 

19 

20 

1  28 

1  31 

1  34 

1  37 

43 

49 

1  55 
1  49 

2  0 

2 

6 

2  10 

2 

13 

2 

19 

2  22 

2  24 

20 

21 

1  25 

1  27 

1  30 

1  33 

38 

44 

1  54 

59 

2  3 

2 

7 

2 

11 

2  14 

2  16 

21 

22 

1  22 

1  24 

1  27 

1  30 

34 

39 

1  44 

1  48 

52 

1  56 

2 

0 

2 

4 

2  6 

2  8 

22 

23 

1  20 

1  22 

1  24 

1  27 

31 

35 

1  40 

1  44 

47 

1  51 

54 

57 

2  0 

2  2 

23 

24 

1  19 

1  20 

1  22 

1  25 

28 

32 

1  36 

1  40 

43 

1  46 

49 

52 

1  54 

1  56 

1  58 

24 

25 

1  18 

1  19 

1  21 

1  23 

26 

29 

1  33 

1  36 

39 

1  42 

44 

47 

1  49 

1  51 

1  53 

25 

26 

1  17 

1  18 

1  19 

1  21 

24 

27 

1  30 

1  33 

35 

1  38 

40 

42 

1  44 

1  46 

1  48 

26 

27 

1  16 

1  17 

1  18 

1  19 

22 

25 

1  27 

1  30 

32 

1  35 

37 

39 

1  40 

1  42 

1  44 

27 

28 

1  16 

1  16 

1  17 

1  18 

20 

23 

1  25 

1  27 

29 

1  32 

34 

36 

1  37 

1  39 

1  40 

1  41 

28 

29 

1  15 

1  15 

1  16 

1  17 

19 

21 

1  23 

1  25 

27 

1  29 

31 

33 

1  34 

1  35 

1  36 

1  37 

29 

30 

1  15 

1  15 

1  16 

1  16 

17 

19 

1  21 

1  23 

25 

1  27 

29 

30 

28 

1  31 

1  32 

1  33 

1  34 

30 

31 

1  14 

1  14 

1  15 

1  15 

16 

18 

1  19 

1  21 

23 

1  25 

27 

1  29 

1  29 

1  30 

1  31 

31 

32 

1  14 

1  14 

1  14 

1  14 

15 

17 

1  18 

1  19 

21 

1  23 

25 

26 

1  27 

1  27 

1  27 

1  28 

32 

33 

1  14 

1  13 

1  13 

1  13 

14 

16 

1  17 

1  18 

20 

1  21 

23 

24 

1  25 

1  25 

1  25 

1  26 

33 

34 

1  14 

1  13 

1  13 

1  13 

14 

15 

1  16 

1  17 

19 

1  20 

21 

22 

1  23 

1  23 

1  23 

1  24 

34 

35 

1  14 

1  13 

1  13 

1  13 

— 

13 
12 

14 

1  15 
1  14 

1  16 

17 

1  18 

19 

20 

1  21 

1  21 

1  21 

1  22 

35 

36 

1  14 

1  13 

1  12 

1  12 

13 

1  15 

16 

1  16 

17 

18 

1  19 

1  19 

1  19 

1  20 

36 

37 

1  14 

1  13 

1  12 

1  12 

12 

12 

1  13 

1  14 

15 

1  15 

16 

16 

1  17 

1  17 

1  17 

1  18 

37 

33 

1  14 

1  13 

1  12 

1  11 

11 

12 

1  13 

1  13 

14 

1  14 

15 

15 

1  16 

1  16 

1  16 

1  17 

38 

39 

1  14 

1  13 

1  12 

1  11 

11 

11 

1  12 

1  12 

13 

1  13 

13 

13 

1  14 

1  14 

1  15 

1  15 

39 

40 

1  14 

1  13 

1  12 

1  11 

10 

10 

1  11 

1  11 

12 

1  12 

12 

12 

1  12 

1  13 

1  13 

1  13 

40 
41 

41 

1  15 

I  14 

1  12 

1  11 

10 

10 

1  10 

1  10 

11 

1  11 

11 

11 

1  11 

1  12 

1  12 

42 

1  15 

1  14 

1  12 

1  11 

9 

9 

1   9 

1  9 

10 

1  10 

10 

10 

1  10 

1  11 

1  11 

42 

43 

1  15 

1  14 

1  12 

1  11 

9 

9 

1  9 

1  9 

9 

1   9 

9 

9 

1  9 

1  10 

1  10 

43 

44 

1  16 

1  14 

1  12 

1  11 

9 

8 

1  8 

1  8 

8 

1  8 

8 

8 

1   8 

1   9 

1  9    1 

44 

46 

1  17 

1  15 

1  13 

1  12 

9 

7 

1   7 

1   7 

6 

1   6 

6 

7 

1  7 

1   7 

46 

48 

1  17 

1  15 

1  13,1  12 

9 

7 

1   6 

1   6 

5 

1   5 

5 

5 

1   5 

1   6 

48 

50 

1  18 

1  16 

1  14 

1  12 

9 

6 

1   5 

1   5 

4 

1  4 

4 

4 

1   4 

50 

52 

1  19 

1  17 

1  15 

1  13 

9 

6 

1  4 

1  4 

3 

1   3 

3 

3 

1   3 

52 

54 

1  20 

1  17 

1  15 

1  13 

9 

6 

1   4 

1   3 

3 

1  2 

2 

2 

54 

56 

1  21 

1  18 

1  16 

1  14 

10 

6 

1   4 

1   2 

2 

1   1 

1 

1 

1 
i 

56 

58 
60 
62 

1  22 
1  23 
1  24 

1  19 
1  19 

1  20 

1  16 
1  16 
1  17 

1  14 
1  14 

1  14 

10 
10 
10 

6 
6 
6 

1  4 
1  4 
1  4 

1  2 

1  2 
1   2 

1 
1 
1 

1  0 
1   0 

1  0 

0 
0 

1 

TABLE  P.  EFFECT  OF  BUN's  PAR 

Add  the  Numbers  above  the 

64 

1  24 

1  20 

1  17 

1  14 

7 

1  4 

1  2 

0 

1  0 

lines  to  3rd  Correction,  sub- 

66 

1  25 

1  21 

1  18 

1  15 

7 

1   4 

1  2 

0 

tract  the  others. 

)'8 
App 
A  t. 

Sun's  Apparent  Altitude. 1  | 

68 

70 

1  25 
1  26 

1  21 
1  22 

1  18 
1  19 

1  15 
1  16 

7 
7 

1   4 
1   4 

1  2 

1   2 

1 

0 

5  10  a 

3  30 

40  5 

0  60 

70^ 

iopo 

72 

1  27 

1  23 

1  19 

1  16 

Hi 

7 

1   4 

1   2 

ft      ft       f 

// 

t      t 

'  " 

" 

n    n 

74 

1  27 

1  23 

1  19 

1  16 

1 

7 

1  4 

5 

0  0  1 

a 

3  4 

I  4 

76 

1  28 

1  23 

1  19 

1  16 

11 

1 
1 

7 
7 

1  4 

10 
20 
30 

1  1  0 
3  3  2 
5  4  3 

1 
1 
2 

2  ; 

0  1 

1  1 

1  i 
2 
0 

2 

0 

I 

78 

1  28 

1  23 

1  20 

1  17 

80 

1  29 

1  24 

1  201 

1  17 

1 

7 

40 

6  6  5 

4 

3  5 

!  2 

1 

1  0 

82 

1  29 

1  24 

1  20 

1  17 

50 

8  7  6 

5 

4  < 

3 

3 

84 
86 

1  29 
1  29 

1  24 
1  24 

1  20 
1  20 

1  17 
1  17 

70  j 

80 

90 

9  8  7 

9  S 

8 

6 

7 
8 
8 

5  t 

6  f 

7 

4 

• 

1 

32° 

Q40 

36° 

38'' 

4 

70 

46° 

50° 

54° 

58°  1 

62° 

fiR° 

70» 

1 

174 

TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  60°                [ 

A.pp. 
Alt. 

APPARENT  ALTITUDE  OF 

THE 

SUN, 

OR  STAR. 

3>'6 

App 

6« 

70 

8° 

9° 

10°  1 

11°  1 

12° 

14°  1 

16°  1 

18° 

20° 

22°  1 

24° 

26°  28° 

30° 

Alt. 

o 

f 

tt 

/  // 

t    It 

/ 

n 

1 

If 

/  // 

1 

n 

/ 

n 

1 

// 

/ 

// 

1 

// 

/  II 

1    II    /    II 

/  // 

0 

6 

1 

22 

1  23 

1  25 

1  28 

33 

40 

1  47 

2 

1 

2 

16 

2 

33 

2 

50 

3 

8 

3  25 

3  41  3  58 

4  15 

6 

7 

24 

1  22 

1  26 

1  25 

28 

33 

1  37 

47 

59 

2 

13 

2 

27 

2 

41 

2  55 

3  9  3  23 

3  37 

7 

8 

28 

1  24 

1  22 

1  23 

25 

28 

1  31 

39 

48 

59 

2 

11 

2 

23 

2  35 

2  48 

3  0 

3  12 

8 

9 

33 

1  28 

1  24 

1  22 

24 

25 

1  27 

33 

40 

49 

58 

2 

8 

2  18 

2  29 

2  39 

2  50 

9 

10 

40 

1  33 

1  27 

1  24 

23 

24 

1  25 

29 

34 

41 

49 

1 

57 

2  6 

2  15 

2  25 

2  34 

iO 

11 

47 

1  38 

1  31 

1  27 

24 

23 

1  24 

26 

30 

36 

42 

49 

1  57 

2  5 

2  13 

2  21 

11 

12 

55 

1  43 

1  36 

1  30 

26 

24 

1  23 

25 

28 

32 

37 

43 

1  49 

1  56 

2  3 

2  11 

12 

13 

2 

3 

1  49 

1  40 

1  34 

29 

26 

1  24 

24 

26 

29 

33 

38 

1  43 

1  49 

1  55 

2  2 

13 

14 

2 

10 

1  55 

1  45 

1  38 

32 

28 

1  25 

23 

25 

27 

30 

34 

1  38 

1  43 

1  49 

1  54 

14 

15 

2 

18 

2  1 

1  50 

1  42 

36 

31 

1  27 

24 

23 

25 

27 

30 

1  34 

1  38 

1  43 

1  48 

15 
16 

16 

2 

26 

2  7 

1  55 

1  46 

39 

34 

1  29 

25 

22 

23 

25 

27 

1  30 

1  34 

1  38 

1  43 

17 

2 

34 

2  13 

2  0 

1  50 

43 

37 

1  31 

26 

22 

22 

23 

25 

1  28 

1  31 

1  34 

1  38 

17 

18 

2 

42 

2  20 

2  5 

1  54 

46 

40 

1  34 

27 

23 

21 

22 

23 

1  25 

1  28 

1  31 

1  34 

18 

19 

2 

50 

2  27 

2  11 

1  59 

50 

43 

1  36 

29 

24 

22 

21 

22 

1  23 

1  26 

1  28 

]  31 

19 

20 

2 

59 

2  34 

2  17 

2  4 

54 

46 

1  39 

31 

25 

22 

20 

21 

1  22 

1  24 

1  26 

1  28 

20 
21 

21 

3 

7 

2  41 

2  23 

2  9 

1 

58 

50 

1  42 

33 

26 

23 

21 

20 

1  21 

1  22 

1  24 

1  25 

22 

3 

15 

2  48 

2  29 

2  14 

2 

2 

53 

1  45 

35 

28 

24 

21 

20 

1  20 

1  21 

1  22 

1  23 

22 

23 

3 

24 

2  55 

2  35 

2  19 

2 

7 

57 

1  48 

37 

30 

25 

22 

20 

1  20 

1  20 

1  21 

1  22 

23 

24 

3 

32 

3  2 

2  41 

2  24 

2 

10 

2 

1 

1  52 

40 

31 

26 

23 

21 

1  20 

1  20 

1  20 

1  21 

24 

25 
26 

3 

41 

3  9 

2  47 

2  29 

2 
2 

15 
20 

2 

4 

1  55 

42 

33 

27 
29 

24 

22 

1  20 

1  19 

1  19 

1  20 

25 

3 

49 

3  16 

2  53 

2  34 

2 

8 

1  59 

45 

35 

25 

22 

1  20 

1  19 

1  19 

1  19 

26 

27 

3 

58 

3  23 

2  59 

2  39 

2 

25 

2 

12 

2  3 

48 

38 

31 

26 

23 

1  21 

1  19 

1  19 

1  19 

27 

28 

4 

6 

3  30 

3  5 

2  44 

2 

29 

2 

16 

2  7 

51 

40 

32 

27 

23 

1  21 

1  19 

1  18 

1  18 

28 

29 

4 

15 

3  37 

3  11 

2  49 

2 

33 

2 

20 

2  11 

53 

42 

34 

28 

24 

1  21 

1  19 

1  18 

1  18 

29 

30 

4 

23 

3  44 

3  17 

2  54 

2 

38 

2 

24 

2  14 

56 

44 

35 

29 

24 

1  21 

1  19 

1  18 

1  18 

30 
31 

31 

4 

31 

3  51 

3  23 

2  59 

2 

42 

2 

28 

2  18 

1 

59 

46 

37 

30 

25 

1  22 

1  20 

1  18 

1  18 

32 

4 

39 

3  58 

3  29 

3  4 

2 

47 

2 

32 

2  21 

2 

2 

48 

38 

31 

26 

1  22 

1  20 

1  19 

1  18 

32 

33 

4 

47 

4  5 

3  34 

3  9 

2 

52 

2 

36 

2  25 

2 

5 

51 

40 

33 

27 

1  23 

1  20 

1  19 

1  18 

33 

34 

4 

55 

4  12 

3  40 

3  14 

2 

56 

2 

40 

2  28 

2 

8 

53 

41 

34 

28 

1  24 

1  21 

1  19 

1  18 

34 

35 

5 

3 

4  18 

3  46 

3  19 

3 

0 

2 

44 

2  32 

2 

11 

55 

43 

35 

29 

1  25 

1  22 

1  20 

1  18 

35 
36 

36 

5 

10 

4  24 

3  52 

3  24 

3 

4 

2 

48 

2  35 

2 

14 

57 

45 

37 

31 

1  26 

1  22 

1  20 

1  18 

37 

<) 

18 

4  31 

3  58 

3  29 

3 

8 

2 

52 

2  39 

2 

17 

59 

47 

38 

32 

1  27 

1  23 

1  21 

1  19 

37 

38 

0 

25 

4  38 

4  4 

3  34 

3 

12 

2 

55 

2  42 

2 

20 

2 

2 

49 

40 

33 

1  28 

1  24 

1  21 

1  19 

38 

39 

5 

32 

4  45 

4  10 

3  39 

3 

17 

2 

59 

2  46 

2 

22 

2 

4 

51 

42 

35 

1  29 

1  25 

1  22 

1  20 

39 

40 
41 

5 

39 

4  51 

4  15 

3  44 

3 

21 

3 

3 

2  49 

2 

25 

2 

6 

53 

43 

36 

1  30 

1  26 

1  22 

1  20 

40 

5 

46 

4  57 

4  21 

3  49 

3 

26 

3 

7 

2  52 

2 

27 

2 

8 

55 

45 

37 

1  31 

1  27 

1  23 

1  20 

41 

42 

5 

53 

5  3 

4  26 

3  53 

3 

30 

3 

11 

2  55 

2 

30 

2 

10 

56 

46 

38 

1  32 

1  28 

1  24 

1  21 

42 

43 

6 

0 

5  9 

4  31 

3  58 

3 

35 

3 

15 

2  58 

2 

32 

2 

13 

58 

48 

40 

1  34 

1  29 

1  25 

1  22 

43 

44 

6 

7 

5  15 

4  36 

4  3 

3 

39 

3 

19 

3   1 

2 

35 

2 

15 

2 

0 

49 

41 

1  35 

1  30 

1  26 

1  22 

44 

46 

48 

6 

21 

5  26 

4  46 

4  12 

3 

47 

3 

26 

3   7 

2 

40 

2 

19 

2 

4 

52 

43 

1  37 

1  31 

1  27 

1  23 

46 

48 

6 

34 

5  37 

4  55 

4  20 

3 

54 

3 

32 

3  13 

2 

45 

2 

23 

2 

8 

56 

46 

1  39 

1  33 

1  28 

1  24 

50 

6 

47 

5  48 

5  4 

4  28 

4 

1 

3 

37 

3  19 

2 

50 

2 

27 

2 

11 

59 

48 

1  41 

1  35 

1  29 

1  25 

50 

52 

6 

59 

5  58 

5  13 

4  36 

4 

8 

3 

43 

3  25 

2 

55 

2 

31 

2 

14 

2 

2 

51 

1  43 

1  36 

1  31 

1  27 

52 

54 

7 

11 

6  8 

5  22 

4  44 

4 

15 

3 

49 

3  30 

2 

59 

2 

35 

2 

18 

2 

4 

53 

1  45 

1  38 

1  33 

1  28 

54 

56 

58 

7 
7 

22 
31 

6  17 

5  30 

4  51 

4 

21 

3 

55 

3  35 

3 

4 

2 

38 

2 

21 

2 

7 

56 

1  47 

1  40 

1  34 

1  29 

56 

6  25 

5  37 

4  58 

4 

27 

4 

1 

3  40 

3 

8 

2 

41 

2 

24 

2 

10 

1 

58 

1  49 

1  41 

1  35 

1  30 

58 

60 

7 

40 

6  32 

5  45 

5  4 

4 

32 

4 

6 

3  45 

3 

12 

2 

44 

2 

27 

2 

12 

2 

0 

1  50 

1  42 

1  36 

1  31 

60 

62 

7 

48 

6  39 

5  52 

5  10 

4 

38 

4 

11 

3  50 

3 

16 

2 

48 

2 

29 

2 

14 

2 

2 

1  52 

1  44 

1  37 

1  32 

62 

64 

7 

56 

6  46 

5  58 

5  16 

4 

43 

4 

15 

3  55 

3 

19 

2 

51 

2 

31 

2 

16 

2 

4 

1  53 

1  45 

1  38 

1  33 

64 

66 

68 

8 

3 

6  53 

6  2 

5  20 

4 

47 

4 

19 

3  59 

3 

22 

2 

54 

2 

33 

2 

18 

2 

5 

1  55 

1  46 

1  39 

1  34 

66 

8 

10 

6  59 

6  6 

5  24 

4 

51 

4 

23 

4  2 

3 

25 

2 

56 

2 

35 

2 

19 

2 

6 

1  56 

1  47 

1  40 

1  34 

68 

70 

6  10 

5  27 

4 

54 

4 

26 

4  4 

3 

27 

2 

58 

2 

36 

2 

20 

2 

7 

1  57 

1  48 

1  41 

1  35 

70 

72 

4 

57 

4 

29 

4  6 

3 

28 

3 

0 

2 

38 

2 

21 

2 

8 

1  58 

1  49 

1  41 

1  35 

72 

74 

4  8 

3 

29 

3 

2 

2 

39 

2 

22 

2 

9 

1  59 

1  50 

1  42 

1  36 

74 

76 

3 

30 

3 

3 

2 

41 

2 

23 

2 

0 

1  59 

1  50 

1  42 

1  36 

76 

78 

3 

4 

2 

42 

2 

24 

2 

11 

2  0 

1  51 

1  43 

1  37 

78 

80 

2 

43 

2 

25 

2 

12 

2  1 

1  51 

1  43 

1  37 

80 

82 

2 

26 

2 

12 

2  1 

1  52 

1  44 

1  38 

82 

84 

2 

12 

2  2 

1  52 

1  44 

1  38 

84 

86 

2  2 

1  52 

1  44 

1  38 

86 

6° 

7° 

8" 

9" 

10° 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 



TABLE  XXXIII. 

r 

17. 

A 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  eo**. 

A.pp. 

Alt. 

o 

APPARENT  ALTITUDE  OF 

THE 

SUN, 

OR 

STAR. 

>'8 

App. 
Alt. 

32° 

340 

36° 

38° 

42° 

46°  1 

50° 

54° 

58°  1 

62° 

66°  1 

70° 

74° 

78° 

82° 

86° 

t    n 

1    n 

1    n 

t    II 

/  // 

/ 

// 

/  II 

/  II 

1 

II 

/ 

// 

/ 

II 

/  II 

1    II 

1    II 

/  // 

/  II 

0 

6 

4  32 

4  48 

5  3 

5  19 

5  49 

6 

17 

6  44 

7  7 

7 

28 

7 

47 

8 

3 

6 

7 

3  51 

4  5 

4  19 

4  32 

4  58 

5 

22 

5  44 

6,  4 

6 

22 

6 

38 

6 

53 

7 

8 

3  23 

3  35 

3  47 

3  59 

4  22 

4 

42 

5  1 

5  19 

5 

35 

5 

50 

6 

2 

6  13 

8 

9 

3  0 

3  10 

3  20 

3  30 

3  49 

4 

8 

4  25 

4  41 

4 

55 

5 

8 

5 

19 

5  30 

9 

10 

2  43 

2  51 

3  0 

3  9 

3  26 

3 

42 

3  58 

4  12 

4 

24 

'4 

35 

4 

45 

4  54 

10 
11 

11 

2  29 

2  37 

2  44 

2  52 

3  7 

3 

21 

3  35 

3  48 

3 

59 

4 

9 

4 

18 

4  26 

12 

2  18 

2  25 

2  32 

2  39 

2  52 

3 

5 

3  17 

3  29 

3 

39 

3 

48 

3 

56 

4  3 

4  8 

12 

13 

2  8 

2  15 

2  21 

2  28 

2  39 

2 

51 

3  2 

3  12 

3 

21 

3 

30 

3 

38 

3  44 

3  48 

13 

14 

2  0 

2  6 

2  12 

2  18 

2  28 

2 

38 

2  48 

2  57 

3 

6 

3 

14 

3 

21 

3  26 

3  29 

14 

15 

1  53 

1  58 

2  3 

2  8 

2  18 

2 

27 

2  36 

2  45 
2  34 

2 

53 

3 

0 

3 

6 

3  11 

3  15 

15 

16 

1  47 

1  51 

1  55 

2  0 

2  9 

2 

18 

2  26 

2 

41 

2 

48 

2 

53 

2  58 

3  2 

3  6 

16 

17 

1  42 

1  45 

1  49 

1  53 

2  M 

2 

9 

2  17 

2  24 

2 

31 

2 

37 

2 

42 

2  46 

2  50 

2  53 

17 

18 

1  37 

1  40 

1  44 

1  47 

1  54 

2 

1 

2  9 

2  16 

2 

22 

2 

27 

2 

32 

2  36 

2  40 

2  42 

18 

•19 

1  33 

1  36 

1  39 

1  42 

1  48 

55 

2  2 

2  9 

2 

15 

2 

19 

2 

24 

2  28 

2  31 

2  33 

19 

20 

1  30 

1  32 

1  35 

1  38 

1  44 

50 

1  56 

2  2 
1  56 

2 

8 

2 

12 

2 

16 

2  20 

2  23 

2  25 

2  27 

20 

21 

1  27 

1  29 

1  32 

1  35 

1  40 

46 

1  51 

2 

1 

2 

6 

2 

10 

2  13 

2  15 

2  17 

2  19 

21 

22 

1  25 

1  27 

1  29 

1  32 

1  37 

42 

1  47 

1  51 

56 

2 

0 

2 

4 

2  6 

2  8 

2  10 

2  12 

22 

23 

1  23 

1  25 

1  27 

1  30 

1  34 

38 

1  43 

1  47 

51 

55 

59 

2   1 

2  3 

2  4 

2  6 

23 

24 

1  22 

1  23 

1  25 

1  27 

1  31 

35 

1  40 

1  44 

47 

*■ 

51 

54 

I  56 

1  58 

1  59 

2  1 

2  3 

24 

25 

1  21 

1  22 

1  23 

1  25 

1  29 
1  26 

32 

1  36 

1  40 

43 

47 

49 

1  51 

1  53 

1  54 

1  56 

1  57 

25 

26 

1  20 

1  21 

1  22 

1  23 

29 

1  33 

1  37 

40 

43 

45 

1  47 

1  49 

1  60 

1  51 

1  52 

26 

27 

1  19 

1  20 

1  21 

1  22 

1  24 

27 

1  30 

1  34 

37 

40 

42 

1  43 

1  45 

1  46 

1  47 

1  48 

27 

28 

1  19 

1  19 

1  20 

1  21 

1  23 

25 

1  28 

1  31 

34 

37 

39 

1  40 

1  41 

1  42 

1  43 

1  44 

28 

29 

1  18 

1  18 

1  19 

1  20 

1  22 

23 

1  26 

1  29 

31 

34 

36 

1  37 

1  38 

1  39 

1  40 

1  41 

29 

30 

1  18 

1  18 

1  18 

1  19 

1  20 

22 

1  24 

1  27 

29 

31 

33 

1  34 
1  31 

1  35 

1  36 

1  37 

1  38 

30 

31 

1  18 

1  18 

1  18 

1  18 

1  19 

20 

1  22 

1  25 

27 

29 

30 

1  32 

1  33 

1  34 

1  35 

31 

32 

1  17 

1  17 

1  17 

1  17 

1  18 

19 

1  21 

1  23 

25 

27 

28 

1  29 

1  30 

1  31 

1  31 

1  32 

32 

33 

1  17 

1  16 

1  16 

1  16 

1  17 

18 

1  19 

1  21 

23 

25 

26 

1  27 

1  28 

1  29 

1  29 

1  30 

33 

34 

1  17 

1  16 

1  16 

1  16 

1  16 

17 

1  18 

1  20 

22 

23 

24 

1  25 

1  26 

1  27 

1  27 

1  28 

34 

35 

1  17 

1  16 

1  16 

1  16 

1  16 

16 

1  17 

1  18 

20 

21 

22 

1  23 

1  24 

1  25 

1  25 

1  26 

35 

36 

1  17 

1  16 

1  15 

1  16 

1  16 

16 

1  16 

1  17 

18 

19 

20 

1  21 

1  22 

1  23 

1  23 

1  24 

36 

37 

1  17 

1  16 

1  15 

1  15 

1  15 

15 

1  15 

1  16 

17 

18 

19 

1  20 

1  21 

1  21 

1  22 

37 

38 

1  17 

1  16 

1  15 

1  14 

1  14 

14 

1  14 

1  15 

16 

17 

18 

1  19 

1  20 

1  20 

1  21 

38 

39 

1  18 

1  16 

1  15 

1  14 

1  13 

13 

1  13 

1  14 

15 

16 

17 

1  17 

1  18 

1  18 

1  19 

39 

40 

1  18 

1  16 

1  15 

1  14 

1  13 

13 

1  13 

1  14 

14 

15 

16 

1  16 

1  17 

1  17 

1  17 

40 
41 

41 

1  18 

1  16 

1  15 

1  14 

1  12 

12 

1  12 

1  13 

13 

14 

15 

1  15 

1  16 

1  16 

42 

1  18 

1  16 

1  15 

1  14 

1  12 

12 

1  12 

1  12 

12 

13 

14 

1  14 

1  15 

1  15 

42 

43 

1  19 

1  17 

1  16 

1  14 

1  12 

11 

1  11 

1  11 

11 

12 

13 

1  13 

1  14 

1  14 

43 

44 

1  19 

1  17 

1  16 

1  14 

1  12 

11 

1  11 

1  11 

11 

11 

12 

1  12 

1  13 

1  13 

44 

4H 

1  20 

1  18 

1  16 

1  14 

1  12 

11 

1  10 

1  10 

10 

10 

11 

1  11 

1  11 

46 

48 

1  21 

1  19 

1  17 

1  15 

1  12 

10 

1   9 

1  9 

9 

9 

10 

1  10 

1  10 

48 

50 

1  22 

1  19 

1  17 

1  15 

1  12 

10 

1   9 

1  8 

8 

8 

8 

1  8 

50 

52 

1  23 

1  20 

1  17 

1  15 

1  12 

10 

1  8 

1  8 

8 

7 

7 

1  7 

52 

54 

1  24 

1  21 

1  18 

1  16 

1  13 

10 

1  8 

1  7 

7 

6 

6 

54 

56 

1  25 

1  22 

1  19 

1  16 

1  13 

10 

1  8 

1  7 

7 

6 

6 

1 

56 

58 
60 
62 
64 

1  26 
1  27 
1  28 
1  29 

1  23 

1  24 
1  24 

1  25 

11? 

1  21 
1  21 

1  17 

1  18 
1  18 
1  18 

1  13 
1  14 
1  14 
1  14 

10 
10 
10 
10 

1  8 
1  8 
1  8 
1  8 

1  7 
1  7 
1  6 
1  6 

6 
6 
5 
5 

5 
5 

'     '    1 

TABLK  P.  KFFKCT  OF  SITn's  PAR  1  1 

Add  the  Numbers  above  th 

lines  to  3rd  Correction,  sub 

tract  th«  others. 

e 

66 

1  29 

1  25 

1  21 

1  18 

1  14 

11 

1  8 

1  6 

App 
Alt. 

Sun's  Apparent  Altituc 

68 
70 

72 

1  2g 

1  3f 
1  3f 

1  25 
.  26 
1  26 

1  22 
1  VI 
1  23 

1  19 
1  19 
1  2C 

1  15 
1  15 
1  15 

11 
11 
11 

1  8 
1  8 
1  8 

1  6 

5 

IUp2( 
II   1 

DOG 
II 

40; 

m 

0  60 

r  tt 

3  4 
2  3 

0  _1_ 
2  1 

70 

80 

90 

* 

II 

74 
76 

1  31 
1  31 

1  27 
1  27 

1  2.'3 
1  23 

1  2r 
1  2(j 

1  15 
1  15 

11 
11 

6 

10 
20 
30 

0 

1 
3 
6 

0  1 

1  0 

3  2 

4  3 

1 
1 
3 

3 
2 

'2  " 

3 
1 

I 

2 
0 

78 

1  as 

!  1  28 

1  24 

1  2C 

1  15 

80 

82 
84 

1  3i 
1  3^ 
1  3S 

!  1  28 
!  1  28 
!  1  28 

1  24 

!  1  24 

1  24 

1  21 
1  21 
1  21 

1  15 

40 
50 
60 
70 

8 

6  .1 

7  6 

8  7 
!)  6 

8 

4 

5 

6 

7 

3 
5 

6 

(i 

3  2 

4  3 

5  4 

2 
.3 

2 

86 

1  3c 

t  1  28 

!  1  24 

80 
90 

8 

8 

7 

32° 

34° 

36° 

38° 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

70° 

12 


176                 TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  W>. 

1 

App. 
Alt. 

APPAKENT  ALTITUDE  OF 

THE  SUN, 

OR  STAR. 

1 

1>*8 

App 

6° 

70 

8° 

90 

10° 

11° 

12° 

14° 

16°  1 

18° 

20« 

22°  1 

24°  1 

26°  1 

28° 

30° 

Alt. 

o 

r  /f 

r    ff 

r    tt 

1    It 

1    II 

/  // 

/  II 

1    II 

1 

II 

/  II 

1 

// 

/ 

// 

f 

II 

1 

// 

/ 

II 

/ 

II 

0 

6 

1  26 

1  27 

1  29 

1  32 

1  36 

1  42 

1  49 

2  3 

2 

19 

2  35 

2 

51 

3 

8 

3 

24 

3 

40 

3 

56 

4 

12 

6 

7  1  28 

1  26 

1  27 

1  29 

1  32 

1  35 

1  40 

1  51 

2 

3 

2  15 

2 

28 

2 

42 

2 

56 

3 

9 

3 

22 

3 

36 

7 

8  1  32 

1  28 

1  26 

1  27 

1  29 

1  31 

1  34 

1  42 

1 

51 

2  2 

2 

13 

2 

24 

2 

36 

2 

48 

3 

0 

3 

11 

8 

9 

1  37 

1  31 

1  28 

1  26 

1  27 

1  28 

1  30 

1  36 

1 

43 

1  52 

2 

1 

2 

10 

2 

20 

2 

31 

2 

41 

2 

51 

9 

10 

1  43 

1  35 

1  30 

1  27 

1  26 

1  27 

1  28 

1  32 

1 

37 

1  44 

1 

51 

59 

2 

8 

2 

17 

2 

26 

2 

36 

10 

11 

1  50 

1  40 

1  33 

1  29 

1  27 

1  26 

1  27 

1  29 

1 

33 

1  38 

44 

51 

59 

2 

7 

2 

14 

2 

22 

11 

12 

1  57 

1  45 

1  37 

1  32 

1  29 

1  27 

1  26 

1  28  1 

30 

1  34 

38 

44 

51 

58 

2 

5 

2 

12 

12 

13 

2  4 

1  50 

1  41 

1  35 

1  31 

1  29 

1  27 

1  27 

28 

1  31 

34 

38 

44 

50 

57 

2 

3 

13 

14 

2  12 

1  56 

1  46 

1  39 

1  34 

1  31 

1  29 

1  26 

27 

1  29 

31 

34 

39 

44 

50 

65 

14 

15 

2  20 

2  2 

1  51 

1  43 

1  37 

1  33 

1  30 

1  27 

26 

1  27 

29 

31 

35 

40 

1 

44 

49 

15 

16 

2  27 

2  8 

1  56 

1  47 

1  41 

1  36 

1  32 

1  28 

25 

1  26 

27 

29 

32 

36 

40 

44 

16 

17 

2  35 

2  14 

2  1 

1  51 

1  45 

1  39 

1  34 

1  29 

26 

1  25 

26 

..* 

28 

30 

33 

36 

40 

17 

18 

2  43 

2  21 

2  6 

1  56 

1  48 

1  42 

1  37 

1  31 

27 

1  2.5 

25 

26 

28 

30 

33 

36 

18 

19 

2  51 

2  27 

2  12 

2  0 

1  52 

1  45 

1  39 

1  32 

28 

1  25 

25 

25 

27 

28 

^ 

30 

33 

19 

20 

2  59 

2  34 

2  17 

2  5 

1  56 

1  49 

1  42 

1  34 

29 

1  26 

24 

24 

1 

25 

26 

^ 

28 

30 

20 
21 

21 

3  7 

2  41 

2  23 

2  10 

2  0 

1  52 

1  45 

1  36 

30 

1  26 

24 

23 

24 

25 

26 

28 

22 

3  15 

2  48 

2  29 

2  15 

2  4 

1  55 

1  48 

1  38 

31 

1  27 

25 

23 

23 

24 

25 

26 

22 

23 

3  23 

2  55 

2  35 

2  20 

2  8 

1  59 

1  51 

1  40 

33 

1  28 

25 

23 

23 

* 

24 

24 

25 

23 

24 

3  31 

3  2 

2  41 

2  25 

2  12 

2  2 

1  54 

1  42 

34 

1  29 

26 

24 

23 

23 

« 

24 

25 

24 

25 
26 

3  39 

3  8 

2  47 

2  30 

2  17 

2  6 

1  57 

1  44 

36 

1  30 

26 

24 

23 

23 

23 

^ 

24 

25 

3  47 

3  15 

2  53 

2  35 

2  21 

2  10 

2  0 

1  47 

38 

1  32 

27 

25 

23 

23 

23 

23 

26 

27 

3  56 

3  22 

2  59 

2  40 

2  26 

2  14 

2  4 

1  50 

40 

1  33 

28 

25 

23 

23 

22 

23 

27 

28 

4  4 

3  29 

3  5 

2  45 

2  30 

2  18 

2  7 

1  53 

42 

1  35 

29 

26 

24 

23 

22 

22 

28 

29 

4  12 

3  36 

3  11 

2  50 

2  35 

2  22 

2  11 

1  55 

44 

1  36 

30 

27 

25 

23 

22 

22 

29 

30 
31 

4  20 

3  42 

3  17 

2  55 

2  39 

2  26 

2  15 

1  58 

46 

1  38 

32 

28 

25 

24 

23 

22 

30 

4  28 

3  49 

3  23 

3  0 

2  43 

2  30 

2  18 

2  0 

48 

1  40 

33 

29 

26 

24 

23 

22 

31 

32 

4  36 

3  55 

3  28 

3  5 

2  48 

2  34 

2  22 

2  3 

50 

1  41 

34 

30 

26 

24 

23 

22 

32 

33 

4  44 

4  2 

3  34 

3  10 

2  52 

2  38 

2  26 

2  6 

53 

1  43 

36 

30 

27 

24 

23 

22 

33 

34 

4  52 

4  8 

3  39 

3  15 

2  56 

2  41 

2  29 

2  8 

55 

1  44 

37 

31 

28 

25 

23 

22 

34 

35 

5  0 

4  15 

3  45 

3  20 

3  1 

2  45 

2  33 

2  11 

57 

1  46 

38 

32 

28 

25 

23 

22 

35 

36 

5  7 

4  21 

3  51 

3  25 

3  5 

2  49 

2  36 

2  14 

1 

59 

1  47 

39 

33 

29 

26 

24 

23 

36 

37 

5  14 

4  28 

3  57 

3  30 

3   9 

2  53 

2  40 

2  17 

2 

2 

1  49 

41 

34 

30 

27 

25 

23 

37 

38 

5  21 

4  34 

4  2 

3  35 

3  14 

2  57 

2  43 

2  20 

2 

4 

1  52 

43 

36 

31 

27 

25 

23 

38 

39 

5  28 

4  41 

4  7 

3  39 

3  18 

3  1 

2  46 

2  23 

2 

6 

1  54 

45 

37 

32 

28 

25 

23 

39 

40 

5  35 

4  47 

4  12 

3  44 

3  22 

3  4 

2  49 

2  26 

2 

9 

1  56 

46 

38 

33 

29 

26 

24 

40 

41 

5  42 

4  53 

4  17 

3  49 

3  26 

3   8 

2  52 

2  29 

2 

11 

1  58 

48 

40 

34 

29 

26 

24 

41 

42 

5  49 

4  59 

4  22 

3  53 

3  30 

3  11 

2  55 

2  31 

2 

13 

2  0 

49 

41 

35 

30 

27 

24 

42 

43 

5  56 

5  5 

4  27 

3  58 

3  34 

3  15 

2  59 

2  34 

2 

15 

2  2 

51 

42 

36 

31 

28 

25 

43 

44 

6  2 

5  11 

4  32 

4  3 

3  38 

3  19 

3  2 

2  36 

2 

16 

2  3 

52 

44 

38 

32 

29 

26 

44 

46 

6  15 

5  21 

4  42 

4  11 

3  45 

3  26 

3  8 

2  41 

2 

22 

2  6 

55 

47 

40 

34 

30 

27 

46 

48 

6  28 

5  32 

4  52 

4  19 

3  53 

3  32 

3  14 

2  45 

2 

26 

2  10 

1 

58 

49 

42 

36 

32 

28 

48 

50 

6  40 

5  42 

5  1 

4  27 

4  0 

3  38 

3  20 

2  50 

2 

29 

2  14 

2 

1 

51 

44 

37 

33 

29 

50 

52 

6  52 

5  52 

5  10 

4  35 

4  7 

3  44 

3  25 

2  55 

2 

33 

2  17 

2 

4 

54 

46 

39 

34 

30 

52 

54 

7  3 

6  1 

5  18 

4  42 

4  14 

3  50 

3  30 

2  59 

2 

37 

2  20 

2 

7 

56 

48 

41 

35 

31 

54 

56 

7  14 

6  10 

5  26 

4  49 

4  20 

3  55 

3  35 

3  3 

2 

41 

2  23 

2 

9 

58 

49 

43 

37 

32 

56 

58 

7  24 

6  18 

5  34 

4  56 

4  25 

4  C 

3  39 

3  7 

2 

44 

2  26 

2 

11 

2 

0 

52 

45 

38 

33 

58 

60 

7  32 

6  26 

5  41 

5  2 

4  30 

4  5 

3  44 

3  11 

2 

47 

2  29 

2 

14 

2 

2 

64 

47 

40 

35 

60 

62 

7  40 

6  33 

5  47 

5  7 

4  35 

4  10 

3  49 

3  15 

2 

50 

2  31 

2 

16 

2 

4 

55 

48 

41 

36 

62 

64 

7  48 

6  40 

5  53 

5  12 

4  40 

4  15 

3  53 

3  19 

2 

52 

2  34 

2 

19 

2 

6 

56 

49 

42 

37 

64 

66 

7  65 

6  47 

5  59 

5  17 

4  45 

4  19 

3  57 

3  22 

2 

54 

2  36 

2 

21 

2 

8 

67 

50 

43 

38 

66 

68 

8  1 

6  53 

6  4 

5  22 

4  49 

4  23 

4  1 

3  24 

2 

56 

2  38 

2 

22 

2 

9 

1 

59 

51 

44 

38 

68 

70 

8  7 

6  59 

6  8 

5  26 

4  53 

4  26 

4  4 

3  26 

2 

58 

2  40 

2 

23 

2 

10 

2 

0 

62 

45 

39 

70 

72 

8  12 

7  4 

6  11 

5  30 

4  56 

4  29 

4  6 

3  28 

3 

0 

2  41 

2 

24 

2 

11 

2 

1 

63 

46 

39 

72 

74 

6  14 

5  33 

4  59 

4  31 

4  8 

3  30 

3 

2 

2  42 

2 

25 

2 

12 

2 

2 

54 

47 

40 

74 

76 

5  1 

4  33 

4  9 

3  32 

3 

4 

2  43 

2 

26 

2 

13 

2 

3 

54 

47 

40 

76 

78 

4  10 

3  33 

3 

6 

2  44 

2 

27 

2 

14 

2 

3 

54 

47 

41 

78 

80 

3  34 

3 

7 

2  45 

2 

28 

2 

15 

2 

4 

65 

47 

41 

80 

82 

3 

8 

2  46 

2 

29 

2 

16 

2 

4 

65 

48 

42 

82 

84 

2  47 

2 

29 

2 

16 

2 

5 

56 

49 

42 

84 

86 

2 

29 

2 

16 

2 

6 

56 

49 

42 

86 

6<» 

70 

8" 

9° 

10° 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

24°  1  2 

r,° 

28° 

30° 

„_ 

TABLE  XXXIIL 

177 

THIRD  COR 

Rl 

ACTION.  TO  APPARE 
T  ALTITUDE  OF  THE 

Ml 

DISTANCE  64°. 

D's 
A.pp. 

Alt. 

APPAR] 

f,  OR  BTAB 

■• 

App. 
Alt. 

32° 

34°  1 

36»  1 

38°  1 

42° 

46°  1 

50° 

54=  1 

58° 

62° 

66° 

70° 

74° 

78° 

82° 

86° 

o 

/  n 

/ 

It 

/ 

// 

/ 

II 

1 

11 

1 

// 

/  II 

/ 

II 

/  II 

/ 

// 

/  // 

r 

II 

/  II 

/  n 

1   II 

/  // 

o 

6 

4  29 

4 

45 

5 

0 

5 

15 

5 

43 

6 

10 

6  36 

6 

59 

7  20 

7 

39 

7  54 

8 

7 

6 

7 

3  49 

4 

2 

4 

15 

4 

28 

4 

53 

5 

16 

5  37 

5 

57 

6  15 

6 

32 

6  46 

6 

59 

7 

8 

3  22 

3 

34 

3 

45 

3 

56 

4 

18 

4 

38 

4  57 

5 

15 

5  31 

5 

46 

5  58 

6 

7 

6  16 

8 

9 

3  6 

3 

10 

3 

20 

3 

30 

3 

49 

4 

7 

4  23 

4 

38 

4  52 

? 

5 

5  16 

5 

26 

5  34 

9 

10 

2  43 

2 

52 

3 

1 

3 

10 

3 

27 

3 

42 

3  56 

4 

9 

4  21 

\ 

32 

4  42 

4 

51 

4  59 

10 

11 

2  30 

2 

37 

2 

45 

2 

54 

3 

9 

3 

22 

3  35 

3 

47 

3  57 

4 

7 

4  16 

4 

24 

4  31 

11 

12 

2  19 

2 

25 

2 

33 

2 

40 

2 

53 

3 

5 

3  17 

3 

27 

3  37 

3 

47 

3  56 

4 

3 

4  8 

4  13 

12 

13 

2  9 

2 

15 

2 

22 

2 

28 

2 

40 

2 

51 

3  1 

3 

11 

3  20 

3 

29 

3  37 

3 

43 

3  47 

3  51 

13 

14 

2  1 

2 

7 

2 

13 

2 

18 

2 

29 

2 

39 

2  48 

2 

57 

3  6 

3 

14 

3  20 

3 

25 

3  29 

3  33 

14 

15 

1  54 

2 

0 

2 

5 

2 

10 

2 

19 

2 

29 

2  37 

2 

45 

2  53 

3 

0 

3  5 

3 

10 

3  14 

3  18 

15 

16 

1  48 

53 

58 

2 

3 

2 

11 

2 

20 

2  28 

2 

35 

2  42 

2 

48 

2  53 

2 

57 

3  1 

3  5 

3  8 

16 

17 

1  43 

47 

52 

56 

2 

4 

2 

12 

2  20 

2 

26 

2  32 

2 

38 

2  43 

2 

47 

2  51 

2  54 

2  56 

17 

18 

1  39 

43 

47 

50 

58 

2 

5 

2  12 

2 

18 

2  24 

2 

30 

2  35 

2 

39 

2  42 

2  44 

2  46 

18 

19 

1  36 

39 

42 

46 

52 

59 

2  5 

2 

11 

2  17 

2 

22 

2  27 

2 

31 

2  34 

2  36 

2  38 

19 

20 

1  33 

36 

38 

42 

— 

48 
44 

54 

1  59 
1  54 

2 

5 

2  11 

2 

15 

2  20 

2 

23 

2  26 

2  28 

2  30 

2  32 

20 

21 

1  30 

33 

35 

38 

49 

2 

0 

2  5 

2 

9 

2  13 

2 

16 

2  18 

2  20 

2  22 

2  23 

21 

22 

1  28 

30 

33 

35 

40 

45 

1  50 

55 

1  59 

2 

3 

2  6 

2 

9 

2  11 

2  13 

2  15 

2  16 

22 

23 

1  27 

28 

30 

32 

37 

41 

1  46 

51 

1  54 

58 

2  1 

2 

3 

2  5 

2  7 

2  9 

2  10 

23 

24 

1  26 

27 

28 

30 

34 

38 

1  42 

47 

1  50 

54 

1  57 

59 

2  0 

2  2 

2  4 

2  5 

24 

25 

1  25 

26 

27 

28 

32 

35 

1  39 

43 

1  47 

50 

1  53 

55 

1  56 

1  58 

1  59 

2  0 

25 

26 

1  24 

25 

1 

26 

27 

30 

33 

1  36 

40 

1  44 

47 

1  49 

51 

1  52 

1  54 

1  55 

1  56 

26 

27 

1  23 

24 

25 

26 

28 

31 

1  34 

37 

1  41 

44 

1  46 

47 

1  49 

1  50 

1  51 

1  52 

27 

28 

1  23 

1 

23 

24 

25 

26 

29 

1  32 

35 

1  38 

41 

1  43 

44 

1  45 

1  46 

1  47 

1  48 

28 

29 

1  22 

22 

23 

24 

25 

27 

1  30 

32 

1  35 

38 

1  40 

41 

1  42 

1  43 

1  44 

1  45 

29 

30 

1  22 

22 

23 

23 

24 

26 

1  28 

30 

1  33 

1  31 

35 

1  37 

38 
35 

1  39 

1  40 

1  41 

1  42 

30 
31 

31 

1  22 

22 

22 

22 

23 

24 

1  26 

28 

33 

1  34 

1  36 

1  37 

1  38 

1  40 

32 

1  21 

21 

21 

21 

22 

23 

1  25 

27 

1  29 

31 

1  32 

33 

1  34 

1  35 

1  36' 1  38 

32 

33 

1  21 

21 

21 

21 

21 

22 

1  24 

26 

1  27 

29 

1  30 

31 

1  32 

1  33 

1  34 

33 

34 

1  21 

20 

20 

20 

20 

21 

1  23 

25 

1  26 

27 

1  28 

29 

1  30 

1  31 

1  32 

34 

35 

1  21 

20 

20 

20 

20 

21 

1  22 

23 

1  24 

25 

1  26 

27 

1  28 

1  29 

1  30 

35 

36 

1  21 

20 

19 

19 

19 

20 

1  21 

22 

1  23 

24 

1  25 

26 

1  26 

1  27 

1  28 

36 

37 

1  21 

20 

19 

19 

19 

19 

1  20 

21 

1  22 

23 

1  24 

25 

1  25 

1  26 

37 

38 

1  21 

20 

19 

18 

18 

18 

1  19 

20 

1  21 

22 

1  23 

24 

1  24 

1  25 

38 

39 

1  21 

20 

19 

18 

18 

18 

1  18 

19 

1  20 

21 

1  21 

22 

1  22 

1  23 

39 

40 

1  22 

20 

19 

18 

17 

17 

1  18 

18 

1  19 

20 

1  20 

21 

1  21 

1  22 

40 
41 

41 

1  22 

20 

19 

18 

17 

17 

1  17 

17 

1  18 

19 

1  19 

20 

1  20 

42 

1  22 

20 

19 

18 

16 

16 

1  16 

17 

1  17 

18 

1  18 

19 

1  19 

42 

43 

1  23 

21 

19 

18 

16 

16 

1  16 

16 

1  16 

17 

1  17 

18 

1  18 

43 

44 

1  23 

21 

19 

18 

16 

16 

1  16 

16 

1  16 

16 

1  16 

17 

1  17 

44 

46 

1  24 

22 

20 

18 

16 

15 

1  15 
1  15 

— 

15 
14 

1  15 

15 

1  15 

16 

46 

48 

1  25 

22 

20 

19 

16 

15 

1  14 

14 

1  14 

1 

14 

48 

50 

1  26 

23 

21 

19 

16 

15 

1  14 

13 

1  13 

13 

1  13 

50 

52 

1  27 

24 

22 

20 

17 

15 

1  13 

12 

1  12 

12 

1  12 

52 

54 

1  28 

25 

22 

20 

17 

15 

1  13 

12 

1  11 

11 

54 

56 

1  29 

26 

1  «3 

21 

17 

15 

1  13 

12 

1  11 

11 

56 

58 
60 
62 

1  29 
1  30 
1  31 

26 

27 
28 

23 

24 
25 

21 

22 
22 

18 
18 
18 

15 
15 
15 

1  13 
1  13 
1  13 

11 
11 
11 

1  10 
1  10 

TABLS  P.  KFFKCT  OF  BUN'b  PAR 

Add  the  Numbers  above  tk* 

64 

1  32 

28 

25 

22 

1 

18 

15 

1  13 

11 

lines  to  3rd  Correction,  sub- 

66 

1  33 

29 

26 

23 

18 

16 

1  13 

i's 

tract  tut  oiners.              ■ 

68 

1  33 

29 

26 

23 

19 

16 

1  13 

^p? 

S 

an  8 
10 -^ 

AjJJ 
1,10 

Dare 
40  fi 

ni  ALU 

0  60  70 

uc 

Ml 

e. 

on 

70 

1  34 

3t 

27 

24 

19 

16 



72 

1  34 

30 

27 

24 

19 

16 

t* 

"  ' 

" 

*/  / 

'  " 

i> 

tt 

" 

74 
76 

1  35 
1  35 

1 

31 

31 

28 

28 

24 
25 

19 

20 

5 
10 
20 

0 

1 

3 

0  1 

1  0 

3  2 

1 

0 

1 

2  . 

1  ' 
1  ( 

J  3 
J  2 

)  0 

3 
2 
1 

1 

78 

1  36 

1 

32 

28 

25 

30 

5 

4  3 

3 

2  1 

l    1 

1 

T 

0 

80 

1  36 

I 

32 

28 

25 

40 

6 

6  5 

4 

4  ; 

)  3 

2 

2 

82 

1  37 

32 

28 

50 

7 

7  6 

5 

5  ' 

t  4 

4 

84 

1  37 

32 

60 

70 

8 
9 

8  7 

9  -^ 

7 

6  . 
7 

5  6 
1 

86 

1  37 

80 

8 

8 

8 

7 

32° 

■3  10 

QGO 

38° 

42° 

\aO 

50° 

54° 

58° 

62° 

66* 

70° 

90 

178                 TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  QS'^. 

1 

D's 

APPARENT  ALTITUDE  OF  THE  SUN,  OR  STAR. 

D's 

App. 
Alt. 

App 

Alt. 

6» 

70 

80 

9° 

10° 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26°  1 

28°  1 

30° 

0 

/  f 

/  // 

/  ff 

r    It 

1     ir 

r    II 

/  n 

/  1' 

/  II 

1    II 

1    II 

/  II 

1 

II 

1 

II 

1 

II 

1    II 

0 

6 

1  29 

1  31 

1  34 

1  37 

1  41 

1  46 

1  52 

2  6 

2  21 

2  36 

2  52 

3  8 

3 

24 

3 

39 

3 

54 

4  10 

6 

7 

1  32 

1  29 

1  31 

1  33 

1  36 

1  39 

1  43 

1  54 

1  5 

2  17 

2  30 

2  43 

2 

56 

3 

9 

3 

22 

3  36 

7 

8 

1  36 

1  31 

1  29 

1  30 

1  32 

1  34 

1  37 

1  45 

1  54 

2  4 

2  14 

2  25 

2 

37 

2 

48 

2 

59 

3  11 

8 

9 

1  41 

1  34 

1  31 

1  29 

1  30 

1  31 

1  33 

1  38 

1  46 

1  54 

2  3 

2  12 

2 

22 

2 

32 

2 

42 

2  52 

9 

10 

1  46 

1  38 

1  33 

1  30 

1  29 

1  30 

1  31 

1  34 

1  40 

1  47 

1  54 

2  2 

2 

10 

2 

19 

2 

28 

2  36 

10 

11 

1  52 

1  43 

1  36 

1  32 

1  30 

1  29 

1  30 

1  32 

1  36 

1  41 

1  47 

1  54 

2 

1 

2 

9 

2 

16 

2  24 

u 

12 

1  59 

1  48 

1  40 

1  35 

1  32 

1  30 

1  29 

1  30 

1  33 

1  37 

1  42 

1  48 

54 

2 

0 

2 

7 

2  14 

12 

13 

2  6 

1  53 

1  44 

1  38 

1  34 

1  32 

1  30 

1  29 

1  31 

1  34 

1  38 

1  43 

48 

53 

59 

2  5 

13 

14 

2  14 

1  59 

I  49 

1  42 

1  37 

1  34 

1  31 

1  29 

1  30 

1  32 

1  35 

1  39 

44 

48 

53 

1  58 

14 

15 

2  21 

2  5 

1  54 

1  46 

1  40 

1  36 

1  33 

1  30 

1  30 

1  31 

1  33 

1  36 

40 

44 

48 

1  53 

15 
16 

16 

2  28 

2  11 

1  59 

1  50 

1  44 

1  39 

1  35 

1  31 

1  29 

1  30 

1  32 

1  34 

37 

40 

44 

1  48 

17 

2  36 

2  17 

2  4 

1  54 

1  47 

1  42 

1  38 

1  32 

1  29 

1  29 

1  30 

1  32 

34 

37 

40 

1  44 

17 

18 

2  44 

2  24 

2  10 

1  59 

1  51 

1  45 

1  40 

1  34 

1  30 

1  28 

1  29 

1  30 

32 

35 

37 

1  40 

18 

19 

2  52 

2  30 

2  15 

2  4 

1  55 

1  48 

1  43 

1  35 

1  31 

1  28 

1  28 

1  29 

31 

33 

* 

35 

1  37 

19 

20 

3  0 

2  36 

2  21 

2  8 

1  59 

1  52 

1  46 

1  37 

1  32 

1  29 

1  28 

1  29 

30 

31 

1 

33 

1  35 

20 

21 

3  8 

2  43 

2  26 

2  13 

2  3 

1  55 

1  48 

1  39 

1  33 

1  30 

1  28 

1  28 

29 

30 

31 

1  33 

21 

22 

3  15 

2  49 

2  32 

2  17 

2  7 

1  58 

1  51 

1  41 

1  35 

1  31 

1  29 

1  27 

28 

29 

30 

1  31 

22 

23 

3  23 

2  56 

2  37 

2  22 

2  11 

2  2 

1  54 

1  43 

1  37 

1  32 

1  29 

1  27 

27 

28 

29 

1  30 

23 

24 

3  31 

3  3 

2  43 

2  27 

2  15 

2  5 

1  57 

1  46 

1  39 

1  34 

1  30 

1  28 

27 

28 

1 

28 

1  29 

24 

25 
26 

3  39 

3  9 

2  48 

2  32 

2  19 

2  9 

2  0 

1  48 

1  41 

1  35 

1  31 

1  29 

27 

27 

27 

1  28 

25 
26 

3  47 

3  16 

2  54 

2  37 

2  23 

2  12 

2  4 

1  51 

1  43 

1  36 

1  32 

1  30 

28 

27 

27 

1  27 

27  3  55 

3  23 

3  0 

2  42 

2  27 

2  16 

2  7 

1  54 

1  44 

1  37 

1  33 

1  30 

28 

27 

26 

1  27 

27 

28 

4  2 

3  29 

3  5 

2  47 

2  31 

2  19 

2  10 

1  56 

1  46 

1  39 

1  34 

1  31 

29 

27 

26 

1  26 

28 

29 

4  10 

3  36 

3  11 

2  52 

2  35 

2  23 

2  14 

1  59 

1  48 

1  41 

1  35 

1  32 

29 

27 

26 

1  26 

29 

30 

4  17 

3  42 

3  16 

2  57 

2  40 

2  27 

2  17 

2  1 

1  50 

1  42 

1  36 

1  32 

29 

27 

26 

1  26 

30 
31 

31 

4  25 

3  49 

3  22 

3  2 

2  44 

2  31 

2  20 

2  3 

1  52 

1  43 

1  37 

1  33 

30 

28 

27 

1  26 

32 

4  32 

3  55 

3  27 

3  7 

2  49 

2  34 

2  23 

2  6 

1  54 

1  45 

1  38 

1  33 

30 

28 

27 

1  26 

32 

33 

4  40 

4  2 

3  33 

3  12 

2  53 

2  38 

2  26 

2  9 

1  56 

1  47 

1  39 

1  34 

31 

29 

27 

1  26 

33 

34 

4  48 

4  8 

3  39 

3  16 

2  57 

2  42 

2  30 

2  12 

1  58 

1  48 

1  41 

1  35 

32 

30 

28 

1  26 

34 

35 

4  55 

4  15 

3  45 

3  21 

3  2 

2  46 

2  34 

2  15 

2  0 

1  50 

1  43 

1  37 

33)1 

30 

28 

1  26 

35 
36 

36 

5  2 

4  21 

3  50 

3  26 

3  6 

2  50 

2  37 

2  17 

2  3 

1  52 

1  44 

1  38 

34 

31 

28 

1  26 

37 

5  10 

4  27 

3  56 

3  30 

3  10 

2  53 

2  41 

2  20 

2  5 

1  54 

1  46 

1  39 

35 

31 

28 

1  26 

37 

38 

5  17 

4  33 

4  1 

3  35 

3  14 

2  57 

2  44 

2  22 

2  7 

1  56 

1  48 

1  41 

36 

32 

29 

1  27 

38 

39 

5  24 

4  39 

4   6 

3  40 

3  18 

3   1 

2  47 

2  25 

2  9 

1  58 

1  50 

1  43 

37 

33 

30 

1  27 

39 

40 

5  31 

4  45 

4  11 

3  45 

3  22 

3  5 

2  50 

2  27 

2  11 

2  0 

1  51 

1  44 

38 

34 

31 

1  28 

40 

41 

5  38 

4  51 

4  16 

3  49 

3  26 

3  9 

2  53 

2  30 

2  14 

2  2 

1  53 

1  45 

39 

35 

31 

1  28 

41 

42 

5  44 

4  57 

4  21 

3  53 

3  30 

3  12 

2  56 

2  32 

2  16 

2  4 

1  54 

1  46 

40 

36 

32 

1  29 

42 

43 

5  50 

5  2 

4  26 

3  58 

3  34 

3  16 

2  59 

2  34 

2  19 

2  6 

1  56 

1  48 

41 

37 

33 

1  30 

43 

44 

5  57 

5  8 

4  31 

4  2 

3  38 

3  19 

3   3 

2  37 

2  21 

2  8 

1  57 

1  49 

43 

38 

34 

1  31 

44 

46 

6  10 

5  19 

4  41 

4  10 

3  46 

3  26 

3  9 

2  42 

2  25 

2  11 

1  59 

1  51 

45 

40 

35 

1  31 

46 

48 

48 

6  22 

5  29 

4  50 

4  18 

3  53 

3  32 

3  15 

2  47 

2  29 

2  14 

2  2 

1  54 

47 

41 

36 

1  32 

50 

6  34 

5  39 

4  59 

4  26 

3  59 

3  38 

3  21 

2  52 

2  33 

2  18 

2  5 

1  56 

49 

43 

38 

1  33 

50 

52 

6  45 

5  48 

5  7 

4  33 

4  6 

3  44 

3  26 

2  56 

2  36 

2  21 

2  8 

1  58 

51 

45 

39 

1  35 

52 

54 

6  56 

5  57 

5  14 

4  40 

4  12 

3  50 

3  31 

3  0 

2  39 

2  24 

2  11 

2  0 

1 

52 

46 

40 

1  36 

54 

56 

7  6 

6  6 

5  21 

4  46 

4  18 

3  55 

3  36 

3  4 

2  42 

2  27 

2  14 

2  2 

54 

47 

41 

1  37 

56 

58 

7  15 

6  14 

5  28 

4  52 

4  24 

4  0 

3  41 

3  8 

2  45 

2  29 

2  16 

2  4 

56 

49 

43 

1  38 

58 

60 

7  24 

6  22 

5  35 

4  58 

4  29 

4  5 

3  4S 

3  12 

2  48 

2  32 

2  18 

2  6 

58 

51 

45 

1  39 

60 

62 

7  33 

6  29 

5  42 

5  3 

4  34 

4  10 

3  49 

3  15 

2  51 

2  34 

2  20 

2  8 

59 

52 

46 

1  40 

62 

64 

7  41 

6  35 

5  48 

5  8 

4  39 

4  14 

3  53 

3  18 

2  54 

2  36 

2  22 

2  10 

2 

1 

53 

47 

1  41 

64 

66 

68 

7  48 

6  41 

5  53 

5  13 

4  43 

4  18 

3  57 

3  21 

2  56 

2  38 

2  24 

2  12 

2 

2 

54 

48 

1  42 

66 

7  55 

6  47 

5  58 

5  17 

4  47 

4  22 

4  0 

3  24 

2  59 

2  40 

2  26 

2  14 

2 

3 

55 

49 

1  43 

68 

70 

8  1 

6  52 

6  3 

5  21 

4  51 

4  25 

4  3 

3  27 

3   1 

2  42 

2  27 

2  15 

2 

4 

56 

50 

1  44 

70 

72 

8  7 

6  57 

6  8 

5  25 

4  55 

4  28 

4  6 

3  30 

3  3 

2  44 

2  28 

2  15 

2 

5 

57 

51 

1  45 

72 

74 

8  12 

7  1 

6  12 

5  29 

4  58 

4  30 

4  8 

3  32 

3   5 

2  45 

2  29 

2  16 

2 

5 

57 

51 

1  45 

74 

76 

8  17 

7  5 

6  15 

5  32 

5   1 

4  32 

4  10 

3  34 

3  7 

2  46 

2  30 

2  17 

2 

6 

58 

51 

1  45 

76 

78 

6  18 

5  35 

5  3 

4  34 

4  12 

3  35 

3  9 

2  47 

2  31 

2  18 

2 

7 

58 

52 

1  46 

78 

80 

5  5 

4  36 

4  13 

3  36 

3  10 

2  48 

2  32 

2  18 

2 

7 

59 

52 

1  46 

80 

82 

4  14 

3  37 

3  11 

2  49 

2  32 

2  19 

2 

8 

59 

52 

1  46 

82 

84 

3  38 

3  11 

2  50 

2  33 

2  20 

2 

9 

2 

0 

53 

1  46 

84 

86 

3  12 

2  50 

2  33 

2  20 

2 

9 

2 

0 

53 

86 

6' 

7° 

8° 

9° 

10° 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30°     1 

TABLE  XXXIII. 

179 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  68°. 

A-pp. 

Alt. 

APPARENT  ALTITUDE  OF 

THE 

SUN,  OR  STAR. 

>'8 

App. 
Alt. 

32° 

34° 

36°  1 

38°  1 

42° 

46°  1 

50° 

54° 

58°  1 

62° 

66° 

70° 

74° 

78° 

82°  1 

86°  1 

o 

1    II 

/  n 

1 

II 

1 

II 

/ 

ri 

1 

II 

/  // 

/  /r 

1 

11 

1 

II 

1    II 

1 

// 

1 

// 

1    II 

1 

// 

1      II          0 

6 

4  25 

4  40 

4 

55 

5 

11 

5 

40 

6 

5 

6  29 

6  51 

7 

11 

7 

29 

7  45 

8 

0 

8 

14 

I  6 

7 

3  49 

4  1 

4 

14 

4 

27 

4 

52 

5 

15 

5  35 

5  53 

6 

10 

6 

25 

6  38 

6 

50 

7 

1 

7 

8 

3  22 

3  33 

3 

44 

3 

55 

4 

17 

4 

37 

4  55 

5  11 

5 

25 

5 

38 

5  51 

6 

2 

6 

10 

6  18 

8 

9 

3  1 

3  11 

3 

21 

3 

30 

3 

48 

4 

6 

4  22 

4  36 

4 

49 

$ 

0 

5  10 

5 

19 

5 

28 

5  30 

9 

10 

2  44 

2  53 

3 

2 

3 

10 

3 

25 

3 

41 

3  55 

4  9 

3  47 

4 

21 

4 

31 

4  40 

4 

49 

4 

57 

5  3 

10 
11 

11 

2  31 

2  39 

2 

47 

2 

54 

3 

8 

3 

22 

3  35 

3 

58 

4 

8 

4  16 

4 

23 

4 

29 

4  34 

12 

2  20 

2  27 

2 

34 

2 

41 

2 

53 

3 

6 

3  18 

3  29 

3 

39 

3 

48 

3  55 

4 

2 

4 

7 

4  11 

4 

15 

12 

13 

2  11 

2  17 

2 

23 

2 

29 

2 

41 

2 

52 

3  2 

3  12 

3 

22 

3 

30 

3  37 

3 

43 

3 

48 

3  52 

3 

56 

13 

14 

2  3 

2  9 

2 

14 

2 

19 

2 

30 

2 

40 

2  49 

2  58 

3 

6 

3 

14 

3  20 

3 

26 

3 

31 

3  35 

3 

38 

14 

15 

1  57 

2  2 

2 

6 

2 

11 

2 

21 

2 

30 

2  38 

2  46 

2 

54 

3 

1 

3  7 

3 

12 

3 

16 

3  20 

3 

23 

15 

16 

1  52 

1  56 

2 

0 

2 

4 

2 

13 

2 

21 

2  29 

2  37 

2 

44 

2 

50 

2  55 

3 

0 

3 

4 

3  8 

3 

10 

3  12 

16 

17 

1  47 

1  51 

55 

58 

2 

6 

2 

14 

2  21 

2  29 

2 

35 

2 

40 

2  45 

2 

49 

2 

53 

2  57 

2 

59 

3  0 

17 

18 

1  43 

1  47 

50 

54 

2 

1 

2 

8 

2  14 

2  21 

2 

27 

2 

32 

2  36 

2 

40 

2 

44 

2  47 

2 

49 

2  50 

18 

19 

1  40 

1  43 

46 

50 

56 

2 

2 

2  8 

2  15 

2 

20 

2 

25 

2  29 

2 

32 

2 

36 

2  39 

2 

41 

2  42 

19 

20 

1  37 

1  40 

43 

46 

— 

52 

48 

1 

57 

2  3 

2  9 

2 

14 

2 

18 

2  22 

2 

25 

2 

28 

2  31 

2 

33 

2  34 

20 

21 

1  35 

1  37 

40 

43 

53 

1  58 

2  3 

2 

8 

2 

12 

2  16 

2 

19 

2 

21 

2  23 

2 

25 

2  26 

21 

22 

1  33 

1  35 

37 

40 

44 

49 

1  54 

1  58 

2 

2 

2 

6 

2  10 

2 

13 

2 

15 

2  17 

2 

19 

2  20 

22 

23 

1  31 

1  33 

35 

37 

41 

46 

1  50 

1  54 

1 

57 

2 

1 

2  5 

2 

8 

2 

10 

2  12 

2 

14 

2  15 

23 

24 

1  30 

1  31 

33 

35 

39 

43 

1  47 

1  50 

53 

57 

2  0 

2 

3 

2 

5 

2  7 

2 

9 

2  10 

24 

25 

1  29 

1  30 

1  29 

31 

33 

37 

40 

1  44 

1  47 

50 

53 

1  56 

1 

59 

2 

1 

2  2 

2 

4 

2  5 

25 

26 

1  28 

30 

32 

35 

38 

1  41 

1  44 

47 

50 

1  53 

55 

57 

1  58 

59 

2  0 

26 

27 

1  27 

1  28 

29 

30 

33 

36 

1  38 

1  41 

44 

47 

1  50 

52 

53 

1  54 

55 

1  56 

27 

28 

1  27 

1  27 

28 

29 

31 

34 

1  36 

1  39 

41 

44 

1  47 

49 

50 

1  51 

52 

1  52 

28 

29 

1  26 

1  26 

27 

28 

29 

32 

1  34 

1  37 

39 

41 

1  44 

46 

47 

1  48 

49 

29 

30 

1  26 

1  26 

26 

27 

28 

30 

1  32 

1  35 

37 

39 

1  41 

— 

43 
40 

44 

1  45 

46 

30 

31 

1  25 

1  25 

26 

26 

27 

29 

1  31 

1  33 

35 

37 

1  39 

41 

1  42 

43 

31 

32 

1  25 

1  25 

25 

25 

26 

28 

1  29 

1  31 

33 

35 

1  37 

38 

39 

1  40 

41 

32 

33 

1  25 

1  24 

25 

25 

26 

27 

1  28 

1  30 

31 

33 

1  35 

36 

37 

1  38 

33 

34 

1  25 

1  24 

24 

24 

25 

26 

1  27 

1  29 

30 

31 

1  33 

34 

35 

1  36 

34 

35 

1  25 

1  24 

24 

24 

24 

25 

1  26 

1  28 

29 

30 

1  31 

32 

33 

1  34 

35 

36 

1  25 

1  24 

23 

23 

23 

24 

1  25 

1  27 

28 

29 

1  30 

30 

31 

1  32 

36 

37 

1  25 

1  24 

23 

23 

23 

23 

1  24 

1  26 

27 

28 

1  29 

29 

30 

37 

38 

1  25 

1  24 

23 

22 

22 

23 

1  24 

1  25 

26 

27 

1  28 

28 

29 

38 

39 

1  25 

1  24 

23 

22 

22 

23 

1  23 

1  24 

25 

26 

1  27 

27 

27 

39 

40 

1  26 

1  25 

24 

23 

22 

22 

1  23 

1  23 

24 

25 

1  26 

26 

26 

40 
41 

41 

1  26 

I  25 

24 

23 

21 

21 

1  22 

1  22 

23 

24 

1  25 

25 

42 

1  27 

1  25 

24 

23 

21 

21 

1  21 

1  22 

23 

23 

1  24 

24 

42 

43 

1  27 

1  25 

24 

23 

21 

21 

1  21 

1  21 

22 

22 

1  23 

23 

43 

44 

1  28 

1  26 

24 

23 

21 

20 

1  20 

1  20 

21 

21 

1  22 

22 

44 

46 

1  28 

1  26 

25 

— 

24 

24 

21 

19 

1  19 
1  18 

1  19 

20 

20 

1  20 

46 

48 

1  29 

1  27 

25 

22 

19 

1  18 

19 

19 

1  19 

48 

50 

1  30 

1  28 

26 

25 

22 

20 

1  18 

1  18 

18 

18 

50 

52 

1  31 

1  29 

27 

25 

22 

20 

1  18 

1  17 

17 

17 

52 

54 

1  32 

1  29 

27 

26 

23 

20 

1  18 

1  17 

16 

54 

56 

1  33 

1  30 

28 

26 

23 

20 

1  18 

1  16 

15 

56 

58 
60 
62 

1  34 
1  35 
1  36 

1  31 
1  32 
1  33 

29 
29 
30 

27 
27 
28 

23 
23 
23 

20 
20 
20 

1  18 
1  18 
1  18 

1  16 
1  16 

1    1 

TABLE  P.  EFFECT  OF  BUN'b  PAR 

Add  tht  Numbers  above  the 

64 
66 

1  37 
1  38 

1  33 
1  34 

30 
31 

28 
28 

24 
24 

20 

20 

1  17 

lines  to  3rd  Correction,  sub- 
tract the  others. 

)'9 

APP 
A  t. 

Sun's  Apparent  Altitude. j 

68 

70 

72 

1  38 
1  39 
1  39 

1  34 
1  35 
1  35 

31 
32 
32 

28 
29 
29 

24 
24 
24 

1 

20 

5 

10  2 

)30 

40|5 

0|60(70l 

n     1 

" 

"  ' 

t   It 

" 

74 
76 

1  4C 
1  4f 

1  3fi 
1  36 

32 
32 

29 
29 

S 
10 
20 
30 

1 
2 
3 
4 

0  u 

1  0 

3  2 

4  4 

1 
0 

1 

3 

1  ' 
1 

1  1 

2  ' 

i    2 

I 

J  0 

2  2 

J 
2 
0 

1 

2 

0  0 

1 

78 

1  41 

1  36 

1 

32 

80 

1  41 

I  3(] 

40 

6 

fi  3 

4 

4  : 

)  3 

3 

82 
84 
86 

1  41 

50 
60 

7 
8 

7  6 

8  7 

6 

7 

5  . 

6  ( 

>  4 

J 

70 
80 
90 

9 

9  8 

7 
8 

7 

32° 

34° 

QftO 

38^ 

42° 

AdO      nno 

54° 

58° 

62° 

66° 

7  no 

1  > 

A 

180                TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  72" 

App. 
Alt. 

APPARENT  ALTITUDE  OF 

THE  SUN, 

OR  STAR. 

3)'s 
App 

Alt. 

6» 

7«   8<»  1 

9* 

10° 

11° 

12° 

14° 

16°  1 

18° 

20°  1  22°  1 

240  1 

26°  1 

28° 

30° 

O         t       1' 

f    n 

/  ft 

t    It 

/  n 

/  n 

/  )) 

>    II 

/ 

II 

/  // 

/ 

// 

/  II 

1 

r/ 

1 

// 

1    II 

1    II 

0 

6 

1  33 

1  35 

1  37 

1  40 

1  44 

1  50 

1  56 

2  9 

2 

23 

2  38 

2 

53 

3  9 

3 

24 

3 

40 

3  56 

4  12 

6 

7 

1  35 

1  33 

1  34 

1  36 

1  39 

1  43 

1  47 

1  56 

2 

8 

2  21 

2 

34 

2  47 

3 

0 

3 

12 

3  25 

3  38 

7 

8 

1  39 

1  35 

1  33 

1  34 

1  36 

1  38 

1  41 

1  48 

58 

2  8 

2 

19 

2  30 

2 

41 

2 

52 

3   3 

3  14 

8 

9 

1  44 

1  38 

1  35 

1  33 

1  34 

1  35 

1  37 

1  42 

50 

1  58 

2 

7 

2  17 

2 

26 

2 

35 

2  44 

2  54 

9 

10 

1  50 

1  42 

1  37 

1  34 

1  33 

1  34 

1  35 

1  38 

44 

1  50 

1 

58 

2  6 

2 

14 

2 

22 

2  30 

2  39 

10 
11 

11 

1  56 

1  46 

1  40 

1  36 

1  34 

1  33 

1  34 

1  36 

40 

1  45 

51 

1  58 

2 

5 

2 

12 

2  20 

2  27 

12 

2  2 

1  51 

1  44 

1  39 

1  36 

1  34 

1  33 

1  35 

37 

1  41 

46 

1  52 

58 

2 

4 

2  11 

2  17 

12 

13 

2  9 

1  56 

1  48 

1  42 

1  39 

1  36 

1  34 

1  34 

35 

1  38 

42 

1  47 

52 

58 

2  4 

2  9 

13 

14 

2  16 

2  2 

1  53 

1  46 

1  42 

1  39 

1  36 

1  33 

34 

1  36 

39 

1  43 

47 

52 

1  57 

2  2 

14 

15 

2  23 

2  8 

1  58 

1  50 

1  45 

1  41 

1  38 

1  34 

33 

1  34 

36 

1  39 

43 

47 

1  51 

1  56 

15 

16 

2  30 

2  14 

2  3 

1  54 

1  48 

1  43 

1  40 

1  35 

33 

1  33 

34 

1  36 

39 

43 

1  47 

1  52 

16 

17 

2  37 

2  20 

2  8 

1  58 

1  51 

1  46 

1  42 

1  36 

34 

1  33 

34 

1  35 

37 

40 

1  44 

1  48 

17 

18 

2  45 

2  27 

2  13 

2  2 

1  54 

1  48 

1  44 

1  37 

34 

1  33 

33 

1  34 

36 

38 

1  41 

1  44 

18 

19 

2  53 

2  33 

2  18 

2  7 

1  58 

1  51 

1  46 

1  39 

35 

1  33 

33 

1  34 

35 

37 

1  39 

1  41 

19 

20 

3  1 

2  40 

2  24 

2  11 

2  2 

1  54 

1  49 

1  41 

36 

1  34 

33 

1  33 

34 

35 

1  37 

1  39 

20 
21 

21 

3  9 

2  46 

2  29 

2  16 

2  6 

1  58 

1  52 

1  43 

37 

1  34 

1 

33 

1  33 

33 

34 

1  35 

1  37 

22 

3  17 

2  53 

2  35 

2  20 

2  10 

2  2 

1  55 

1  45 

39 

1  35 

33 

1  32 

33 

33 

1  34 

1  35 

22 

23 

3  25 

2  59 

2  40 

2  25 

2  14 

2  5 

1  58 

1  47 

40 

1  36 

34 

1  32 

32 

33 

1  33 

1  34 

23 

24 

3  33 

3  6 

2  46 

2  30 

2  18 

2  8 

2  1 

1  50 

42 

1  37 

34 

1  32 

32 

32 

1  33 

1  34 

24 

25 

26 

3  41 

3  12 

2  51 

2  35 

2  23 

2  12 

2  4 

1  52 

44 

1  38 

35 

1  33 

32 

32 

1  32 

1  33 

25 
26 

3  48 

3  18 

2  57 

2  40 

2  27 

2  16 

2  8 

1  55 

46 

1  40 

36 

1  33 

32 

31 

1  31 

1  32 

27 

3  56 

3  25 

3  2 

2  45 

2  31 

2  20 

2  12 

1  57 

48 

1  41 

37 

1  34 

32 

31 

1  31 

1  31 

27 

28 

4  3 

3  31 

3  7 

2  49 

2  35 

2  24 

2  15 

2  .0 

50 

1  43 

38 

1  34 

32 

31 

1  30 

1  31 

28 

29 

4  11 

3  37 

3  13 

2  54 

2  39 

2  27 

2  18 

2  2 

52 

1  45 

39 

1  35 

33 

32 

1  31 

1  30 

29 

30 

4  18 

3  44 

3  19 

2  59 

2  43 

2  31 

2  21 

2  5 

54 

1  46 

40 

1  36 

34 

32 

1  31 

1  30 

30 
31 

31 

4  26 

3  50 

3  24 

3  4 

2  47 

2  34 

2  24 

2  8 

56 

1  48 

41 

1  37 

34 

32 

1  31 

1  30 

32 

4  33 

3  56 

3  29 

3  9 

2  51 

2  38 

2  27 

2  11 

58 

1  50 

43 

1  38 

35 

33 

1  32 

1  31 

32 

33 

4  40 

4  2 

3  35 

3  14 

2  56 

2  42 

2  30 

2  14 

2 

0 

1  51 

44 

1  39 

35 

33 

I  32 

1  31 

33 

34 

4  47 

4  9 

3  41 

3  18 

3  0 

2  45 

2  33 

2  16 

2 

2 

1  53 

46 

1  40 

36 

34 

1  32 

1  31 

34 

35 

4  54 

4  15 

3  46 

3  23 

3  4 

2  49 

2  37 

2  18 

2 

4 

1  54 

47 

1  41 

37 

34 

1  32 

1  31 

35 
36 

36 

5  1 

4  21 

3  51 

3  27 

3  8 

2  53 

2  40 

2  20 

2 

7 

1  56 

48 

1  42 

38 

35 

1  33 

1  32 

37 

5  9 

4  27 

3  56 

3  32 

3  12 

2  57 

2  43 

2  23 

2 

9 

1  58 

50 

1  44 

39 

36 

1  33 

1  32 

37 

38 

5  16 

4  33 

4  1 

3  37 

3  16 

3   0 

2  47 

2  26 

2 

11 

2  0 

52 

1  45 

40 

37 

1  34 

1  32 

38 

39 

5  23 

4  39 

4  6 

3  41 

3  20 

3   4 

2  50 

2  28 

2 

13 

2  2 

53 

1  46 

41 

38 

1  34 

1  32 

39 

40 

5  30 

4  45 

4  11 

3  46 

3  24 

3   7 

2  54 

2  30 

2 

15 

2  4 

54 

1  48 

— 

43 
44 

39 

1  35 

1  33 

40 

41 

5  37 

4  51 

4  16 

3  50 

3  28 

3  11 

2  57 

2  32 

2 

18 

2  6 

56 

1  49 

40 

1  36 

1  33 

41 

42 

5  44 

4  57 

4  21 

3  54 

3  32 

3  15 

3  0 

2  35 

2 

20 

2  8 

58 

1  50 

45 

41 

1  37 

1  34 

42 

43 

5  51 

5  2 

4  26 

3  59 

3  36 

3  18 

3  3 

2  37 

2 

22 

2  10 

59 

1  51 

46 

42 

1  38 

1  34 

43 

44 

5  57 

5  7 

4  30 

4  3 

3  40 

3  22 

3   6 

2  41 

2 

24 

2  12 

2 

1 

1  53 

47 

43 

1  39 

1  35 

44 

46 

6  9 

5  17 

4  39 

4  11 

3  47 

3  29 

3  12 

2  45 

2 

28 

2  15 

2 

4 

1  55 

49 

44 

1  40 

1  36 

46 

48 

48 

6  21 

5  27 

4  48 

4  19 

3  54 

3  35 

3  18 

2  50 

2 

32 

2  18 

2 

7 

1  58 

51 

45 

1  41 

]  38 

50 

6  32 

5  37 

4  57 

4  26 

4  1 

3  41 

3  23 

2  55 

2 

35 

2  21 

2 

10 

2  0 

53 

47 

1  43 

1  39 

50 

52 

6  43 

5  46 

5  6 

4  33 

4  7 

3  46 

3  28 

2  59 

2 

39 

2  24 

2 

12 

2  2 

55 

49 

1  44 

1  40 

52 

54 

6  54 

5  55 

5  14 

4  40 

4  13 

3  52 

3  33 

3  3 

2 

43 

2  27 

2 

15 

2  5 

57 

50 

1  45 

1  41 

54 

56 

7  4 

6  4 

5  22 

4  47 

4  19 

3  57 

3  38 

3  7 

2 

47 

2  31 

2 

18 

2  7 

59 

52 

1  46 

1  42 

56 

58 

7  13 

6  12 

5  29 

4  53 

4  25 

4  2 

3  43 

3  11 

2 

50 

2  34 

2 

21 

2  9 

2 

0 

53 

1  47 

1  43 

58 

60 

7  22 

6  20 

5  35 

4  58 

4  30 

4  7 

3  47 

3  15 

2 

53 

2  37 

2 

23 

2  11 

2 

2 

54 

1  49 

1  44 

60 

62 

7  31 

6  27 

5  41 

5  3 

4  35 

4  11 

3  51 

3  19 

2 

56 

2  39 

2 

25 

2  13 

2 

4 

56 

1  50 

1  45 

62 

64 

7  39 

6  33 

5  47 

5  8 

4  40 

4  15 

3  55 

3  22 

2 

59 

2  41 

2 

27 

2  15 

2 

5 

57 

1  51 

1  46 

64 

66 

7  46 

6  39 

5  53 

5  13 

4  44 

4  19 

3  59 

3  25 

3 

1 

2  43 

2 

29 

2  16 

2 

6 

58 

1  52 

1  47 

66 

68 

7  52 

6  45 

5  58 

5  18 

4  48 

4  23 

4  2 

3  28 

3 

3 

2  45 

2 

30 

2  18 

2 

7 

1 

59 

1  52 

1  47 

68 

70 

7  58 

6  50 

6  3 

5  22 

4  52 

4  26 

4  4 

3  30 

3 

5 

2  47 

2 

31 

2  19 

2 

8 

2 

0 

1  53 

1  48 

70 

72 

8  4 

6  55 

6  7 

5  26 

4  55 

4  29 

4  7 

3  32 

3 

7 

2  48 

2 

33 

2  20 

2 

9 

2 

1 

1  54 

1  48 

72 

74 

8  9 

7  ( 

6  10 

5  30 

4  58 

4  31 

4  9 

3  34 

3 

9 

2  49 

2 

34 

2  21 

2 

10 

2 

2 

1  55 

1  49 

74 

76 

8  13 

7  4 

6  14 

6  33 

5  1 

4  33 

4  11 

3  35 

3 

11 

2  50 

2 

35 

2  22 

2 

11 

2 

2 

1  56 

1  49 

76 

78 

8  16 

7  7 

6  17 

5  36 

5  3 

4  35 

4  12 

3  37 

3 

12 

2  51 

2 

36 

2  23 

2 

12 

2 

3 

1  56 

1  50 

78 

80 

8  19 

7  10 

6  19 

5  38 

5  5 

4  37 

4  14 

3  38 

3 

13 

2  52 

2 

37 

2  24 

2 

13 

2 

4 

1  57 

1  51 

80 

82 

6  21 

5  40 

5  7 

4  39 

4  16 

3  39 

3 

13 

2  53 

2 

38 

2  24 

2 

13 

2 

4 

1  57 

82 

84 

5  9 

4  41 

4  17 

3  40 

3 

14 

2  54 

2 

38 

2  24 

2 

14 

2 

5 

84 

86 

4  18 

3  41 

3 

15 

2  54 

2 

38 

2  24 

2 

14 

86 

6° 

7» 

8« 

g' 

10° 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

TABLE  XXXIil. 

181 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  72°. 

J>'8 

App. 

Alt. 

APPARENT  ALTITUDE  OF  THE 

SUN, 

OR  STAR. 

>'8 

App. 
Alt. 

32° 

34° 

36° 

38° 

42° 

46° 

50° 

54° 

58° 

62* 

66°  1 

70° 

74° 

78°  1 

82°  86° 

0 

/  // 

r  n 

/  rr 

/    n 

/  It 

t    // 

f     rr 

/  // 

/    II 

1 

// 

r 

// 

1   II 

1    II 

1 

// 

1    II 

'  "I 

o 

6 

4  27 

4  41 

4  56 

5  11 

5   38 

6  3 

6  27 

6  48 

7  8 

7 

27 

7 

42 

7  55 

8  6 

8 

16 

e 

7 

3  51 

4  3 

4  16 

4  28 

4  51 

5  12 

5  32 

5  51 

6  8 

6 

23 

6 

36 

6  48 

6  58 

7 

7 

7 

8 

3  25 

3  36 

3  47 

3  58 

4  18 

4  36 

4  54 

5  11 

5  26 

5 

39 

5 

51 

6  1 

6  9 

6 

16 

6  22 

8 

9 

3  4 

3  14 

3  24 

3  33 

3  51 

4  8 

4  23 

4  37 

4  50 

5 

1 

5 

11 

5  20 

5  28 

5 

35 

5  41 

9 

10 

2  48 

•2  57 

3  6 

3  14 

3  29 

3  44 

3  58 

4  10 

4  22 

4 

33 

4 

42 

4  50 

4  57 

5 

3 

5  7 

10 
11 

11 

2  35 

2  43 

2  51 

2  58 

3  11 

3  25 

3  37 

3  48 

3  59 

4 

9 

4 

17 

4  24 

4  30 

4 

35 

4  39 

12 

2  24 

2  31 

2  38 

2  45 

2  57 

3  9 

3  20 

3  31 

3  41 

3 

49 

3 

57 

4  3 

4  8 

4 

12 

4  16 

4  20 

12 

13 

2  15 

2  21 

2  27 

2  33 

2  45 

2  56 

3  6 

3  16 

3  24 

3 

32 

3 

39 

3  45 

3  49 

3 

53 

3  56 

3  59 

13 

14 

2  7 

2  13 

2  18 

2  24 

2  34 

2  44 

2  54 

3  2 

3  10 

3 

18 

3 

24 

3  29 

3  33 

3 

36 

3  39 

3  41 

14 

15 

2  1 

2  6 

2  11 

2  16 

2  25 

2  34 

2  43 

2  51 

2  58 

3 

5 

3 

11 

3  16 

3  20 

3 

23 

3  25 

3  27 

15 

16 

1  56 

2  1 

2  5 

2  9 

2  18 

2  26 

2  33 

2  41 

2  48 

2 

54 

2 

59 

3  4 

3  8 

3 

11 

3  13 

3  15 

16 

17 

1  52 

1  56 

1  59 

2  3 

2  11 

2  19 

2  25 

2  32 

2  39 

2 

45 

2 

50 

2  54 

2  57 

3 

0 

3  2 

3  4 

17 

18 

1  48 

1  51 

1  54 

1  58 

2  6 

2  13 

2  19 

2  25 

2  31 

2 

37 

2 

42 

2  46 

2  48 

2 

50 

2  52 

2  54 

18 

19 

1  44 

1  47 

1  50 

1  54 

2  1 

2  7 

2  13 

2  19 

2  25 

2 

30 

2 

35 

2  38 

2  40 

2 

42 

2  44 

2  45 

19 

20 

1  41 

1  44 

1  47 

1  50 

1  56 

2  2 

2  7 

2  13 

2  19 

2 

23 

2 

28 

2  31 

2  33 

2 

35 

2  36 

2  37 

20 

21 

1  39 

1  41 

1  44 

1  46 

1  52 

1  57 

2  2 

2  8 

2  13 

2 

17 

2 

21 

2  24 

2  26 

2 

28 

2  29 

2  30 

21 

22 

1  37 

1  39 

1  41 

1  43 

1  48 

1  53 

1  58 

2  3 

2  7 

2 

11 

2 

15 

2  18 

2  20 

2 

22 

2  23 

2  24 

22 

23 

1  36 

1  37 

1  39 

1  41 

1  45 

1  50 

1  54 

1  59 

2  2 

2 

6 

2 

10 

2  13 

2  15 

2 

16 

2  17 

2  18 

23 

24 

1  35 

1  36 

1  37 

1  39 

1  43 

1  47 

1  51 

1  55 

1  58 

2 

2 

2 

5 

2  8 

2"  10 

2 

11 

2  12 

2  13 

24 

25 

1  34 

1  35 

1  36 

1  38 

1  41 

1  44 

1  48 

1  51 

1  54 

1 

58 

2 

1 

2  3 

2  5 

2 

6 

2  8 

25 

26 

1  33 

1  34 

1  35 

1  36 

1  39 

1  42 

1  45 

1  48 

1  51 

54 

57 

1  59 

2  1 

2 

2 

2  4 

26 

27 

1  32 

1  33 

1  34 

1  35 

1  37 

1  40 

1  43 

1  45 

1  48 

51 

54 

1  56 

1  57 

58 

2  0 

27 

28 

1  32 

1  32 

1  33 

1  34  1  35 

1  38 

1  41 

1  43 

1  46 

48 

51 

1  53 

1  54 

55 

1  56 

28 

29 

1  31 

1  32 

1  i2 

1  33  1  34 

1  36 

1  39 

1  41 

1  44 

46 

48 

1  50 

1  52 

53 

29 

30 

1  31 

1  31 
1  .■?! 

i  32 
1  31 

1  32 
1  31 

1  33 

1  35 

1  37 

1  39 

1  42 

44 

46 

1  47 

1  49 

50 

30 
31 

31 

1  30 

1  32 

1  34 

1  36 

1  38 

1  40 

42 

44 

1  45 

1  46 

47 

32 

I  29 

1  30 

1  30 

1  30 

1  31 

1  33 

1  35 

1  36 

1  38 

40 

42 

1  43 

1  44 

45 

32 

33 

1  29 

1  29 

1  29 

1  30 

1  31 

1  32 

1  33 

1  34 

1  36 

38 

40 

1  41 

1  42 

33 

34 

1  30 

1  29 

]  29 

1  29 

1  30 

1  31 

1  32 

1  33 

1  34 

36 

38 

1  39 

1  40 

34 

35 

1  30 

1  29 

1  29 

1  29 

1  30 

1  30 

1  31 

1  32 

1  33 

35 

36 

1  37 

1  38 

35 
36 

36 

1  31 

I  29 

1  28 

1  28 

1  29 

1  30 

1  31 

1  32 

1  33 

34 

35 

1  36 

1  36 

37 

1  31 

1  30 

1  28 

1  28 

1  29 

1  29 

1  30 

1  31 

1  32 

33 

34 

1  35 

37 

38 

1  31 

1  30 

1  28 

1  27 

1  29 

1  28 

1  30 

1  31 

1  32 

33 

33 

1  34 

38 

39 

1  31 

1  30 

1  29 

1  28 

1  28 

1  28 

1  29 

1  30 

1  31 

32 

32 

1  32 

39 

40 

1  31 

1  30 

1  29 

1  28 

1  27 

1  28 

1  28 

1  29 

1  30 

30 

30 

1  30 

40 
41 

41 

1  31 

1  30 

1  29 

1  28 

1  27 

1  27 

1  27 

1  28 

1  28 

29 

29 

42 

1  32 

1  31 

1  29 

1  28 

1  26 

1  26 

1  26 

1  27 

1  27 

28 

28 

42 

43 

1  32 

1  31 

1  29 

1  28 

1  26 

1  26 

1  26 

1  26 

1  26 

27 

27 

43 

44 

1  33 

1  31 

1  30 

1  28 

1  26 

1  26 

1  25 

1  25 

1  25 

26 

26 

44 

46 

1  34 

1  32 

1  30 

1  29 

1  27 

1  25 

1  25 
1  24 

1  25 

1  25 

25 

46 

48 

1  35 

1  32 

1  30 

1  29 

1  27 

1  25 

1  24 

1  24 

1 

24 

48 

50 

1  36 

1  33 

1  31 

1  30 

1  27 

1  25 

1  24 

1  23 

1  23 

60 

52 

1  37 

1  34 

1  31 

1  30 

1  27 

1  25 

1  23 

1  22 

1  23 

62 

54 

1  37 

1  34 

1  32 

1  31 

1  28 

1  25 

1  23 

1  22 

64 

56 

1  38 

1  35 

1  33 

1  31 

1  28 

1  25 

1  23 

1  22 

6b 

58 
60 
62 
64 
66 

1  39 
1  39 
1  40 
1  41 

1  42 

1  36 
1  36 
1  37 
1  38 
1  38 

1  34 
1  34 
1  35 
1  36 
1  36 

1  32 
1  32 
1  32 
1  33 
1  33 

1  28 
1  28 
1  28 
1  28 
1  28 

1  25 
1  25 
1  25 
1  25 

1  23 
1  23 

TABLK 

P.  BrFBCT  o»  sun's  pa  r  I 

Add  the  Numbers  above  th 

lines  to  Srd  Correction,  sub 

tract  the  others. 

e 

App 
Alt. 

s 

5 

, 

68 
70 

1  43 
1  4S 

1  39 
1  39 

1  36 
1  1  36 

1  34 
1  34 

1  29 

10  2 

130 

40.^ 

()()() 

70 

80 

00 

72 
74 
76 

1  i4 
1  44 
1  At 

\  1  4C 
[   1  4C 
)  1  4C 

)  1  36 
>  1  36 
» 

1  34 

10 
20 
30 
40 

n 

1 

2 
3 
4 

6 

//  # 

0  0 

1  1 

3  2 

4  4 

6  S 

1 
'  0 
2 
3 
5 

1 
0 

1  ' 
3 
4 

2  2 
1  1 

1  1 

2  2 
4  4 

2 

j_ 
1 
2 
3 

1 

0 
2 

0 

78 
80 

1  4t 

> 

sc 

50  7 

7  6 

6 

5 

5  5 

60  8 

8  7 

7 

6 

S 

84 
86 

1 

70  9 

80 
90 

8  e 

9  8 

7 

8 

7 

32° 

34° 

36° 

38° 

A  oo  A  cO  1  ftnO 

54° 

58° 

coO 

6fi° 

70° 

1 

1   lU 

f  tjyj 

182                 TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  76". 

D's 

App. 
Alt. 

APPARENT  ALTITUDE  OF  THE  SON, 

OR  STAR. 

App. 

Alt. 

6° 

7° 

8° 

90 

10° 

11° 

12° 

14° 

16° 

18° 

20°  1 

22°  1 

24°  1 

26°  1 

28°  1  30°  1 

o 

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/  // 

/  // 

1    n 

/  n 

/  // 

/  II 

/  n 

/  n 

/  It 

/ 

// 

1 

// 

1 

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1 

// 

1 

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II 

0 

6 

1  37 

1  39 

1  41 

1  44 

1  48 

1  54 

2  0 

2  13 

2  27 

2  42 

2 

57 

3 

13 

3 

28 

3 

43 

3 

58  4 

13 

6 

7 

1  40 

1  37 

1  38 

1  40 

1  43 

1  47 

1  51 

2  1 

2  12 

2  24 

2 

37 

2 

50 

3 

3 

3 

15 

3 

28 

3 

40 

7 

8 

1  44 

1  40 

1  37 

1  38 

1  40 

1  42 

1  45 

1  52 

2  2 

2  12 

2 

22 

2 

33 

2 

44 

2 

54 

3 

5 

3 

16 

8 

9 

1  49 

1  43 

1  39 

1  37 

1  38 

1  39 

1  41 

1  46 

1  54 

2  2 

2 

11 

2 

20 

2 

30 

2 

39 

2 

48 

2 

58 

9 

10 

1  54 

1  46 

1  41 

1  39 

1  37 

1  38 

1  39 

1  42 

1  48 

1  55 

2 

2 

2 

10 

2 

18 

2 

26 

2 

34 

2 

43 

10 

11 

2  0 

1  50 

1  44 

1  41 

1  39 

1  37 

1  38 

1  40 

1  44 

1  49 

55 

2 

2 

2 

9 

2 

16 

2 

23 

2 

31 

11 

12 

2  6 

1  55 

1  48 

1  44 

1  41 

1  38 

1  37 

1  38 

1  41 

1  45 

50 

56 

2 

2 

2 

8 

2 

15 

2 

21 

12 

13 

2  12 

2  0 

1  52 

1  47 

1  43 

1  40 

1  38 

1  37 

1  39 

1  42 

46 

51 

56 

2 

2 

2 

8 

2 

13 

13 

14 

2  19 

2  6 

1  56 

1  50 

1  45 

1  42 

1  40 

1  37 

1  38 

1  40 

43 

47 

52 

57 

2 

2 

2 

7 

14 

15 

2  26 

2  12 

2  1 

1  54 

1  48 

1  44 

1  42 

1  38 

1  37 

1  39 

41 

45 

49 

53 

1 

57 

2 

1 

15 

16 

2  34 

2  18 

2  6 

1  58 

1  51 

1  47 

1  44 

1  39 

1  37 

1  38 

40 

43 

46 

49 

53 

56 

16 

17 

2  41 

2  24 

2  11 

2  4 

1  54 

1  49 

1  46 

1  40 

1  38 

1  37 

39 

41 

43 

46 

49 

52 

17 

18 

2  49 

2  30 

2  17 

2  6 

1  58 

1  52 

1  48 

1  42 

1  39 

1  36 

38 

39 

41 

43 

46 

49 

18 

19 

2  57 

2  36 

2  22 

2  10 

2  2 

1  55 

1  50 

1  43 

1  40 

1  37 

37 

38 

39 

41 

43 

46 

19 

20 

3  5 

2  43 

2  27 

2  15 

2  6 

1  58 

1  52 

1  49 

1  41 

1  38 

36 

37 

38 

39 

41 

43 

20 

21 

3  12 

2  49 

2  33 

2  20 

2  10 

2  2 

1  55 

1  47 

1  42 

1  39 

37 

36 

37 

38 

39 

41 

21 

22 

3  20 

2  50 

2  38 

2  24 

2  14 

2  5 

1  58 

1  49 

1  44 

1  40 

38 

36 

36 

37 

38 

39 

22 

23 

3  28 

3  3 

2  44 

2  39 

2  18 

2  9 

2  1 

1  51 

1  45 

1  41 

38 

36 

35 

36 

37 

38 

23 

24 

3  36 

3  9 

2  49 

2  34 

2  22 

2  12 

2  4 

1  54 

1  47 

1  42 

39 

37 

1 

35 

36 

1 

36 

37 

24 

25 
26 

3  44 

3  15 

2  54 

2  39 

2  26 

2  16 

2  7 
2  11 

1  56 

1  45 

I  44 

40 

37 

36 

36 

36 

37 

25 
26 

3  51 

3  21 

3  0 

2  44 

2  30 

2  20 

1  59 

1  51 

1  45 

41 

38 

36 

35 

35 

36 

27 

3  59 

3  28 

3  5 

2  49 

2  34 

2  23 

2  14 

2  2 

1  53 

1  47 

42 

39 

37 

36 

35 

35 

27 

28 

4  6 

3  34 

3  10 

2  54 

2  38 

2  27 

2  17 

2  4 

1  54 

1  48 

43 

39 

37 

36 

35 

35 

28 

29 

4  13 

3  40 

3  15 

2  58 

2  42 

2  31 

2  21 

2  7 

1  56 

1  49 

44 

40 

38 

36 

35 

34 

29 

30 

4  20 

3  46 

3  52 

3  21 

3  3 

2  47 

2  34 

2  24 

2  9 

1  58 

1  51 

45 

41 

— 

39 
39 

37 

35 

34 

30 

31 

4  27 

3  26 

3  7 

2  51 

2  38 

2  28 

2  12 

2  0 

1  52 

46 

42 

37 

35 

34 

31 

32 

4  34 

3  58 

3  31 

3  12 

2  55 

2  42 

2  31 

2  14 

2  2 

1  54 

48 

43 

40 

38 

36 

35 

32 

33 

4  41 

4  4 

3  37 

3  16 

2  59 

2  45 

2  34 

2  17 

2  4 

1  55 

49 

44 

41 

38 

36 

35 

33 

34 

4  48 

4  10 

3  42 

3  20 

3  3 

2  49 

2  37 

2  19 

2  6 

1  57 

50 

45 

42 

39 

37 

35 

34 

35 
36 

4  55 

4  16 
4  22 

3  47 

3  25 

3  7 
3  11 

2  52 

2  41 

2  22 

2  8 

1  59 

52 

46 

42 

39 

37 

35 

35 
36 

5  2 

3  53 

3  29 

2  56 

2  44 

2  24 

2  11 

2  1 

53 

47 

43 

40 

38 

36 

37 

5  9 

4  27 

3  58 

3  34 

3  15 

3  0 

2  47 

2  27 

2  13 

2  3 

55 

48 

44 

41 

38 

36 

37 

38 

5  16 

4  33 

4  3 

3  38 

3  19 

3  3 

2  50 

2  29 

2  15 

2  4 

56 

49 

45 

42 

39 

37 

38 

39 

5  23 

4  38 

4  8 

3  43 

3  23 

3  7 

2  53 

2  31 

2  17 

2  6 

58 

51 

46 

42 

39 

37 

39 

40 

5  30 

4  44 

4  13 

3  47 

3  27 

3  10 

2  56 

2  34 

2  19 

2  8 

59 

52 

47 

43 

40 

38 

40 

41 

5  37 

4  50 

4  18 

3  51 

3  31 

3  14 

2  59 

2  36 

2  22 

2  10 

2 

0 

53 

48 

44 

41 

38 

41 

42 

5  43 

4  55 

4  23 

3  55 

3  34 

3  17 

3  2 

2  39 

2  24 

2  12 

2 

1 

54 

49 

45 

42 

39 

42 

43 

5  49 

5  1 

4  28 

3  59 

3  38 

3  20 

3  5 

2  41 

2  26 

2  14 

2 

3 

56 

50 

46 

43 

40 

43 

44 

5  55 

5  6 

4  33 

4  3 

3  41 

3  24 

3  8 

2  44 

2  28 

2  15 

2 

4 

57 

51 

47 

43 

40 

44 

46 

6  7 

5  16 

4  42 

4  11 

3  49 

3  31 

3  14 

2  49 

2  32 

2  18 

2 

7 

59 

53 

48 

44 

41 

46 

48 

6  19 

5  26 

4  51 

4  19 

3  56 

3  37 

3  20 

2  54 

2  35 

2  21 

2 

10 

2 

2 

55 

50 

46 

43 

48 

50 

6  30 

5  36 

4  59 

4  27 

4  3 

3  43 

3  25 

2  58 

2  39 

2  25 

2 

13 

2 

4 

57 

51 

47 

44 

50 

52 

6  41 

5  46 

5  7 

4  34 

4  10 

3  49 

3  30 

3  3 

2  43 

2  28 

2 

16 

2 

6 

59 

53 

49 

45 

52 

54 

6  51 

5  55 

5  15 

4  41 

4  17 

3  55 

3  35 

3  7 

2  47 

2  31 

2 

19 

2 

9 

2 

1 

55 

50 

46 

54 

56 

58 

7  1 

6  4 

5  22 

4  48 

4  23 

4  0 

3  40 

3  11 

2  50 

2  34 

2 

22 

2 

12 

2 

3 

56 

51 

47 

56 

7  11 

6  12 

5  29 

4  54 

4  28 

4  5 

3  45 

3  15 

2  53 

2  37 

2 

25 

2 

14 

2 

5 

57 

52 

48 

58 

60 

7  20 

6  20 

5  36 

5  0 

4  33 

4  9 

3  49 

3  19 

2  56 

2  40 

2 

27 

2 

16 

2 

6 

59 

53 

49 

60 

62 

7  28 

6  27 

5  42 

5  5 

4  37 

4  14 

3  53 

3  22 

2  59 

2  43 

2 

29 

2 

18 

2 

8 

2 

0 

54 

50 

62 

64 

7  3fc 

6  34 

5  48 

5  10 

4  41 

4  18 

3  57 

3  25 

3  2 

2  45 

2 

31 

2 

20 

2 

10 

2 

2 

56 

51 

64 

66 

68 

7  43 

6  40 

5  54 

5  15 

4  45 

4  22 

4  1 

3  28 

3  5 

2  47 

2 

33 

2 

21 

2 

11 

2 

3 

57 

52 

66 

7  49 

6  45 

5  59 

5  19 

4  49 

4  26 

4  5 

3  31 

2  8 

2  49 

2 

35 

2 

23 

2 

13 

2 

4 

58 

53 

68 

70 

7  5.'} 

6  50 

6  3 

5  23 

4  53 

4  29 

4  8 

3  34 

2  10 

2  51 

2 

36 

2 

24 

2 

14 

2 

5 

58 

ill  70  1 

72 

8   1 

6  54 

6  7 

5  27 

4  57 

4  32 

4  11 

3  37 

3  12 

2  52 

2 

37 

2 

25 

2 

15 

2 

6 

59 

54 

72 

74 

8  e 

6  58 

6  10 

5  30 

5  0 

4  34 

4  13 

3  39 

3  13 

2  53 

2 

38 

2 

26 

2 

16 

2 

7 

2 

0 

54 

74 

76 

78 

8  11 

7  2 

6  13 

5  33 

5  3 

4  36 

4  15 

3  41 

3  14 

2  54 

2 

39 

2 

26 

2 

16 

2 

7 

2 

1 

55 

76 

8  1£ 

.  7  € 

6  16 

5  36 

5  5 

4  38 

4  17 

3  42 

3  15 

2  55 

2 

40 

2 

27 

2 

17 

2 

8 

2 

1 

78 

80 

8  1? 

!  7  9 

6  19 

5  38 

5  7 

4  40 

4  19 

3  43 

3  16 

2  56 

2 

40 

2 

28 

2 

18 

2 

9 

80 

82 

8  2C 

17  11 

6  21 

5  40 

5  9 

4  42 

4  2( 

3  44 

3  17 

2  57 

2 

41 

2 

28 

2 

18 

82 

84 

8  2£ 

!  7  13 

6  23 

5  42 

5  10 

4  43 

4  21 

3  45 

3  18 

2  58 

2 

41 

2 

28 

84 

86 

6  25 

5  44 

5  11 

4  44 

4  22 

3  45 

3  18 

2  58 

2 

42 

86 

6° 

70 

g' 

9° 

10° 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

^_^ 

TABLE  XXXllI. 

183  1 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  76" 

D's 
App. 

Alt. 

APPARENT  ALTITUDE  OF 

THE 

SUN, 

OR  STAR. 

App. 

Alt. 

0 

32" 

340 

36° 

38° 

42° 

46° 

50° 

54° 

58°  1 

62° 

66°  1 

70° 

74° 

78° 

82° 

86° 

0 

1    n 

»    II 

1    II 

/  // 

/  // 

/  II 

/  II 

/  // 

1 

II 

/ 

// 

1 

// 

'  II 

/  II 

1    II 

1    II 

/  II 

6 

4  28 

4  42 

4  57 

5  11 

5  37 

6  2 

6  26 

6  47 

7 

6 

7 

24 

7 

40 

7  54 

8  6 

8  13 

8  20 

6 

7 

3  53 

4  5 

4  17 

4  29 

4  52 

5  13 

5  33 

5  52 

6 

9 

6 

24 

6 

37 

6  48 

6  57 

7  5 

7  12 

7 

8 

3  27 

3  38 

3  49 

3  59 

4  19 

4  38 

4  56 

5  12 

5 

26 

5 

39 

5 

51 

6   1 

6  9 

6  16 

6  21 

6  26 

8 

9 

3  8 

3  17 

3  26 

3  35 

3  52 

4  8 

4  24 

4  38 

4 

51 

5 

3 

5 

13 

5  22 

5  29 

5  35 

5  40 

5  44 

9 

10 
11 

2  52 

3  0 

3  8 

3  16 

3  31 

3  46 

4  1 

4  14 

4 

25 

4 

35 

4 

44 

4  52 

4  59 

5  4 

5  8 

5  11 

10 
11 

2  39 

2  46 

2  53 

3  0 

3  14 

3  27 

3  40 

3  51 

4 

2 

4 

12 

4 

20 

4  27 

4  33 

4  38 

4  42 

4  45 

12 

2  28 

2  34 

2  41 

2  47 

3  0 

3  12 

3  23 

3  34 

3 

43 

3 

52 

4 

0 

4  6 

4  11 

4  15 

4  19 

4  22 

12 

13 

2  19 

2  25 

2  30 

2  36 

2  48 

2  59 

3  9 

3  19 

3 

28 

3 

36 

3 

43 

3  48 

3  53 

3  57 

4  0 

4  2 

13 

14 

2  12 

2  17 

2  22 

2  27 

2  38 

2  48 

2  58 

3  6 

3 

14 

3 

22 

3 

28 

3  33 

3  37 

3  41 

3  43 

3  45 

14 

15 
16 

2  5 

2  10 

2  15 

2  19 

2  29 

2  38 

2  47 

2  55 

3 

3 

3 

9 

3 

16 

3  20 

3  24 

3  27 

3  29 

3  31 

15 

2  0 

2  4 

2  9 

2  13 

2  21 

2  29 

2  37 

2  45 

2 

52 

2 

58 

3 

4 

3  8 

3  12 

3  15 

3  17 

3  19 

16 

17 

1  56 

1  59 

2  3 

2  7 

2  14 

2  22 

2  29 

2  36 

2 

43 

2 

49 

2 

54 

2  58 

3  2 

3  4 

3  6 

3  8 

17 

18 

1  52 

1  55 

1  58 

2  2 

2  9 

2  16 

2  23 

2  30 

2 

36 

2 

42 

2 

46 

2  50 

2  53 

2  55 

2  57 

2  58 

18 

19 

1  49 

1  51 

1  54 

1  58 

2  4 

2  11 

2  17 

2  24 

2 

30 

2 

35 

2 

39 

2' 42 

2  45 

2  47 

2  49 

2  5C 

19 

20 
21 

1  46 

1  48 

1  51 

1  54 

2  0 
1  56 

2  6 

2  12 

2  18 

2 

24 

2 

28 

2 

32 

2  35 

2  37 

2  39 

2  41 

2  42 

20 

1  43 

1  45 

1  48 

1  51 

2  2 

2  7 

2  13 

2 

18 

2 

22 

2 

26 

2  29 

2  31 

2  33 

2  34 

21 

22 

1  41 

1  43 

1  46 

1  48 

1  53 

1  58 

2  3 

2  8 

2 

13 

2 

17 

2 

20 

2  23 

2  25 

2  27 

2  28 

22 

23 

1  40 

1  42 

1  44 

1  46 

1  50 

1  55 

1  59 

2  3 

2 

8 

2 

12 

2 

15 

2  17 

2  19 

2  21 

2  23 

23 

24 

1  39 

1  40 

1  42 

1  44 

1  48 

1  52 

1  56 

1  59 

2 

4 

2 

7 

2 

10 

2  12 

2  14 

2  16 

2  18 

24 

25 

1  38 

1  39 

1  40 

1  42 

1  46 

1  49 

1  53 

1  56 

2 

0 

2 

3 

2 

6 

2  8 

2  10 

2  12 

25 

26 

1  37 

1  38 

1  39 

1  41 

1  44 

1  47 

1  50 

1  53 

56 

69 

2 

2 

2  4 

2  6 

2  8 

26 

27 

1  36 

1  37 

1  38 

1  40 

1  42 

1  45 

1  48 

1  50 

53 

66 

59 

2  1 

2  3 

2  5 

27 

28 

1  36 

1  37 

1  38 

1  39 

1  41 

1  43 

1  46 

1  48 

50 

53 

56 

1  58 

2  0 

2  2 

28 

29 

1  35 

1  36 

1  37 

1  38 

1  40 

1  42 

1  44 

1  46 

48 

50 

53 

1  55 

1  57 

29 

30 

1  35 

1  35 

1  36 

1  37 

1  38 

1  40 

1  42 

1  44 

1  42 

46 

48 

50 

1  52 
1  50 

1  54 

30 

31 

1  34 

1  34 

1  35 

1  36 

1  37 

1  39 

1  40 

44 

46 

48 

1  52 

31 

32 

1  34 

1  34 

1  34 

1  35 

1  36 

1  38 

1  39 

1  41 

43 

44 

46 

1  48 

1  60 

32 

33 

1  34 

1  33 

1  34 

1  35 

1  35 

1  37 

1  38 

1  40 

42 

43 

45 

1  46 

33 

34 

1  34 

1  33 

1  33 

1  34 

1  35 

1  36 

1  37 

1  39 

41 

42 

44 

1  46 

34 

35 

1  34 

1  33 

1  33 

1  33 

1  34 

1  35 

1  36 

1  38 

39 

40 

42 

I  43 

35 

36 

1  35 

1  34 

1  33 

1  33 

1  33 

1  34 

1  35 

1  37 

38 

39 

40 

1  41 

36 

37 

1  35 

1  34 

1  33 

1  32 

1  33 

1  33 

1  34 

1  36 

37 

38 

39 

37 

38 

I  35 

1  34 

1  33 

1  32 

1  32 

1  33 

1  34 

1  35 

36 

37 

38 

38 

39 

1  36 

1  34 

1  33 

1  32 

1  32 

1  33 

1  33 

1  34 

35 

36 

36 

39 

40 

1  36 

1  35 

1  34 

1  33 

1  32 

1  32 

1  33 

1  34 

34 

35 

35 

40 
41 

41 

1  37 

I  35 

1  34 

1  33 

1  32 

1  32 

1  32 

1  33 

33 

34 

42 

1  37 

1  35 

1  34 

1  33 

1  31 

1  31 

1  32 

1  32 

33 

33 

42 

43 

1  37 

1  35 

1  34 

1  33 

1  31 

1  30 

1  31 

1  31 

32 

32 

43 

44 

1  38 

1  36 

1  34 

1  33 

1  31 

1  30 

1  30 

1  31 

31 

31 

44 

46 

1  39 

1  37 

1  35 

1  34 

1  31 

1  29 

1  29 
1  29 

1  30 

30 

- 

46 

48 

1  40 

1  38 

1  36 

1  34 

1  31 

1  29 

1  29 

1 

29 

48 

50 
52 
54 
56 

1  41 
1  42 
1  43 
1  44 

1  38 
1  39 
1  40 
1  41 

1  ;i7 
1  37 
1  38 
1  38 

1  35 
1  35 
1  36 
1  36 

1  32 
1  32 
1  33 
1  33 

1  30 
1  30 
1  30 
1  30 

1  29 
1  29 
1  29 
1  29 

1  29 
1  28 

1    1    1 

50 
52 
54 
56 

58 
60 

62 

TABLE  P.  EFFECT  OF  SUn's  Pi 

LR 

t 
e. 

Add  the  Numbers  above  th 

lines  to  3rd  Correction,  sub 

tract  the  others. 

58 
60 

62 

1  45 
1  46 
1  46 

1  42 
1  43 

1  43 

1  39 
1  40 

1  40 

1  37 

1  37 
1  37 

1  33 
1  33 
1  33 

1  30 
1  30 

)'8 

App 
Alt. 

Sun's  Apparent  Altitud 

5 

lU-i 

3  30 

40  .'5 

0  60  7C 

80 

90 

64 

1  47 

1  44 

1  41 

1  38 

1  33 

ft 

fl      * 

1" 

^^  ~ 

»  It        n 

— 

64 

66 

68 
70 
72 
74 
76 

1  48 

1  44 

1  41 

1  38 

5 

10 
15 

20 
25 
.30 
35 
40 
45 
50 
55 
60 
65 
70 
75 
80 
90 

1 

1 
2 
3 
4 
4 
5 

6 
6 
7 
7 
8 
8 
8 
9 
9 

1  CI 

1  1 

2  2 

3  2 

4  :) 

4  4 

5  4 

6  .1 

6  e 

7  (i 

7  1 

8  ; 

8  ? 

8  6 

9  i. 
9  i 

Q  F 

0 
'  0 

1 

2 

3 
3 
4 
6 

5 
6 
6 
7 

7 
8 

)  8 

) 

1 
0 
1 
2 
2 
3 
4 
4 
5 
6 
6 
7 
7 

I  ]  _1_ 

J  0  "o 

1)  0  0 

1  1  1 

2  2  2 

3  3  3 

4  3  3 

4  4 

5  5 
5 

6 

1 

1 

0 

1 

2 

0 

66 

68 
70 
72 
74 
76 

1  49 
1  4£ 
1  4S 
1  5C 

1  45 
1  4S 

1  1  45 

> 

1  41 
1  41 

1  38 

78 

80 

82 

'  84 

>  86 

78 
80 
82 
84 
86 

32° 

34° 

36° 

38° 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

1 

184                 TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  80«. 

App. 
Alt. 

APPARENT  ALTITUDE  OF  THE  SUN, 

OR  STAR. 

D's 

App. 

6° 

70 

8° 

9^ 

10° 

11° 

12° 

14° 

16° 

18° 

20°  1 

22°  1 

24°  1 

26°  1 

28* 

30° 

Alt. 

o 

r  II 

/  // 

/  II 

1    II 

/  // 

1    II 

/  // 

1     n 

/  // 

/  II 

1 

// 

/ 

// 

t 

f/ 

/ 

// 

/ 

// 

/ 

II       0  * 

6 

1  41 

1  43 

1  46 

1  50 

1  54 

1  59 

2  4 

2  17 

2  32 

2  47 

3 

2 

3 

17 

3 

32 

3 

47 

4 

2 

4 

16   6 

7 

1  44 

1  41 

1  43 

1  45 

1  48 

1  51 

1  55 

2  5 

2  17 

2  29 

2 

41 

2 

54 

3 

6 

3 

19 

3 

31 

3 

441  7 

8 

1  48 

1  43 

1  41 

1  42 

1  44 

1  46 

1  49 

1  56 

2  6 

2  16 

2 

26 

2 

37 

2 

48 

2 

59 

3 

10 

3 

20   8 

9 

1  52 

1  46 

1  43 

1  41 

1  42 

1  44 

1  46 

1  51 

1  58 

2  6 

2 

15 

2 

25 

2 

34 

2 

43 

2 

62 

3 

1 

9 

10 

1  57 

1  50 

1  46 

1  43 

1  41 

1  42 

1  44 

1  47 

1  54 

1  59 

2 

6 

2 

14 

2 

22 

2 

30 

2 

38 

2 

46 

10 

11 

2  3 

1  54 

1  49 

1  45 

1  43 

1  41 

]  42 

1  45 

1  49 

1  54 

59 

2 

6 

2 

13 

2 

20 

2 

27 

2 

34 

11 

12 

2  9 

1  59 

1  52 

1  48 

1  45 

1  43 

1  41 

1  43 

1  46 

1  50 

54 

2 

0 

2 

6 

2 

12 

2 

19 

2 

25 

12 

13 

2  16 

2  4 

1  56 

1  51 

1  48 

1  45 

1  42 

1  42 

1  44 

1  47 

51 

56 

2 

1 

2 

6 

2 

12 

2 

18 

13 

14 

2  23 

2  10 

2  0 

1  54 

1  50 

1  47 

1  44 

1  41 

1  43 

1  45 

48 

52 

57 

2 

2 

2 

7 

2 

12 

14 

15 

2  30 

2  16 

2  5 

1  58 

1  53 

1  49 

1  46 

1  42 

1  42 

1  44 

46 

49 

53 

1 

58 

2 

2 

2 

7 

15 

16 

2  37 

2  22 

2  10 

2  2 

1  56 

1  52 

1  48 

1  43 

1  41 

1  43 

45 

47 

50 

54 

58 

2 

2 

16 

17 

2  45 

2  2» 

2  15 

2  6 

1  59 

1  54 

1  50 

1  45 

1  42 

1  42 

43 

45 

48 

51 

54 

58 

17 

18 

2  53 

2  34 

2  21 

2  11 

2  3 

1  57 

1  52 

1  47 

1  43 

1  41 

42 

44 

46 

48 

51 

54 

18 

19 

3  0 

2  41 

2  26 

2  15 

2  7 

2  0 

1  54 

1  48 

1  44 

1  42 

41 

43 

44 

46 

49 

61 

19 

20 

3  8 

2  47 

2  31 

2  20 

2  10 

2  3 

1  57 

1  50 

1  46 

1  43 

41 

42 

43 

45 

47 

49 

20 
21 

21 

3  16 

2  54 

2  37 

2  24 

2  14 

2  6 

1  59 

1  52 

1  47 

1  44 

42 

41 

42 

1 

43 

45 

47 

22 

3  23 

3  0 

2  43 

2  29 

2  18 

2  9 

2  2 

1  54 

1  49 

1  45 

42 

40 

41 

42 

43 

45 

22 

23 

3  31 

3  6 

2  47 

2  33 

2  22 

2  13 

2  5 

1  57 

1  51 

1  47 

43 

41 

40 

41 

42 

44 

23 

24 

3  38 

3  12 

2  53 

2  38 

2  25 

2  16 

2  8 

1  59 

1  52 

1  48 

44 

41 

40 

41 

42 

43 

24 

25 
26 

3  46 

3  18 

2  58 

2  42 

2  29 

2  19 

2  12 

2  1 

1  54 

1  49 

45 

42 

40 

.. 

40 

41 

42 

25 
26 

3  53 

3  24 

3  4 

2  47 

2  33 

2  23 

2  15 

2  3 

1  55 

1  50 

46 

43 

41 

40 

41 

^ 

42 

27 

4  1 

3  31 

3  10 

2  52 

2  37 

2  26 

2  19 

2  6 

1  57 

1  51 

47 

43 

41 

40 

40 

41 

27 

28 

4  8 

3  37 

3  15 

2  56 

2  41 

2  30 

2  22 

2  8 

1  59 

1  53 

48 

44 

42 

41 

40 

40 

28 

29 

4  15 

3  43 

3  20 

3  1 

2  46 

2  34 

2  26 

2  11 

2  1 

1  55 

49 

45 

43 

41 

40 

39 

29 

30 
31 

4  22 

3  49 

3  25 

3  5 

2  50 

2  38 

2  29 

2  14 

2  3 

1  56 

50 

46 

44 

42 

40 

39 

30 
31 

4  29 

3  55 

3  30 

3  10 

2  54 

2  41 

2  32 

2  17 

2  5 

1  58 

52 

47 

44 

42 

40 

39 

32 

4  36 

4  1 

3  35 

3  14 

2  58 

2  45 

2  35 

2  19 

2  7 

1  59 

53 

48 

45 

43 

41 

39 

32 

33 

4  43 

4  7 

3  40 

3  19 

3  2 

2  49 

2  38 

2  22 

2  9 

2  1 

54 

49 

46 

44 

42 

40 

33 

34 

4  50 

4  12 

3  45 

3  23 

3  6 

2  52 

2  41 

2  24 

2  11 

2  2 

56 

50 

47 

44 

42 

40 

34 

35 

4  57 

4  18 

3  50 

3  28 

3  10 

2  56 

2  44 

2  27 

2  14 

2  4 

57 

51 

47 

44 

42 

40 

35 
36 

36 

5  4 

4  24 

3  55 

3  32 

3  14 

3  0 

2  47 

2  29 

2  16 

2  6 

58 

52 

48 

45 

43 

41 

37 

5  11 

4  29 

4  0 

3  37 

3  19 

3  3 

2  50 

2  32 

2  18 

2  8 

2 

0 

53 

49 

46 

44 

42 

37 

38 

5  18 

4  35 

4  5 

3  42 

3  23 

3  7 

2  54 

2  34 

2  20 

2  9 

2 

1 

54 

49 

46 

44 

42 

38 

39 

5  25 

4  41 

4  10 

3  46 

3  27 

3  11 

2  58 

2  36 

2  22 

2  10 

2 

2 

55 

50 

47 

45 

43 

39 

40 
41 

5  31 

4  47 

4  15 

3  50 

3  31 

3  14 

3  1 

2  38 

2  24 

2  12 

2 

4 

57 

51 

47 

45 

43 

40 

5  38 

4  52 

4  20 

3  54 

3  35 

3  18 

3  4 

2  41 

2  26 

2  14 

2 

5 

58 

52 

48 

46 

44 

41 

42 

5  44 

4  57 

4  25 

3  58 

3  3S 

3  21 

3  7 

2  44 

2  28 

2  16 

2 

7 

59 

53 

49 

46 

44 

42 

43 

5  51 

5  3 

4  30 

4  2 

3  42 

3  25 

3  10 

2  46 

2  30 

2  17 

2 

8 

2 

1 

55 

50 

47 

45 

43 

44 

5  57 

5  8 

4  35 

4  6 

3  46 

3  28 

3  13 

2  48 

2  32 

2  19 

2 

10 

2 

2 

56 

51 

48 

45 

44 

46 

6  9 

5  18 

4  44 

4  14 

3  53 

3  35 

3  19 

2  53 

2  36 

2  23 

2 

13 

2 

4 

58 

53 

49 

46 

46 

48 

6  20 

5  28 

4  53 

4  22 

4  0 

3  41 

3  25 

2  58 

2  39 

2  26 

2 

15 

2 

7 

2 

0 

55 

51 

48 

48 

50 

6  31 

5  38 

5  1 

4  30 

4  6 

3  47 

3  30 

3  3 

2  43 

2  29 

2 

18 

2 

9 

2 

2 

56 

52 

49 

60 

52 

6  41 

5  47 

5  9 

4  37 

4  12 

3  53 

3  35 

3  7 

2  47 

2  32 

2 

21 

2 

12 

2 

4 

58 

54 

50 

52 

54 

6  51 

5  56 

5  17 

4  44 

4  18 

3  58 

3  39 

3  11 

2  51 

2  35 

2 

24 

2 

14 

2 

6 

59 

55 

52 

54 

56 

7  1 

6  5 

5  24 

4  50 

4  24 

4  3 

3  44 

3  15 

2  54 

2  38 

2 

26 

2 

17 

2 

8 

2 

1 

57 

53 

56 

58 

7  11 

6  14 

5  31 

4  56 

4  30 

4  8 

3  49 

3  19 

2  57 

2  41 

2 

29 

2 

19 

2 

10 

2 

3 

58 

54 

68 

60 

7  20 

6  22 

5  38 

5  2 

4  35 

4  13 

3  54 

3  23 

3  0 

2  44 

2 

31 

2 

21 

2 

12 

2 

5 

59 

55 

60 

62 

7  28 

6  29 

5  44 

5  7 

4  40 

4  18 

3  58 

3  27 

3  3 

2  47 

2 

3o 

2 

22 

2 

13 

2 

6 

2 

0 

56 

62 

64 

7  36 

6  35 

5  50 

5  12 

4  44 

4  22 

4  2 

3  31 

3  6 

2  49 

2 

3.5 

2 

24 

2 

15 

2 

7 

2 

1 

56 

64 

66 

68 

7  43 

6  41 

5  55 

5  17 

4  49 

4  26 

4  6 

3  34 

3  9 

2  51 

2 

37 

2 

26 

2 

16 

2 

8 

2 

2 

57 

66 

7  49 

6  46 

6  0 

5  21 

4  53 

4  30 

4  9 

3  37 

3  12 

2  53 

2 

39 

2 

27 

2 

17 

2 

9 

2 

3 

68 

68 

70 

7  55 

6  51 

6  5 

5  25 

4  57 

4  33 

4  12 

3  39 

3  14 

2  55 

2 

41 

2 

29 

2 

19 

2 

10 

2 

4 

59 

70 

72 

8  0 

6  55 

6  9 

5  29 

5  0 

4  36 

4  14 

3  41 

3  16 

2  57 

2 

42 

2 

30 

2 

20 

2 

11 

2 

5 

2 

0 

72 

74 

8  5 

6  59 

6  13 

5  32 

5  3 

4  38 

4  16 

3  43 

3  18 

2  58 

2 

43 

2 

31 

2 

21 

2 

12 

2 

5 

74 

76 

8  9 

7  3 

6  16 

5  35 

5  6 

4  40 

4  18 
4  19 

3  44 

3  19 

2  59 

2 

44 

2 

32 

2 

22 

2 

13 

76 

78 

8  13 

7  6 

6  19 

5  37 

5  8 

4  42 

3  45 

3  20 

3  0 

2 

45 

2 

32 

2 

22 

78 

80 

8  16 

7  9 

6  21 

5  40 

5  10 

4  44 

4  21 

3  46 

3  21 

3  1 

2 

45 

2 

33 

80 

82 

8  19 

7  12 

6  23 

5  42 

5  12 

4  45 

4  22 

3  47 

3  22 

3  2 

2 

46 

82 

84 

8  22 

7  14 

6  25 

5  44 

5  13 

4  46 

4  23 

3  48 

3  23 

3  3 

84 

86 

8  24 

7  16 

6  27 

5  46 

5  14 

4  47 

4  24 

3  49 

3  24 

86 

6=* 

70 

%" 

9° 

10° 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

^^^_ 

TABLE  XXXUI. 

185  1 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  80<».               | 

App. 

Alt. 

APPARENT  ALTITUDE  OF 

THE 

SUN, 

OR  STAR. 

App. 

Alt. 

0 

32" 

340  1 

3  50 

38°  1 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

70° 

74° 

78° 

82<» 

86° 

o 

/  // 

f 

f  f 

/  1  r 

/ 

// 

/ 

ff 

/     n 

/  // 

/  // 

1 

II 

1 

II 

/ 

// 

'  II 

1   II 

1    II 

1    II 

/  /; 

6 

4  30 

4 

44 

4  58 

5 

12 

5 

39 

6  4 

6  28 

6  49 

7 

8 

7 

26 

7 

41 

7  54 

8  5 

8  13 

8  19 

8  1A 

\      6 

p 
t 

3  56 

4 

8 

4  19 

4 

30 

4 

52 

5  14 

5  35 

5  54 

6 

11 

6 

26 

6 

39 

6  50 

6  59 

7  6 

7  12 

7  H 

)  7 

8 

3  31 

3 

41 

3  52 

4 

2 

4 

23 

4  42 

4  59 

5  15 

5 

29 

5 

42 

5 

54 

6  4 

6  12 

6  18 

6  23 

6  27 

8 

9 

3  11 

3 

21 

3  30 

3 

39 

3 

56 

4  12 

4  28 

4  42 

4 

54 

5 

5 

5 

15 

5  24 

5  32 

5  38 

5  43 

5  46 

;    9 

10 

2  54 

3 

3 

3  12 

3 

20 

3 

35 

3  50 

4  4 

4  16 

4 

28 

4 

39 

4 

48 

4  56 

5  2 

5  7 

5  11 

5  \A 

\  10 
11 

11 

2  42 

2 

49 

2  57 

3 

5 

3 

19 

3  32 

3  44 

3  56 

4 

7 

4 

16 

4 

24 

4  31 

4  36 

4  41 

4  45 

4  47 

12 

2  32 

2 

38 

2  45 

2 

52 

3 

5 

3  17 

3  28 

3  38 

3 

48 

3 

57 

4 

5 

4  11 

4  15 

4  19 

4  22 

4  11 

)  12 

13 

2  24 

2 

30 

2  36 

2 

42 

2 

53 

3  4 

3  14 

3  23 

3 

32 

3 

40 

3 

47 

3  53 

3  57 

4  1 

4  4 

4  i 

)  13 

14 

2  18 

2 

23 

2  28 

2 

33 

2 

43 

2  53 

3  2 

3  11 

3 

19 

3 

26 

3 

32 

3  38 

3  42 

3  46 

3  48 

3  4c 

)  14 

15 
16 

2  12 

2 

16 

2  21 

2 

25 

2 

34 

2  43 
2  34 

2  52 

3  0 

3 

7 

3 

13 

3 

19 

3  25 

3  29 

3  32 

3  34 

3  3( 

)  15 

2  6 

2 

10 

2  14 

2 

18 

2 

26 

2  42 

2  50 

2 

56 

3 

2 

3 

8 

3  13 

3  17 

3  20 

3  22 

3  2- 

1  16 

17 

2  1 

2 

4 

2  8 

2 

12 

2 

20 

2  27 

2  34 

2  41 

2 

47 

2 

53 

2 

58 

3  3 

3  6 

3  9 

3  11 

17 

18 

1  57 

2 

0 

2  3 

2 

7 

2 

14 

2  21 

2  28 

2  34 

2 

40 

2 

46 

2 

50 

2  54 

2  57 

3  0 

3  2 

18 

19 

1  54 

56 

1  59 

2 

2 

2 

9 

2  16 

2  22 

2  28 

2 

34 

2 

39 

2 

43 

2  47i 

^  50 

2  52 

2  53 

19 

20 

1  51 

53 

1  56 

1 

58 

2 

5 

2  11 

2  17 

2  22 

2 

28 

2 

33 

2 

37 

2  40 

2  43 

2  45 

2  46 

20 

21 

1  49 

51 

1  53 

55 

2 

1 

2  7 

2  12 

2  17 

2 

22 

2 

27 

2 

31 

2  34 

2  37 

2  38 

21 

22 

1  47 

49 

1  51 

53 

58 

2  3 

2  8 

2  13 

2 

17 

2 

21 

2 

25 

2  28 

2  31 

2  32 

22 

23 

1  46 

47 

1  49 

51 

55 

2  0 

2  4 

2  9 

2 

13 

2 

17 

2 

20 

2  23 

2  26 

2  27 

23 

24 

1  45 

46 

1  47 

49 

53 

1  57 

2  1 

2  5 

2 

9 

2 

13 

2 

16 

2  19 

2  21 

2  22 

24 

25 

1  44 

45 

1  46 

48 

51 

1  54 

1  58 

2  1 

2 

5 

2 

9 

2 

12 

2  14 

2  16 

25 

26 

1  43 

44 

1  45 

46 

49 

1  52 

1  55 

1  58 

2 

2 

2 

5 

2 

8 

2  10 

2  12 

26 

27 

1  42 

43 

1  44 

45 

47 

1  50 

1  53 

1  56 

59 

2 

2 

2 

5 

2  7 

2  8 

27 

28 

1  41 

42 

1  43 

■'■ 

44 

46 

1  48 

1  51 

1  54 

57 

59 

2 

2 

2  4 

2  5 

28 

29 

1  40 

41 

1  41 

42 

44 

1  46 

1  49 

1  52 

55 

57 

59 

2  1 

29 

30 

1  39 

40 

1  40 

41 

43 

1  45 

1  48 

1  51 

53 

55 

57 

1  59 

30 

31 

1  39 

4Q 

1  40 

41 

42 

1  44 

1  46 

1  49 

51 

53 

55 

1  57 

31 

32 

1  39 

39 

1  39 

40 

41 

1  43 

1  45 

1  47 

49 

51 

53 

1  5^ 

32 

33 

1  39 

39 

1  39 

40 

41 

1  42 

1  44 

1  46 

48 

49 

51 

33 

34 

1  39 

39 

1  39 

40 

41 

1  42 

1  43 

1  45 

47 

48 

49 

34 

35 

1  39 

39 

1  39 

39 

40 

1  41 

1  42 

1  44 

45 

46 

47 

35 

36 

1  40 

39 

1  39 

39 

40 

1  41 

1  42 

1  43 

44 

45 

1 

46 

36 

37 

1  41 

40 

1  39 

38 

39 

1  40 

1  41 

1  42 

43 

44 

37 

38 

1  41 

40 

1  39 

38 

39 

1  40 

1  41 

1  42 

42 

43 

38 

39 

1  41 

40 

1  39 

38 

39 

1  39 

1  40 

1  41 

41 

42 

39 

40 

1  41 

40 

1  39 

38 

38 

1  38 

1  39 

1  40 

40 

41 

40 

41 

1  42 

41 

1  40 

39 

38 

1  38 

1  38 

1  39 

39 

41 

42 

1  42 

41 

1  40 

39 

37 

1  37 

1  37 

1  38 

38 

42 

43 

1  43 

41 

1  40 

39 

37 

1  37 

1  37 

1  37 

38 

43 

44 

1  43 

42 

1  40 

39 

37 

1  37 

1  36 

1  37 

37 

44 

46 

1  44 

42 

1  41 

40 

38 

1  37 

1  36 

1  36 

46 

48 

1  45 

43 

1  41 

40 

38 

1  37 

1  36 

1  36 

48 

50 
52 
54 
56 

1  46 
1  47 
1  48 
1  49 

44 
45 
46 
47 

1  42 
1  43 
1  44 
1  44 

41 

38 

1  36 

1  36 

'    1    1 

50 

41 

42 
42 

38 
38 
38 

1  36 
1  36 
1  36 

1  35 

TABLB  P.  EFFECT  OF  SUN't  PAK 

52 
54 
56 

Add  the  Numbers  above  the 
lines  to  3rd  Correction,  sub- 
tract the  others. 

58 

1  50 

A7 

1  45 

42 
43 
43 

38 

58 
60 
62 
64 
66' 

60 

62 

1  51 
1  52 

48 
49 

1  45 
1  46 

38 

App 
Alt. 

Snn's  Apparent  Altitude. 1 

5 

10  2( 

3  30 

40  5 

0  60 

70  f 

!U90 

64 

1  52 

49 

1  46 

43 

„ 

tl      1 

1* 

"  t 

»  n 

It 

ft    n 

66 

1  53 

49 

1  46 

5 

10 
15 

20 
25 
30 
35 
40 
45 
50 
55 
60 
65 
70 
75 
80 
90 

1 

1 
2 
3 
4 
4 
5 
6 
6 
7 
7 
8 
8 
8 
9 
9 

1  I 

1  1 

2  2 

3  3 

4  :t 

4  4 
6  5 

6  5 

6  6 

7  6 

7  7 

8  7 

8  8 

8  8 

9  8 
9  8 

0 

1 
2 
2 
3 
4 
4 
5 
6 
6 
7 
7 

e 

8 

0 

1  ( 
1 
3  ' 

3  ; 

4  : 

4  . 

5  , 
«  < 

7 

1 

)  0 

I 

I  2 

3  3 
}  3 
t  4 

5  4 

5 
3 

\ 
0  ' 

2 
2 
3 

1 

0 
1  0 

2 

68 
70 
72 
74 

76 

1  54 
1  55 

1 

50 

68 
70 
72 
74 
76 

78 
80 
82 
84 
86 

78 
80 
82 
84 
86 

^^^ 

32° 

38" 

42° 

58° 

62° 

66° 

»  1 

1 

i54" 

36° 

46° 

50° 

54° 

186                 TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE 

84°. 

J  '8 

APPARENT  ALTITUDE  OF 

THE 

SUN, 

OR  STAR. 

D's 

App 
Alt. 

App. 

Alt. 

6° 

70 

8<» 

9«» 

100 

II* 

12° 

14° 

16°  1 

18°  1 

20° 

22°  1 

24° 

26° 

28° 

30° 

1 

o 

1     II 

1    If 

1    II 

1    II 

/  II 

/  // 

1    It 

/  II 

/ 

// 

1 

11 

/ 

// 

1 

r/ 

f 

// 

/ 

^/ 

1 

// 

/ 

// 

0 

l 

6 

1  47 

1  49 

1  51 

1  54 

1  59 

2  4 

2  10 

2  22 

2 

36 

2 

50 

3 

5 

3 

20 

3 

35 

3 

50 

4 

5 

4 

20 

6 

1 

7 

1  50 

1  47 

1  48 

1  50 

1  53 

1  56 

2  0 

2  10 

2 

21 

2 

33 

2 

45 

2 

57 

3 

10 

3 

23 

3 

35 

3 

48 

7 

8 

1  53 

1  49 

1  47 

1  48 

1  50 

1  52 

1  55 

2  2 

2 

11 

2 

21 

2 

31 

2 

42 

2 

53 

3 

3 

3 

14 

3 

25 

8 

9 

1  57 

1  52 

1  49 

1  47 

1  48 

1  50 

1  52 

1  57 

2 

4 

2 

12 

2 

21 

2 

30 

2 

39 

2 

48 

2 

58 

3 

7 

9 

10 

2  2 

1  55 

1  51 

1  49 

1  47 

1  48 

1  50 

1  53 

1 

59 

2 

5 

2 

12 

2 

20 

2 

27 

2 

35 

2 

44 

2 

52 

10 

11 

2  8 

1  59 

1  54 

1  51 

1  49 

1  47 

1  48 

1  51 

55 

59 

2 

5 

2 

12 

2 

18 

2 

36 

2 

33 

2 

41 

11 

12 

2  14 

2  4 

1  57 

1  53 

1  51 

1  48 

1  47 

1  49 

52 

55 

59 

2 

5 

2 

11 

2 

18 

2 

25 

2 

31 

12 

13 

2  20 

2  9 

2  1 

1  56 

1  53 

1  50 

1  48 

1  48 

1 

50 

52 

55 

2 

0 

2 

6 

2 

11 

2 

17 

2 

23 

13 

14 

2  27 

2  14 

2  5 

1  59 

1  55 

1  52 

1  50 

1  47 

48 

50 

53 

57 

2 

2 

2 

6 

2 

11 

2 

16 

14 

15 

2  34 

2  20 

2  10 

2  3 

1  58 

1  54 

1  51 

1  48 

47 

49 

51 

54 

1 

58 

2 

2 

2 

7 

2 

11 

15 

16  2  42 

2  26 

2  15 

2  7 

2  1 

1  56 

1  53 

1  49 

47 

48 

50 

52 

55 

59 

2 

3 

2 

7 

16 

17  2  49 

2  32 

2  20 

2  11 

2  4 

1  59 

1  55 

1  50 

48 

47 

48 

50 

53 

56 

2 

0 

2 

3 

17 

18  2  57 

2  38 

2  25 

2  16 

2  8 

2  2 

1  57 

1  52 

49 

46 

47 

49 

51 

54 

57 

2 

0 

18 

19  3  4 

2  44 

2  31 

2  20 

2  12 

2  5 

1  59 

1  53 

50 

47 

46 

48 

49 

52 

54 

67 

19 

20  3  12 

2  50 

2  36 

2  25 

2  15 

2  8 

2  2 

1  55 

51 

48 

46 

47 

48 

50 

52 

55 

20 

21  3  20 

2  57 

2  42 

2  29 

2  19 

2  11 

2  5 

1  57 

52 

49 

47 

46 

47 

48 

50 

52 

21 

22  3  27 

3  3 

2  47 

2  34 

2  23 

2  14 

2  8 

1  59 

54 

50 

47 

46 

46 

47 

49 

50 

22 

23  3  35 

3  9 

2  52 

2  38 

2  27 

2  18 

2  11 

2  1 

56 

52 

48 

46 

46 

47 

48 

49 

23 

24  3  42 

3  15 

2  57 

2  42 

2  30 

2  21 

2  14 

2  3 

57 

53 

49 

46 

46 

46 

47 

48 

24 

25 
26 

3  49 

3  21 

3  3 

2  47 

2  34 

2  25 

2  17 

2  6 

59 

54 
~55 

50 

47 

46 

46 

46 

47 

25 
26 

3  56 

3  27 

3  8 

2  52 

2  38 

2  28 

2  20 

2  8 

2 

0 

51 

48 

47 

46 

46 

46 

27 

4  4 

3  34 

3  13 

2  56 

2  42 

2  32 

2  24 

2  11 

2 

2 

56 

52 

49 

47 

46 

45 

46 

27 

28 

4  11 

3  40 

3  18 

3  1 

2  46 

2  35 

2  27 

2  13 

2 

4 

58 

53 

49 

47 

46 

45 

45 

28 

29 

4  19 

3  47 

3  24 

3  5 

2  51 

2  39 

2  30 

2  16 

2 

6 

59 

54 

50 

48 

46 

45 

45 

29 

30 
31 

4  26 

3  53 

3  29 

3  10 

2  55 

2  43 

2  33 

2  18 

2 

8 

2 

1 

55 

51 

49 

47 

46 

45 

30 
31 

4  33 

3  59 

3  35 

2  14 

2  59 

2  46 

2  36 

2  21 

2 

10 

2 

3 

57 

52 

49 

47 

46 

45 

32 

4  40 

4  5 

3  40 

3  19 

3  3 

2  50 

2  39 

2  24 

2 

12 

2 

4 

58 

53 

50 

48 

46 

45 

32 

33 

4  47 

4  11 

3  45 

3  24 

3  7 

2  54 

2  42 

2  27 

2 

14 

2 

5 

59 

54 

50 

48 

46 

45 

33 

34 

4  54 

4  16 

3  50 

3  28 

3  11 

2  57 

2  45 

2  29 

2 

16 

2 

7 

2 

0 

55 

51 

48 

47 

46 

34 

35 

5  1 

4  22 

3  55 

3  33 

3  15 

3  1 

2  49 

2  32 

2 

19 

2 

9 

2 

2 

56 

52 

49 

47 

46 

35 
36 

36 

5  8 

4  28 

4  0 

3  37 

3  19 

3  5 

2  52 

2  34 

2 

21 

2 

10 

2 

3 

58 

53 

49 

47 

46 

37 

5  15 

4  34 

4  5 

3  42 

3  23 

3  8 

2  56 

2  37 

2 

23 

2 

12 

2 

4 

59 

54 

50 

48 

47 

37 

38 

5  21 

4  40 

4  10 

3  46 

3  27 

3  12 

2  59 

2  39 

2 

25 

2 

14 

2 

6 

2 

0 

55 

51 

49 

47 

38 

39 

5  28 

4  45 

4  15 

3  51 

3  31 

3  15 

3  2 

2  42 

2 

27 

2 

16 

2 

7 

2 

1 

56 

52 

49 

47 

39 

40 

5  34 

4  51 

4  20 

3  55 

3  35 

3  19 

3  5 

2  44 

2 

29 

2 

18 

2 

9 

2 

3 

57 

52 

49 

47 

40 

41 

5  41 

4  56 

4  25 

3  59 

3  39 

3  23 

3  8 

2  47 

2 

31 

2 

20 

2 

11 

2 

4 

58 

53 

50 

48 

41 

42 

5  47 

5  1 

4  30 

4  3 

3  43 

3  26 

3  11 

2  49 

2 

33 

2 

21 

2 

12 

2 

5 

59 

54 

51 

49 

42 

43 

6  53 

5  7 

4  35 

4  7 

3  47 

3  30 

3  14 

2  52 

2 

35 

2 

23 

2 

13 

2 

7 

2 

0 

55 

52 

50 

43 

44 

6  0 

5  12 

4  40 

4  11 

3  50 

3  34 

3  17 

2  54 

2 

37 

2 

25 

2 

15 

2 

8 

2 

1 

56 

53 

51 

44 

46 

48 

6  12 

5  22 

4  49 

4  19 

3  57 

3  40 

3  23 

2  59 

2 

41 

2 

29 

2 

18 

2 

10 

2 

3 

58 

55 

52 

46 

6  24 

5  32 

4  58 

4  27 

4  4 

3  46 

3  29 

3  4 

2 

45 

2 

32 

2 

21 

2 

12 

2 

5 

2 

0 

56 

53 

48 

50 

6  35 

5  42 

5  6 

4  35 

4  11 

3  52 

3  35 

3  9 

2 

49 

2 

35 

2 

24 

2 

15 

2 

8 

2 

2 

58 

55 

50 

52 

6  45 

5  51 

5  14 

4  42 

4  17 

3  58 

3  40 

3  13 

2 

53 

2 

38 

2 

27 

2 

18 

2 

10 

2 

4 

2 

0 

57 

52 

54 

6  55 

6  0 

5  22 

4  49 

4  23 

4  4 

3  45 

3  17 

2 

57 

2 

41 

2 

30 

2 

20 

2 

12 

2 

6 

2 

2 

58 

54 

56 

58 

7  5 

6  9 

5  29 

4  55 

4  29 

4  9 

3  50 

3  21 

3 

1 

2 

44 

2 

32 

2 

22 

2 

14 

2 

8 

2 

3 

59 

56 

7  14 

6  17 

5  36 

5  1 

4  34 

4  14 

3  55 

3  25 

3 

4 

2 

47 

2 

35 

2 

24 

2 

16 

2 

9 

2 

4 

2 

0 

58 

60 

7  22 

6  25 

5  42 

5  6 

4  39 

4  19 

3  59 

3  29 

3 

7 

2 

50 

2 

37 

2 

26 

2 

17 

2 

10 

2 

5 

2 

1 

60 

62 

7  30 

6  32 

5  48 

5  11 

4  44 

4  23 

4  3 

3  33 

3 

10 

2 

53 

2 

39 

2 

28 

2 

19 

2 

12 

2 

7 

2 

2 

62 

64 

7  38 

6  39 

5  54 

5  16 

4  49 

4  27 

4  7 

3  36 

3 

13 

2 

56 

2 

41 

2 

29 

2 

20 

2 

13 

2 

8 

2 

3 

64 

66 

7  45 

6  45 

6  0 

5  21 

4  54 

4  31 

4  11 

3  39 

3 

16 

2 

58 

2 

43 

2 

31 

2 

22 

2 

15 

2 

9 

2 

3 

66 

68 

7  51 

6  60 

6  5 

5  25 

4  58 

4  35 

4  15 

3  41 

3 

19 

3 

0 

2 

45 

2 

33 

2 

24 

2 

16 

2 

10 

2 

4 

68 

70 

7  57 

6  54 

6  9 

5  29 

5  2 

4  39 

4  18 

3  44 

3 

21 

3 

2 

2 

46 

2 

34 

2 

25 

2 

17 

2 

10 

70 

72 

8  2 

6  58 

6  13 

5  33 

5  6 

4  42 

4  21 

3  46 

3 

23 

3 

3 

2 

47 

2 

35 

2 

26 

2 

18 

72 

74 

8  fi 

7  2 

6  17 

5  36 

5  9 

4  44 

4  23 

3  48 

3 

24 

3 

4 

2 

48 

2 

36 

2 

27 

74 

76 

8  10 

7  5 

6  20 

5  39 

5  11 

4  46 

4  25 

3  50 

3 

25 

3 

5 

2 

49 

2 

37 

76 
78 

78 

8  14 

7  8 

6  23 

5  42 

5  13 

4  48 

4  26 

3  51 

3 

26 

3 

6 

2 

50 

80 

8  18 

7  11 

6  26 

5  45 

5  15 

4  50 

4  27 

3  52 

3 

27 

3 

7 

80 

82 

8  21 

7  14 

6  28 

5  47 

5  17 

4  51 

4  28 

3  53 

3 

28 

82 

84 

8  24 

T  17 

6  30 

5  49 

5  18 

4  52 

4  29 

3  54 

84 

86 

8  26 

7  19 

6  31 

5  50 

5  19 

4  53 

4  30 

86 

6° 

7" 

8°  1  9°  i  10° 

11" 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

TABLE  XXXUI. 

18,  1' 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  84". 

- 

App. 

Alt. 

0 

APPARENT  ALTITUDE  OF  THE  SUN, 

OR  STAR. 

•  '8 

App 
Alt. 

32° 

34*  (  36° 

38° 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

70° 

74° 

78° 

82° 

86° 

1    It 

1    II    1    II 

/  n 

/    // 

/  II 

/  II 

1    II 

/  // 

/  /' 

1 

// 

/  // 

/  II 

;  II 

/  II 

1    II 

o 

6 

4  34 

4  48^ 

5  2 

5  15 

5  41 

6  6 

6  29 

6  51 

7  10 

7  27 

7 

42 

7  55 

8  6 

8  14 

8  21 

8  27 

6 

7 

4  0 

4  12 

4  24 

4  36 

4  58 

5  19 

5  39 

5  58 

6  15 

6  30 

6 

42 

6  53 

7  2 

7  9 

7  15 

7  19 

7 

8 

3  36 

3  47 

3  57 

4  7 

4  27 

4  46 

5  4 

5  20 

5  34 

5  46 

5 

58 

6  9 

6  17 

6  23 

6  28 

6  31 

8 

9 

3  16 

3  25 

3  34 

3  43 

4  0 

4  17 

4  33 

4  47 

4  59 

5  10 

5 

20 

5  29 

5  36 

5  42 

5  47 

5  50 

9 

10 

3  1 

3  9 

3  17 

3  25 

3  41 

3  55 

4  9 

4  21 

4  as 

4  43 

4 

53 

5  1 

5  7 

5  13 

5  17 

5  19 
4  54 

10 
11 

11 

2  48 

2  55 

3  3 

3  10 

3  24 

3  37 

3  50 

4  2 

4  12 

4  21 

4 

30 

4  37 

4  43 

4  48 

4  51 

12 

2  38 

2  44 

2  51 

2  58 

3  10 

3  22 

3  34 

3  45 

3  54 

4  2 

4 

10 

4  16 

4  22 

4  26 

4  28 

4  30 

12 

13 

2  29 

2  35 

2  41 

2  47 

2  58 

3  9 

3  20 

3  29 

3  38 

3  45 

3 

52 

3  58 

4  3 

4  7 

4  9 

13 

14 

2  22 

2  27 

2  33 

2  38 

2  48 

2  58 

3  8 

3  16 

3  24 

3  31 

3 

37 

3  43 

3  47 

3  51 

3  53 

14 

15 

2  16 

2  21 

2  26 

2  30 

2  39 

2  48 
2  40 

2  57 

3  5 

3  12 

3  19 

3 

25 

3  30 

3  34 

3  37 

3  40 

15 

16 

2  11 

2  15 

2  20 

2  24 

2  32 

2  48 

2  56 

3  2 

3  9 

3 

15 

3  19 

3  23 

3  26 

3  29 

16 

17 

2  7 

2  10 

2  14 

2  18 

2  26 

2  34 

2  41 

2  48 

2  54 

3  0 

3 

5 

3  9 

3  13 

3  15 

17 

18 

2  3 

2  6 

2  10 

2  13 

2  21 

2  28 

2  34 

2  40 

2  46 

2  52 

2 

57 

3  1 

3  4 

3  6 

18 

19 

2  0 

2  3 

2  6 

2  9 

2  16 

2  23 

2  29 

2  34 

2  40 

2  45 

2 

49 

2  53 

2  56 

2  58 

19 

20 

1  57 

2  0 

2  2 

2  5 

2  12 

2  18 

2  24 

2  29 

2  34 

2  38 

2 

42 

2  45 

2  48 

2  50 

20 

21 

1  54 

1  57 

1  59 

2  2 

2  8 

2  13 

2  19 

2  24 

2  29 

2  33 

2 

36 

2  39 

2  41 

21 

22 

1  52 

1  54 

1  56 

1  59 

2  4 

2  9 

2  14 

2  19 

2  24 

2  28 

2 

31 

2  34 

2  36 

22 

23 

1  50 

1  52 

1  54 

1  56 

2  1 

2  5 

2  10 

2  15 

2  19 

2  23 

2 

26 

2  29 

2  32 

23 

24 

1  49 

1  50 

1  52 

1  54 

1  58 

2  2 

2  7 

2  11 

2  15 

2  19 

2 

22 

2  25 

2  28 

24 

25 

1  48 

1  49 

1  50 

1  52 

1  56 
1  54 

2  0 

2  4 

2  8 

2  12 

2  15 

2 

18 

2  21 

25 

26 

1  47 

1  48 

1  49 

1  51 

1  58 

2  2 

2  5 

2  9 

2  12 

2 

15 

2  17 

26 

27 

1  47 

1  48 

1  49 

1  50 

1  53 

1  56 

2  0 

2  3 

2  6 

2  9 

2 

12 

2  14 

27 

28 

1  46 

1  47 

1  48 

1  49 

1  51 

1  64 

1  58 

2  1 

2  3 

2  6 

2 

9 

2  11 

28 

29 

1  46 

1  47 

1  47 

1  48 

1  50 

1  53 

1  56 

1  59 

2  1 

2  4 

2 

6 

29 

30 

1  45 

1  46 

1  46 

1  47 

1  49 

1  52 

1  55 

1  57 
1  56 

2  0 

2  2 

2 

3 

30 

31 

1  45 

1  45 

1  46 

1  47 

1  49 

1  51 

1  54 

1  58 

2   0 

2 

1 

31 

32 

1  45 

1  45 

1  45 

1  46 

1  48 

1  50 

1  52 

1  54 

1  56 

1  58 

1 

59 

32 

33 

1  45 

1  45 

1  45 

1  46 

1  47 

1  49 

1  51 

1  53 

1  54 

1  56 

33 

34 

1  45 

1  44 

1  44 

1  45 

1  46 

1  48 

1  50 

1  52 

1  53 

1  54 

34 

35 

1  45 

1  44 

1  44 

1  45 

1  46 

1  47 

1  49 

1  50 

1  51 

1  52 

35 

36 

1  46 

1  45 

1  44 

1  44 

1  45 

1  46 

1  48 

1  49 

1  50 

1  50 

«6 

37 

1  46 

1  45 

1  44 

1  44 

1  45 

1  45 

1  47 

1  48 

1  49 

37 

38 

1  46 

1  45 

1  44 

1  44 

1  44 

1  45 

1  46 

1  47 

1  48 

38 

39 

1  46 

1  45 

1  44 

1  44 

1  44 

1  44 

1  45 

1  46 

1  47 

39 

40 

1  46 

1  45 

1  45 

1  45 

1  44 

1  44 

1  45 

1  45 

1  46 

40 

41 

1  47 

1  46 

1  45 

1  45 

1  44 

1  44 

1  44 

1  44 

41 

42 

1  48 

1  47 

1  46 

1  45 

1  43 

1  43 

1  44 

1  44 

42 

43 

1  49 

1  48 

1  46 

1  45 

1  43 

1  43 

1  44 

1  44 

43 

44 

1  49 

1  48 

1  47 

1  45 

1  43 

1  43 

1  43 

44 

46 

1  50 

1  49 

1  47 

1  45 

1  43 

1  43 

1  43 

46 

48 

1  51 

1  50 

1  48 

1  46 

1  44 

1  43 

1  42 

48 

50 
52 
54 
56 

1  53 
1  54 
1  55 

1  56 

1  51 

1  51 
1  52 
1  53 

1  49 

1  49 
1  49 
1  50 

1  47 
1  47 
1  47 
1  48 

1  44 
1  44 
1  44 
1  44 

1  43 
1  42 

'    1 

50 
52 
54 

TABLE  P.  EFFECT  OF  SON's  PAR . 

To  be.  subtracted  from  the 
Third  Correction. 

56 

58 
60 

62 

58 
60 

62 

1  56 

1  57 
1  58 

1  53 
1  54 
1  54 

1  50 
1  51 
1  51 

1  48 
1  48 

)8 

App 
Alt. 

Sun's  Apparent  Altitude.  1 

5 

10  2 

0  30 

40  5 

0  60 

70 

80 

90 

64 

1  59 

1  55 

n 

/*   # 

~  "^ 

If 

f    n 

It 

~~ 



64 

66 

1  59 

5 

10 
15 
20 
25 
30 
35 
40 
45 
50 
55 
60 
65 
70 
75 
80 
90 

1 
1 

o 
3 
4 
4 

5 

6 
6 
7 
7 
8 
8 
8 
9 
9 
9 

1  1 

1 

2  '. 

3  C 

4  r 

4  4 

5  t 

6  ; 

6  e 

7  ' 

7  ' 

8  ' 
8  i 

8  t 

9  i 
9 

0 

1 

!  2 
t  3 
I  3 
4 
»  5 

>  5 

>  6 
J   6 

r  7 

r  7 

i   8 
) 

0 

1 

I 
3 
4 
5 
5 
6 
6 
7 

B  0 

1  1 

2  2 

2  2 

3  3 
1  4 

4  4 

5  5 
8 

0 
1 

2 
2 
3 
4 

0 

1 
1 

0 

66 

68 
70 
72 
74 
76 

78 
80 
82 
84 
86 

1 

68 
70 
72 
74 
76 

78 
80 
82 
84 
86 

1 

32° 

34° 

36° 

38° 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

■  ,  , 

188                 TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  88° 

• 

i 

J  '8 

APPARENT  ALTITUDE  OF  THE  SUN,  OR  STAR. 

J  "6 

App. 

Alt. 

App. 
Alt. 

0^ 

6° 

70 

8° 

9° 

10" 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26°  1 

28° 

3 

o 

/  n 

1    It 

1    n 

/  n 

/  II 

1    II 

/  II 

1    II 

/  // 

1    II 

1    II 

/  // 

1    II 

1 

// 

/  // 

1 

/r 

0 

6 

1  53 

1  54 

1  56 

1  59 

2  4 

2  10 

2  16 

2  28 

2  42 

2  56 

2  11 

3  26 

3  41 

3 

56 

4  11 

4 

25 

6 

7 

1  55 

1  53 

1  54 

1  56 

1  59 

2  3 

2  7 

2  16 

2  27 

2  39 

2  51 

3  4 

3  16 

3 

28 

3  40 

3 

52 

7 

8 

1  58 

1  55 

1  53 

1  54 

1  56 

1  59 

2  2 

2  8 

2  17 

2  27 

2  37 

2  48 

2  59 

3 

9 

3  19 

3 

30 

8 

9 

2  2 

1  58 

1  55 

1  53 

1  54 

1  56 

1  58 

2  3 

2  10 

2  18 

2  26 

2  35 

2  45 

2 

54 

3  3 

3 

12 

9 

10 

2  7 

2  I 

1  57 

1  55 

1  53 

1  54 

1  56 

2  0 

2  5 

2  11 

2  18 

2  25 

2  34 

2 

43 

2  50 

2 

58 

10 

11 

2  13 

2  5 

2  0 

1  57 

1  55 

1  53 

1  54 

1  57 

2  1 

2  6 

2  12 

2  18 

2  25 

2 

32 

2  39 

2 

47 

11 

12 

2  19 

2  10 

2  4 

2  0 

1  57 

1  54 

1  53 

1  55 

1  58 

2  2 

2  7 

2  12 

2  18 

2 

24 

2  30 

2 

37 

12 

13 

2  26 

2  15 

2  8 

2  3 

1  59 

1  56 

1  54 

1  54 

1  56 

1  59 

2  3 

2  7 

2  12 

2 

18 

2  23 

2 

29 

13 

14 

2  33 

2  21 

2  12 

2  6 

2  1 

1  58 

1  56 

1  53 

1  55 

1  57 

2  0 

2  3 

2  7 

2 

12 

2  17 

2 

22 

14 

15 

2  40 

2  26 

2  16 

2  9 

2  4 

2  0 

1  57 

1  54 

1  54 

1  55 

1  58 

2  0 

2  4 

2 

8 

2  13 

2 

17 

15 

16 

2  47 

2  32 

2  20 

2  13 

2  7 

2  2 

1  59 

1  55 

1  53 

1  54 

1  56 

1  58 

2  1 

2 

5 

2  9 

2 

13 

16 

17 

2  54 

2  37 

2  25 

2  17 

2  10 

2  5 

2   1 

1  56 

1  53 

1  53 

1  55 

1  57 

1  59 

2 

2 

2  5 

2 

9 

17 

18 

3  2 

2  43 

2  30 

2  21 

2  13 

2  7 

2  3 

1  58 

1  54 

1  52 

1  54 

1  56 

1  58 

2 

0 

2  2 

2 

5 

18 

19 

3  10 

2  49 

2  35 

2  25 

2  16 

2  10 

2  5 

1  59 

1  55 

1  53 

1  53 

1  54 

1  56 

58 

2  0 

2 

3 

19 

20 

3  17 

2  55 

2  41 

2  29 

2  20 

2  13 

2  8 

2   1 

1  56 

1  54 

1  52 

1  53 

1  54 

56 

1  58 

2 

1 

20 
21 

21 

3  25 

3  2 

2  46 

2  34 

2  24 

2  17 

2  11 

2  3 

1  58 

1  55 

1  53 

1  52 

I  53 

55 

1  57 

59 

22 

3  32 

3  8 

2  52 

2  39 

2  28 

2  20 

2  14 

2  5 

1  59 

1  56 

1  53 

1  52 

1  53 

54 

1  55 

57 

22 

23 

3  40 

3  15 

2  57 

2  43 

2  32 

2  24 

2  17 

2  7 

2  1 

1  57 

1  54 

1  52 

1  52 

53 

1  54 

55 

23 

24 

3  47 

3  21 

3  2 

2  48 

2  36 

2  27 

2  20 

2  9 

2  2 

1  58 

1  55 

1  53 

1  52 

52 

1  53 

54 

24 

25 
26 

3  55 

3  27 

3  8 

2  52 

2  40 

2  31 

2  23 
2  27 

2  11 

2  4 

2  0 

1  56 

1  53 

1  52 

52 

1  53 

54 

25 
26 

4  2 

3  33 

2  13 

2  57 

2  44 

2  35 

2  14 

2  6 

2  1 

1  57 

1  54 

1  53 

52 

1  52 

53 

27 

4  10 

3  39 

3  18 

3  2 

2  48 

2  38 

2  30 

2  17 

2  8 

2  2 

1  58 

1  55 

1  53 

52 

1  52 

52 

27 

28 

4  17 

3  45 

3  23 

3  6 

2  52 

2  42 

2  33 

2  19 

2  10 

2  4 

1  59 

1  55 

1  53 

52 

1  52 

52 

28 

29 

4  24 

3  51 

3  28 

3  11 

2  56 

2  46 

2  37 

2  22 

2  12 

2  5 

2  0 

1  56 

1  53 

52 

1  52 

52 

29 

30 

4  31 

3  57 

3  34 

3  15 

3  0 

2  49 

2  40 

2  24 

2  14 

2  6 

2  1 

1  57 

1  54 

53 

1  52 

52 

30 

31 

4  39 

4  3 

3  40 

3  20 

3  4 

2  53 

2  43 

2  27 

2  16 

2  8 

2  2 

1  58 

1  55 

53 

1  52 

52 

31 

32 

4  46 

4  9 

3  45 

3  25 

3  8 

2  56 

2  46 

2  29 

2  18 

2  9 

2  3 

1  59 

1  56 

54 

1  53 

52 

32 

33 

4  53 

4  15 

3  51 

3  29 

3  12 

3  0 

2  50 

2  31 

2  20 

2  11 

2  5 

2  0 

1  56 

54 

1  53 

53 

33 

.14 

5  0 

4  21 

3  56 

3  34 

3  17 

3  4 

2  53 

2  34 

2  22 

2  13 

2  7 

2  1 

1  57 

55 

1  54 

53 

34 

35 

5  7 

4  27 

4  1 

3  38 

3  21 

3  7 

2  56 

2  37 

2  24 

2  15 

2  8 

2  2 

1  58 

56 

1  54 

53 

35 
36 

3ff 

5  13 

4  33 

4  6 

3  43 

3  25 

3  11 

2  59 

2  40 

2  26 

2  17 

2  10 

2  4 

1  59 

56 

1  54 

53 

37 

5  20 

4  39 

4  11 

3  48 

3  29 

3  15 

3  2 

2  43 

2  28 

2  19 

2  11 

2  5 

2  0 

57 

1  55 

54 

37 

38 

5  27 

4  45 

4  16 

3  52 

3  33 

3  18 

3  5 

2  46 

2  31 

2  21 

2  13 

2  6 

2  1 

58 

1  56 

54 

38 

39 

5  34 

4  51 

4  21 

3  57 

3  37 

3  22 

3  8 

2  49 

2  33 

2  22 

2  14 

2  7 

2  2 

58 

1  56 

55 

39 

40 
41 

5  40 

4  56 

4  26 

4  1 

3  41 

3  25 

3  11 

2  51 

2  35 

2  24 

2  16 
2  17 

2  9 

2  3 

59 

1  57 

55 

40 

5  47 

5  2 

4  31 

4  5 

3  45 

3  29 

3  14 

2  54 

2  38 

2  26 

2  10 

2  4 

2 

0 

1  57 

65 

41 

42 

5  53 

5  7 

4  36 

4  9 

3  49 

3  32 

3  17 

2  56 

2  40 

2  28 

2  19 

2  11 

2  5 

2 

1 

1  58 

56 

42 

43 

6  0 

5  13 

4  41 

4  14 

3  53 

3  36 

3  20 

2  59 

2  42 

2  30 

2  20 

2  12 

2  6 

2 

2 

)  59 

57 

43 

44 

6  6 

5  19 

4  46 

4  18 

3  57 

3  39 

3  23 

3   1 

2  44 

2  32 

2  22 

2  13 

2  7 

2 

3 

2  0 

58 

44 

46 
48 

6  18 

5  29 

4  55 

4  26 

4  4 

3  46 

3  29 

3   6 

2  48 

2  35 

2  25 

2  16 

2  9 

2 

5 

2  2 

59 

46 

6  29 

5  39 

5  4 

4  34 

4  11 

3  52 

3  35 

3  11 

2  52 

2  39 

2  28 

2  18 

2  11 

2 

7 

2  3 

2 

0 

48 

50 

6  40 

5  48 

5  12 

4  41 

4  17 

3  58 

3  41 

3  15 

2  56 

2  42 

2  31 

2  21 

2  13 

2 

9 

2  5 

2 

2 

50 

52 

6  51 

5  57 

5  20 

4  48 

4  23 

4  2 

3  47 

3  19 

2  59 

2  45 

2  34 

2  24 

2  16 

2 

10 

2  6 

2 

3 

52 

54 

7   1 

6  6 

5  28 

4  55 

4  29 

4  8 

3  52 

3  23 

3  3 

2  48 

2  36 

2  27 

2  18 

2 

12 

2  8 

2 

4 

54 

56 

7  10 

6  15 

5  35 

5  1 

4  35 

4  14 

3  57 

3  27 

3  7 

2  51 

2  39 

2  29 

2  20 

2 

14 

2  9 

2 

5 

56 

58 

7  19 

6  23 

5  42 

5  7 

4  40 

4  19 

4  2 

3  31 

3  10 

2  54 

2  42 

2  31 

2  22 

1 

16 

2  11 

2 

6 

58 

60 

7  28 

6  31 

5  48 

5  12 

4  45 

4  24 

4  6 

3  35 

3  13 

2  57 

2  44 

2  33 

2  24 

1 

17 

2  12 

2 

7 

60 

62 

7  36 

6  38 

5  54 

5  17 

4  50 

4  29 

4  10 

3  38 

3  16 

2  59 

2  46 

2  35 

2  26 

2 

19 

2  13 

2 

8 

62 

64 

7  44 

6  45 

6  0 

5  22 

4  55 

4  33 

4  14 

3  42 

3  19 

3  2 

2  48 

%   37 

2  28 

2 

20 

2  14 

2 

9 

64 

66 

68 

7  51 

6  51 

6  5 

5  27 

5  0 

4  37 

4  18 

3  45 

3  22 

3  4 

2  50 

2  39 

2  30 

2 

22 

2  15 

66 

7  58 

6  56 

6  10 

5  32 

5  4 

4  41 

4  21 

3  48 

3  25 

3  6 

2  51 

2  40 

2  31 

2 

23 

68 

70 

S  4 

7  1 

6  15 

5  36 

5  8 

4  44 

4  23 

3  50 

3  27 

3  8 

2  53 

2  41 

2  32 

70 

72 

•'  IC 

7  S 

6  19 

5  40 

5  11 

4  47 

4  25 

3  52 

3  29 

3  9 

2  53 

2  42 

72 

74 

>  If 

>  7  9 

6  23 

5  43 

5  14 

4  49 

4  27 

3  54 

3  30 

3  10 

2  54 

74 

76 

78 

8  ^<3 

7  13 

6  26 

5  46 

5  17 

4  51 

4  29 

3  56 

3  31 

3  11 

76 

8  2S 

!  7  16 

6  29 

5  49 

5  19 

4  53 

4  31 

3  57 

3  32 

78 

80 

8  21 

i  7  19 

6  31 

5  52 

5  21 

4  55 

4  33 

3  58 

80 

82 

8  26 

!  7  22 

6  33 

5  54 

5  23 

4  57 

4  35 

82 

84 

8  3( 

)  7  24 

6  35 

5  56 

5  15 

84 

86 

8  35 

5  7  26 

6  37 

86 

&'' 

70 

8° 

9<» 

10° 

11" 

12° 

14° 

16° 

18° 

20° 

22°  24° 

26° 

28° 

30° 

_ 

TABLE  XXXIII. 

189  1 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  899 

A.pp. 
Alt. 

APPARENT  ALTITUDE  OP  THE  SUN, 

OR  STAR. 

>'8 

App 
Alt. 

o 

32° 

34" 

36°  1 

38° 

42° 

46° 

50° 

54° 

58° 

62° 

66°  1 

70° 

74° 

78° 

82° 

86° 

o 

1    ti 

/  // 

1 

// 

r     II 

/  II 

1    II 

/  II 

/  II 

/  II 

/  II 

/ 

II 

/  II 

/  // 

/  // 

1    II 

/  II 

6 

4  40 

4  54 

5 

8 

5  22 

5  48 

6  13 

6  36 

6  57 

7  16 

7  34 

7 

49 

8  2 

8  13 

8  21 

8  27 

8  32 

6 

7  4  4 

4  16 

4 

28 

4  40 

5  3 

5  25 

5  45 

6  4 

6  21 

6  36 

6 

49 

7  0 

7  9 

7  16 

7  22 

7  27 

7 

8  3  41 

3  52 

4 

3 

4  13 

4  33 

4  52 

5  10 

5  26 

5  40 

5  53 

6 

5 

6  15 

6  23 

6  29 

6  34 

6  37 

8 

9  3  22 

3  31 

3 

41 

3  50 

4  8 

4  24 

4  39 

4  53 

5  5 

5  16 

5 

26 

5  35 

5  43 

5  49 

5  54 

9 

10 

3  6 

3  14 

3 

22 

3  30 

3  46 

4  1 

4  15 

4  27 

4  38 

4  49 

4 

58 

5  7 

5  14 

5  19 

5  23 

10 
11 

11 

2  54 

3  2 

3 

9 

3  16 

3  30 

3  43 

3  56 

4  7 

4  17 

4  27 

4 

36 

4  43 

4  49 

4  53 

4  57 

12 

2  44 

2  51 

2 

58 

3  4 

3  16 

3  28 

3  40 

3  50 

4  0 

4  8 

4 

16 

4  23 

4  28 

4  32 

4  36 

12 

13 

2  35 

2  41 

2 

47 

2  53 

3  4 

3  15 

3  26 

3  35 

3  44 

3  52 

3 

59 

4  5 

4  10 

4  13 

13 

14 

2  27 

2  33 

2 

38 

2  44 

2  54 

3  4 

3  14 

3  22 

3  30 

3  37 

3 

44 

3  50 

3  54 

3  57 

14 

15 
16 

2  22 

2  27 

2 

32 

2  36 

2  46 

2  55 

3  4 

3  11 

3  18 

3  25 

3 

31 

3  37 

3  41 

3  44 

15 

2  17 

2  21 

2 

26 

2  30 

2  39 

2  47 

2  55 

3  2 

3  9 

3  15 

3 

21 

3  26 

3  30 

3  33 

16 

17 

2  12 

2  16 

2 

21 

2  25 

2  33 

2  40 

2  47 

2  54 

3  0 

3  6 

3 

12 

3  16 

3  19 

17 

18 

2  8 

2  12 

2 

16 

2  20 

2  27 

2  34 

2  41 

2  47 

2  53 

2  58 

2 

3 

3  7 

3  10 

18 

19 

2  5 

2  8 

2 

12 

2  16 

2  22 

2  29 

2  35 

2  41 

2  47 

2  52 

2 

56 

2  59 

3  2 

19 

20 

2  3 

2  6 

2 

9 

2  12 

2  18 

2  24 

2  30 

2  35 

2  41 

2  46 

2 

49 

2  52 

2  54 

20 

21 

2  1 

2  3 

2 

6 

2  8 

2  14 

2  19 

2  25 

2  30 

2  35 

2  40 

2 

43 

2  46 

21 

22 

1  59 

2  1 

2 

3 

2  5 

2  10 

2  15 

2  20 

2  25 

2  30 

2  35 

2 

38 

2  41 

22 

23 

1  57 

1  59 

2 

1 

2  3 

2  7 

2  12 

2  16 

2  21 

2  26 

2  30 

2 

33 

2  36 

23 

24 

1  56 

1  57 

59 

2  1 

2  5 

2  9 

2  13 

2  17 

2  22 

2  26 

2 

29 

2  31 

24 

25 

1  55 

1  56 

57 

1  59 

2  3 

2  6 

2  10 

2  14 

2  18 

2  22 

2 

25 

25 

26 

1  54 

1  55 

56 

1  58 

2  1 

2  4 

2  8 

2  12 

2  15 

2  18 

2 

21 

26 

27 

1  53 

1  54 

1 

55 

1  57 

2  0 

2  3 

2  6 

2  10 

2  13 

2  15 

2 

17 

27 

28 

1  53 

1  54 

55 

1  56 

1  58 

2  1 

2  4 

2  8 

2  11 

2  13 

2 

14 

28 

29 

1  52 

1  53 

54 

1  55 

1  57 

2  0 

2  3 

2  6 

2  8 

2  10 

29 

30 

1  52 

1  53 

53 

1  54 

1  56 

1  59 

2  2 

2  4 

2  6 

2  8 

30 

31 

1  52 

1  52 

52 

1  53 

1  55 

1  58 

2  0 

2  2 

2  4 

2  5 

31 

32 

1  51 

1  52 

52 

1  53 

1  55 

1  57 

1  59 

2  1 

2  2 

2  3 

32 

33 

1  52 

1  51 

51 

1  52 

1  54 

1  56 

1  58 

1  59 

2  0 

33 

34 

1  52 

1  51 

51 

1  52 

1  53 

1  55 

1  57 

1  58 

1  69 

34 

35 

1  52 

1  51 

51 

1  51 

1  52 

1  54 

1  56 

1  57 

1  57 

35 

36 

1  53 

1  52 

51 

1  51 

1  52 

1  53 

1  55 

1  56 

1  56 

36 

37 

1  53 

1  52 

51 

1  51 

1  51 

1  52 

1  54 

1  56 

37 

38 

1  53 

1  52 

51 

1  50 

1  51 

1  52 

1  53 

1  54 

38 

39 

1  54 

1  52 

51 

'l  50 

1  51 

1  52 

1  52 

1  53 

39 

40 

1  54 

1  53 

52 

1  51 

1  50 

1  51 

1  52 

1  52 

40 
41 

41 

1  54 

1  53 

52 

1  51 

1  50 

1  51 

1  51 

42 

1  54 

1  53 

52 

1  51 

1  50 

1  51 

1  51 

42 

43 

1  55 

1  54 

53 

1  52 

1  51 

1  51 

1  51 

43 

44 

1  56 

1  54 

53 

1  52 

1  51 

1  50 

1  50 

44 

46 

1  57 

1  55 

53 

1  52 

1  51 

1  50 

46 

48 

1  58 

1  56 

54 

1  53 

1  51 

1  50 

48 

*50 
52 
54 

1  59 

2  0 
2  1 

1  57 
I  58 
1  58 

55 
55 
56 
56 

1  53 
1  53 
1  54 
1  54 

1  51 
1  52 

'    1 

50 
52 
54 

TABLE  P.  BF FBCT  OF  IDN's  PAK . 

56 

58 
60 
62 

2  2 

1  59 

To  be  subtracted  from  th« 
Third  Correction. 

56 

58 
60 
62 

2  3 
2  3 
2  4 

1  59 
1  59 

1 

56 

APP 
A  t. 

Sun's  Apparent  Altitude. 1 

5 

10  2 

0  30 

40  5 

0  60  7( 

)8C 

90 

64 



ft 



'  t* 

ft 



— 

— 

64 

66 

5 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 
60 
65 
70 
75 
80 
90 

1 
2 
2 

3 
4 
4 

5 
6 
6 
7 
7 
8 
8 
8 
9 
9 
9 

1  1 

1 

2  S 

3  C 

4  4 

4  4 

5  i 

6  C 

6  i 

7  • 

7  ' 

8  i 
8  i 
8  i 
9 

9 

1 

1 

!  2 

3 

4 

4 

5 

6 

!  0 

r  7 

r  7 

)  8 

i 
i 

1 

1 
2 
3 
4 
4 
5 
6 
6 
7 
7 

I  1  0 

1  1  1 

2  2  2 

3  3  3 

4  4  4 

4  4 

5  5 

0 

1 
2 

0 

66 

68 
70 
72 
74 
7ti 

78 
80 
82 
84 
86 

68 
70 
72 
74 
76 

! 

78 
80 
82 
84 
86 

36° 

38° 

50° 

54° 

58° 

62° 

66° 

32° 

34° 

42° 

46° 

190 

TABLE  XXXIIl. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  92". 

2>'8 

App. 
Alt. 

APPARENT  ALTITUDE  OF 

THE 

SUN, 

OR  STAR. 

App. 
Alt. 

6» 

70 

8° 

9 

0 

10° 

11 

I" 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

0 

/  // 

t    ti 

1   tt 

t 

n 

1 

// 

/ 

n 

1    It 

I 

II 

; 

II 

t 

II 

/ 

II 

/  // 

'  ." 

r 

// 

t 

rf 

1 

II 

0 

6 

1  id 

2  1 

2  3 

2 

6 

2 

10 

2 

15 

2  21 

2 

34 

2 

48 

3 

3 

3 

18 

3  33 

3  48 

4 

3 

4 

18 

4 

33 

6 

7 

2  1 

1  59 

2  1 

2 

3 

2 

5 

2 

9 

2  13 

2 

22 

2 

33 

2 

45 

2 

58 

3  11 

3  24 

3 

36 

3 

48 

4 

0 

7 

8 

2  4 

2  1 

1  59 

2 

0 

2 

2 

2 

4 

2  7 

2 

14 

2 

23 

2 

33 

2 

44 

2  55 

3   5 

3 

16 

3 

26 

3 

37 

8 

9 

2  8 

2  4 

2  1 

1 

59 

2 

0 

2 

2 

2  4 

2 

9 

2 

16 

2 

24 

2 

33 

2  42 

2  51 

3 

1 

3 

10 

3 

19 

9 

10 

2  13 

2  7 

2  3 

2 

1 

1 

59 

2 

0 

2  2 

2 

6 

2 

11 

2 

17 

2 

24 

2  32 

2  40 

2 

48 

2 

57 

3 

5 

10 

11 

2  19 

2  11 

2  6 

2 

3 

2 

1 

1 

59 

2  0 

2 

3 

2 

7 

2 

12 

2 

18 

2  24 

2  31 

2 

39 

2 

46 

2 

54 

11 

12 

2  25 

2  16 

2  10 

2 

6 

2 

3 

2 

1 

1  59 

2 

1 

2 

4 

2 

8 

2 

13 

2  18 

2  24 

2 

31 

2 

37 

2 

44 

12 

13 

2  32 

2  21 

2  14 

2 

9 

2 

5 

2 

2 

2  0 

2 

0 

2 

2 

2 

5 

2 

9 

2  14 

2  19 

2 

24 

2 

30 

2 

36 

13 

14 

2  39 

2  27 

2  18 

2 

12 

2 

7 

2 

4 

2  2 

1 

59 

2 

1 

2 

3 

2 

6 

2  10 

2  14 

2 

19 

2 

24 

2 

29 

14 

15 

2  46 

2  32 

2  22 

2 

15 

2 

10 

2 

6 

2  3 

2 

0 

2 

0 

2 

1 

2 

4 

2  7 

2  10 

2 

15 

2 

19 

2 

24 

15 

16 

2  53 

2  38 

2  27 

2 

19 

2 

13 

2 

8 

2  5 

2 

1 

1 

59 

2 

0 

2 

2 

2  4 

2  7 

2 

11 

2 

15 

2 

19 

16 

17 

3  0 

2  44 

2  32 

2 

23 

2 

16 

2 

11 

2  7 

2 

3 

2 

0 

1 

59 

2 

1 

2   3 

2  5 

2 

8 

2 

12 

2 

15 

17 

18 

3  8 

2  50 

2  37 

2 

27 

2 

19 

2 

14 

2  9 

2 

4 

2 

1 

1 

59 

2 

0 

2  2 

2  4 

2 

6 

2 

9 

2 

12 

18 

19 

3  16 

2  56 

2  42 

2 

31 

2 

22 

2 

16 

2  11 

2 

6 

2 

2 

2 

0 

2 

0 

2   1 

2  2 

2 

4 

2 

7 

2 

10 

19 

20 

3  23 

3  2 

2  48 

2 

36 

2 

26 

2 

19 

2  14 

2 

8 

2 

3 

2 

0 

1 

59 

2  0 

2  1 

2 

3 

2 

5 

2 

8 

20 

21 

3  31 

8  9 

2  54 

2 

41 

2 

30 

2 

23 

2  17 

2 

10 

2 

5 

2 

1 

1 

59 

1  59 

2  0 

2 

2 

2 

4 

2 

6 

21 

22 

3  38 

3  15 

2  59 

2 

45 

2 

34 

2 

26 

2  20 

2 

12 

2 

6 

2 

2 

2 

0 

1  59 

2  0 

2 

1 

2 

2 

2 

4 

22 

23 

3  46 

3  22 

3  4 

2 

50 

2 

38 

2 

30 

2  23 

2 

14 

2 

8 

2 

3 

2 

0 

1  59 

1  59 

2 

0 

2 

1 

2 

2 

23 

24 

3  53 

3  28 

3  9 

2 

54 

2 

42 

2 

34 

2  27 

2 

16 

2 

9 

2 

4 

2 

1 

2  0 

1  59 

59 

2 

0 

2 

1 

24 

25 
26 

4   1 

3  34 

3  15 

2 

59 

2 

46 

2 

37 

2  30 

2 

19 

2 

11 

2 

5 

~1 

2 

2 

2  0 

1  59 

59 

2 

0 

2 

0 

25 
26 

4  9 

3  40 

3  20 

3 

3 

2 

50 

2 

41 

2  33 

2 

22 

2 

13 

2 

2 

4 

2   1 

1  59 

59 

59 

2 

0 

27 

4  17 

3  46 

3  26 

3 

8 

2 

55 

2 

45 

2  36 

2 

24 

2 

15 

2 

9 

2 

5 

2  2 

2  0 

59 

59 

2 

0 

27 

28 

4  24 

3  52 

3  31 

3 

13 

2 

59 

2 

48 

2  39 

2 

27 

2 

17 

2 

11 

2 

6 

2  2 

2  0 

59 

59 

59 

28 

29 

4  31 

3  58 

3  36 

3 

18 

3 

3 

2 

52 

2  43 

2 

29 

2 

19 

2 

12 

2 

7 

2  3 

2  1 

2 

0 

59 

59 

29 

30 

4  38 

4   4 

3  41 

3 

22 

3 

7 

2 

56 

2  46 

2 

32 

2 

21 

2 

13 

2 

8 

2  4 

2  1 

2 

0 

59 

59 

30 
31 

31 

4  46 

4  10 

3  47 

3 

27 

3 

12 

3 

0 

2  50 

2 

35 

2 

23 

2 

15 

2 

9 

2  5 

2  2 

2 

0 

1 

59 

59 

32 

4  53 

4  16 

3  52 

3 

32 

3 

16 

3 

4 

2  53 

2 

37 

2 

25 

2 

16 

2 

11 

2  7 

2  3 

2 

1 

2 

0 

59 

32 

33 

5  0 

4  22 

3  58 

3 

37 

3 

20 

3 

8 

2  57 

2 

40 

2 

27 

2 

18 

2 

12 

2  8 

2  4 

2 

1 

2 

0 

59 

33 

34 

5  7 

4  28 

4  3 

3 

41 

3 

24 

3 

11 

3   0 

2 

42 

2 

29 

2 

20 

2 

14 

2  9 

2  5 

2 

2 

2 

1 

2 

0 

34 

35 

5  14 

4  34 

4  8 

3 

46 

3 

28 

3 

15 

3   3 

2 

45 

2 

31 

2 

22 

2 

15 

2  10 

2  6 

2 

3 

2 

1 

2 
2 

0 

1 

35 
36 

36 

5  21 

4  40 

4  13 

3 

50 

3 

32 

3 

18 

3   6 

2 

47 

2 

33 

2 

24 

2 

17 

2  11 

2  7 

2 

4 

2 

2 

37 

5  28 

4  46 

4  18 

3 

55 

3 

36 

3 

22 

3   9 

2 

50 

2 

36 

2 

25 

2 

18 

2  12 

2  8 

2 

5 

2 

3 

2 

1 

37 

38 

5  34 

4  52 

4  23 

4 

0 

3 

40 

3 

25 

3  12 

2 

53 

2 

38 

2 

27 

2 

20 

2  14 

2  9 

2 

6 

2 

4 

2 

2 

38 

39 

5  41 

4  58 

4  28 

4 

4 

3 

44 

3 

29 

3  15 

2 

55 

2 

40 

2 

29 

2 

21 

2  15 

2  10 

2 

7 

2 

4 

2 

2 

39 

40 
41 

5  47 

5  J 

4  33 

4 

8 

3 

48 

3 

32 

3  18 

2 

58 

2 

42 

2 

31 

2 

22 

2  16 

2  11 

2 

• 

2 

5 

2 

3 

40 

5  54 

5  9 

4  38 

4 

12 

3 

52 

3 

35 

3  21 

3 

0 

2 

45 

2 

33 

2 

24 

2  17 

2  12 

2 

8 

2 

5 

2 

3 

41 

42 

6  0 

5  14 

4  43 

4 

16 

3 

55 

3 

39 

3  24 

3 

2 

2 

47 

2 

34 

2 

25 

2  18 

2  13 

2 

9 

2 

6 

2 

4 

42 

43 

6  7 

5  20 

4  48 

4 

21 

3 

59 

3 

42 

3  27 

3 

5 

2 

49 

2 

36 

2 

27 

2  20 

2  14 

2 

10 

2 

7 

2 

4 

43 

44 

6  13 

5  25 

4  53 

4 

25 

4 

3 

3 

46 

3  30 

3 

8 

2 

51 

2 

38 

2 

28 

2  21 

2  15 

2 

11 

2 

8 

2 

5 

44 

45 
46 

6  19 

5  31 

4  58 

4 

29 

4 

7 

3 

49 

3  33 

3 

11 

0 

53 

2 

40 

2 

30 

2  22 

2  16 

2 

12 

2 

8 

2 

5 

45 

6  25 

5  36 

5   2 

4 

33 

4 

10 

3 

52 

3  36 

3 

13 

2 

55 

2 

42 

2 

31 

2  24 

2  18 

2 

13 

2 

9 

2 

6 

46 

47 

6  31 

5  41 

5  7 

4 

37 

4 

13 

3 

55 

3  39 

3 

16 

2 

57 

2 

44 

2 

33 

2  25 

2  19 

2 

14 

2 

10 

2 

7 

4f 

48 

6  37 

5  46 

5  11 

4 

41 

4 

17 

3 

59 

3  42 

3 

18 

2 

59 

2 

46 

2 

35 

2  27 

2  20 

2 

15 

2 

11 

2 

8 

48 

50 

6  47 

5  56 

5  19 

4 

48 

4 

24 

4 

5 

3  48 

3 

22 

3 

4 

2 

49 

2 

37 

2  29 

2  22 

2 

16 

2 

12 

2 

9 

50 

52 

54 

6  57 

7  7 

6  5 

5  27 

4 

55 

4 

30 

4 

11 

3  53 

3 

26 

3 

8 

2 

53 

2 

41 

2  32 

2  24 

2 

18 

2 

13 

2 

10 

52 

6  14 

5  35 

5 

2 

4 

36 

4 

16 

3  58 

3 

30 

3 

11 

2 

56 

2 

44 

2  34 

2  26 

2 

20 

2 

15 

2 

11 

54 

56 

7  17 

6  23 

5  42 

5 

9 

4 

42 

4 

21 

4  3 

3 

34 

3 

14 

2 

59 

2 

47 

2  37 

2  29 

2 

22 

2 

16 

2 

12 

56 

58 

7  27 

6  31 

5  49 

5 

15 

4 

47 

4 

26 

4  8 

3 

38 

3 

17 

3 

2 

2 

49 

2  39 

2  31 

2 

24 

2 

18 

2 

13 

58 

lO 

7  36 

6  39 

5  56 

5 

21 

4 

53 

4 

31 

4  13 

3 

42 

3 

20 

3 

5 

2 

52 

2  41 

2  32 

2 

25 

2 

20 

2 

14 

60 

(i2 
64 

7  45 

6  46 

6  2 

5 

26 

4 

58 

4 

36 

4  17 

3 

46 

3 

23 

3 

8 

2 

54 

2  43 

2  34 

2 

26 

2 

21 

62 

7  53 

6  53 

6  8 

5 

31 

5 

3 

4 

41 

4  21 

3 

50 

3 

26 

3 

10 

2 

56 

2  44 

2  35 

2 

27 

64 

66 

8  1 

6  59 

6  13 

5 

36 

5 

8 

4 

45 

4  25 

3 

53 

3 

29 

3 

12 

2 

57 

2  45 

2  37 

66 

68 

8  8 

7  5 

6  18 

5 

41 

5 

12 

4 

49 

4  28 

3 

56 

3 

32 

3 

14 

2 

58 

2  46 

68 

70 

8  14 

7  10 

6  23 

5 

45 

5 

16 

4 

52 

4  31 

3 

58 

3 

34 

3 

15 

2 

59 

70 

72 

8  20 

7  15 

6  28 

5 

49 

5 

19 

4 

55 

4  33 

4 

0 

3 

35 

3 

16 

72 
74 

74 

8  25 

7  19 

6  31 

5 

53 

5 

22 

4 

57 

4  35 

4 

1 

3 

36 

76 

8  29 

7  23 

6  34 

5 

56 

5 

25 

4 

59 

4  37 

4 

2 

76 

78 

8  32 

7  26 

6  37 

5 

58 

5 

27 

5 

1 

4  39 

78 

80 

8  34 

7  28 

6  39 

6 

0 

5 

1^9 

80 

82 

8  36 

7  30^6  41 

82 

6' 

7°   ^' 

9° 

10° 

11" 

12" 

14" 

16" 

18" 

20" 

22° 

24" 

26° 

28° 

30° 

TABLE  XXXlll. 

191   1 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  92°.                                     1 

App. 

Alt. 

APPARENT   ALTITUDE    OF    THE    SUN, 

OR    STAR. 

^'8 

App 
Alt 

0 

32^ 

34° 

36° 

38° 

40° 

42° 

46° 

50° 

54° 

58° 

62° 

66° 

70° 

74° 

78° 

82° 
/    II 

0 

/     II 

>    // 

1    II 

/    // 

/    // 

/    II 

t    II 

1    II 

1    II 

/    II 

/ 

II 

'    II 

1    II 

1    II 

t    II 

6 

4  47 

5     2 

5   16 

5  30 

5  44 

5  57 

6  21 

6  44 

7     5 

7   24 

7 

42 

7  59 

8   12 

8  22 

8  30 

8  36 

6 

7 

4   12 

4  24 

4  36 

4  48 

5     0 

5   11 

5  33 

5  53 

6   12 

6  29 

6 

44 

6  58 

7   10 

7   18 

7   25 

7  30 

7 

8 

3  48 

3   59 

4   10 

4   20 

4  30 

4  40 

4  59 

5   17 

5  33 

5  48 

6 

1 

6    13 

6  23 

6  31 

6  37 

6  41 

8 

9 

3   29 

3   38 

3  48 

3   57 

4     6 

4   14 

4  30 

4  45 

5     0 

5  13 

5 

25 

5  35 

5  44 

5  52 

5  58 

9 

10 
11 

3   13 
3     1 

3   21 

3  30 

3   38 

3  45 

3  52 

4     8 

4   22 

4  34 

"4  46 

4 

57 

5     7 

5  15 

5  22 

5  27 

10 
11 

3     8 

3   16 

3  22 

3  29 

3  36 

3  50 

4     3 

4   14 

4  24 

4 

34 

4  43 

4  51 

4  57 

5     2 

12 

2  51 

2  57 

3     4 

3   10 

3   17 

3  23 

3   35 

3  47 

3  57 

4     6 

4 

15 

4  23 

4  30 

4  36 

4  41 

12 

13 

2  42 

2  47 

2  53 

2  59 

3     6 

3    12 

3   23 

3   33 

3  42 

3  51 

4 

0 

4     7 

4   13 

4  17 

13 

14 

2  34 

2  39 

2  44 

2  50 

2  56 

3      2 

3   12 

3   21 

3   30 

3  38 

3 

46 

3  52 

3  57 

4     1 

14 

15 
16 

2  28 

2  33 

2  38 

2  43 

2  37 

2  48 

2   53 

3     2 

3    11 

3   19 

3  26 

3 

33 

3  39 

3  44 

3  49 

15 
16 

2  23 

2  28 

2  32 

2  42 

2  46 

2  54 

3      2 

3     9 

3   16 

3 

22 

3  28 

3  33 

3  38 

17 

2   19 

2  23 

2  27 

2  32 

2  36 

2  40 

2  47 

2  54 

3     1 

3     7 

3 

13 

3   19 

3  24 

17 

18 

2   16 

2   19 

2  23 

2  27 

2   31 

2  34 

2  41 

2  48 

2  54 

3     0 

3 

6 

3   11 

3   15 

18 

19 

2   13 

2   16 

2   19 

2  23 

2  26 

2  29 

2  36 

2  42 

2  48 

2  54 

2 

59 

3     4 

3     7 

19 

20 

2  10 

2   13 

2   16 

2   19 

2  22 
2   18 

2  25 

2  31 

2  37 

2  43 

2  48 

2 

53 

2  57 

3     0 

20 

21 

2     8 

2   10 

2   13 

2   16 

2  21 

2  26 

2  32 

2  38 

2  43 

2 

47 

2  51 

21 

22 

2     6 

2     8 

2   10 

2   13 

2  15 

2   17 

2  22 

2  28 

2  33 

2  38 

2 

42 

2  45 

22 

23 

2     4 

2     6 

2     8 

2   10 

2   12 

2  14 

2   19 

2  24 

2  29 

2  34 

2 

38 

2  41 

23 

24 

2     2 

2     4 

2     6 

2     8 

2   10 

2   12 

2   16 

2  21 

2  26 

2  30 

2 

34 

2  38 

24 

25 

2     1 

2     3 

2     4 

2     6 

2     8 

2   10 

2   14 

2   18 

2  22 

2  26 

2 

30 

25 

26 

2     1 

2     2 

2     3 

2     5 

2     6 

2     8 

2   12 

2   15 

2   19 

2  23 

2 

26 

26 

27 

2     0 

2     1 

2     2 

2     4 

2     5 

2     7 

2   10 

2   13 

2   16 

2  20 

2 

23 

27 

28 

1   59 

2     0 

2     1 

2     3 

2     4 

2     6 

2     8 

2   11 

2   14 

2   17 

2 

20 

28 

29 

1    59 

1   59 

2     0 

2     2 

2     3 

2     5 

2     7 

2   10 

2   12 

2   15 

29 

30 

1   59 

1   59 

2     0 

2     1 

2     2 

2     4 

2     6 

2     9 

2   11 

2  13 

— ^ 

30 
31 

31 

1   59 

1   59 

1   59 

2     0 

2     1 

2     3 

2     5 

2     7 

2     9 

2   11 

32 

1   59 

1   59 

1   59 

2     0 

2     1 

2     2 

2     4 

2     6 

2     7 

2     9 

32 

33 

1   59 

1   59 

1   59 

1   59 

2     0 

2     1 

2     3 

2     5 

2     6 

33 

34 

1   59 

1   58 

1   59 

1   59 

2     0 

2     1 

2     2 

2     4 

2     5 

34 

35 

1   59 

1   58 

1   59 

1   59 

2     0 

2     0 

2     1 

2     3 

2     4 

- 

35 
36 

36 

2     0 

1   59 

1   59 

1   59 

2     0 

2     0 

2     1 

2     2 

2     3 

37 

2     0 

1   59 

1   59 

1   58 

1   59 

1   59 

2     0 

2     1 

37 

38 

2     0 

1   59 

1   59 

1   58 

1   59 

1   59 

2     0 

2     1 

38 

39 

2     1 

2     0 

1   59 

1   58 

1   58 

1   59 

1   59 

2     0 

39 

40 

2     1 

2     0 

1   59 

1   58 

1  58 

1   58 

1   59 

2     0 



40 
41 

41 

2     1 

2     0 

1   59 

1   59 

1   58 

1   58 

1   58 

42 

2     2 

2     0 

1   59 

1   59 

1   58 

1   58 

1   58 

42 

43 

2     2 

2     1 

2     0 

1   59 

1   58 

1   58 

1   58 

43 

44 

2     3 

2     1 

2     0 

1   59 

1   58 

1   58 

1   57 

44 

45 

2     3 

2     2 

2     1 

2     0 

1   59 

1   58 

45 

46 

2     4 

2     2 

2     1 

2     0 

1   59 

1   58 

46 

47 
48 
50 

2     4 
2     5 

2     fi 
2     7 

2     2 
2     3 
2     4 
2     5 

2     1 
2     2 
2     2 
2     3 

2     0 
2     1 
2     1 
2     1 

1   59 

1  59 

2  0 

1   58 
1   59 

1          '          1 

47 
48 
50 

TABLS  P.  EFFECT  OF  BITN's  PAR 

52 

To  be  subtracted  from  the 

52 

54 

56 
5P 
60 

54 
56 

2     8 
2     9 

2     5 

2     5 

2     3 

e. 

)'e 

App 
Aft. 

Sun's  Apparent  Altituc 

6S    2  lO' 

5 

IU2 

0  30 

tt 

40  5 

tt 

0  60  70 

80 

90 

tl 

60 

„ 

62 

5 
10 
15 
20 
25 
30 
35 
40 
45 
50 
55 
60 
65 
70 
75 
80 
90 

I 
2 

o 
3 
4 
4 
5 
6 
6 
7 
7 
8 
8 
9 
9 
9 

1  1 

2  S 

2  '. 

3  C 

4  4 

4  £ 

5  fi 

6  f. 

6  t 

7  ' 

7  ' 

8  i 
8  i 
8  i 
9 

9 

1 
2 

.    2 
3 
4 
5 
5 
6 

)   7 

r  7 
r  8 

i   8 

\ 

1 

2 
3 
3 
4 
S 
5 
fi 
7 
7 

1  1      1 

2  2  2 

3  3   3 
13   3 
1   4 

5   5 

5 

6 

't 

0 

i  62 

64 
66 
68 
70 
72 

64 
66 

68 
70 
72 

74 

76 
78 
80 
82 

74 
76 
78 
80 
82 

32« 

34° 

36° 

38° 

40° 

42° 

46° 

50° 

54° 

58° 

62° 

13 


192                 TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE 

96° 

D's 

App. 
Alt. 

APPARENT  ALTITUDE  OF  THE 

3UN,  OR  STAR. 

])'s 

_  App., 

6" 

70 

8° 

9° 

10°  11°  12° 

14° 

16° 

18°  1 

20° 

22° 

24 

1° 

26°  1 

28°  1 

30°  1 

Alt. 

o 

t     II 

1-  II 

/  // 

1    II 

1    II    f    1,     t    II 

/  II 

1    II 

1 

// 

1    II 

1    II 

/ 

II 

> 

II 

1 

^r 

/ 

// 

0 

6 

2  6 

2  8 

2  10 

2  13 

2  17 

2  22  2  28 

2  41 

2  55 

3 

10 

3  26 

3  41 

3 

56 

4 

11 

4 

26 

4 

41 

6 

7 

2  9 

2  6 

2  8 

2  10 

2  12 

2  16  2  20 

2  29 

2  40 

2 

52 

3  5 

3  18 

3 

31 

3 

43 

3 

56 

4 

8 

7 

8 

2  12 

2  8 

2  6 

2  7 

2  9 

2  12 

2  15 

2  22 

2  31 

2 

40 

2  51 

2  2 

3 

13 

3 

24 

3 

35 

3 

45 

8 

9 

2  16 

2  11 

2  8 

2  6 

2  7 

2  9 

2  12 

2  17 

2  24 

2 

31 

2  40 

2  49 

2 

59 

3 

8 

3 

18 

3 

27 

9 

10 
11 

2  20 

2  14 

2  10 

2  8 

2  6 

2  7 

2  9 

2  13 

2  18 

2 

24 

2  32 

2  40 

2 

48 

2 

56 

3 

4 

3 

12 

10 

2  26 

2  18 

2  13 

2  10 

2  7 

2  6 

2  7 

2  10 

2  14 

2 

19 

2  25 

2  32 

2 

39 

2 

46 

2 

53 

3 

1 

11 

12 

2  32 

2  23 

2  17 

2  13 

2  9 

2  7 

2  6 

2  8 

2  11 

2 

15 

2  20 

2  26 

2 

32 

2 

38 

2 

45 

2 

52 

12 

13 

2  39 

2  28 

2  21 

2  16 

2  12 

2  9 

2  7 

2  7 

2  9 

2 

12 

2  16 

2  21 

2 

26 

2 

32 

2 

38 

2 

44 

13 

14 

2.46 

2  33 

2  25 

2  19 

2  14 

2  11 

2  9 

2  6 

2  8 

2 

10 

2  13 

2  18 

2 

22 

2 

27 

2 

32 

2 

37 

14 

15 

2  53 

2  39 

2  29 

2  22 

2  17 

2  14 

2  11 

2  7 

2  7 

2 

9 

2  11 

2  15 

2 

19 

2 

23 

2 

28 

2 
2 

32 

28 

15 
16 

16 

3  1 

2  45 

2  34 

2  26 

2  20 

2  16 

2  13 

2  8 

2  5 

2 

8 

2  10 

2  13 

2 

16 

2 

20 

2 

24 

17 

3  8 

2  51 

2  39 

2  30 

2  23 

2  19 

2  15 

2  9 

2  7 

2 

7 

2  9 

2  11 

2 

14 

2 

17 

2 

21 

2 

24 

17 

18 

3  15 

2  57 

2  44 

2  34 

2  26 

2  21 

2  17 

2  11 

2  8 

2 

6 

2  8 

2  10 

2 

12 

2 

15 

2 

18 

2 

21 

18 

19 

3  23 

3  3 

2  49 

2  38 

2  30 

2  24 

2  19 

2  13 

2  9 

2 

7 

2  7 

2  8 

2 

10 

2 

13 

2 

15 

2 

18 

19 

20 

3  30 

3  9 

2  54 

2  43 

2  34 

2  27 

2  22 

2  15 

2  11 

2 

8 

2  6 

2  7 

2 

9 

2 

11 

2 

13 

2 

15 

20 

21 

3  38 

3  16 

3  0 

2  48 

2  37 

2  30 

2  25 

2  17 

2  12 

2 

9 

2  7 

2  7 

2 

8 

2 

9 

2 

11 

2 

13 

21 

22 

3  46 

3  22 

3  5 

2  52 

2  41 

2  33 

2  28 

2  19 

2  14 

2 

10 

2  8 

2  6 

2 

7 

2 

8 

2 

10 

2 

12 

22 

23 

3  54 

3  28 

3  11 

2  57 

2  45 

2  37 

2  31 

2  21 

2  15 

2 

11 

2  8 

2  6 

2 

6 

2 

7 

2 

q 

2 

11 

23 

24 

4  1 

3  34 

3  16 

3   I 

2  49 

2  41 

2  35 

2  23 

2  17 

2 

12 

2  9 

2  7 

2 

6 

2 

7 

2 

8 

2 

10 

24 

25 
26 

4  9 

3  41 

3  22 

3  6 

2  53 

2  45 

2  38 

2  26 

2  19 

2 

14 
16 

2  11 

2  8 

2 

6 

2 

7 

2 

8 

2 

9 

25 
26 

4  16 

3  47 

3  27 

3  11 

2  57 

2  48 

2  41 

2  29 

2  21 

2 

2  12 

2  9 

2 

7 

2 

6 

2 

7 

2 

8 

27 

4  24 

3  53 

3  33 

3  15 

3   1 

2  52 

2  44 

2  31 

2  23 

2 

17 

2  13 

2  10 

2 

8 

2 

6 

2 

6 

2 

7 

27 

28 

4  31 

4  0 

3  38 

3  20 

3  fi 

2  55 

2  47 

2  34 

2  24 

2 

18 

2  14 

2  11 

2 

9 

2 

7 

2 

6 

2 

7 

28 

29 

4  39 

4  6 

3  44 

3  25 

3  10 

2  59 

2  50 

2  36 

2  26 

2 

20 

2  15 

2  12 

2 

10 

2 

8 

2 

7 

2 

6 

29 

30 

4  46 

4  12 

3  49 

3  29 

3  14 

3  3 

2  53 

2  38 

2  28 

2 

21 

2  16 

2  13 

2 

10 

2 

8 

2 

7 

2 

6 

30 

31 

4  53 

4  18 

3  55 

2  34 

3  18 

3  7 

2  57 

2  41 

2  30 

2 

23 

2  18 

2  14 

2 

11 

2 

9 

2 

8 

2 

7 

31 

32 

5  0 

4  24 

4  0 

3  39 

3  23 

3  11 

3  1 

2  44 

2  32 

2 

25 

2  19 

2  15 

2 

12 

2 

9 

2 

8 

2 

7 

32 

33 

5  7 

4  30 

4  5 

3  44 

3  27 

3  15 

3  4 

2  46 

2  34 

2 

26 

2  20 

2  16 

2 

13 

2 

10 

2 

8 

2 

7 

33 

34 

5  14 

4  36 

4  11 

3  49 

3  32 

3  19 

3  7 

2  48 

2  36 

2 

28 

2  21 

2  17 

2 

14 

2 

11 

2 

9 

2 

8 

34 

35 
36 

5  21 

4  42 

4  16 

3  54 

3  36 

3  23 

3  11 

2  51 

2  38 

2 

30 

2  23 

2  18 

2 

15 

2 

12 

2 

10 

2 

8 

35 
36 

5  28 

4  48 

4  21 

3  59 

3  40 

3  26 

3  14 

2  54 

2  40 

2 

32 

2  25 

2  20 

2 

16 

2 

13 

2 

11 

2 

9 

37 

5  35 

4  54 

4  26 

4  3 

3  44 

3  29 

3  17 

2  57 

2  43 

2 

33 

2  26 

2  21 

2 

17 

2 

14 

2 

11 

2 

9 

37 

38 

5  42 

5  0 

4  31 

4  8 

3  48 

3  33 

3  20 

2  59 

2  45 

2 

35 

2  27 

2  22 

2 

18 

2 

15 

2 

12 

2 

10 

38 

39 

5  49 

5  6 

4  36 

4  12 

3  52 

3  36 

3  23 

3  2 

2  47 

2 

37 

2  29 

2  23 

2 

19 

2 

16 

2 

13 

2 

11 

39 

40 
41 

5  55 

5  12 

4  41 

4  16 

3  56 

3  40 

3  26 

3  5 

2  50 

2 

39 

2  30 

2  24 

2 

20 

2 

16 

2 

13 

2 

11 

40 

6  2 

5  18 

4  46 

4  20 

4  0 

3  44 

3  30 

3  7 

2  52 

2 

41 

2  32 

2  25 

2 

21 

2 

17 

2 

14 

2 

12 

41 

42 

6  8 

5  23 

4  51 

4  24 

4  4 

3  47 

3  33 

3  10 

2  54 

2 

43 

2  34 

2  27 

2 

22 

2 

18 

2 

15 

2 

13 

42 

43 

6  14 

5  29 

4  56 

4  29 

4  8 

3  51 

3  36 

3  13 

2  55 

2 

45 

2  35 

2  28 

2 

23 

2 

19 

2 

16 

2 

13 

43 

44 

6  20 

5  34 

5  1 

4  33 

4  11 

3  54 

3  39 

3  16 

2  59 

2 

47 

2  37 

2  29 

2 

24 

2 

20 

2 

17 

2 

14 

44 

45 
46 

6  26 

5  39 

5  6 

4  37 

4  14 

3  57 

3  42 

3  19 

3   1 

2 

48 

2  38 

2  30 

2 

25 

2 

21 

2 

17 

2 

14 

45 

6  32 

5  44 

5  10 

4  41 

4  18  4  0 

3  45 

3  21 

3   3 

2 

50 

2  39 

2  31 

2 

26 

2 

22 

2 

18 

2 

15 

46 

47 

6  38 

5  49 

5  15 

4  45 

4  22 

4  3 

3  48 

3  24 

3  5 

2 

52 

2  41 

2  33 

2 

27 

2 

23 

2 

19 

2 

16 

47 

48 

6  44 

5  54 

5  19 

4  49 

4  25 

4  7 

3  51 

3  26 

3  7 

2 

53 

2  42 

2  34 

2 

28 

2 

24 

2 

20 

2 

16 

48 

49 

6  50 

5  59 

5  23 

4  53 

4  29 

4  10 

3  54 

3  28 

3  9 

2 

55 

2  44 

2  36 

2 

29 

2 

25 

2 

21 

2 

17 

49 

50 
51 

6  55 

7  C 

6  4 

5  27 

4  57 

4  32 

4  13 

3  57 

3  30 

3  11 

2 

56 

2  45 

2  37 

2 

31 

2 

26 

2 

21 

2 

17 

50 

6  9 

5  31 

5  1 

4  36 

4  16 

4  0 

3  32 

3  13 

2 

58 

2  47 

2  38 

2 

32 

2 

27 

2 

22 

2 

18 

51 

52 

7  £ 

6  14 

5  35 

5  4 

4  39 

4  19 

4  3 

3  34 

3  15 

3 

0 

2  48 

2  39 

2 

33 

2 

28 

2 

23 

2 

18 

52 

54 

7  \t 

.  6  23 

5  43 

5  11 

4  45 

4  25 

4  8 

3  38 

3  19 

3 

2 

2  51 

2  42 

2 

35 

2 

29 

2 

24 

2 

19 

54 

56 

7  11 

.  6  31 

5  51 

5  18 

4  51 

4  30 

4  13 

3  42 

3  22 

3 

6 

2  54 

2  45 

2 

37 

2 

30 

2 

25 

2 

19 

56 

58 
60 

7  3f 

i  6  39 

5  58 

5  24 

4  56 

4  35 

4  17 

3  46 

3  26 

3 

9 

2  57 

2  47 

2 

39 

2 

31 

2 

25 

58 

7  M 

)  6  46 

6  4 

5  3C 

5   1 

4  39 

4  21 

3  50 

3  29 

3 

12 

2  59 

2  49 

2 

41 

2 

32 

60 

62 

7  5t\ 

I  6  53 

6  IC 

5  35 

5  6 

4  44 

4  25 

3  54 

3  32 

3 

15 

3   1 

2  50 

2 

42 

62 

64 

8  S 

!  7  0 

6  16 

5  40 

5  11 

4  48 

4  29 

3  58 

3  35 

3 

17 

3  3 

2  51 

64 

66 

8  1( 

)  7  7 

6  21 

5  45 

5  16 

4  52 

4  33 

4  1 

3  38 

3 

19 

3  4 

66 

68 
70 

8  Vi 

'  7  13 

6  26 

5  5C 

5  21 

4  56 

4  36 

4  3 

3  40 

3 

21 

68 

8  2-: 

1  7  18 

6  31 

5  54 

5  25 

5  0 

4  39 

4  5 

3  42 

70 

72 

8  2t 

)  7  23 

6  36 

!  5  5S 

!  5  28 

5  3 

4  41 

4  7 

72 

74 

8  3: 

5  7  27 

6  4C 

)  6  1 

5   31 

5  6 

4  43 

74 

7* 

8  3' 

r  7  21 

6  4c 

!  6  4 

5  34 

76 

7. 

8  41 

)  7  34 

6  46 

' 

78 

1  «' 

-0 

8° 

9" 

10° 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

124° 

26° 

28° 

30° 

_^ 

TABLE  XXXUI. 

193   1 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  96".                                     1 

S's 
App. 

Alt. 

APPARENT    ALTITUDE    OF    THE    SUN, 

OR    STAR. 

>'8 

App. 

Alt. 

32» 

34» 

36° 

38° 

40° 

42° 

44° 

46° 

50° 

54° 

58°  1 

62° 

66° 

70° 

74° 

78° 

o 

r     tt 

/     n 

^    ti 

/    // 

^    // 

^    It 

/    // 

/    II 

r    /> 

/    // 

/ 

II 

/    II 

/     II 

1    II 

1    II 

/   // 

o 

6 

4  56 

5   10 

5  24 

5  38 

5   51 

6     4 

6   17 

6  29 

6  52 

7   14 

7 

34 

7  52 

8     9 

8  23 

8  33 

8  40 

6 

7 

4  20 

4  32 

4  44 

4  56 

5     8 

5  20 

5  31 

5  42 

6     2 

6  20 

6 

37 

6  52 

7     6 

7   18 

7   28 

7  35 

7 

8 

3  56 

4     7 

4   18 

4   29 

4   39 

4  49 

4  59 

5     8 

5  26 

5  42 

5 

56 

6     9 

6  21 

6  31 

6  40 

6  47 

8 

9 

3  37 

3  46 

3  55 

4     4 

4   13 

4  23 

4  32 

4  40 

4  56 

5  10 

5 

23 

5  34 

5  44 

5  53 

6     1 

9 

10 
11 

3   22 

3  30 

3  37 

3   45 

3   53 
3  38 

4     2 

4   10 

4   17 

4  31 

4  43 

4 

55 

5     6 

5  16 

5  24 

5  31 

10 
11 

3     9 

3   17 

3   24 

3  31 

3  45 

3  52 

3  59 

4  11 

4  22 

4 

33 

4  43 

4  52 

5     0 

5     7 

12 

2  59 

3     6 

3   12 

3    19 

3   25 

3  32 

3   38 

3  45 

3  55 

4     5 

4 

15 

4  24 

4  32 

4  39 

4  46 

12 

13 

2  50 

2  56 

3     2 

3     8 

3   14 

3  20 

3  26 

3  32 

3  42 

3  51 

4 

0 

4     8 

4   15 

4  21 

13 

14 

2  42 

2  48 

2  53 

2   58 

3     4 

3     9 

3   15 

3  20 

3  30 

3  39 

3 

48 

3  55 

4     1 

4     6 

14 

15 
16 

2  36 

2  41 

2  46 

2  50 

2   55 

3     0 

3     5 

3   10 

3   19 

3  28 

3 

36 

3  43 

3  49 

3  54 

15 

2  32 

2  36 

2  40 

2  44 

2   48 

2  53 

2  57 

3     2 

3   10 

3  18 

3 

25 

3  32 

3  38 

3  44 

16 

17 

2  28 

2   31 

2   35 

2   39 

2  43 

2  47 

2  51 

2  55 

3     3 

3   10 

3 

16 

3  22 

3  28 

17 

18 

2  24 

2  27 

2   31 

2  35 

2  38 

2  42 

2  45 

2  49 

2  56 

3     2 

3 

8 

3   14 

3   19 

18 

19 

2  21 

2  24 

2  27 

2  31 

2  34 

2  37 

2  40 

2  44 

2  50 

2  56 

3 

2 

3     7 

3   11 

19 

: 

20 

2  18 

2  21 

2  24 

2  27 

2  30 
2   26 

2  33 

2  36 

2  39 

2  45 

2  51 

2 

56 

3     1 

3     4 

20 

21 

2   16 

2   19 

2  21 

2  24 

2  29 

2  32 

2  35 

2  41 

2  46 

2 

51 

2  55 

21 

22 

2   14 

2   17 

2   19 

2  21 

2  23 

2  26 

2  28 

2  31 

2  37 

2  42 

2 

46 

2  50 

22 

23 

2   13 

2   15 

2   17 

2   19 

2  21 

2  23 

2  25 

2  28 

2  33 

2  38 

2 

42 

2  45 

23 

24 

2  11 

2   13 

2   15 

2   17 

2   19 

2  21 

2  23 

2  25 

2  30 

2  35 

2 

38 

2  41 

24 

25 

2   10 

2   11 

2   13 

2   15 

2   17 

2   19 

2  21 

2  23 

2  27 

2  31 

2 

35 

25 

26 

2     9 

2   10 

2   12 

2   13 

2  15 

2   17 

2   19 

2  21 

2  25 

2  28 

2 

31 

26 

27 

2     8 

2     9 

2   11 

2   12 

2   14 

2   16 

2   18 

2  20 

2  23 

2  25 

2 

27 

27 

28 

2     8 

2     9 

2   10 

2   11 

2   13 

2   15 

2  17 

2  18 

2  21 

2  23 

2 

24 

28 

29 

2     7 

2     8 

2     9 

2   10 

2   12 

2   13 

2   15 

2   17 

2   19 

2  21 

29 

30 

2     7 

2     8 

2     9 

2   10 

2   11 

2   12 

2   14 

2   15 

2   17 

2  19 

30 
31 

31 

2     6 

2     7 

2     8 

2     9 

2   10 

2   11 

2  12 

2   14 

2  16 

2   17 

32 

2     6 

2     7 

2     7 

2     8 

2     9 

2   10 

2  11 

2   12 

2  14 

2   16 

32 

33 

2     6 

2     6 

2     7 

2     7 

2     8 

2     9 

2   10 

2   11 

2  13 

33 

34 

2     7 

2     6 

2     7 

2     7 

2     8 

2     9 

2   10 

2   11 

2   12 

34 

35 

2     7 

2     6 

2     6 

2     7 

2     7 

2     8 

2     9 

2  10 

2  11 

35 

36 

2     8 

2     7 

2     6 

2     6 

2     7 

2     8 

2     9 

2     9 

2   10 

36 

37 

2     8 

2     7 

2     6 

2     6 

2     7 

2     7 

2     8 

2     8 

37 

38 

2     9 

2     8 

2     7 

2     6 

2     6 

2     7 

2     8 

2     8 

38 

39 

2     9 

2     8 

2     7 

2     6 

2     6 

2     7 

2     7 

2     8 

39 

40 

2   10 

2     8 

2     7 

2     6 

2     6 

2     6 

2     7 

2     7 

40 
41 

41 

2   10 

2     9 

2     8 

2     7 

2     7 

2     6 

2     6 

42 

2   11 

2     9 

2     8 

2     7 

2     7 

2     6 

2     6 

42 

43 

2   11 

2   10 

2     8 

2     7 

2     7 

2     (i 

43 

44 

2   12 

2   10 

2     8 

2     7 

2     7 

2     6 

44 

45 

2   12 

2  10 

2     9 

2     8 

2     7 

45 

46 

2   13 

2   11 

2     9 

2     8 

2     7 

46 

47 
48 
49 

2   13 
2   13 
2  14 

2  11 
2  11 
2  12 

2     9 
2     9 
2   10 
2  10 

2     8 
2     8 

' 

47 
48 
49 

TABLK  P.  EFFECT  OF  BUN'b  r  AB  . 

50 

2   14 

2   12 

To  be  subtracted  from  the 
Third  Correction. 

50 

51 

52 
54 

51 
52 
54 

2   14 
2   15 
2  15 

2   12 
2   12 

> 

)'8 

App 
Alt. 

Sun's  Apparent  Altitude. 1 

5ll0  2( 

)30 

40  5 

0  60 

70  J 

?0  90 

56 

7, 

//       f 

*  ■"■ 

tt      f 

'      »/ 

// 

//      // 

56 

58 

5 

10 
15 
20 
25 
30 
35 
40 
45 
50 
55 
60 
65 
70 
75 
80 
90 

1 
2 
o 

3 
4 

5 
5 
6 
6 
7 
7 
8 
8 
9 
9 
9 

1  t 

2  2 

2  3 

3  3 

4  4 

5  5 

5  5 

6  6 

7  7 

7  ^ 

8  8 
8   8 
8  8 
9 

9 

1 

2 
3 
4 
4 
5 
6 
6 
7 
7 
8 

1 

2  i 

3  . 

4  ' 
4 

5  . 

6  ( 
6 

7 

1  1 

2  2 
}  3 
1   4 

5  5 

5 
S 

2 

3 
3 

8 

68 

60 
62 
64 
66 
68 

70 
72 
74 
76 
78 

60 
62 
64 
66 
68 

70 
72 
74 
76 
7g 

44° 

46° 

50° 

54° 

58° 

' 

32** 

34° 

36° 

38" 

40° 

42° 

194                 TABLE  XXXIII. 

THIRD  OORREOTION,  TO  APPARENT  DISTANCE 

100°. 

J's 

App. 
Alt. 

APPARENT  ALTITUDE  OF 

THE 

SUN, 

OR  STAR. 

App- 

6° 

70 

80 

9° 

\0° 

11* 

12<» 

140 

16° 

18° 

20°  1 

22° 

24°  1 

26° 

28°  1 

30°  1 

Alt. 

o 

t     II 

/  // 

/  n 

1    II 

1    II 

1    II 

/  n 

1    II 

1 

II 

/ 

II 

/ 

II 

/  // 

f 

// 

/  n 

1 

// 

/ 

// 

0 

fi 

2  13 

2  15 

2  18 

2  21 

2  25 

2  31 

2  37 

2  49 

3 

3 

3 

18 

3 

33 

3  48 

4 

4 

4  19 

4 

34 

4 

49 

6 

7 

2  16 

2  13 

2  15 

2  17 

2  20 

2  24 

2  29 

2  38 

2 

49 

3 

1 

3 

13 

3  25 

3 

38 

3  50 

4 

3 

4 

16 

7 

8 

2  19 

2  15 

2  13 

2  14 

2  16 

2  19 

2  23 

2  31 

2 

39 

2 

49 

2 

59 

3  10 

3 

21 

3  32 

3 

43 

3 

54 

8 

9 

2  23 

2  18 

2  15 

2  13 

2  14 

2  16 

2  19 

2  25 

2 

32 

2 

40 

2 

48 

2  58 

3 

7 

3  16 

3 

26 

3 

35 

9 

10 

2  28 

2  22 

2  18 

2  15 

2  13 

2  14 

2  16 

2  21 

2 

26 

2 

33 

2 

40 

2  48 

2 

56 

3   4 

3 

13 

3 

21 

10 

11 

2  33 

2  26 

2  21 

2  17 

2  15 

2  13 

2  14 

2  18 

2 

22 

2 

27 

2 

33 

2  40 

2 

47 

2  54 

3 

2 

3 

10 

11 

12 

2  40 

2  30 

2  24 

2  20 

2  17 

2  14 

2  13 

2  16 

2 

19 

2 

23 

2 

28 

2  34 

2 

40 

2  46 

2 

53 

3 

0 

12 

13 

2  47 

2  35 

2  28 

2  23 

2  19 

2  16 

2  14 

2  14 

2 

17 

2 

20 

2 

24 

2  29 

2 

34 

2  40 

2 

45 

2 

51 

13 

14 

2  54 

2  40 

2  32 

2  26 

2  21 

2  18 

2  16 

2  13 

2 

15 

2 

18 

2 

21 

2  25 

2 

30 

2  35 

2 

39 

2 

44 

14 

15 

3   1 

2  46 

2  36 

2  29 

2  24 

2  '/I 

2  18 

2  14 

2 

14 

2 

16 

2 

19 

2  22 

2 

26 

2  30 

2 

34 

2 

39 

15 

16 

3  8 

2  52 

2  41 

2  33 

2  27 

2  23 

2  20 

2  16 

2 

13 

2 

15 

2 

17 

2  20 

2 

23 

2  26 

2 

30 

2 

35 

16 

17 

3  15 

2  58 

2  46 

2  37 

2  30 

2  25 

2  22 

2  17 

2 

14 

2 

14 

2 

16 

2  18 

2 

21 

2  24 

2 

27 

2 

31 

17 

18 

3  23 

3  4 

2  51 

2  41 

2  33 

2  28 

2  24 

2  19 

2 

15 

2 

13 

2 

15 

2  17 

2 

19 

2  22 

2 

25 

2 

28 

18 

19 

3  30 

3  11 

2  56 

2  45 

2  37 

2  31 

2  26 

2  20 

2 

16 

2 

14 

2 

14 

2  16 

2 

17 

2  20 

2 

22 

2 

25 

19 

20 

3  38 

3  17 

3  2 

2  50 

2  41 

2  34 

2  29 

2  22 

2 

18 

2 

15 

2 

13 

2  15 

2 

16 

2  18 

2 

20 

2 

23 

20 

21 

3  45 

3  24 

3  8 

2  54 

2  45 

2  38 

2  32 

2  24 

2 

19 

2 

16 

2 

14 

1  14 

2 

15 

2  17 

2 

19 

2 

21 

21 

22 

3  53 

3  30 

3  13 

2  59 

2  49 

2  41 

2  35 

2  26 

2 

21 

2 

18 

2 

15 

1  13 

2 

14 

2  1© 

2 

18 

2 

20 

22 

23 

4  1 

3  36 

3  19 

3  4 

2  53 

2  45 

2  38 

2  28 

2 

23 

2 

19 

2 

16 

1  13 

2 

13 

2  15 

2 

17 

2 

19 

23 

24 

4  9 

3  42 

3  24 

3  9 

2  58 

2  49 

2  42 

2  31 

2 

24 

2 

20 

2 

17 

2  14 

2 

13 

2  14 

2 

16 

2 

18 

24 

25 
26 

4  16 

3  49 

3  30 

3  14 

3  2 

2  53 

2  45 

2  33 

2 

26 

2 

21 
23 

2 

18 

2  15 

2 

14 

2  14 

2 

15 

2 

17 

25 
26 

4  24 

3  55 

3  35 

3  19 

3  6 

2  56 

2  48 

2  36 

2 

28 

2 

2 

19 

2  16 

2 

14 

2  14 

2 

15 

2 

16 

27 

4  31 

4  2 

3  41 

3  24 

3  11 

3  0 

2  51 

2  38 

2 

30 

2 

24 

2 

20 

2  17 

2 

15 

2  14 

2 

14 

2 

15 

27 

28 

4  39 

4  8 

3  46 

3  28 

3  15 

3  4 

2  54 

2  40 

2 

32 

2 

25 

2 

21 

2  18 

2 

16 

2  15 

2 

14 

2 

15 

28 

29 

4  46 

4  14 

3  52 

3  33 

3  19 

3  7 

2  58 

2  43 

2 

34 

2 

26 

2 

22 

2  19 

2 

17 

2  15 

2 

14 

2 

14 

29 

30 

4  54 

4  20 

3  57 

3  38 

3  23 

3  11 

3   1 

2  45 

2 

36 

2 

28 

2 

24 

2  21 

2 

18 

2  16 

2 

15 

2 

14 

30 
31 

31 

5  1 

4  26 

4  3 

3  42 

3  27 

3  15 

3  5 

2  48 

2 

38 

2 

30 

2 

25 

2  22 

2 

19 

2  17 

2 

15 

2 

14 

32 

5  8 

4  33 

4  8 

3  47 

3  31 

3  18 

3  8 

2  51 

2 

40 

2 

32 

2 

27 

2  23 

2 

20 

2  17 

2 

16 

2 

15 

32 

33 

5  16 

4  39 

4  14 

3  52 

3  36 

3  22 

3  11 

2  54 

2 

42 

2 

33 

2 

28 

2  24 

2 

21 

2  18 

2 

16 

2 

15 

33 

34 

5  23 

4  45 

4  19 

3  57 

3  40 

3  26 

3  15 

2  56 

2 

44 

2 

35 

2 

29 

2  25 

2 

22 

2  19 

2 

17 

2 

16 

34 

35 

5  30 

4  51 

4  24 
4  29 

4  2 
4  7 

3  44 

3  30 

3  18 

2  59 

2 

46 

2 

37 

2 

31 

2  26 

2 

23 

2  20 

2 

18 

2 

16 

35 
36 

36 

5  37 

4  57 

3  48 

3  34 

3  22 

3  2 

2 

49 

2 

39 

2 

32 

2  28 

2 

24 

2  20 

2 

18 

2 

17 

37 

5  44 

5  3 

4  35 

4  12 

3  52 

3  38 

3  25 

3  5 

2 

51 

2 

41 

2 

34 

2  29 

2 

25 

2  21 

2 

19 

2 

18 

37 

38 

5  51 

5  9 

4  40 

4  16 

3  56 

3  41 

3  28 

3  8 

2 

54 

2 

43 

2 

36 

2  30 

2 

26 

2  22 

2 

20 

2 

18 

38 

39 

5  58 

5  15 

4  45 

4  21 

4  0 

3  45 

3  31 

3  11 

2 

56 

2 

45 

2 

37 

2  31 

2 

27 

2  23 

2 

21 

2 

19 

39 

40 

6  4 

5  21  4  50 

4  25 

4  4 

3  48 

3  34 

3  14 

2 

58 

2 

47 

2 

38 

2  32 

2 

28 

2  24 

2 

22 

2 

20 

40 

41 

6  11 

5  27 

4  55 

4  29 

4  8 

3  52 

3  38 

3  17 

3 

1 

2 

49 

2 

40 

2  34 

2 

29 

2  25 

2 

22 

2 

20 

41 

42 

6  18 

5  33 

5  0 

4  33 

4  12 

3  55 

3  41 

3  19 

3 

3 

2 

51 

2 

41 

2  35 

2 

30 

2  26 

2 

23 

2 

21 

42 

43 

6  24 

5  38 

5  5 

4  38 

4  16 

3  59 

3  44 

3  22 

3 

6 

2 

53 

2 

43 

2  36 

2 

31 

2  27 

2 

24 

2 

22 

43 

44 

6  30 

5  44 

5  9 

4  42 

4  20 

4  2 

3  47 

3  24 

3 

8 

2 

55 

2 

45 

2  38 

2 

32 

2  28 

2 

25 

2 

22 

44 

45 
46 

6  36 

5  49 

5  14 

4  46 

4  24 

4  6 

3  50 

3  27 

3 

10 

2 

57 

2 

47 

2  39 

2 

33 

2  29 

2 

26 

2 

23 

45 

6  42 

5  54 

5  18 

4  50 

4  27 

4  9 

3  53 

3  29 

3 

12 

2 

59 

2 

48 

2  41 

2 

35 

2  30 

2 

27 

2 

24 

46 

47 

6  48 

5  59 

5  23 

4  54 

4  31 

4  12 

3  56 

3  32 

3 

14 

3 

0 

2 

50 

2  42 

2 

36 

2  31 

2 

28 

2 

25 

47 

48 

6  54 

6  4 

5  27 

4  58 

4  34 

4  15 

3  59 

3  34 

3 

16 

3 

2 

2 

51 

2  43 

2 

37 

2  32 

2 

28 

2 

25 

48 

49 

7  -0 

6  9 

5  32 

5  2 

4  38 

4  18 

4  2 

3  37 

3 

18 

3 

4 

2 

53 

2  45 

2 

38 

2  33 

2 

29 

2 

26 

49 

50 
51 

7  5 

6  14 

5  36 

5  6 

4  41 

4  31 

4  5 

3  39 

3 

20 

3 

5 

2 

54 

2  46 

2 

39 

2  34 

2 

30 

2 

26 

50 

7  11 

6  19 

5  41 

5  10 

4  45 

4  24 

4  8 

3  42 

3 

22 

3 

7 

2 

55 

2  47 

2 

40 

2  35 

2 

31 

2 

27 

51 

52 

7  16 

6  24 

5  45 

5  14 

4  48 

4  27 

4  11 

3  44 

3 

24 

3 

9 

2 

57 

2  49 

2 

42 

2  36 

2 

31 

2 

27 

52 

53 

7  21 

6  29 

5  49 

5  17 

4  52 

4  30 

4  14 

3  46 

3 

26 

3 

11 

2 

59 

2  50 

2 

43 

2  37 

2 

32 

53 

54 

7  26 

6  34 

5  53 

5  21 

4  55 

4  33 

4  16 

3  48 

3 

28 

3 

12 

3 

0 

2  51 

2 

44 

2  37 

2 

32 

54 

55 
56 

7  31 

6  39 

5  57 

5  24 

4  58 

4  36 

4  19 

3  50 

3 

30 

3 

14 

3 

1 

2  52 

2 

45 

2  38 

55 

7  3€ 

6  43 

6  0 

5  27 

5  1 

4  39 

4  22 

3  52 

3 

32 

3 

16 

3 

2 

2  53 

2 

46 

2  39 

56 

58 

7  4f 

6  51 

6  7 

5  33 

5  7 

4  44 

4  26 

3  56 

3 

36 

3 

19 

3 

5 

2  55 

2 

47 

58 

60 

7  56 

;  6  58 

6  14 

5  39 

5  12 

4  49 

4  31 

4  0 

3 

39 

3 

22 

3 

8 

2  57 

60 

62 

8  t 

>  7  0 

6  10 

5  45 

5  17 

4  54 

4  36 

4   4 

3 

42 

3 

24 

3 

10 

62 

64 

8  12 

7  12 

6  26 

5  51 

5  22 

4  59 

4  40 

4  7 

3 

45 

3 

26 

64 

66 

8  21 

7  IS 

6  32 

5  57 

5  27 

5  3 

4  43 

4  10 

3 

47 

66 

68 

8  26 

\  7  2£ 

6  38 

6  2 

5  32 

5  7 

4  45 

4  13 

68 

70 

8  3f 

)  7  3C 

1  6  43 

6  7 

5  36 

5  11 

4  4S 

70 

72 

8  4( 

)  7  21 

►  6  47 

6  11 

5  40 

72 

74 

8  4^ 

I  7  4C 

)  6  51 

74 

6° 

70 

8° 

9° 

10° 

11° 

120 

14° 

16° 

18° 

20° 

22° 

24" 

26° 

28° 

30° 

TABLE  XXXIll. 

195  1 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  lOO^. 

D's 
A.pp. 

Alt. 

APPARENT  ALTITUDE  OF  THE  8CN, 

OR 

STAR. 

Api^ 
Alt. 

e 

32° 

34° 

36° 

38° 

40° 

42° 

44° 

46° 

48° 

60° 

54°, 

58° 

62° 

66° 

70°  [  74° 

o 

/  II 

f  // 

/  // 

1    It 

/  // 

/  // 

/  II 

/  // 

1    II 

/  f/ 

1 

II 

1    II 

1    II 

1    II 

1   II 

/  II 

6 

5  4 

5  19 

6  34 

5  48 

6  2 

6  15 

6  28 

6  41 

6  63 

7  4 

7 

26 

7  46 

8  5 

8  20 

8  33 

8  44 

ti 

7 

4  29 

4  41 

4  54 

5  6 

5  18 

5  30 

5  41 

5  52 

6  3 

6  13 

6 

32 

6  60 

7  6 

7  19 

7  30 

7  40 

7 

8 

4  5 

4  16 

4  27 

4  38 

4  48 

4  58 

5  8 

5  17 

5  26 

6  35 

5 

62 

6  7 

6  20 

6  32 

6  43 

7  52 

|i: 

9 

3  45 

3  55 

4  5 

4  15 

4  24 

4  32 

4  41 

4  49 

4  57 

«  4 

5 

19 

6  33 

5  45 

5  56 

6  7 

(1 

10 
11 

3  30 

3  39 

3  47 

3  55 

4  3 

4  11 

4  la 

4  26 

4  33 

4  40 

4 

54 

5  6 

5  16 

5  26 

6  36 

lO 

11 

3  18 

3  26 

3  33 

3  40 

3  47 

3  54 

4  1 

4  8 

4  15 

4  21 

4 

33 

4  44 

4  54 

5  3 

6  12 

12 

3  7 

3  14 

3  21 

3  27 

3  34 

3  40 

3  47 

3  53 

3  59 

4  4 

4 

15 

4  25 

4  34 

4  43 

4  52 

12 

13 

2  58 

3  4 

3  10 

3  16 

3  22 

3  28 

3  34 

3  40 

3  46 

3  51 

4 

0 

4  9 

4  17 

4  25 

13 

14 

2  50 

2  56 

2  1 

3  7 

3  12 

3  18 

3  23 

3  29 

3  34 

3  39 

3 

48 

3  56 

4  4 

4  10 

14 

15 
16 

2  44 

2  49 

2  54 

2  59 
2  52 

3  4 

3  9 

3  14 

3  19 

3  24 

3  28 

3 

37 

3  45 

3  52 

3  69 

15 

2  39 

2  44 

2  48 

2  57 

3  2 

3  7 

3  11 

3  16 

3  19 

3 

27 

3  35 

3  42 

3  49 

16 

17 

2  35 

2  39 

2  43 

2  47 

2  51 

2  56 

3  0 

3  4 

3  8 

3  12 

3 

19 

3  26 

3  33 

17 

18 

2  31 

2  35 

2  38 

2  42 

2  46 

2  50 

2  54 

2  68 

3  1 

3  6 

3 

12 

3  18 

3  24 

18 

19 

2  28 

2  31 

2  34 

2  38 

2  42 

2  45 

2  49 

2  52 

2  55 

2  59 

3 

5 

3  11 

3  16 

19 

20 

2  25 

2  28 

2  31 

2  35 

2  38 
2  35 

2  41 

2  44 

2  47 

2  50 

2  54 

3 

0 

3  5 

3  10 

20 

21 

2  23 

2  26 

2  29 

2  32 

2  38 

2  40 

2  43 

2  46 

2  49 

2 

66 

3  0 

21 

22 

2  22 

2  24 

2  27 

2  29 

2  32 

2  35 

2  37 

2  40 

2  43 

2  45 

2 

50 

2  55 

22 

23 

2  21 

2  23 

2  25 

2  27 

2  29 

2  32 

2  34 

2  37 

2  40 

2  42 

2 

46 

2  60j 

23 

24 

2  20 

2  22 

2  23 

2  25 

2  27 

2  29 

2  32 

2  35 

2  37 

2  39 

2 

43 

2  46 

24 

25 

2  19 

2  20 

2  21 

2  23 

2  25 
2  23 

2  27 

2  30 

2  32 

2  34 

2  36 

2 

40 

25 

26 

2  18 

2  19 

2  20 

2  21 

2  25 

2  28 

2  30 

2  32 

2  34 

2 

37 

26 

27 

2  17 

2  18 

2  19 

2  20 

2  22 

2  24 

2  26 

2  28 

2  30 

2  32 

2 

34 

27 

28 

2  16 

2  17 

2  18 

2  19 

2  21 

2  23 

2  24 

2  26 

2  28 

2  30 

2 

31 

28 

29 

2  15 

2  16 

2  17 

2  18 

2  20 

2  22 

2  23 

2  25 

2  26 

2  28 

29 

30 

2  15 

2  16 

2  17 

2  18 

2  19 

2  21 

2  22 

2  24 

2  25 

2  26 

30 

31 

2  14 

2  15 

2  16 

2  17 

2  18 

2  20 

2  21 

2  22 

2  23 

2  24 

31 

32 

2  14 

2  15 

2  16 

2  17 

2  18 

2  19 

2  20 

2  21 

2  22 

2  23 

32 

33 

2  15 

2  15 

2  15 

2  16 

2  17 

2  18 

2  19 

2  20 

2  21 

33 

34 

2  15 

2  15 

2  15 

2  16 

2  17 

2  18 

2  19 

2  19 

2  20 

34 

35 

2  15 

2  15 

2  15 

2  15 

2  16 

2  17 

2  18 

2  18 

35 
36 

36 

2  16 

2  15 

2  15 

2  15 

2  16 

2  17 

2  17 

2  18 

37 

2  17 

2  16 

2  15 

2  15 

2  16 

2  16 

2  17 

37 

38 

2  17 

2  16 

2  16 

2  15 

2  16 

2  16 

2  17 

38 

39 

2  18 

2  17 

2  16 

2  16 

2  16 

2  16 

39 

40 

2  18 

2  17 

2  16 

2  16 

2  16 

2  16 

I    1 

40 
41 

41 

2  19 

2  18 

2  17 

2  16 

2  16 

42 

2  19 

2  18 

2  17 

2  16 

2  16 

42 

43 

2  20 

2  18 

2  17 

2  16 

43 

44 

2  20 

2  19 

2  17 

2  16 

44 

45 

2  21 

2  19 

2  17 

45 

46 

2  21 

2  19 

2  17 

46 

47 

2  22 

2  19 

47 

48 
49 
60 

2  22 
2  23 
2  23 

2  19 

48 
49 
50 

TABLK  P.  XrFZCTOF  IVN'b  PAR. 

To  be  subtracted  from  the 
Third  Correction. 

51 
62 
53 
54 

51 
52 
53 
54 

APP 
A  t. 

Sun's  Appuant  Altitnde.  1 

5 

10  2( 

3  30 

40  5 

O60  7C 

76 

80 

55 

5 
10 
15 
20 
25 
30 
35 
10 
45 
50 
55 
60 
65 
70 
75 

1 
2 
2 

3 

4 
5 
5 

6 

7 
7 
8 
8 
8 
9 
9 

*f      * 

1  t 

2  2 

S  4 

4  4 

5  5 

5  6 

6  C 

7  : 

7  '' 

8  6 
8  i 
9 

9 

H 

2 

2 
3 
4 
.  5 
5 
6 
7 

r  7 
r  6 
) 

} 

2 
3 
3 
4 
5 
« 
6 
7 

2  S  2 

3  3  3 

4  4  4 
1  4 

5  5 
3 

9 

8 

65 

56 
58 
60 
62 
64 

66 
68 
60 
62 
64 

66 
68 
70 
72 
74 

66 
68 
70 

72 
74 

320 

34° 

36° 

38° 

40° 

42° 

44° 

46° 

48° 

60° 

54° 

196                 TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE 

104" 

J) '8 

APPARENT  ALTITUDE  OF 

THE 

SUN, 

OR  STAR. 

D'8 

App. 
Alt. 

App. 

Alt. 

6<» 

70 

8° 

9° 

10° 

11°  12° 

14°  1 

16° 

18° 

20° 

22°  1 

24°  1 

26° 

28° 

30° 

o 

r    II 

/  n 

1    n 

1    II 

/  II 

1    II    1    II 

1 

II 

1 

II 

1 

II 

1 

II 

/ 

II 

1 

// 

1 

II 

/  II 

1 

II 

0 

6 

2  20 

2  22 

2  25 

2  29 

2  33 

2  39 

2  45 

2 

58 

3 

13 

3 

28 

3 

43 

3 

59 

4 

15 

4 

30 

4  46 

5 

1 

6 

7 

2  23 

2  20 

2  22 

2  25 

2  28 

2  32 

2  36 

2 

46 

2 

57 

3 

10 

3 

23 

3 

36 

3 

48 

4 

1 

4  14 

4 

27 

7 

8 

2  26 

2  22 

2  20 

2  22 

2  24 

2  27 

2  30 

2 

38 

2 

47 

2 

57 

3 

8 

3 

20 

3 

31 

3 

42 

3  53 

4 

4 

8 

9 

2  30 

2  25 

2  22 

2  21 

2  22 

2  24 

2  26 

2 

32 

2 

39 

2 

48 

2 

57 

3 

7 

3 

17 

3 

26 

3  36 

3 

46 

9 

10 

2  36 

2  29 

2  25 

2  22 

2  21 

2  22 

2  24 

2 

28 

2 

34 

2 

41 

2 

48 

2 

56 

3 

5 

3 

14 

3  23 

3 

31 

10 

11 

2  42 

2  34 

2  28 

2  24 

2  22 

2  21 

2  22 

2 

25 

2 

30 

2 

35 

2 

41 

2 

48 

2 

55 

3 

4 

3  11 

3 

19 

11 

12 

2  48 

2  39 

2  32 

2  27 

2  24 

2  22 

2  21 

2 

23 

2 

27 

2 

31 

2 

36 

2 

42 

2 

48 

2 

56 

3  2 

3 

9 

12 

13 

2  56 

2  44 

2  36 

2  30 

2  26 

2  24 

2  22 

2 

22 

2 

25 

2 

28 

2 

32 

2 

38 

2 

43 

2 

49 

2  55 

3 

1 

13 

14 

3  2 

2  49 

2  40 

2  33 

2  29 

2  26 

2  24 

2 

22 

2 

23 

2 

26 

2 

30 

2 

34 

2 

39 

2 

43 

2  48 

2 

54 

14 

15 

3  9 

2  54 

2  45 

2  37 

2  32 

2  28 

2  26 

2 

23 

2 

22 

2 

25 

2 

28 

2 

31 

2 

35 

2 

39 

2  43 

2 

48 

15 

16 

3  16 

3  0 

2  50 

2  41 

2  35 

2  31 

2  28 

2 

24 

2 

22 

2 

24 

2 

26 

2 

29 

2 

32 

2 

35 

2  39 

2 

44 

16 

17 

3  23 

3  6 

2  55 

2  45 

2  38 

2  33 

2  30 

2 

26 

2 

23 

2 

23 

2 

25 

2 

27 

2 

30 

2 

33 

2  36 

2 

40 

17 

18 

3  31 

3  13 

3  0 

2  49 

2  41 

2  36 

2  33 

2 

27 

2 

24 

2 

22 

2 

24 

2 

26 

2 

28 

2 

31 

2  34 

2 

37 

18 

19 

3  38 

3  19 

3  5 

2  53 

2  45 

2  39 

2  35 

2 

29 

2 

25 

2 

23 

2 

23 

2 

24 

2 

26 

2 

29 

2  31 

2 

34 

19 

20 

3  46 

3  25 

3  11 

2  58 

2  49 

2  43 

2  38 

2 

31 

2 

27 

2 

24 

2 

22 

2 

23 

2 

25 

2 

27 

2  29 

2 

32 

20 

21 

3  54 

3  32 

3  16 

3  3 

2  53 

2  46 

2  41 

2 

33 

2 

28 

2 

25 

2 

23 

1 

22 

2 

24 

2 

26 

2  28 

2 

30 

21 

22 

4  2 

3  38 

3  22 

3  8 

2  57 

2  50 

2  44 

2 

35 

2 

30 

2 

26 

2 

24 

1 

22 

2 

23 

2 

25 

2  27 

2 

29 

22 

23 

4  10 

3  45 

3  27 

3  13 

3  2 

2  54 

2  47 

2 

38 

2 

32 

2 

28 

2 

25 

1 

23 

2 

22 

2 

24 

2  26 

2 

28 

23 

24 

4  18 

3  51 

3  33 

3  18 

3  6 

2  57 

2  50 

2 

40 

2 

33 

2 

29 

2 

26 

2 

24 

2 

22 

2 

23 

2  25 

2 

27 

24 

25 
26 

4  26 

3  58 

3  39 

3  22 

3  10 

3   1 

2  54 

2 

42 

2 

35 

2 

30 
31 

2 

27 

2 

24 

2 

23 

2 

23 

2  24 

2 

26 

25 
26 

4  33 

4  4 

3  44 

3  27 

3  15 

3  5 

2  57 

2 

44 

2 

36 

2 

2 

28 

2 

25 

2 

24 

2 

23 

2  24 

2 

26 

27 

4  41 

4  11 

3  50 

3  32 

3  19 

3  9 

3  0 

2 

47 

2 

38 

2 

32 

2 

29 

2 

26 

2 

24 

2 

23 

2  24 

2 

25 

27 

28 

4  49 

4  18 

3  56 

3  37 

3  23 

3  12 

3  3 

2 

49 

2 

40 

2 

34 

2 

30 

2 

27 

2 

25 

2 

24 

2  24 

2 

25 

28 

29 

4  57 

4  24 

4   1 

3  42 

3  28 

3  16 

3  7 

2 

52 

2 

42 

2 

35 

2 

31 

2 

28 

2 

26 

2 

25 

2  24 

2 

25 

29 

30 

5  4 

4  30 

4  7 

3  47 

3  32 

3  20 

3  10 

2 

55 

2 

44 

2 

37 

2 

33 

2 

30 

2 

27 

2 

25 

2  24 

2 

24 

30 

31 

5  12 

4  37 

4  13 

3  52 

3  3b  3  24 

3  14 

2 

58 

2 

46 

2 

39 

2 

34 

2 

31 

2 

28 

2 

26 

2  25 

2 

24 

31 

32 

5  19 

4  44 

4  19 

3  57 

3  41 

3  28 

3  17 

3 

0 

2 

49 

2 

41 

2 

36 

2 

32 

2 

29 

2 

27 

2  26 

2 

25 

32 

33 

5  27 

4  51 

4  25 

4  2 

3  46 

3  32 

3  21 

3 

3 

2 

51 

2 

43 

2 

37 

2 

33 

2 

30 

2 

28 

2  26 

2 

25 

33 

34 

5  34 

4  58 

4  30 

4  7 

3  50 

3  36 

3  24 

3 

5 

2 

54 

2 

45 

2 

39 

2 

34 

2 

31 

2 

29 

2  27 

2 

26 

34 

35 

5  42 

5  4 

4  36 

4  12 

3  55 

3  40 

3  27 

3 

8 

2 

56 

2 

47 

2 

40 

2 

35 

2 

32 

2 

30 

2  28 

2 
2 

27 
27 

35 
36 

36 

5  49 

5  10 

4  41 

4  17 

3  59 

3  44 

3  31 

3 

11 

2 

58 

2 

49 

2 

42 

2 

37 

2 

33 

2 

30 

2  28 

37 

5  56 

5  16 

4  46 

4  21 

4  3 

3  47 

3  35 

3 

14 

3 

1 

2 

51 

2 

43 

2 

38 

2 

34 

2 

31 

2  29 

2 

27 

37 

38 

6  3 

5  22 

4  51 

4  26 

4  7 

3  51 

3  38 

3 

17 

3 

4 

2 

53 

2 

45 

2 

39 

2 

35 

2 

32 

2  30 

2 

28 

38 

39 

6  10 

5  28 

4  56 

4  31 

4  11 

3  55 

3  41 

3 

20 

3 

6 

2 

55 

2 

47 

2 

41 

2 

36 

2 

33 

2  31 

2 

29 

39 

40 

6  16 

5  33 

5  1 

4  36 

4  15 

3  59 

3  45 

3 

23 

3 

9 

2 

57 

2 

49 

2 

42 

2 

37 

2 

34 

2  32 

2 

30 

40 

41 

6  23 

5  39 

5  6 

4  40 

4  19 

4  3 

3  49 

3 

26 

3 

11 

2 

59 

2 

51 

2 

44 

2 

39 

2 

35 

2  32 

2 

30 

41 

42 

6  30 

5  44 

5  11 

4  44 

4  23 

4  6 

3  53 

3 

29 

3 

13 

3 

1 

2 

52 

2 

45 

2 

40 

2 

36 

2  33 

2 

31 

42 

43 

6  37 

5  50 

5  16 

4  49 

4  27 

4  10 

3  56 

3 

32 

3 

15 

3 

3 

2 

54 

2 

47 

2 

41 

2 

37 

2  34 

2 

31 

43 

44 

6  43 

5  55 

5  21 

4  53 

4  31 

4  13 

3  59 

3 

35 

3 

18 

3 

5 

2 

55 

2 

48 

2 

42 

2 

38 

2  35 

2 

32 

44 

45 
46 

6  50 

6  1 

5  26 

4  58 

4  35 

4  17 

,4  2 

3 

38 

3 

20 

3 

6 

2 

57 

2 

50 

2 

44 

2 

39 

2  35 

2 

32 

45 

6  56 

6  6 

5  31 

5  2 

4  39 

4  20 

4  5 

3 

40 

3 

22 

3 

8 

2 

58 

2 

51 

2 

45 

2 

40 

2  36 

2 

33 

46 

47 

7  2 

6  12 

5  36 

5  6 

4  43 

4  24 

4  8 

3 

43 

3 

24 

3 

10 

3 

0 

2 

52 

2 

46 

2 

41 

2  37 

2 

34 

47 

48 

7  8 

6  17 

5  40 

5  10 

4  46 

4  27 

4  11 

3 

45 

3 

26 

3 

12 

3 

1 

2 

53 

2 

48 

2 

42 

2  38 

2 

34 

48 

49 

7  14 

6  23 

5  45 

5  14 

4  50 

4  30 

4  14 

3 

47 

3 

28 

3 

14 

3 

3 

2 

55 

2 

49 

2 

43 

2  38 

49 

50 

7  20 

6  28 

5  49 

5  18 

4  53 

4  33 

4  17 

3 

50 

3 

30 

3 

16 

3 

4 

2 

56 

2 

50 

2 

44 

2  39 

50 

51 

7  26 

6  33 

5  53 

5  22 

4  57 

4  36 

4  20 

3 

52 

3 

32 

3 

18 

3 

6 

2 

58 

2 

51 

2 

45 

51 

52 

7  32 

6  38 

5  57 

5  26 

5  0 

4  39 

4  23 

3 

54 

3 

34 

3 

20 

3 

8 

2 

59 

2 

52 

2 

45 

52 

53 

7  37 

6  43 

6  2 

5  29 

5  4 

4  42 

4  26 

3 

56 

3 

36 

3 

22 

3 

9 

3 

0 

2 

52 

53 

54 

7  42 

6  48 

6  6 

5  33 

5  7 

4  45 

4  29 

3 

58 

3 

38 

3 

23 

3 

10 

3 

1 

2 

53 

54  t 

55 
56 

7  47 

6  53 

6  10 

5  36 

5  10 

4  48 

4  32 

4 

0 

3 

40 

3 

25 

3 

12 

3 

1 

55  1 

7  52 

6  57 

6  14 

5  40 

5  13 

4  51 

4  34 

4 

0 
0 

3 

42 

3 

26 

3 

13 

3 

2 

56 

57 

7  57 

7   1 

6  18 

5  44 

5  16 

4  54 

4  37 

4 

5 

3 

44 

3 

28 

3 

14 

57 

58 

8  2 

7  5 

6  22 

5  47 

5  19 

4  57 

4  39 

4 

7 

3 

46 

3 

29 

3 

15 

58 

59 

8  6 

7  9 

6  26 

5  50 

5  22 

5  0 

4  41 

4 

9 

3 

48 

3 

31 

59 

60 

8  10 

7  13 

6  30 

5  53 

5  25 

5  2 

4  43 

4 

11 

3 

50 

3 

3? 

60 

62 

8  19 

7  19 

6  36 

5  59 

5  30 

5  6 

4  47 

4 

15 

3 

52 

62 

64 

8  27 

7  26 

6  42 

6  4 

5  35 

5  10 

4  51 

4 

19 

64 

66 

8  35 

7  33 

6  47 

6  9 

5  40 

5  14 

4  54 

1 

66 

68 

8  43 

7  39 

6  52 

6  14 

5  45 

68 

70 

8  49 

7  45 

6  57 

, 

1 

70 

6° 

70 

8° 

9° 

10° 

11° 

12° 

14° 

16° 

18° 

20°  1  22°  1  24^ 1 

26° 

28^ 

30° 



TABLE  XXXIII. 

197  1 

THIRD  CORREOTION,  TO  APPARENT  DISTA^''CE  104". 

- 

1 

D'K 

APPARENT    ALTITUDE    OF    THE    SUN, 

OR    STAR. 

>'s 

App. 

All. 
o 

App 
Alt. 
0 

32° 

34<» 

36° 

38° 

40° 

42° 

440 

46° 

48° 

50° 

52°  1 

54° 

58° 

62° 

66° 

70° 

/     // 

/    11 

/    // 

r     11 

1    II 

1    II 

/    II 

1    II 

/    II 

/    II 

1 

II 

/    /' 

1    II 

1    II 

/    // 

/    II 

6 

5    16 

5  31 

5  45 

6     0 

6   14 

6  28 

6  41 

6  54 

7     6 

7   18 

7 

29 

7   40 

8     0 

8   19 

8  35 

8  4S 

6 

; 

4   42 

4   56 

5     8 

5  20 

5  31 

5  42 

5  53 

6     4 

6   15 

6   26 

6 

37 

6  47 

7     4 

7    19 

7  33 

7  4t 

i      7 

s 

4    Iti 

4  28 

4  39 

4  49 

4  59 

5     9 

5   19 

5  28 

5  38 

5  47 

5 

57 

6     6 

6  21 

6  34 

6  46 

6  57 

8 

9 

3  55 

4     5 

4   15 

4   25 

4   34 

4  43 

4  52 

5     0 

5     8 

5   16 

5 

24 

5  32 

5  46 

5  58 

6     9 

9 

10 
11 

3  40 

3   49 

3  58 

4     7 

4    15 

4   23 

4  31 

4   38 

4  45 

4  52 

4 

59 

5     6 

5   18 

5  30 

5  40 

10 
11 

3   27 

3  35 

3  43 

3  51 

3  58 

4     5 

4   12 

4   19 

4  26 

4  32 

4 

38 

4  44 

4  55 

5     6 

5   16 

12 

3    16 

3  23 

3   30 

3  37 

3  44 

3  51 

3  58 

4     4 

4   10 

4   17 

4 

23 

4  28 

4  38 

4  47 

4  56 

12 

13 

3     7 

3    13 

3  20 

3  26 

3  33 

3  39 

3  45 

3   51 

3  56 

4     2 

4 

7 

4   12 

4  22 

4  30 

13 

14 

2  59 

2     5 

3   11 

3   17 

3  23 

3  29 

3  34 

3   39 

3  44 

3  49 

3 

54 

3  59 

4     8 

4   15 

14 

15 

2  53 

2  58 

3     4 

3     9 

3    15 

3  20 

3  25 

3   29 

3  34 

3  38 

3 

43 

3   47 

3  56 

3     3 

15 
16 

16 

2   48 

2  53 

2  58 

3     3 

3     8 

3   12 

3   17 

3   21 

3  25 

3  29 

3 

33 

3  37 

3  45 

3  52 

17 

i  44 

2  49 

2  53 

2  58 

3     2 

3     6 

3   10 

3   14 

3   17 

3  21 

3 

25 

3  29 

3  3b 

17 

18 

i  41 

2  45 

2  49 

2  53 

2  57 

3     1 

3     4 

3     8 

3   11 

3   15 

3 

18 

3  22 

3  29 

18 

19 

Z  3% 

2  41 

2  45 

2  49 

2  53 

2  56 

2  59 

3     3 

3     6 

3     9 

3 

12 

3   16 

3  22 

19 

20 
21 

i  35 
2  33 

2  38 

2  42 

2  45 

2  49 

2  52 

2  55 

2  58 

3     1 

3     4 

3 

7 

3   10 

3  lb 

20 

2  36 

2  39 

2  42 

2  45 

2  48 

2  51 

2  54 

2  57 

3     0 

3 

3 

3     5 

21 

22 

2  31 

2  34 

2  36 

2  39 

2  42 

2  45 

2  47 

2  50 

2  53 

2  56 

2 

59 

2     1 

22 

23 

2  30 

2  32 

2  34 

2  37 

2  39 

2  42 

2  44 

2  47 

2  50 

2  53 

2 

55 

2  57 

23 

24 

2  29 

2  31 

2  33 

2  35 

2  37 

2  40 

2  42 

2  44 

2  47 

2  50 

2 

52 

2  54 

24 

26 

2  28 

2  29 

2  31 

2  33 

2  35 

2  38 

2  40 

2  42 

2  44 

2  47 

2 

49 

25 

26 

2  27 

2  28 

2   30 

2  32 

2  34 

2  36 

2  38 

2  40 

2  42 

2  44 

2 

46 

26 

27 

2  26 

2  27 

2  29 

2  31 

2  32 

2  34 

2  36 

2  38 

2  40 

2  41 

27 

28 

2  26 

2  27 

2  28 

2  30 

2  31 

2  33 

2  35 

2  36 

2  38 

2  39 

28 

29 

2  25 

2  26 

2  27 

2  29 

2  30 

2  32 

2  33 

2  34 

2  36 

29 

30 

2  25 

2  26 

2  27 

2  28 

2  29 

2  31 

2  32 

2  33 

2  34 

30 
31 

31 

2  24 

2  25 

2  20 

2  27 

2  28 

2  30 

2  31 

2  32 

32 

2  24 

2  25 

2  26 

2  27 

2  28 

2  29 

2  30 

2  31 

32 

33 

2  24 

2  24 

2  25 

2  26 

2  27 

2  28 

2  29 

33 

34 

2  25 

2  24 

2  25 

2  26 

2  27 

2  27 

2  28 

34 

35 

2  26 

2   25 

2  25 

2  26 

2  26 

2  27 

35 

36 

2   26 

2  25 

2  25 

2  26 

2  26 

2  27 

36 

37 

2  26 

2  25 

2  25 

2  26 

2  26 

37 

38 

2  27 

2  26 

2  26 

2  26 

2  26 

38 

39 

2  27 

2  26 

2  26 

2  26 

39 

40 

2  28 

2  27 

2  26 

2  26 

40 
41 

41 

2  28 

2  27 

2  26 

42 

2  29 

2  27 

2  26 

42 

43 

2  29 

2  27 

43 

44 

2  30 

2  28 

44 

45 

2  30 

45 

46 

2  31 

46 

47 

47 

48 
49 
50 

48 
49 

50 

51 

TABLE  P.  KFFSCTOFIUN'BPAR- 

51 

ro  be  subtracted  from  tA« 

52 
53 
54 

TMrd  Correction. 

52 
53 
54 

Afp- 
Alt. 

8n  n'»  Apparent  Altitude .  1 

55 

5  10 -if 

)30 

40  5 

0  60 

70S 

0  90 

65 

56 

5 

1    1    2 

2 

2   S 

!  3 

3 

rf     n 

56 

57 

10 

2   2   2 

3 

3  ; 

1  4 

4 

57 

58 

IS 

20 

2  3   3 

3  4   4 

3 
4 

4  i 

5  .' 

1   4 
t   5 

4 

58 

59 

25 

4    4    5 

5 

5   ( 

5 

69 

60 

30 
35 
40 

5  5   5 

6  6  e 
6   6   1 

6 
6 
7 

6   ( 
7 

7 

i 

60 
62 

62 

45 

7   7   • 

H 

64 

. 

50 

7  8   6 

64 

66 

55 

8  8  e 

! 

66 

68 

80 
65 

8  8 

9  9 

68 

70 

50° 

70 

9 

70 

3  2° 

340 

36° 

38"» 

40° 

42° 

44° 

46° 

48° 

52° 

198 

TABLE  XXXIII. 

THIRD  pORRECTION,  TO  APPARENT  DISTANCE  108» 

J '8 

App. 
Alt. 

APPARENT  ALTITUDE  OF 

THE 

SUN, 

OR  STAR. 

J>'8 

App 

Alt. 

6°    7" 

80 

9° 

lO* 

11°  1 

12° 

14°  1 

16° 

18° 

20° 

22°  1 

24°  1 

26° 

28° 

30° 

o 

t    II    1    fi 

/  // 

r    II 

/  ;/ 

1 

// 

1    n 

/ 

n 

1 

II 

1 

II 

/ 

II 

1 

II 

/ 

// 

/ 

// 

1 

'f 

1 

/' 

0 

6 

2  30 

•2  32 

2  35 

2  39 

2  44 

2 

50  2  56 

3 

9 

3 

24 

3 

39 

3 

55 

4 

11 

4 

27 

4 

43 

4 

59 

5 

15 

6 

7 

2  33 

2  30 

2  32 

2  35 

2  39 

2 

43 

2  48 

2 

58 

3 

10 

3 

22 

3 

35 

3 

48 

4 

2 

4 

15 

4 

28 

4 

41 

7 

8 

2  36 

2  32 

2  30 

2  32 

2  35 

2 

38 

2  42 

2 

49 

2 

58 

3 

9 

3 

20 

3 

31 

3 

42 

3 

54 

4 

6 

4 

17 

8 

9 

2  40 

2  35 

2  32 

2  31 

2  33 

2 

35 

2  38 

2 

43 

2 

50 

2 

58 

3 

8 

3 

18 

3 

28 

3 

38 

3 

48 

3 

58 

9 

10 

2  46 

2  39 

2  35 

2  33 

2  31 

2 

33 

2  35 

2 

39 

2 

44 

2 

51 

2 

59 

3 

7 

3 

16 

3 

25 

3 

34 

3 

43 

10 

11 

2  52 

2  44 

2  38 

2  35 

2  33 

2 

32 

2  33 

2 

37 

2 

41 

2 

46 

2 

53 

3 

0 

3 

7 

3 

15 

3 

23 

3 

30 

11 

12 

2  59 

2  49 

2  42 

2  38 

2  35 

2 

33 

2  32 

2 

35 

2 

39 

2 

43 

2 

48 

2 

54 

3 

0 

3 

7 

3 

14 

3 

20 

12 

13 

3  6 

2  54 

2  46 

2  41 

2  37 

2 

35 

2  33 

2 

34 

2 

37 

2 

40 

2 

44 

2 

49 

2 

54 

3 

0 

3 

6 

3 

L2 

13 

14 

3  13 

2  59 

2  54 

2  44 

2  40 

2 

37 

2  35 

2 

33 

2 

35 

2 

38 

2 

41 

2 

45 

2 

49 

2 

54 

2 

59 

3 

5 

14 

15 

3  20 

3  5 

2  56 

2  48 

2  43 

2 

39 

2  37 

2 

34 

2 

34 

2 

36 

2 

39 

2 

42 

2 

46 

2 

50 

2 

54 

2 

59 

15 

16 

3  28 

3  11 

3  1 

2  52 

2  46 

2 

42 

2  39 

2 

35 

2 

33 

2 

35 

2 

37 

2 

40 

2 

43 

2 

46 

2 

50 

2 

54 

16 

17 

3  35 

3  17 

3  6 

2  56 

2  49 

2 

45 

2  42 

2 

37 

2 

34 

2 

34 

2 

35 

2 

38 

2 

40 

2 

43 

2 

47 

2 

50 

17 

x8 

3  43 

3  24 

3  11 

3  0 

2  53 

2 

48 

2  44 

2 

39 

2 

35 

2 

33 

2 

34 

2 

36 

2 

38 

2 

41 

2 

44 

2 

47 

18 

19 

3  50 

3  31 

3  17 

3  5 

2  57 

2 

51 

2  46 

2 

40 

2 

36 

2 

34 

2 

33 

2 

35 

2 

37 

2 

39 

2 

42 

2 

45 

19 

20 

3  58 

3  37 

3  22 

3  10 

3  1 

2 

54 

2  49 

2 

42 

2 

38 

2 

35 

2 

33 

2 

34 

2 

36 

2 

38 

2 

40 

2 

43 

20 

21 

4  6 

3  44 

3  28 

3  14 

3  4 

2 

57 

2  52 

2 

44 

2 

39 

2 

36 

2 

34 

2 

34 

2 

35 

2 

37 

2 

39 

2 

41 

21 

22 

4  14 

3  51 

3  31 

3  19 

3  8 

3 

0 

2  55 

2 

46 

2 

41 

2 

37 

2 

35 

2 

34 

2 

35 

2 

36 

2 

38 

2 

40 

22 

23 

4  22 

3  58 

3  40 

3  24 

3  12 

3 

4 

2  58 

2 

48 

2 

42 

2 

38 

2 

36 

2 

34 

2 

34 

2 

35 

2 

37 

2 

39 

23 

24 

4  30 

4  4 

3  46 

3  29 

3  17 

3 

8 

3  1 

2 

50 

2 

44 

2 

40 

2 

37 

2 

35 

2 

34 

2 

35 

2 

36 

2 

38 

24 

25 
26 

4  38 

4  11 

3  51 

3  34 

3  22 

3 

12 

3  4 

2 

53 

2 

46 

2 

41 
'43 

2 

38 

2 

36 

2 

34 

2 

34 

2 

35 

2 

37 

25 
26 

4  46 

4  18 

3  57 

3  39 

3  26 

3 

16 

3  8 

2 

55 

2 

48 

2 

2 

39 

2 

37 

2 

35 

2 

34 

2 

35 

2 

36 

27 

4  54 

4  25 

4  3 

3  44 

3  31 

3 

20 

3  11 

2 

58 

2 

50 

2 

44 

2 

40 

2 

38 

2 

36 

2 

35 

2 

34 

2 

35 

27 

28 

5  2 

4  31  4  9 

3  49 

3  35 

3 

24 

3  15 

3 

0 

2 

52 

2 

46 

2 

42 

2 

39 

2 

37 

2 

35 

2 

34 

2 

35 

28 

29 

5  10 

4  37 

4  15 

3  54 

3  40 

3 

28 

3  18 

3 

3 

2 

54 

2 

47 

2 

43 

2 

40 

2 

38 

2 

36 

2 

35 

2 

35 

29 

30 

5  18 

4  44 

4  21 

3  59 

3  44 

3 

32 

3  22 

3 

6 

2 

56 

2 

49 

2 

45 

2 

41 

2 

38 

2 

36 

2 

35 

2 

35 

30 
31 

31 

5  26 

4  51 

4  27 

4  4 

3  48 

3 

36 

3  25 

3 

9 

2 

58 

2 

50 

2 

46 

2 

42 

2 

39 

2 

37 

2 

36 

2 

35 

32  5  33 

4  58 

4  33 

4  9 

3  52 

3 

40 

3  28 

3 

11 

3 

0 

2 

52 

2 

47 

2 

43 

2 

40 

2 

38 

2 

37 

2 

36 

32 

33  5  41 

5  5 

4  38 

4  14 

3  57 

3 

44 

3  32 

3 

14 

3 

2 

2 

54 

2 

48 

2 

44 

2 

41 

2 

39 

2 

37 

2 

36 

33 

34 

f  48 

5  11 

4  43 

4  19 

4  1 

3 

47 

3  36 

3 

17 

3 

5 

2 

56 

2 

50 

2 

45 

2 

42 

2 

40 

2 

38 

2 

37 

34 

35 

5  56 

5  18 

4  49 

4  24 

4  5 

3 

51 

3  39 

3 

20 

3 

7 

2 

58 

2 

51 

2 

46 

2 

43 

2 

41 

2 

39 

2 

2 

37 
38 

35 
36 

36 

6  3 

5  24 

4  55 

4  29 

4  10 

3 

55 

3  42 

3 

23 

2 

9 

3 

0 

2 

53 

2 

48 

2 

44 

2 

42 

2 

40 

37 

6  10 

5  30 

5  0 

4  34 

4  14 

3 

59 

3  46 

3 

26 

3 

12 

3 

2 

2 

55 

2 

49 

2 

45 

2 

42 

2 

40 

2 

38 

37 

38 

6  17 

5  36 

5  5 

4  39 

4  19 

4 

3 

3  50 

3 

29 

3 

15 

3 

4 

2 

57 

2 

51 

2 

46 

2 

43 

2 

41 

2 

39 

38 

39 

6  24 

5  42 

5  10 

4  44 

4  24 

4 

7 

3  54 

3 

32 

3 

17 

3 

6 

2 

58 

2 

52 

2 

47 

2 

44 

2 

42 

2 

40 

39 

40 

6  31 

5  48 

5  15 

4  49 

4  28 

4 

11 

3  57 

3 

35 

3 

20 

3 

8 

3 

0 

2 

54 

2 

49 

2 

45 

2 

43 

2 

40 

40 

41 

6  38 

5  54 

5  20 

4  54 

4  33 

4 

15 

4  1 

3 

38 

3 

22 

3 

10 

3 

1 

2 

55 

2 

50 

2 

46 

2 

43 

2 

41 

41 

42 

6  45 

5  59 

5  25 

4  58 

4  37 

4 

18 

4  5 

3 

41 

3 

24 

3 

12 

3 

3 

2 

56 

2 

51 

2 

47 

2 

44 

2 

41 

42 

43 

6  52 

6  5 

5  30 

5  3 

4  41 

4 

22 

4  9 

3 

44 

3 

27 

3 

14 

3 

5 

2 

58 

2 

52 

2 

48 

2 

45 

2 

42 

43 

44 

6  59 

6  11 

5  36 

5  7 

4  45 

4 

26 

4  12 

3 

47 

3 

29 

3 

16 

3 

6 

2 

59 

2 

53 

2 

49 

2 

46 

2 

43 

44 

45 
46 

7  6 

6  17 

5  41 

5  12 

4  49 

4 

30 

4  16 

3 

50 

3 

31 

3 

18 

3 

8 

3 

1 

2 

55 

2 

50 

2 

47 

45 

7  12 

6  22 

5  46 

5  16 

4  53 

4 

34 

4  19 

3 

52 

3 

33 

3 

20 

2 

10 

3 

2 

2 

56 

2 

51 

2 

47 

46 

47 

7  18 

6  27 

5  51 

5  20 

4  57 

4 

37 

4  22 

3 

55 

3 

36 

3 

22 

3 

12 

3 

4 

2 

58 

2 

52 

47 

48 

7  24 

6  32 

5  56 

5  24 

5  0 

4 

41 

4  25 

3 

57 

3 

38 

3 

24 

3 

13 

3 

5 

2 

59 

2 

53 

48 

49 

7  30 

6  37 

6  1 

5  28 

5  4 

4 

44 

4  28 

4 

0 

3 

41 

3 

26 

3 

15 

3 

7 

3 

0 

49 

50 

7  36 

6  42 

6  5 

5  32 

5  7 

4 

47 

4  31 

4 

2 

3 

43 

3 

28 

3 

17 

3 

8 

3 

1 

50 

51 

7  42 

6  47 

6  10 

5  36 

4  11 

4 

50 

4  34 

4 

5 

3 

45 

3 

30 

3 

18 

3 

9 

51 

62 

7  47 

6  52 

6  14 

5  40 

5  14 

4 

53 

4  37 

4 

7 

3 

47 

3 

32 

3 

19 

3 

10 

52 

63 

7  53 

6  57 

6  18 

5  43 

5  18 

4 

56 

4  39 

4 

1© 

3 

49 

3 

34 

3 

20 

53 

54 

7  68 

7  2 

6  22 

5  47 

5  21 

4 

59 

4  42 

4 

12 

3 

51 

3 

35 

3 

21 

54 

65 
56 

8  4 

7  7 

6  26 

5  51 

5  24 

5 

2 

4  45 

4 

14 

3 

53 

3 

36 

5f 

8  9 

7  11 

6  30 

5  54 

5  27 

5 

5 

4  47 

4 

16 

3 

55 

3 

38 

56 

57 

8  14 

7  16 

6  34 

5  58 

5  30 

5 

8 

4  50 

4 

18 

3 

57 

67 

58 

8  19 

7  20 

6  38 

6  1 

5  33 

5 

11 

4  52 

4 

20 

3 

58 

58 

59 

8  24 

7  25 

6  42 

6  4 

5  36 

5 

14 

4  54 

4 

22 

69 

60 

8  28 

7  29 

6  45 

6  8 

5  39 

5 

16 

4  56 

4 

24 

60 

fil 

8  33 

7  33 

6  48 

6  11 

5  42 

5 

19 

4  58 

61 

62 

8  37 

7  37 

6  51 

6  14 

5  45 

5 

21 

5  0 

62 

63 

8  41 

7  40 

6  54 

6  17 

5  48 

5 

23 

63 

64 

8  45 

7  43 

6  57 

6  20 

64 

66 

8  53 

7  46 

7  0 

66 

6» 

7° 

8» 

9° 

10« 

11" 

120 

14° 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

TABLE  XXXUl.                                  ,                199 
THIRD  CORRECTION,  TO  APPARENT  DISTANCE  108". 

J)  '8 

App. 

Alt. 

APPARENT    ALTITUDE    OF    THB    SUN,    OR    STAR. 

D'B 

App 
Alt. 

o 

6 
7 
8 
9 
10 

11 
12 
13 
14 
15 

32<» 

34<» 

36" 

38° 

40° 

42° 

44° 

46° 

48° 

50° 

52° 

54° 

56° 

58° 

62° 

66° 

0 

6 

7 

8 

9 

10 

/    n 

5  30 
4  55 

4  29 
4     8 
3  52 

1     n 

5  45 
5     8 
4  41 
4   18 
4     0 

6     0 
5  21 
4  52 
4  28 
4     9 

t    n 

6  15 
5  34 
5     3 

4  38 
4   18 

6  29 
5  46 
5   13 
4  48 
4  27 

/    II 

6  44 
5  58 
5  23 
4  57 
4  36 

1    II 

6  58 
6   10 
5  34 
5     6 
4  44 

1    n 

7   11 

6  22 
5  44 
5   15 
4  52 

7  23 
6  33 
5  54 
5  23 
4  59 

/    II 

7  34 
6  43 
6     4 
5  31 
5     6 

/    II 

7   45 
6  53 
6   13 
5  38 

5      I 

1    II 

7  56 
7     2 
6  22 
5  45 
5  20 

1    II 

8     6 
7   11 
6  30 
5  53 

5  27 

1    II 

8  16 
7   20 
6  38 
6     1 
5  33 

1    n 

8  35 
7  35 
6  51 
6   14 
5  45 

8  63 

7  47 
7     1 

11 
12 
13 
14 
15 

3  38 
3  27 
3  18 
3   10 
3     4 

3  46 
3  34 
3  24 
3   16 
3     9 

3  54 
3   41 
3   30 
3  22 
3   14 

4     2 
3  48 
3  37 
3  28 
3  20 

4   10 
3  56 
3  44 
3  34 
3  25 

4   18 
4     4 
3  51 
3  40 
3  31 

4  25 
4   11 

3  58 
3  46 
3  36 

4  33 
4   18 
4     4 
3  52 
3  42 

4  40 
4  21 
4   10 
3  58 
3  47 

4  47 
4  30 
4  15 
4     3 
3  52 

4  53 
4  36 
4  21 
4     8 
3  56 

4  59 
4  42 
4  26 
4  12 
4     1 

5     5 

4  47 
4  30 
4   16 
4     5 

5  11 

4  52 
4  34 
4  20 
4     8 

5  20 
5     0 

16 
17 
18 
19 
20 

2  59 
2  54 
2  51 
2  48 
2  46 

3     3 
2  58 
2  54 
2  51 
2  49 

2  47 
2  45 
2  43 
2  42 
2  40 

3     8 
3     3 

2   59 
2  55 
2  52 

2  50 
2  48 
2  46 
2  44 
2  42 

2  41 

2  40 
2  39 
2  38 
2  37 

3   13 

3     7 
3     3 
2  59 
2  56 

3   18 
3   12 
3     7 
3     3 
2  59 

3  23 
3   17 
3   11 
3     6 
3     2 

3  28 
3  21 
3   15 
3   10 
3     6 

3  33 
3  26 
3  20 
3   14 
3     9 

3  38 
3  30 
3  24 
3   18 
3   13 

3  43 
3  35 

3  28 
3  22 
3   16 

3  47 
3  39 
3  32 
3   25 
3   19 

3  51 
3  43 
3  35 
3  28 
3  22 

3  55 
3  46 
3  38 

3  58 

16 
17 
18 
19 
20 

21 
22 
23 
24 
25 

2  44 
2  42 
2  41 
2  40 
2  39 

2  53 
2  50 

2  48 
2  46 
2  44 

2  56 
2  53 
2  50 
2  48 
2  46 

2  45 

2  44 
2  42 
2  41 
2  40 

2  59 
2  56 
2  53 
2  51 
2  49 

3     2 

2  59 
2  56 
2  53 
2  51 

3     5 
3     2 

2  59 
2  56 
2  53 

3     9 
3     5 
3     2 
2  59 
2  56 

3   12 
3     8 
3     4 
3      1 

3   14 
3   10 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

2  38 
2  37 
2  36 
2  36 
2  35 

2  39 
2  38 
2  38 
2  37 
2  36 

2  43 
2  42 
2  41 
2  40 
2  39 

2  47 
2  45 
2  44 
2  42 
2  41 

2  49 
2  47 
2  46 
2  44 
2  43 

2  51 
2  49 
2  47 

2  54 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

2  35 
2  35 
2  36 

2  36 
2  36 

2  36 
2  36 
2  36 
2  36 
2  36 

2  37 
2  37 
2  36 
2  36 
2  36 

2  38 
2  38 
2  37 
2  37 
2  37 

2  39 
2  39 
2  38 
2  38 

2  40 
2  40 

31 
32 
33 
34 
35 

36 
37 
38 
39 
40 

41 

42 
43 
44 
45 

36 
37 
38 
39 
40 

2  37 

2  38 
2  38 
2  39 
2  39 

2  36 
2  37 
2  37 
2  38 
2  38 

2  36 
2  36 
2  36 

2  36 

41 
42 
43 
44 
45 

2  40 
2  40 

46 
47 
48 
49 
50 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 

56 
57 
58 
59 
60 

61 
62 
63 
64 
66 

r  ABLB  P.  KFFICT  01  SUN'b  FAR 

51 
52 
53 
54 
55 

To  be  subu*tttd  from  the 
Third  Correction. 

>'8 

App  - 
A  t. 

5 

10 
15 
20 
25 
30 
35 
40 
45 
50 
55 
60 
65 
70 

Snn's  Apparent  Altitude .  j 

5  tOpO 

1  1    2 

2  2   3 
13   3 
4   4   4 

4  4    5 

5  5   6 

6  6  6 

6  7   7 

7  7   8 

8  8   8 
8   8   9 
8    9 

9 

30 

** 

2 
3 
4 

5 
6 
6 
7 
8 
8 

40  5 

#/       t 

3  : 

4  ^ 

4  ; 

5  ; 
a  ( 

7  • 
7 

0  60 
>  II 

i  3 

1  4 
5   5 

) 
5 

65  8 

It 

3 

0  90 

56 
57 
58 
59 
60 

' 

61 
62 
63 
64 
66 

1 

. 

32° 

34<»     36» 

38" 

40° 

42° 

44° 

46° 

48° 

50° 

52° 

200   •             TABLE  XXXllI. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  112* 

A-PP. 
Alt. 

APPARENT  ALTITUDE  OF  THE  SUN,  OR  STAR. 

D's 

App. 

Alt. 

6° 

70 

8° 

9° 

10° 

11° 

12° 

14° 

16° 

18° 

20° 

22° 

24° 

28° 

28° 

30° 

o 

6 
7 
8 
9 
10 

2  40 
2  42 
2  46 
2  51 
2  57 

2  42 
2  40 
2  42 
2  45 
2  49 

/  // 

2  43 
2  42 
2  41 
2  43 
2  45 

1  II 

2  45 
2  42 
2  43 
2  41 
2  43 

/  II 

2  51 
2  49 
2  45 
2  43 

2  42 

/  II 

3  0 
2  53 
2  48 
2  45 
2  43 

/  II 

3  7 
2  08 
2  52 
2  48 
2  45 

1  II 

3  21 
3  8 
3  0 

2  54 
2  49 

1  II 

3  36 
3  20 
3  9 
3  1 

2  55 

/  II 

3  52 
3  33 
3  19 
3  9 

3  2 

/  II 

4  8 
3  46 
3  31 
3  19 
3  10 

1    II 

4  24 
3  59 
3  42 
3  29 
3  19 

1    II 

4  40 
4  13 
3  54 
3  40 

3  28 

1    II 

4  56 
4  26 
4  6 
3  50 
3  37 

1    II 

5   12 
4  40 
4  18 
4  0 
3  46 

'  " 
5  28 
4  54 
4  30 
4  11 
3  56 

0 

6 

7 

8 

9 

10 

11 
12 
13 
14 
15 

3  3 

3  9 
3  16 
3  23 
3  31 

2  54 

2  59 

3  4 
3  10 
3  16 

2  48 
2  52 

2  56 

3  0 
3  5 

2  45 

2  48 
2  51 
2  54 

2  58 

2  43 

2  45 
2  47 
2  50 
2  53 

2  42 
2  43 
2  45 
2  47 
2  49 

2  43 
2  42 
2  43 
2  45 

2  47 

2  46 
2  44 
2  43 
2  43 

2  44 

2  50 
2  47 
2  45 
2  44 
2  44 

2  56 
2  52 
2  49 
2  47 
2  46 

3  3 

2  58 
2  54 
2  51 
2  49 

3  11 
3  5 
3  0 
2  56 
2  53 

3  19 
3  12 
3  6 
3  1 

2  57 

3  27 
3  19 
3  12 
3   6 
3   1 

3  55 
3  26 
3  18 
3  12 
3  6 

3  44 
3  34 
3  25 
3  17 
3  11 

11 
12 
13 
14 
15 

16 
17 
18 
19 
20 

21 
22 
23 

24 
25 

26 

27 
28 
29 
30 

3  39 
3  47 

3  55 

4  3 
4  11 

3  22 
3  29 
3  35 

3  41 

4  48 

3  10 
3  15 
3  20 
3  26 
3  32 

3  2 
3  6 
3  10 
3  15 
3  20 

2  56 

2  59 

3  2 
3  6 
3  10 

2  51 
2  54 

2  57 

3  0 
3  3 

2  48 
2  50 
2  53 
2  56 
2  58 

2  45 
2  46 
2  48 
2  50 
2  52 

2  43 
2  44 
2  45 

2  46 
2  48 

2  45 
2  44 
2  44 
2  45 
2  45 

2  47 
2  46 
2  45 
2  44 
2  44 

2  50 
2  48 
2  47 
2  46 
2  45 

2  54 
2  51 
2  49 
2  48 

2  47 

2  57 
2  54 
2  52 
2  50 
2  49 

3  2 
2  58 
2  55 
2  53 
2  51 

3  6 

3  2 
2  59 
2  56 
2  54 

2  52 
2  51 
2  50 
2  49 
2  48 

16 
17 
18 
19 

20 

21 

22 
23 
24 
25 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

36 
37 
38 
39 
40 

4  19 

4  27 
4  35 
4  43 
4  52 

3  54 

4  1 
4  8 
4  15 
4  22 

3  38 
3  44 
3  50 

3  56 

4  3 

3  25 
3  30 
3  35 
3  40 
3  46 

3  15 
3  20 
3  24 
3  28 
3  33 

3  7 
3  11 
3  15 
3  19 
3  23 

3  1 
3  5 
3  8 
3  11 
3  15 

2  54 
2  56 

2  58 

3  1 
3  3 

2  49 
2  51 
2  52 
2  54 
2  55 

2  46 
2  47 
2  48 
2  49 
2  51 

2  44 

2  45 
2  46 
2  47 
2  48 

2  44 
2  44 
2  45 
2  45 
2  46 

2  46 
2  45 
2  44 
2  44 
2  45 

2  48 
2  47 
2  46 
2  45 
2  44 

2  50 
2  49 

2  48 
2  47 
2  46 

5  0 
5  8 
5  16 
5  24 
5  32 

4  29 
4  37 
4  44 
4  51 

4  57 

4  9 
4  15 

4  21 
4  27 
4  33 

3  51 

3  56 

4  2 

4  7 
4  12 

3  38 
3  42 
3  47 
3  52 
3  57 

3  27 
3  31 
3  36 
3  40 
3  45 

3  18 
3  22 
3  26 
3  31 
3  35 

3  5 

3  8 
3  11 
3  14 
3  17 

2  57 

2  59 

3  2 
3  5 
3  7 

2  52 
2  54 
2  56 

2  58 

3  0 

2  49 
2  51 
2  52 
2  53 
2  55 

2  47 
2  48 
2  49 
2  50 
2  52 

2  45 
2  45 
2  46 
2  46 
2  47 

2  44 
2  45 
2  46 
2  46 

2  47 

2  45 
2  45 
2  45 
2  45 
2  46 

2  47 
2  46 

2  46 

3  46 
3  46 

31 
32 
33 
34 
35 

5  40 
5  48 

5  56 

6  4 
6  11 

5  4 
5  10 
5  17 
5  24 
5  31 

4  39 

4  45 

5  51 
5  56 
5  2 

4  17 
4  22 
4  28 
4  33 
4  38 

4  2 
4  7 
4  12 
4  16 
4  21 

3  49 
3  54 

3  58 

4  2 
4  6 

3  39 
3  43 
3  46 
3  50 
3  53 

3  20 
3  23 
3  26 
3  29 
3  32 

3  9 
3  12 
3  14 
3  17 
3  19 

3  2 
3  4 
3  6 
3  8 
3  10 

2  57 

2  58 

3  0 
3  2 
3  4 

2  53 
2  54 
2  55 
2  57 
2  59 

2  49 
2  51 
2  52 
2  53 
2  55 

2  48 
2  49 
2  50 
2  51 
2  52 

2  47 
2  47 
2  48 
2  49 
2  50 

2  46 
2  46 
2  47 
2  48 
2  49 

36 
37 
38 
39 
40 

6  19 
6  26 
6  33 
6  41 
6  48 

5  37 
5  44 

5  50 

5  56 

6  2 

5  7 
5  13 
5  18 
5  24 
5  29 

4  43 
4  48 
4  53 

4  58 

5  3 

4  25 
4  29 
4  33 
4  37 
4  41 

4  10 
4  14 
4  17 
4  21 
4  25 

3  57 

4  1 
4  4 
4  8 
4  11 

3  35 
3  38 
3  41 
3  44 

3  47 

3  21 
3  24 
3  26 
3  29 
3  32 

3  12 
3  14 
3  16 
3  18 
3  20 

3  5 
3  7 
3  9 
3  10 
3  12 

3  0 
3  1 
3  3 
3  4 
3  B 

2  56 

2  57 

2  cy 

2  59 

3  1 

2  53 
2  54 
2  55 
2  56 
2  57 

2  51 
2  52 
2  53 
2  54 
2  55 

2  49 
2  50 
2  51 
2  52 
2  53 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 

56 

n 

58 
59 
60 

6  55 

7  2 
7  8 
7  15 
7  22 

6  8 
6  14 
6  20 
6  26 
6  32 

5  35 
5  40 
5  46 
5  51 
5  56 

5  8 
5  13 

5  18 
5  23 

5  28 

4  45 
4  49 
4  53 

4  58 

5  3 

4  28 
4  32 
4  36 
4  40 
4  44 

4  15 

4  18 
4  22 
4  25 
4  28 

3  50 
3  53 
3  56 

3  59 

4  2 

3  35 
3  38 
3  40 
3  42 
3  45 

3  22 
3  25 
3  27 
3  29 
3  31 

3  13 
3  15 
3  17 
3  19 
3  21 

3  7 
3  8 
3  10 
3  12 
3  14 

3  2 
3  3 
3  5 
3  6 
3  8 

2  58 

2  59 

3  0 
3  1 

2  55 
2  56 

41 
42 
43 
44 
45 

7  28 
7  35 
7  42 
7  48 
7  55 

6  38 
6  44 
6  49 
6  54 
6  59 

6  2 
6  7 
6  12 
6  16 
6  21 

5  33 
5  37 
5  41 
5  45 
5  49 

5  8 
5  12 
5  16 
5  20 
5  23 

4  47 
4  51 
4  55 

4  58 

5  2 

4  31 
4  34 
4  38 
4  41 
4  44 

4  5 
4  8 
4  11 
4  14 
4  17 

3  47 
3  50 
3  52 
3  55 
3  57 

3  33 
3  36 
3  38 
3  40 
3  42 

3  23 

3  25 
3  26 
3  28 
3  29 

3  15 
3  16 
3  17 

3  9 

46 
47 
48 
49 
50 

8  1 
8  7 
8  13 
8  19 

8  25 

7  4 
7  9 
7  14 
7  19 

7  23 

6  25 
6  29 
6  34 
6  38 
6  42 

5  53 

5  57 

6  1 
6  5 
6  8 

5  27 
5  30 
5  34 
5  37 
5  41 

5  5 
5  8 
5  12 
5  15 
5  18 

4  47 
4  50 
4  53 
4  56 
4  59 

4  19 
4  22 
4  24 
4  26 
4  28 

3  59 

4  1 
4  3 
4  4 

3  44 
3  46 

51 

52 
53 
54 
55 

8  30 
8  35 
8  40 
8  45 
8  5C 

7  28 
7  33 
7  38 
7  43 
7  48 

6  47 
6  51 

6  55 

6  59 

7  2 

6  12 
6  15 
6  19 
6  22 
6  25 

5  44 
5  47 
5  50 
5  53 
5  56 

5  21 

5  24 
5  27 
5  29 

5  1 
5  4 
5  6 

4  30 

56 
57 
58 
59 
60 

61 
62 
63 
64 
65 

8  54 

8  58 

9  2 
9  5 

7  52 
7  56 
7  5S 

7  5 
7  8 

6  28 

61 
62 
63 
64 
66 

1  6° 

7° 

8° 

9° 

10° 

11° 

12° 

140 

16° 

18° 

20° 

22° 

24° 

26° 

28° 

30° 

1                                                          TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  112°. 

201 

App. 
Alt. 

APPARENT   ALTITUDE    OF   THE    SUN,    OR    STAR. 

>'8 

App 
Alt. 

32° 

34° 

36° 

38° 

40° 

42° 

44° 

46° 

48° 

50° 

52° 

54° 

56° 

58° 

60° 

62° 

o 

6 
7 
8 
9 
10 

/     It 

5  44 
5     7 
4  42 
4  21 
4     5 

t    It 

6     0 
5  21 
4  54 
4  32 

4   14 

t    n 

6   16 
5  34 
5     5 
4  42 
4  23 

/    If 

6  31 
5  47 
5   16 
4  52 
4  32 

1    II 

6  46 
6     0 

5  27 
5      1 
4  40 

/    II 

7     0 
6   13 
5  38 
5   11 
4  49 

/    II 

7    14 
6   25 
5  49 
5  21 
4  58 

1    II 

7  27 
6  37 
6     0 
5  31 

5     7 

1    II 

7  40 
6  49 
6   10 
5  140 
5   15 

1    II 

7  53 
7     0 

6  20 
5  48 
5  23 

/    n 

8     5 
7   10 
6  29 
5  56 
5  31 

1    II 

8   18 
7   20 
6  38 
6     4 
5  38 

1     II 

8  30 
7  30 
6  47 
6  11 
5  44 

1    II 

8  41 
7  39 
6  55 
6   18 
5  50 

/    // 

8  50 
7  47 
7     2 
6  24 
5  55 

/    // 

8  58 
7  55 

7     8 

o 

6 
7 
8 
9 
10 

11 
12 
13 
14 
15. 

11 
12 
13 
14 
15 

3  52 
3  41 

3  31 
3  23 
3   16 

4     0 

3  48 
3  38 
3  29 
3  21 

4     8 
3  55 
3  44 
3  35 

3  27 

4   16 
4     2 
3   50 
3  41 
3   33 

4  23 
4     9 

3  57 
3  47 
3  38 

4  31 
4   16 

4     4 
3  53 
3  44 

4  39 
4  24 
4   10 
3  59 
3  50 

4  47 
4  31 
4   17 
4     6 
3  56 

4  55 
4  38 
4  23 
4  12 
4     1 

5     2 
4  44 
4  29 
4  17 
4     6 

5     8 
4  50 
4  35 
4  22 
4  10 

5  14 
4  56 
4  40 
4  26 
4   14 

5  19 
5     1 

4  45 
4  30 

5  24 
5     5 

16 
17 
18 
19 
20 

3   10 
3     6 
3     3 
3     0 

2  57 

3   15 
3   11 
3     7 
3     4 
3      1 

3  21 
3   16 
3   12 
3     8 
3     5 

3   26 
3  20 
3    16 
3   12 
3     8 

3  31 
3  25 
3  20 
3   16 
3   12 

3     9 
3     6 
3     3 
3     1 

2  59 

2  57 
2  56 
2  55 
2  54 
2  53 

3  37 
3  30 
3  25 
3  20 
3   16 

3  42 
3  35 
3  29 
3  24 
3  20 

3   47 
3  40 
3  34 
3   28 
3  23 

3   19 
3   15 
3   12 
3     9 

3  52 
3  45 
3  38 
3  32 
3  26 

3  22 
3   18 

3  57 
3  49 
3  42 
3  35 
3  29 

4     1 
3  53 
3  46 

4     4 

16 
17 
18 
19 
20 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

2  55 
2  53 
2  52 
2  51 
2  50 

2  58 
2  56 
2  55 
2  53 
2  52 

3     2 
3     0 
2  5S 
2  56 
2  54 

3     5 
3     3 
3      1 

2  59 
2  57 

3   12 
3     9 
3     6 
3     4 
3     1 

3   16 
3   12 
3     9 
3     7 
3     4 

21 
22 
23 
24 
25 

26 

27 
28 
29 
30 

31 
32 
33 
34 
35 

2  49 
2  48 

2  47 
2  47 
2  47 

2  51 

2  50 
2  49 

2  48 
2  48 

2  53 

2  52 
2  51 
2  50 
2  49 

2  55 
2   54 
2  53 
2  52 
2  51 

2  59 
2  57 
2  56 

3     1 

31 
32 
33 
34 
35 

2  47 
2  47 
2  47 
2  48 
2  48 

2  48 
2  48 
2  48 
2  48 
2  48 

2  49 
2  49 
2  49 
2  49 

2  50 
2  50 

36 
37 
38 
39 
40 

2  49 
2  49 
2  50 

2  48 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

41 
42 
43 
44 
45 

46 

47 

48 
49 
50 

46 
47 
48 
49 
50 

51 

52 
53 
54 
55 

56 
57 
58 
59 
60 

61 
62 
63 
64 
65 

TABLE  P.  EFFECT  OF  iOW'i  PAR . 

51 
52 
53 
54 
55 

To  bt  subtraettd  from  tht 
Third  Correction. 

)'8 

App 

Ah. 

5 

10 
15 
20 
25 
30 
35 
40 
45 
50 
55 
60 
05 

Sun's  Apparent  Altitnde.l 

5 

1 
2 
3 
4 
4 
5 
0 
7 
7 
8 
8 
9 
9 

10  2( 

2   S 

2  3 

3  4 

4  4 

5  £ 

5  ( 

6  1 

7  - 
7   f 

e  i 

9 
9 

)30 

It 

3 

4 

4 

5 

>   C 

)   7 

r  7 
r  8 

) 

405 

tf      1 

3   ' 

4 

5  . 
6 
8 
7 

0  60 

1  4 

5   5 

5 
S 

65 
4 

80 

n 

90 

56 
57 
58 
59 
fiO 

61 
62 
63 
64 
65 

32° 

34° 

36° 

38° 

40° 

42° 

44° 

46° 

48° 

50° 

52° 

1     202                TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  116» 

App. 

APPARENT  ALTITUDE  OF  THE  8UK,  OR  STAR. 

App. 

Alt. 

6° 

70 

8» 

90 

lOO 

\V* 

12° 

13° 

140 

15° 

160 

18° 

20° 

22° 

240 

26° 

Alt. 

o 

6 
7 
8 
9 
10 

2  50 
2  62 

2  56 

3  1 

3  7 

2  62 
2  50 
2  62 
2  55 
2  59 

t   // 

2  55 
2  62 
2  50 
2  62 
2  55 

/  // 

2  59 
2  55 
2  62 
2  60 
2  52 

t    n 

3  4 

2  58 
2  54 
2  62 
2  51 

1  n 

3  10 
3  2 

2  67 

2  54 
2  52 

1  n 

3  17 
3  8 
3  1 

2  57 
2  54 

t    n 

3  25 
3  13 
3  5 
3  0 
2  57 

/  // 

3  33 
3  19 
3  10 
3  4 
3  0 

/  // 

3  41 
3  25 
3  15 
3  8 
3  3 

3  49 
3  32 
3  21 
3  13 
3  7 

/  It 

4  6 
3  46 
3  32 
3  21 
3  14 

1    II 

4  22 
4  0 
3  44 
3  31 
3  22 

1    It 

4  39 
4  14 
3  56 
3  42 
3  31 

1    It 

4  56 
4  28 
4  8 
3  53 
3  41 

t    II 

5   13 
4  42 
4  20 
4  4 
3  50 

0 

6 
7 
8 
9 
10 

11 
12 
13 
14 
15 

3  13 

3  20 
3  27 
3  35 
3  43 

3  4 
3  9 
3  15 

3  21 
3  27 

2  68 

3  2 
3  6 
3  11 
3  16 

2  54 

2  67 

3  1 
3  5 
3  9 

2  62 
2  64 

2  57 

3  0 
3  4 

2  51 
2  53 
2  55 

2  57 

3  0 

2  53 
2  52 
2  53 
2  55 
2  57 

2  55 
2  53 
2  52 
2  53 
2  55 

2  67 
2  55 
2  53 
2  52 
2  53 

3  0 
2  57 
2  55 
2  54 
2  53 

3  3 
3  0 

2  58 
2  56 
2  54 

3  9 
3  5 
3  2 
2  59 
2  57 

3  16 
3  10 
3  6 
3  3 
3  0 

3  23 
3  16 
3  11 

3  7 
3  4 

3  31 
3  23 
3  17 
3  12 
3  8 

3  39 
3  30 
3  23 
3  18 
3  14 

11 
12 
13 
14 
15 

16 
17 
18 

19 
20 

3  51 

3  59 

4  7 
4  16 
4  24 

3  33 
3  40 
3  47 

3  64 

4  1 

3  21 
3  27 
3  33 
3  39 
3  45 

3  13 
3  17 
3  22 
3  27 
3  32 

3  7 
3  11 
3  14 

3  18 

3  22 

3  3 
3  6 
3  9 
3  12 
3  16 

3  0 
3  2 
3  5 
3  8 
3  11 

2  57 

2  59 

3  1 
3  4 
3  7 

2  55 
2  57 

2  59 

3  1 
3  3 

2  54 
2  55 
2  56 

2  58 

3  0 

2  53 
2  54 
2  55 
2  56 
2  58 

2  55 
2  55 
2  54 
2  55 
2  56 

2  58 
2  57 
2  56 
2  55 
2  55 

3  1 

2  59 
2  58 
2  57 
2  57 

3  5 
3  3 
3   1 
3  0 
2  59 

3  10 
3  7 
3  5 
3   3 
3   2 

16 
17 
18 
19 

20 

21 
22 
23 
24 
25 

26 

27 
28 
29 
30 

31 
32 
33 
34 
35 

4  33 
4  41 
4  49 

4  58 

5  6 

4  8 
4  15 
4  22 
4  29 
4  36 

3  51 

3  57 

4  4 
4  10 
4  16 

3  37 
3  43 
3  49 

3  54 

4  0 

3  27 
3  32 
3  37 
3  42 
3  47 

3  20 
3  24 
3  28 
3  32 
3  37 

3  14 
3  17 
3  21 
3  24 
3  28 

3  32 
3  35 
3  39 
3  43 
3  47 

3  9 
3  12 
3  15 
3  18 
3  21 

3  5 
3  7 
3  10 
3  13 
3  16 

3  2 
3  4 
3  7 
3  10 
3  12 

3  0 
3  2 
3  4 
3  7 
3  9 

2  57 

2  59 

3  0 
3  2 
3  4 

2  56 
2  57 
2  58 

2  59 

3  1 

2  57 
2  56 
2  57 
2  58 
2  59 

2  59 
2  58 
2  58 
2  57 
2  68 

3   1 
3  0 
3   0 

2  59 
2  59 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

5  15 
5  23 
5  31 
5  39 
5  47 

4  43 
4  50 

4  57 

5  4 

6  11 

4  22 
4  28 
4  34 
4  40 
4  46 

4  5 
4  11 
4  16 
4  21 
4  26 

3  52 

3  57 

4  1 
4  6 
4  10 

3  41 
3  45 
3  49 
3  54 

3  58 

3  24 
3  27 
3  31 
3  34 
3  38 

3  18 
3  21 
3  24 
3  27 
3  30 

3  14 

3  16 
3  19 
3  21 
3  24 

3  11 
3  13 
3  15 
3  17 
3  19 

3  6 
3  8 
3  9 
3  11 
3  13 

3  2 
3  4 
3  5 
3  7 
3  8 

3  0 
3  2 
3  3 
3  4 
3  5 

2  69 

3  0 
3  1 
3  2 
3  3 

2  58 
2  59 

2  59 

3  0 
3   1 

3  2 
3  3 
3  4 
3  5 
3  6 

5  55 

6  3 

6  12 
6  20 
6  29 

5  18 

6  26 
6  33 
5  40 
5  47 

4  52 

4  58 

5  5 

6  11 
5  17 

4  32 
4  37 
4  42 
4  47 
4  53 

4  15 
4  20 
4  25 
4  30 
4  35 

4  2 
4  6 
4  11 
4  15 
4  20 

3  51 
3  55 

3  59 

4  2 
4  6 

4  10 
4  14 
4  18 

4  22 
4  26 

3  42 
3  46 
3  48 
3  52 
3  55 

2  34 

3  37 
3  40 
3  43 
3  47 

3  27 
3  30 
3  33 
3  36 
3  40 

3  22 
3  25 
3  27 
3  30 
3  33 

3  15 
3  17 
3  19 
3  21 
3  24 

3  10 
3  12 
3  13 
3  15 
3  17 

3  6 
3  8 
3  9 
3  10 
3  12 

3  4 
3  5 
3  6 
3  7 
3  9 

36 
37 
38 
39 
40 

6  37 

6  45 

6  63 

7  1 
7  8 

5  55 

6  2 
6  9 
6  16 
6  23 

5  23 
5  29 

5  35 

6  41 
5  47 

4  58 

5  4 

6  9 
5  15 
5  20 

4  40 
4  45 
4  50 
4  54 
4  58 

4  24 
4  29 
4  33 
4  37 
4  41 

3  59 

4  2 
4  6 
4  10 
4  13 

3  50 
3  53 

3  57 

4  0 
4  3 

3  43 
3  46 
3  49 
3  52 
3  54 

3  36 
3  39 
3  42 
3  45 

3  47 

3  26 
3  29 
3  31 
3  33 
3  36 

3  19 
3  21 
3  23 
3  25 

3  27 

3  14 
3  15 
3  17 
3  19 
3  20 

3  10 
3  11 
3  13 
3  15 
3  16 

3  7 
3  8 
3  9 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 

7  15 
7  22 
7  30 
7  37 
7  45 

6  29 
6  35 
6  41 
6  47 
6  63 

6  53 

5  58 

6  4 
6  9 
6  15 

5  25 
5  30 
5  35 
5  40 
5  45 

5  3 
5  7 
5  12 

5  16 

6  21 

4  45 
4  49 
4  53 

4  57 

5  ] 

4  30 
4  33 
4  37 
4  41 
4  44 

4  17 
4  20 
4  23 
4  27 
4  30 

4  6 
4  9 
4  12 
4  15 
4  18 

3  57 

4  0 
4  3 
4  6 
4  9 

3  50 
3  53 
3  55 

3  68 

4  1 

3  39 
3  41 
3  43 
3  45 
3  47 

3  29 
3  31 
3  33 
3  34 

3  21 
3  23 

41 
42 
43 
44 
45 

7  52 

7  69 

8  6 
8  12 
8  18 

6  69 

7  5 
7  10 
7  15 
7  20 

6  20 
6  25 
6  30 
6  35 
6  40 

6  49 

5  54 

6  69 
6  4 
6  8 

6  25 
6  29 
6  33 
5  37 
5  41 

5  6 

6  9 

5  13 

6  16 
5  20 

4  48 
4  52 
4  55 
4  58 
6  1 

4  33 
4  37 
4  40 
4  43 
4  46 

4  21 
4  24 
4  27 
4  30 
4  33 

4  11 
4  14 
4  17 
4  19 

4  3 
4  6 

4  8 

3  49 

46 
47 
48 
49 
50 

51 
52 
53 
54 
65 

56 
57 
58 
69 
60 

8  24 

8  30 
8  36 
8  42 
8  48 

7  26 
7  31 
7  37 
7  42 
7  47 

6  45 
6  60 
6  55 

6  59 

7  3 

6  12 
6  16 

6  20 
6  24 
6  28 

5  45 

5  49 

6  53 
6  50 

5  23 
5  27 
5  30 

5  4 

6  7 

4  49 

51 
52 
53 
54 
55 

8  54 

8  5S 

9  2 

7  62 

7  57 

7  7 

56 
57 
68 
69 
60 

61 
62 
63 
64 
65 

61 
62 
63 
64 
65 

6« 

70 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

18°^ 

20° 

22° 

24° 

26° 

_^,^ 

TABLE  XXXllI.                                                   203 
THIRD  CORRECTION,  TO  APPARENT  DISTANCE  116° 

])'8 

App. 
Alt. 

APPARENT   ALTITUDE    OP    THE    SUN,    OR    STAR. 

App 
Alt 
o 

6 
7 
8 
9 
10 

11 
12 
13 
14 
15 

28°     30°  1 

32° 

34° 

36° 

38° 

40° 

42° 

44° 

46° 

48° 

50° 

52° 

54° 

56° 

58° 
1    II 

9     3 

0 

6 
7 
8 
9 
10 

5  30 
4  56 
4  33 
4   15 
4     0 

5  46 

5   10 
4  45 
4  26 
4   10 

/    II 

6     3 
5  25 
4  58 
4  37 
4  20 

/    II 

6    19 
5   40 
5    11 
4   47 
4   29 

/    II 

6  36 
5  55 

5  24 
4  58 
4  39 

1    II 

6   52 
6     9 
5   36 
5     8 
4  48 

/    II 

7     7 
6  22 
5  47 
5   19 
4  58 

1    II 

7  22 
6   34 
5   58 
5   29 
5     7 

/    // 

7  36 
6  46 
6     8 
5  39 
5   16 

1    II 

7   51 
6  58 
6   18 
5  49 
5  25 

1    >i 

8     5 
7     9 
6  28 
5  59 
5  33 

/•  II 

8  18 
7  20 
6  38 
6     8 
5  41 

1     II 

8  30 
7  31 
6  48 
6  16 
5  49 

8  42 
7  42 
6  58 
6  24 
5  56 

1    II 

8  53 
7  52 
7     8 

11 
12 
13 
14 
15 

3  48 
3  38 
3   30 
3  24 
3   19 

3  57 
3  46 
3   37 
3  30 
3  25 

4     6 
3   54 
3  44 
3  37 
3   31 

4   15 
4     2 
3  52 
3  44 
3  37 

4  23 
4   10 
4     0 
3  51 
3  43 

4  32 
4   18 
4     7 
3  57 
3  49 

4  41 
4  26 
4   14 
4     4 
3  55 

4  49 
4  34 
4  21 
4   10 
4      1 

4  57 
4  41 
4  27 
4   16 
4     6 

5     5 

4  48 
4  33 
4  21 
4   1] 

5   12 
4  54 
4  39 

4  27 
4  17 

5  19 
5     1 
4  45 
4  33 

5  25 
5     7 

16 
17 
18 
19 
20 

3   15 
3   12 
3     9 
3     7 
3     5 

3  20 
3   16 
3  13 
3    10 
3     8 

3  26 
3  21 
3   17 
3   14 
3   11 

3   31 
3  26 
3  22 
3   18 
3   15 

3   37 
3  31 
3  26 
3   22 
3   19 

3   16 
3   14 
3  12 
3    10 
3     9 

3  42 
3  36 
3  31 
3  27 
3  23 

3  47 
3  41 
3  36 
3  31 
3  27 

3  53 
3  46 
3  40 
3  35 

3  31 

3  58 
3  51 
3  45 
3  39 
3  34 

4     2 
3  55 
3  49 

4     8 

^ 

16 

17 
18 
19 
20 

21 
22 
23 
24 
25 

3     4 
3     3 
3     2 
3     1 
3     0 

3     6 
3     5 
3     4 
3     3 

3     2 

3     9 
3     7 
3     6 
3     5 
3     4 

3   12 
3   10 
3     9 
3     8 
3     7 

3  20 
3   17 
3   15 
3   13 
3   11 

3  23 
3  20 
3   18 
3   16 

3  27 
3  23 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

3     0 

3     0 
2  59 

2  59 

3  0 

3     2 
3     1 
3     0 
3     0 
3     0 

3     4 
3     3 
3     2 
3     1 
3     1 

3     6 
3     5 
3     4 
3     3 
3     3 

3     7 
3     6 
3     5 

3     9 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

31 
32 
33 
34 
35 

3      1 
3     2 
3     2 
3     3 
3     4 

3     0 
3      1 
3      1 
3     2 

3     1 

3     2 

36 
37 
38 
39 
40 

3     5 

36 
37 
38 
39 
40 

41 

42 
43 
44 
45 

41 
42 
43 
44 
45 

46 

47 
48 
49 
50 

• 

46 
47 
48 
49 

50 

51 

52 
53 
54 
'.ih 

56 
57 
58 
59 
60 

61 
62 
63 
64 
65 

I 

TABLB  P.  xrracT  or  aini'i  fab. 

51 
52 
53 
54 
55 

To  be  subtracted  from  th* 
Third  Correction. 

)'8 

App 
A  t. 

5 
10 
15 
20 
2.5 
.30 
35 
40 
45 
50 
55 
60 

Snn't  Apparent  Altitade.  i 

5 

'* 

2 
2 
3 
'4 
5 
5 
6 
7 
7 
8 
9 
9 

10  2( 

a  2 

2  3 

3  i 

4  5 

5  6 

6  6 
8  7 

7  8 

8  8 
8 

9 

)30 

3 
4 

5 
6 
6 
7 
8 

40  5 
If   » 

4  4 

5  S 
5   t 
6 

7 

D60 
tt 
5 

1 

70 

80 

It 

BO 

56 
57 
58 
59 
60 

61 
62 
63 
64 
65 

34° 

38° 

44° 

28" 

30° 

32« 

36° 

40° 

42° 

46° 

48° 

J '8 

App. 

Alt 


204  TABLE  XXXIII. 

THIRD  CORRECTION,  TO  APPARENT  DISTANCE  120°. 

APPARENT  ALTITUDE  OF  THE  SUN,  OR  STAR. 


6° 


6  3  1 

7  3  3 

8  3  7 


9 

10 


11 
12 
13 
14 
15 


16 
17 
18 
19 
20 

21 
22 
23 
24 
25 

26 

27 
28 
29 
30 


3  12 
3  18 


3  25 
3  33 

3  41 
3  49 
3  57 


3 
3 
3 
3 
3  12 


8» 


t    It 


3  17 
3  23 
3  28 
3  34 
3  41 


14 
23 
32 
40 


4  49 

4  58 

5  7 
5  16 
5  25 


31 
32 
33 
34 
35 


36 
37 
38 
39 
40 


41 
42 
43 
44 
45 


5  34 
5  42 

5  51 

6  0 
6  8 


48 
55 
3 
10 
17 


4  24 
4  31 
4  39 
4  46 
4  53 


12 
16 
20 
25 
30 


3  11 

3  7 
3  5 
3  4 
3  6 


8 
11 
15 
19 
23 


3  36 

3  42 
3  48 

3  54 

4  1 


10"  ll"  12°  13 


/  It 

3  17 
3  11 
3  8 
3  6 
3  5 


3 

3 

3  11 
3  14 
3  18 


24 

16 

11 

8 

6 


5 
5 

5  16 
5  24 
5  31 


6  17 
6  25 
6  34 
6  43 
6  51 


59 

8 
16 
24 
32 


46 
47 
48 
49 
50 


51 
52 
53 
54 
55 


40 
47 
55 
3 
11 


5  39 
5  46 

5  54 

6  2 
6  9 


4  7 
4  14 
4  21 
4  27 
4  33 


3  28 
3  32 
3  37 
3  42 
3  48 


4  40 
4  47 

4  53 

5  0 
5  6 


5  12 
5  18 
5  25 
5  31 
5  38 


16 
23 
30 
37 
44 


50 

56 

2 

9 

15 


18 
25 
32 
39 
45 


ffi 
57 
58 
59 
60 


8  51 

8  57 

9  3 
9  9 


61 
62 
63 
64 
65 


21 
27 
33 
39 
45 


44 
50 
56 


3  53 

3  58 

4  4 
4  10 
4  15 


4  20 
4  25 
4  31 
4  37 
4  43 


3  22 
3  25 
3  29 
3  33 
3  38 


3  42 
3  47 
3  52 

3  57 

4  2 


3  5 
3  6 
3  8 
3  11 
3  14 


3  32 
3  22 
3  15 
3  11 
3  8 


3  6 
3  5 
3  6 
3  8 
3  11 


3  17 
3  20 
3  23 
3  26 
3  30 


3  34 
3  39 
3  43 

3  47 
3  51 


4  48 

4  54 

5  0 
5  6 
5  l2 


5 

5 
5 
5 

85 


6  14 
6  19 
6  25 
6  31 
6  36 


6  41 
6  46 
6  52 

6  57 

7  2 


7  51 

7  57 

8  3 


18 
23 

28 
34 
39 


44 

50 

55 

0 

5 


10 
15 
20 
25 
30 


4 

4  12 
4  17 

4  22 
4  27 


4  32 
4  37 
4  42 
4  47 
4  52 


57 

2 

7 

12 

17 


22 
27 
32 
37 
42 


8  6  34 
13 


56 
1 
5 

10 


13 
15 
18 
21 


3  39 

3  28 
3  20 
3  14 
3  10 


14= 


47 
34 
25 
18 
14 


3  11 

3  9 
3  8 
3  7 
3  8 


3  24  3  20 


28 
32 
36 
39 
43 


3  11 
3  12 
3  14 
3  17 


3  47 
3  51 
3  55 
3  59 


15  4  3 


4  19 
4  23 
4  27 
4  32 
4  37 


4  42 
4  46 
4  50 
4  55 
4  59 


5 
5 

5  13 
5  17 
5  22 


46 
51 
55 
59 
3 


26 
30 
34 
37 


23 
26 
30 
33 
36 


9 

10 


15= 


55 

40 
29 
22 
17 


3  13 
3  11 
3  9 
3  8 
3  7 


3  12 
3  15 
3  17 


3  19 

3  22 
3  25 
3  28 
3  31 


3  39 
3  43 
3  47 
3  50 
3  54 


4  7 
4  11 
4  15 
4  19 
4  24 


4  28 
4  32 
4  36 
4  40 
4  44 


4  48 
4  52 

4  56 

5  0 
5  4 


70 


go 


8 
11 
14 


3  57 

4  1 
4  5 
4  9 
4  12 


4  15  4 


34 
37 
40 
43 
46 


3 
3 

3  11 
3  13 


16°  17°  18°  19 


4 
47 
35 
26 

20 


16 

13 

11 

9 

8 


3  15  3  13 


3  17 
3  19 
3  21 
3  23 
3  26 


3  49 
3  52 
3  56 

3  59 

4  2 


4  19 
4  23 
4  27 
4  31 


4  35 
4  39 
4  42 
4  46 
4  49 


53 
56 


4 

4  13 
4  16 

4  20 


4  24 
4  28 
4  31 
4  34 
4  37 


4  40 


29 
32 
35 
37 
40 


3  43 
3  46 
3  49 
3  52 
3  55 


3 

3  9 
3  10 
3  11 


12 
54 
40 
31 
24 


3  19 
3  15 
3  13 
3  11 
3  9 


3  15 
3  16 

3  18 
3  20 
3  23 


3  25 
3  28 
3  30 
3  33 
3  36 


3  38 
3  41 
3  44 
3  47 
3  50 


3  58 

4  2 


15 
18 
21 
24 
27 


10°  11°  12°  13°  14°  15°  16° 


3 
3 

3  9 
3  10 
3  12 


21 
1 
46 
36 
28 


3  22 
3  1 
3  15 
3  12 
3  11 


30 
8 
52 
41 
33 


20« 


22= 


>'8 

App 
Alt. 


39 
15 
59 

47 
38 


3  26 
3  21 
3  17 
3  14 
3  12 


3  10 
3  9 
3  9 
3  10 
3  11 


13 
14 
16 
18 
20 


3  22 
3  25 
3  27 
3  29 
3  32 


3  34 
3  36 
3  39 
3  42 
3  46 


53 

56 

59 

1 

4 


4  7 
4  10 
4  13 
4  16 


47 
50 
53 
55 
58 


12 
13 
14 
16 
18 


11 
10 
10 
9 
10 


3  30 
3  24 
3  20 
3  17 
3  14 


47 
30 
12 

58 
47 


3  38 
3  31 
3  26 
3  22 
3  1 


3  20 

3  22 
3  24 
3  26 

3  28 


11 
12 
13 
15 

17 


12 
11 
11 
10 
10 


3  30 
3  32 
3  35 
3  37 
3  40 


4  1 
4  3 
4  6 


42 
45 
47 
50 
52 


3  18 
3  20 
3  22 
3  23 
3  25 


3  27 
3  29 
3  32 
3  34 
3  36 


38 
41 
43 
45 
47 


10 
11 
12 
14 


3  16  16 


6 
7 
8 
9 
10 


11 
12 
13 
14 
15 


3  ]4 
3  13 
3  12 
3  12 


17 
18 
19 
20 


3  15 


16 

18 
20 
21 
23 


3  25 
3  27 
3  29 
3  31 
3  33 


55 

57 


3  49 


35 
37 
39 
41 
43 


11 
11 
12 
13 
14 


21 

22 
23 
24 
25 


3  15 

3  16 
3  17 
3  18 
3  19 


3  20 
3  22 
3  24 
3  26 
3  28 


30 
31 
33 


26 
27 
28 
29 
30 


31 
32 
33 
34 
35 


36 
37 
38 
39 
40 

41 
42 
43 
44 
45 


TABLK  P.  EFFECT  OF  SHN's  PAR. 

To  be  subtracted  from  the 

Third  Correction. 

At)P 

Sun's  Apparent  Altitnd*.  | 

A  t. 

5 

10 

20 

30 

40 

50 

55 

If 

70 

80 

90 

5 

2 

2 

3 

3 

4 

5 

5 

10 

2 

3 

3 

4 

5 

6 

15 

3 

4 

4 

5 

ti 

7 

20 

4 

4 

5 

6 

7 

25 

5 

5 

6 

7 

7 

30 

6 

6 

7 

8 

35 

6 

7 

8 

40 

7 

8 

8 

45 

8 

8 

1  50 

8 

9 

1  55 

9 

46 
47 
48 
49 
50 

51 
52 
53 
54 
65 

56 
57 
58 
59 
60 

61 
62 
63 
64 
66 


TABLE  XXXIII.                    205 
THIRD  CORRECTION.  TO  APPARENT  DISTANCE  120». 

D'8 

App. 
Alt. 

APPARENT  ALTITUDE  OF  THE  SUN,  OR  STAR. 

App. 

Alt. 

24« 

26° 

280 

30° 

32° 

34° 

36° 

38° 

40° 

42° 

44° 

46° 

48° 

50° 

62° 

54° 

o 

6 
7 
8 
9 
10 

11 
12 
13 
14 
15 

/  n 

5   15 

4  45 
4  25 
4  9 
3  57 

5  32 
5  0 
4  38 
4  20 
4  7 

1    II 

5  49 
5  15 
4  51 
4  31 
4  17 

t    n 

6  6 
5  30 
5  4 
4  43 

4  27 

1    n 

6  23 
5  45 
5  17 
4  55 
4  37 

1    II 

6  41 
6  0 
5  30 

5  7 

4  47 

/  II 

6  58 
6  15 
5  43 
5  18 
4  57 

4  42 
4  28 
4  16 
4  6 
3  58 

/  II 

7  14 
6  29 
5  56 
5  28 
5  7 

/  II 

7  30 
6  43 
6  8 
5  38i 
5  17 

7  46 
6  56 
6  20 
5  49 

5  27 

1    II 

8  2 
7  8 
6  31 
6  0 
5  37 

8  17 
7  21 
6  42 
6  10 
5  46 

1    II 

8  31 

7  33 
6  53 
6  20 
5  55 

1    II 

8  44 
7  45 
7  3 
6  29 
6  3 

/  n 

8  57 
7  57 
7  13 

1    II 
9  9 

0 

6 

7 

8 

9 

10 

3  47 
3  39 
3  32 
3  27 
3  23 

3  56 
3  47 
3  39 
3  33 

3  29 

4  5 
3  55 
3  46 
3  39 
3  34 

4  14 
4  3 
3  53 
3  46 
3  40 

4  23 
4  11 
4  0 
3  52 
3  46 

4  32 
4  19 
4  8 
3  59 
3  52 

4  51 

4  36 
4  24 
4  13 
4  4 

4  59 
4  44 
4  31 
4  20 
4  11 

5  8 
4  52 
4  38 
4  27 
4  18 

5  17 

5  0 
4  46 
4  34 
4  24 

5  25 
5  7 
4  53 
4  40 

5  33 
5  14 

11 
12 
13 
14 
15 

16 
17 

18 
19 
20 

3  20 
3  18 
3  16 
3  15 
3  14 

3  25 
3  22 
3  20 
3  18 
3  16 

3  30 
3  27 
3  24 
3  21 
3  19 

3  36 
3  32 
3  28 
3  25 
3  23 

3  41 
3  36 
3  32 
3  29 
3  27 

3  46 
3  41 
3  37 
3  33 
3  31 

3  52 
3  47 
3  42 
3  38 
3  35 

3  58 
3  52 
3  47 
3  43 
3  39 

4  4 
3  58 
3  52 
3  47 
3  43 

4  10 
4  3 
3  57 

4  16 

16 
17 
18 
19 

20 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

3  13 
3  12 
3  12 
3  12 
3  12 

3  15 
3  14 
3  13 
3  13 
3  13 

3  17 
3  16 
3  15 
3  15 
3  15 

3  21 
3  19 
3  18 
3  17 
3  17 

3  24 
3  22 
3  21 
3  20 
3  19 

3  28 
3  26 
3  24 
3  23 
3  21 

3  32 
3  29 
3  27 
3  26 

3  36 
3  33 

21 
22 
23 
24 
25 

26 
27 
28 
29 
30 

31 
32 
33 
34 
35 

3  13 
3  14 

3  15 
3  16 
3  17 

3  14 
3  14 
3  14 
3  15 
3  16 

3  15 
3  15 
3  15 
3  15 
3  16 

3  16 
3  16 
3  16 
3  16 
3  16 

3  18 
3  18 
3  18 

3  20 

3  18 
3  19 
3  21 
3  22 
3  24 

3  17 
3  18 
3  19 
3  20 

3  17 
3  18 

36 
37 
38 
39 
40 

3  26 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 

41 
42 
43 
44 
45 

46 
47 
48 
49 
50 

46 
47 
48 
49 
50 

51 
52 
53 
54 
55 

56 

57 
58 
59 
60 

51 

52 
53 
54 
55 

56 
57 
58 
59 
60 

fil 
62 
63 
64 
65 

61 
62 
63 
64 
65 

24° 

26o 

28" 

30° 

32° 

34° 

380 

40° 

42° 

440 

46° 

48° 

50° 

52° 

54° 

206 

TABLE 

XXXIV 

• 

PROPORTIONAL  LOGARITHMS. 

1.  I 

I.    m.  h.    m. 

b.    m. 

1.    in. 

D            1 

h.    m. 

a        , 

1.    m. 

o         ' 

ix.    m. 

o        > 

h.    m. 

h.    m 

h.    m. 

a. 

( 

)    o|< 

)     1 

0     2 

0     3 

0     4 

0     50     6 

0     7 

0     8  0     9| 

0 

i 

i 

J. 2553 

1.9542 

1.7782 

1.6532 

1.5563 

1.4771 

1.4102 

1.3522 

1.3010 

0 

1    < 

1.0334 

2481 

9506 

7757 

6514 

5549 

4759 

4091 

3513 

3002 

1 

2    : 

J.7324 

2410 

9471 

7734 

6496 

5534 

4747 

4081 

3504 

2994 

2 

3 

5563 

2341 

9435 

7710 

6478 

5520 

4735 

4071 

3495 

2986 

3 

4 

4314 

2272 

9400 

7686 

6460 

5506 

4723 

4061 

3486 

2978 

4 

5  . 

J. 3345 

2.2205 

1.9365 

1.7663 

1.6443 

1.5491 

1.4711 

1.4050 

1.3477 

1.2970 

5 

6 

2553 

2139 

9331 

7639 

6425 

5477 

4699 

4040 

3468 

2962 

6 

7 

1883 

2073 

9296 

7616 

6407 

5463 

4688 

4030 

3459 

2954 

7 

8 

1303 

2009 

9262 

7593 

6390 

5449 

4676 

4020 

3450 

2946 

8 

9 

0792 

1946 

9228 

7570 

6372 

5435 

4664 

4010 

3441 

2939 

9 

10 

3.0334 

2.1883 

1.9195 

1.7547 

1.6355 

1.5421 

1.4652 

1.4000 

1.3432 

1.2931 

10 

11 

2.9920 

1822 

9162 

7524 

6338 

5407 

4640 

3989 

3423 

2923 

11 

12 

9542 

1761 

9128 

7501 

6320 

5393 

4629 

3979 

3415 

2915 

12 

13 

9195 

1701 

9096 

7479 

6303 

5379 

4617 

3969 

3406 

2907 

13 

14 

8873 

1642 

9063 

7456 

6286 

5365 

4606 

3959 

3397 

2899 

14 

15 

2.8573 

2.1584 

1.9031 

1.7434 

1.6269 

1.5351 

1.4594 

1.3949 

1.3388 

1.2891 

15 

16 

8293 

1526 

8999 

7412 

6252 

5337 

4582 

3939 

3379 

■  2883 

16 

17 

8030 

1460 

8967 

7390 

6235 

5324 

4571 

3929 

3371 

2876 

17 

18 

7782 

1413 

8935 

7368 

6218 

5310 

4559 

3919 

3362 

2868 

18 

19 

7547 

1358 

8904 

7346 

6201 

5296 

4548 

3910 

3353 

2860 

19 

20 

2.7324 

2.1303 

1.8873 

1.7324 

1.6185 

1.5283 

1.4536 

1.3900 

1.3345 

1.2852 

20 

21 

7112 

1249 

8842 

7302 

6168 

5269 

4525 

3890 

3336 

2845 

21 

22 

6910 

1196 

8811 

7281 

6151 

5256 

4514 

3880 

3327 

2837 

22 

23 

6717 

1143 

8781 

7259 

6135 

5242 

4502 

3870 

3319 

2829 

23 

24 

6532 

1091 

8751 

7238 

6118 

5229 

4491 

3860 

3310 

2821 

24 

25 

2.6355 

2.1040 

1.8721 

1.7217 

1.6102 

1.5215 

1.4480 

1.3851 

1  3301 

1.2814 

25 

26 

6185 

0989 

8691 

7196 

6085 

5202 

4468 

3841 

3293 

2806 

26 

27 

6021 

0939 

8661 

7175 

6069 

5189 

4457 

3831 

3284 

2798 

27 

28 

5863 

0889 

8632 

7154 

6053 

5175 

4446 

3821 

3276 

2791 

28 

29 

5710 

0840 

8602 

7133 

6037 

5162 

4435 

3812 

3267 

2783 

29 
30 

30 

2.5563 

2.0792 

1.8573 

1.7112 

1.6021 

1.5149 

1.4424 

1.3802 

1  3259 

1.2775 

31 

5421 

0744 

8544 

7091 

6005 

5136 

4412 

3792 

3250 

2768 

31 

32 

5283 

0696 

8516 

7071 

5989 

5123 

4401 

3783 

3242 

2760 

32 

33 

5149 

0649 

8487 

7050 

5973 

5110 

4390 

3773 

3233 

2753 

33 

34 

5019 

0603 

8459 

7030 

5957 

5097 

4379 

3764 

3225 

2745 

34 
35 

35 

2.4894 

2.0557 

1.8431 

1.7010 

1.5941 

1.5084 

1.4368 

1.3754 

1.3216 

1.2738 

36 

4771 

0512 

8403 

6990 

5925 

5071 

4357 

3745 

3208 

2730 

36 

37 

4652 

0467 

8375 

6970 

5909 

5058 

4346 

3735 

3199 

2722 

37 

38 

4536 

0422 

8348 

6950 

5894 

5045 

4335 

3726 

3191 

2715 

38 

39 

4424 

0378 

8320 

6930 

5878 

5032 

4325 

3716 

3183 

2707 

39 

40 

2.4314 

2.0334 

1.8293 

1.6910 

1.5863 

1.5019 

1.4314 

1.3707 

1.3174 

1.2700 

40 

41 

4206 

0291 

8266 

6890 

5847 

5007 

4303 

3697 

3166 

2692 

41 

42 

4102 

0248 

8239 

6871 

5832 

4994 

4292 

3688 

3158 

2685 

42 

43 

4000 

0206 

8212 

6851 

5816 

4981 

4281 

3678 

3149 

2678 

43 

44 

3900 

0164 

8186 

6832 

5801 

4969 

4270 

3669 

3141 

2670 

44 

45 

2.3802 

2.0122 

1.8159 

1.6812 

1.5786 

1.4956 

1.4260 

1.3660 

1.3133 

1.2663 

45 

46 

3707 

0081 

8133 

6793 

5771 

4943 

4249 

3650 

3124 

2655 

46 

47 

3613 

0040 

8107 

6774 

5755 

4931 

4238 

3641 

3116 

2648 

47 

48 

3522 

0000 

8081 

6755 

5740 

4918 

4228 

3632 

3108 

2640 

48 

49 

3432 

1.9960 

8055 

6736 

5725 

4906 

4217 

3623 

3100 

2633 

49 

50 

2.3345 

1.9920 

1.8030 

1.6717 

1.5710 

1.4894 

1.4206 

1.3613 

1  3091 

1.2626 

50 

51 

3259 

9881 

8004 

6698 

5695 

4881 

4196 

3604 

3083 

2618 

51 

52 

3174 

9842 

7979 

6679 

5680 

4869 

4185 

3595 

3075 

2611 

52 

53 

3091 

9803 

7954 

6661 

5666 

4856 

4175 

3586 

3067 

2604 

53 

54 
55 

3010 

9765 

7929 

6642 

5651 

4844 

4164 

3576 

3059 

2596 

54 

2.2931 

1.9727 

1.7904 

1.6624 

1.5636 

1.4832 

1.4154 

1.3567 

1.3051 

1.2589 

55 

56 

2852 

9690 

7879 

6605 

5621 

4820 

4143 

3558 

3043 

2582 

56 

57 

2775 

9652 

7855 

6587 

5607 

4808 

4133 

3549 

3034 

2574 

57 

58 

2700 

9615 

7830 

6568 

5592 

4795 

4122 

3540 

3026 

2567 

58 

59 

2626 

9579 

7806 

6550 

5578 

4783 

4112 

3531 

3018 

2560 

59 

0     0 

0     ] 

0     2 

0     3 

0     4 

0     5 

0     6 

0     7 

0     8 

0     9 

207 

TABLE 

XXXIV 

• 

• 

PROPORTIONAL  LOGARITHMS 

— tl      1 

/  ' 

»     1 

o         ' 

0         1 

o          . 

6                      I 

o         ' 

o         , 

Q                          1 

■.  1 

L.    m.l 

1.     m. 

b.    m. 

b.    m. 

1.     m. 

h.    m. 

b.     m. 

h.     m. 

h.     m. 

h.     m. 

• 

( 

3    100    11 

0    12 

0    13 

0    14 

0     15  0     16 

0    17 

0    18 

0     19 

0 

1.2553 

1.2139 

1.1761 

1.1413 

1.1091 

1.0792 

1.0512 

1.0248 

1.0000 

0.9765 

0 

1 

2545 

2132 

1755 

1408 

1086 

07»7 

0507 

0244 

0.9996 

9761 

1 

2 

2538 

2126 

1749 

1402 

1081 

0782 

0502 

0240 

9992 

9758 

2 

3 

2531 

2119 

1743 

1397 

1076 

0777 

0498 

0235 

9988 

9754 

3 

4 

2524 

2113 

1737 

1391 

1071 

0773 

0493 

0231 

9984 

9750 

4 
5 

5 

1.2517 

1.2106 

1.1731 

1.1386 

1.1066 

1.0768 

1.0489 

1.0227 

0.9980 

0.9746 

6 

2510 

2099 

1725 

1380 

1061 

0763 

0484 

0223 

9976 

9742 

6 

7 

2502 

2093 

1719 

1374 

1055 

0758 

0480 

0219 

9972 

9739 

7 

8 

2495 

2086 

1713 

1369 

1050 

0753 

0475 

0214 

9968 

9735 

8 

9 

2488 

2080 

1707 

1363 

1045 

0749 

0471 

0210 

9964 

9731 

9 

10 

1.2481 

1.2073 

1.1701 

1.1358 

1.1040 

1.0744 

1.0467 

1.0206 

0.9960 

0.9727 

10 

11 

2474 

2067 

1695 

1352 

1035 

0739 

0462 

0202 

9956 

9723 

11 

12 

2467 

2061 

1689 

1347 

1030 

0734 

0458 

0197 

9952 

9720 

12 

13 

2460 

2054 

1683 

1342 

1025 

0730 

0453 

0193 

9948 

9716 

13 

14 

2453 

2048 

1677 

1336 

1020 

0725 

0449 

0189 

9944 

9712 

14 

15 

1.2445 

1.2041 

1.1671 

1.1331 

1.1015 

1.0720 

1.0444 

1.0185 

0.9940 

0.9708 

15 

16 

2438 

2035 

1665 

1325 

1009 

0715 

0440 

0181 

9936 

9705 

16 

17 

2431 

2028 

1660 

1320 

1004 

0711 

0435 

0176 

9932 

9701 

17 

18 

2424 

2022 

1654 

1314 

0999 

0706 

0431 

0172 

9928 

9697 

18 

19 

2417 

2016 

1648 

1309 

0994 

0701 

0426 

0168 

9924 

9693 

19 

20 

1.2410 

1.2009 

1.1642 

1.1303 

1.0989 

1.0696 

1.0422 

1.0164 

0.9920 

0.9690 

20 

21 

2403 

2003 

1636 

1298 

0984 

0692 

0418 

0160 

9916 

9686 

21 

22 

2396 

1996 

1630 

1292 

0979 

0687 

0413 

0156 

9912 

9682 

22 

23 

2389 

1990 

1624 

1287 

0974 

0682 

0409 

0151 

9908 

9678 

23 

24 

2382 

1984 

1619 

1282 

0969 

0678 

0404 

0147 

9905 

9675 

24 
25 

25 

1.2375 

1.1977 

1.1613 

1.1276 

1.0964 

1.0673 

1.0400 

1.0143 

0.9901 

0.9671 

26 

2368 

1971 

1607 

1271 

0959 

0668 

0395 

0139 

9897 

9667 

26 

27 

2362 

1965 

1601 

1266 

0954 

0663 

0391 

0135 

9893 

9664 

27 

28 

2355 

1958 

1595 

1260 

0949 

0659 

0387 

0131 

9889 

9660 

28 

29 

2348 

1952 

1589 

1255 

0944 

.  0654 

0382 

0126 

9885 

9656 

29 

30 

1.2341 

1.1946 

1.1584 

1.1249 

1.0939 

1.0649 

1.0378 

1.0122 

0.9881 

0.9652 

30 

31 

2334 

1939 

1578 

1244 

0934 

0645 

0374 

0118 

9877 

9649 

31 

32 

2327 

1933 

1572 

1239 

0929 

0640 

0369 

0114 

9873 

9645 

32 

33 

2320 

1927 

1566 

1233 

,0924 

0635 

0365 

0110 

9869 

9641 

33 

34 
35 

2313 

1921 

1561 

1228 

0919 

0631 

0360 

0106 

9865 

9638 

34 

1.2307 

1.1914 

1.1555 

1.1223 

1.0914 

1.0626 

1.0356 

1.0102 

0.9861 

0.9634 

35 

36 

2300 

1908 

1549 

1217 

0909 

0621 

0352 

0098 

9858 

9630 

36 

37 

2293 

1902 

1543 

1212 

0904 

0617 

0347 

0093 

9854 

9626 

37 

38 

2286 

1896 

1538 

1207 

0899 

0612 

0343 

0089 

9850 

9623 

38 

39 

2279 

1889 

1532 

1201 

0894 

0608 

0339 

0085 

9846 

9619 

39 

40 

1.2272 

1.1883 

1.1526 

1.1196 

1.0889 

1.0603 

1.0334 

1.0081 

0.9842 

0.9615 

40 

41 

2266 

1877 

1520 

1191 

0884 

0598 

0330 

0077 

9838 

9612 

41 

42 

2259 

1871 

1515 

1186 

0880 

0594 

0326 

0073 

9834 

9608 

42 

43 

2252 

1865 

1509 

1180 

0875 

0589 

0321 

0069 

9830 

9604 

43 

44 

2245 

1859 

1503 

1175 

0870 

0585 

0317 

0065 

9827 

9601 

44 

45 

1.2239 

1.1852 

1.1498 

1.1170 

1.0865 

1.0580 

1.0313 

1.0061 

0.9823 

0.9597 

45 

46 

2232 

1846 

1492 

1164 

0860 

0575 

0308 

0057 

9819 

9593 

46 

47 

'2-225 

1840 

1486 

1159 

0855 

0571 

0304 

0053 

9815 

9590 

47 

48 

2218 

1834 

1481 

1154 

0850 

0566 

0300 

0049 

9811 

9586 

48 

49 

2212 

1.1828 

1475 

1149 

0845 

0562 

0295 

0044 

9807 

9582 

49 
50 

50 

1.2205 

1.1822 

1.1469 

1.1143 

1.0840 

1.0557 

1.0291 

1.0040 

0,9803 

0.9579 

51 

2198 

1816 

1464 

1138 

0835 

0552 

0287 

0036 

9800 

9575 

51 

52 

2192 

1809 

1458 

1133 

0831 

0548 

0282 

0032 

9796 

9571 

52 

53 

2185 

1803 

1452 

1128 

0826 

0543 

0278 

0028 

9792 

9568 

53 

54 

2178 

1797 

1447 

1123 

0821 

0539 

0274 

0024 

9788 

9564 

54 

55 

1.2172 

1.1791 

1.1441 

1.1117 

1.0816 

1.0534 

1.0270 

1.0020 

0.9784 

0.9561 

55 

56 

2165 

1785 

1436 

1112 

0811 

0530 

0265 

0016 

9780 

9557 

56 

57 

2159 

1779 

1430 

1107 

0806 

0525 

0261 

0012 

9777 

9553 

57 

58 

2152 

1773 

1424 

1102 

0801 

0521 

0257 

0008 

9773 

9550 

58 

59 

2145 

1767 

1419 

1097 

0797 

0516 

0252 

0004 

9769 

9546 

59 

0    10 

0    11 

0    12 

0    13 

0    14 

0    15 

0    16 

0    17 

0    18 

0    19 

14 

208 

TABLE  XXXIV. 

PROPORTIONAL  LOGARITHMS. 

• 

1  • 
I.    m.  ii 

1  < 

>.   m.  i 

•  •    >  < 
1.    m.  b.    m.  1 

1         I      c 

1.    m.  1 

*   0         ' 

1.    m.  h.    m. 

a.   m. 

o       « 

h.    m. 

O         t 

h.        m. 

o       / 

h.   m. 

O          1 

h.   m. 

C 

>    20( 

)       21  ( 

)   22  ( 

)   23  0   24  ( 

)    25 

0   26 

0   27  0   28l0   29|0   30| 

0   31 

0  ( 

).9542 

9331 

9128 

8935 

8751 

8573 

8403 

8239 

8081 

7929 

7782 

7639 

0 

1 

9539 

9327 

9125 

8932 

8748 

8570 

8400 

8236 

8079 

7926 

7779 

7637 

1 

2 

9535 

9324 

9122 

8929 

8745 

8568 

8397 

8234 

8076 

7924 

7777 

7634 

2 

3 

9532 

9320 

9119 

8926 

8742 

8565 

8395 

8231 

8073 

7921 

7774 

7632 

3 

4 
"  5  ( 

9528 

9317 

9115 

8923 

8739 

8562 

8392 

8228 

8071 

7919 

7772 

7630 

4 
6 

3.9524 

9313 

9112 

8920 

8736 

8559 

8389 

8226 

8068 

7916 

7769 

7627 

6 

9521 

9310 

9109 

8917 

8733 

8556 

8386 

8223 

8066 

7914 

7767 

7625 

6 

7 

9517 

9306 

9106 

8913 

8730 

8253 

8384 

8220 

8063 

7911 

7765 

7623 

7 

8 

9514 

9303 

9102 

8910 

8727 

8550 

8381 

8218 

8061 

7909 

7762 

7620 

8 

9 
10 

9510 

9300 

9099 

8907 

8724 

8547 

8378 

8215 

8058 

7906 

7760 

7618 

9 

0.9506 

9296 

9096 

8904 

8721 

8544 

8375 

8212 

8055 

7904 

7757 

7616 

10 

11 

9503 

9293 

9092 

8901 

8718 

8542 

8372 

8210 

8053 

7901 

7755 

7613 

11 

12 

9499 

9289 

9089 

8898 

8715 

8539 

8370 

8207 

8050 

7899 

7753 

7611 

12 

13 

9496 

9286 

9086 

8895 

8712 

8536 

8367 

8204 

8048 

7896 

7750 

7609 

13 

14 
16 

9492 

9283 

9083 

8892 

8709 

8533 

8364 

8202 

8045 

7894 

7748 

7607 

14 
15 

0.9488 

9279 

9079 

8888 

8706 

8530 

8361 

8199 

8043 

7891 

7745 

7604 

16 

9485 

9276 

9076 

8885 

8703 

8527 

8359 

8196 

8040 

7889 

7743 

7602 

16 

17 

9481 

9272 

9073 

8882 

8700 

8524 

8356 

8194 

8037 

7887 

7741 

7600 

17 

18 

9478 

9269 

9070 

8879 

8697 

8522 

8353 

8191 

8035 

7884 

7738 

7597 

18 

19 
20 

9474 

9266 

9066 

8876 

8694 

8519 

8350 

8188 

8032 

7882 

7736 

7595 

19 
20 

0.9471 

9262 

9063 

8873 

8691 

8516 

8348 

8186 

8030 

7879 

7734 

7593 

21 

9467 

9259 

9060 

8870 

8688 

8513 

8345 

8183 

8027 

7877 

7731 

7590 

21 

22 

9464 

9255 

9057 

8867 

8685 

8510 

8342 

8181 

8025 

7874 

7729 

7588 

22 

23 

9460 

9252 

9053 

8864 

8682 

8507 

8339 

8178 

8022 

7872 

7726 

7586 

23 

24 

9456 

9249 

9050 

8861 

8679 

8504 

8337 

8175 

8020 

7869 

7724 

7583 

24 
25 

25 

0.9453 

9245 

9047 

8857 

8676 

8502 

8334 

8173 

8017 

7867 

7722 

7581 

26 

9449 

9242 

9044 

8854 

8673 

8499 

8331 

8170 

8014 

7864 

7719 

7579 

26 

27 

9446 

9238 

9041 

8851 

8670 

8496 

8328 

8167 

8012 

7862 

7717 

7577 

27 

28 

9442 

9235 

9037 

8848 

8667 

8493 

8326 

8165 

8009 

7859 

7714 

7574 

28 

29 
30 

9439 

9232 

9034 

8845 

8664 

8490 

8323 

8162 

8007 

7857 

7712 

7572 

29 
30 

0.9435 

9228 

9031 

8842 

8661 

8487 

8320 

8159 

8004 

7855 

7710 

7570 

31 

9432 

9225 

9028 

8839 

8658 

8484 

8318 

8157 

8002 

7852 

7707 

7567 

31 

32 

9428 

9222 

9024 

8836 

8655 

8482 

8315 

8154 

7999 

7850 

7705 

7565 

32 

33 

9425 

9218 

9021 

8833 

8652 

8479 

8312 

8152 

7997 

7847 

7703 

7563 

33 

34 
35 

9421 

9215 

9018 

8830 

8649 

8476 

8309 

8149 

7994 

7845 

7700 

7560 

34 

0.9418 

9212 

9015 

8827 

8646 

8473 

8307 

8146 

7992 

7842 

7698 

7558 

35 

36 

9414 

9208 

9012 

8824 

8643 

8470 

8304 

8144 

7989 

7840 

7696 

7556 

36 

37 

9411 

9205 

9008 

8821 

8640 

8467 

8301 

8141 

7987 

7837 

7693 

7554 

37 

38 

9407 

9201 

9005 

8817 

8637 

8465 

8298 

8138 

7984 

7835 

7691 

7551 

38 

39 
40 

9404 

9198 

9002 

8814 

8635 

8462 

8296 

8136 

7981 

7832 

7688 

7549 

39 
40 

0.9400 

9195 

8999 

8811 

8632 

8459 

8293 

8133 

7979 

7830 

7686 

7547 

41 

9397 

9191 

8996 

8808 

8629 

8456 

8290 

8131 

7976 

7828 

7684 

7544 

41 

42 

9393 

9188 

8992 

8805 

8626 

8453 

8288 

8128 

7974 

7825 

7681 

7542 

42 

43 

9390 

9185 

8989 

8802 

8623 

8451 

8285 

8125 

7971 

7823 

7679 

7540 

43 

44 

45 

9386 

9181 

8986 

8799 

8620 

8448 

8282 

8123 

7969 

7820 

7677 

7538 

44 

0.9383 

9178 

8983 

8796 

8617 

8445 

8279 

8120 

7966 

7818 

7674 

7535 

45 

46 

9379 

9175 

8980 

8793 

8614 

8442 

8277 

8117 

7964 

7815 

7672 

7533 

46 

47 

9376 

9172 

8977 

8790 

8611 

8439 

8274 

8115 

7961 

7813 

7670 

7531 

47 

48 

9372 

9168 

8973 

8787 

8608 

8437 

8271 

8112 

7959 

7811 

7667 

7528 

48 

49 
50 

9369 

9165 

8970 

8784 

8605 

8434 

8269 

8110 

7956 

7808 

7665 

7526 

49 

0.9365 

9162 

8967 

8781 

8602 

8431 

8266 

8107 

7954 

7806 

7663 

7524 

50 

51 

9362 

9158 

8964 

8778 

8599 

8428 

8263 

8104 

7951 

7803 

7660 

7522 

61 

52 

9358 

9155 

8961 

8775 

8597 

8425 

8261 

8102 

7949 

7801 

7658 

7519 

52 

53 

3955 

9152 

8958 

8772 

8594 

8423 

8258 

8099 

7946 

7798 

7655 

7517 

53 

54 
55 

9351 

9148 

8954 

8769 

8591 

8420 

8255 

8097 

7944 

7796 

7653 

7515 

54 
55 

0.9348 

9145 

8951 

8766 

8588 

8417 

8253 

8094 

7941 

7794 

7651 

7513 

56 

9344 

9142 

8948 

8763 

8585 

8414 

8250 

8091 

7939 

7791 

7648 

7510 

56 

57 

9341 

9138 

8945 

8760 

8582 

8411 

8247 

8089 

7936 

7789 

7646 

7508 

57 

58 

9337 

9135 

8942 

8757 

8579 

8409 

8244 

8086 

7934 

7786 

7644 

7506 

58 

59 

9334 

9132 

8939 

8754 

8576 

8406 

8242 

8084 

7931 

7784 

7641 

7503 

59 

0    2G 

0   21 

0   22 

0   23 

0   24 

0   25 

0   26 

0   27 

0   28 

0   29 

0   30 

0   31 

- 

TABLE  XXXIV. 

' 

209 

PROPORTIONAL  LOGARITHMS 

"  1 

>     1 

O           ' 

»    ' 

>    1   < 

>   1  < 

'1 

b    /  < 

>    / 

i    / 

'         1 

«    1 

" 

..  1 

n.    m. 

h.         m. 

li.   m. 

1.       m. : 

1.   m.  h.   m.| 

1.   m.  1 

1.   m. 

h.   m.  1 

1.   nL. 

h.        m. 

1.    m. 

a 

( 

)    32 

3   33 

3   34 

3   35  ( 

3   36 

)   37  ( 

)  -38 

3   39 

3   40  0   4110   42| 

0   43 

0  ( 

3.7501 

7368 

7238 

7112 

6990 

6871 

6755 

6642 

6532 

6425 

6320 

6218 

0 

1 

7499 

7365 

7236 

7110 

6988 

6869 

6753 

6640 

6530 

6423 

6319 

6216 

1 

2 

7497 

7363 

7234 

7108 

6986 

6867 

6751 

6638 

6529 

6421 

6317 

6215 

2 

3 

7494 

7361 

7232 

7106 

6984 

6865 

6749 

6637 

6527 

6420 

6315 

6213 

3 

4 
5 

7492 

7359 

7229 

7104 

6982 

6863 

6747 

6635 

6525 

6418 

6313 

6211 

4 

J. 7490 

7357 

7227 

7102 

6980 

6861 

6745 

6633 

6523 

6416 

6312 

6210 

5 

6 

7488 

7354 

7225 

7100 

6978 

6859 

6743 

6631 

6521 

6414 

6310 

6208 

6 

7 

7485 

7352 

7223 

7098 

6976 

6857 

6742 

6629 

6519 

6413 

6308 

6206 

7 

8 

7483 

7350 

7221 

7096 

6974 

6855 

6740 

6627 

6518 

6411 

6306 

6205 

8 

9 
10 

7481 

7348 

7219 

7093 

6972 

6853 

6738 

6625 

6516 

6409 

6305 

6203 

9 

3.7479 

7346 

7217 

7091 

6970 

6851 

6736 

6624 

6514 

6407 

6303 

6201 

10 

11 

7476 

7344 

7215 

7089 

6968 

6849 

6734 

6622 

6612 

6406 

6301 

6200 

11 

12 

7474 

7341 

7212 

7087 

6966 

6847 

6732 

6620 

6510 

6404 

6300 

6198 

12 

13 

7472 

7339 

7210 

7085 

6964 

6845 

6730 

6618 

6509 

6402 

6298 

6196 

13 

14 
15 

7470 

7337 

7208 

7083 

6962 

6843 

6728 

6616 

6507 

6400 

6296 

6195 

14 

0.7467 

7335 

7206 

7081 

6960 

6841 

6726 

6614 

6505 

6398 

6294 

6193 

15 

16 

7465 

7333 

7204 

7079 

6958 

6840 

6725 

6612 

6503 

6397 

6293 

6191 

16 

17 

7463 

7330 

7202 

7077 

6956 

6838 

6723 

6611 

6501 

6395 

6291 

6190 

17 

18 

7461 

7328 

7200 

7075 

6954 

6836 

6721 

6609 

6500 

6393 

6289 

6188 

18 

19 

20 

7458 

7326 

7198 

7073 

6952 

6834 

6719 

6607 

6498 

6391 

6288 

6186 

19 

20 

0.7456 

7324 

7196 

7071 

6950 

6832 

6717 

6605 

7496 

6390 

6286 

6185 

21 

7454 

7322 

7193 

7069 

6948 

6830 

6715 

6603 

6494 

6388 

6284 

6183 

21 

22 

7452 

7320 

7191 

7067 

6946 

6828 

6713 

6601 

6492 

6386 

6282 

6181 

22 

23 

7450 

7317 

7189 

7065 

6944 

6826 

6711 

6600 

6491 

6384 

6281 

6179 

23 

24 
25 

.7447 

7315 

7187 

7063 

6942 

6824 

6709 

6598 

6489 

6383 

6279 

6178 

24 

0.7445 

7313 

7185 

7061 

6940 

6822 

6708 

6596 

6487 

6381 

6277 

6176 

25 

26 

7443 

7311 

7183 

7059 

6938 

6820 

6706 

6594 

6485 

6379 

6276 

6174 

26 

27 

7441 

7309 

7181 

7057 

6936 

6818 

6704 

6592 

6484 

6377 

6274 

6173 

27 

28 

7438 

7307 

7179 

7055 

6934 

6816 

6702 

6590 

6482 

6376 

6272 

6171 

28 

29 
30 

7436 

7304 

7177 

7052 

6932 

6814 

6700 

6589 

6480 

6374 

6271 

6169 

29 

0.7434 

7302 

7175 

7050 

6930 

6812 

6698 

6587 

6478 

6372 

6269 

6168 

30 

31 

7432 

7300 

7172 

7048 

6928 

6810 

6696 

6585 

6476 

6371 

6267 

6166 

31 

32 

7429 

7298 

7170 

7046 

6926 

6809 

6694 

6583 

6475 

6369 

6265 

6165 

32 

33 

7427 

7296 

7168 

7044 

6924 

6807 

6692 

6581 

6473 

6367 

6264 

6163 

33 

34 
35 

7425 

7294 

7166 

7042 

6922 

6805 

6691 

6579 

6471 

6365 

6262 

6161 

34 
35 

0.7423 

7291 

7164 

7040 

6920 

6803 

6689 

6578 

6469 

6364 

6260 

6160 

36 

7421 

7289 

7162 

7038 

6918 

6801 

6687 

6576 

6467 

6362 

6259 

6158 

36 

37 

7418 

7287 

7160 

7036 

6916 

6799 

6685 

6574 

6466 

6360 

6257 

6156 

37 

38 

7416 

7285 

7158 

7034 

6914 

6797 

6683 

6572 

6464 

6358 

6255 

6155 

38 

39 

~40 

7414 

7283 

7156 

7032 

6912 

6795 

6681 

6570 

6462 

6357 

6354 

6153 

39 

0.7412 

7281 

7154 

7030 

6910 

6793 

6679 

6568 

6460 

6355 

6252 

6151 

40 

41 

7409 

7279 

7152 

7028 

6908 

6791 

6677 

6567 

6459 

6353 

6250 

6150 

41 

42 

7407 

7276 

7149 

7026 

6906 

6789 

6676 

6565 

6457 

6351 

6248 

6148 

42 

43 

7405 

7274 

7147 

7024 

6904 

6787 

6674 

6563 

6455 

6350 

6247 

6146 

43 

44 

45 

7403 

7272 

7145 

7022 

6902 

6785 

6672 

6561 

6453 

6348 

6245 

6145 

44 

0.7401 

7270 

7143 

7020 

6900 

6784 

6670 

6559 

6451 

6346 

6243 

6143 

45 

46 

7398 

7268 

7141 

7018 

6898 

6782 

6668 

6558 

6450 

6344 

6242 

6141 

46 

47 

7396 

7266 

7139 

7016 

6896 

6780 

6666 

6556 

6448 

6343 

6240 

6140 

47 

48 

7394 

7264 

7137 

7014 

6894 

6778 

6664 

6554 

6446 

6341 

6238 

6138 

48 

49 
50 

7392 

7261 

7135 

7012 

6892 

6776 

6663 

6552 

6444 

6339 

6237 

6136 

49 

0.7390 

7259 

7133 

7010 

6890 

6774 

6661 

6550 

6443 

6338 

6235 

6135 

50 

51 

7387 

7257 

7131 

7008 

6888 

6772 

6659 

6548 

6441 

6336 

6233 

6133 

51 

52 

7385 

7255 

7129 

7006 

6886 

6770 

6657 

6547 

6439 

6334 

6232 

6131 

52 

53 

7383 

7253 

7127 

7004 

6884 

6768 

6655 

6545 

6437 

6332 

6230 

6130 

53 

54 
55 

7381 

7251 

7124 

7002 

6882 

6766 

6653 

6543 

6435 

6331 

6228 

6128 

54 

0.7379 

7249 

7122 

7000 

6881 

6764 

6651 

6541 

6434 

6329 

6226 

6126 

55 

56 

7376 

7246 

7120 

6998 

6879 

6763 

6650 

6539 

6432 

6327 

6225 

6125  '56 

57 

7374 

7244 

7118 

6996 

6877 

6761 

6648 

6538 

6430 

6325 

6223 

6123  57 

58 

7372 

7242 

7116 

6994 

6875 

6759 

6646 

6536 

6428 

6324 

6221 

6121  58 

59 

7370 

7240 

7114 

6992 

6873 

6757 

6644 

6534 

6427 

6322 

6220 

6120 

59 

- 

0      as 

0   33 

0   34 

0   3£ 

0   36 

0   37 

0   38 

0   39 

0   40 

0   41 

0   42 

0   43 

210 

TABLE  XXXIV. 
PROPORTIONAL  LOGARITHMS 

11 

9          1 

' 

' 

°     1 

1       /  6       , 

0         1 

»    y 

•    / 

'1 

«   "'  1 

i} 

•.  1 

k.    m. 

li.    m. 

h.    m. 

1.   m. 

li.   m.h.    m. 

tt.   m. 

1.   m. 

li.   m. 

ti.   m.i 

b.   m.| 

h.       m- 

t. 

( 

)    44 

0        45 

0   460   47  0   480*  49  0   50 

0   51 

0   520   53  0   54 

0   55 

0 

J. 6118 

6021 

5925 

5832 

5740 

5651 

5563 

5477 

5393 

5310 

5229 

5149 

0 

1 

6117 

6019 

5924 

5830 

5739 

5649 

5562 

5476 

5391 

5309 

5227 

5148 

1 

2 

6115 

6017 

5922 

5829 

5737 

5648 

5560 

5474 

5390 

5307 

5226 

5146 

2 

3 

6113 

6016 

5920 

5827 

5736 

5646 

5559 

5473 

5389 

5306 

5225 

5145 

3 

4 
5 

6112 

6014 

5919 

5826 

5734 

5645 

5557 

5471 

5387 

5305 

5223 

5144 

4 

[)-6110 

6013 

5917 

5824 

5733 

5643 

5556 

5470 

5386 

5303 

5222 

5143 

5 

6 

6108 

6011 

5916 

5823 

5731 

5642 

5554 

5469 

5384 

5302 

5221 

5141 

6 

7 

6107 

6009 

5914 

5821 

5730 

5640 

5553 

5467 

5383 

5300 

5219 

5140 

7 

8 

6105 

6008 

5913 

5819 

5728 

5639 

5551 

5466 

5382 

5299 

5218 

5139 

8 

9 
10 

6103 

6006 

5911 

5818 

5727 

5637 

5550 

5464 

5380 

5298 

5217 

5137 

9 

0.6102 

6005 

5909 

5816 

5725 

5636 

5549 

5463 

5379 

5296 

5215 

5136 

10 

11 

6100 

6003 

5908 

5815 

5724 

5635 

5547 

5461 

5377 

5295 

5214 

5135 

11 

12 

6099 

6001 

5906 

5813 

5722 

6633 

5546 

5460 

5376 

5294 

5213 

5133 

12 

13 

6097 

6000 

5905 

5812 

5721 

5632 

5544 

5459 

5375 

5292 

5211 

5132 

13 

14 
15 

6U95 

5998 

5903 

5810 

5719 

5630 

5543 

5457 

5373 

5291 

5210 

5131 

14 

0.6094 

5997 

5902 

5809 

5718 

5629 

5541 

5456 

5372 

5290 

5209 

5129 

15 

16 

6092 

5995 

5900 

5807 

5716 

5627 

5540 

5454 

5370 

5288 

5207 

5128 

16 

17 

6090 

5993 

5898 

5806 

5715 

5626 

5538 

5453 

5369 

5287 

5206 

5127 

17 

18 

6089 

5992 

5897 

5804 

5713 

5624 

5537 

5452 

5368 

5285 

5205 

5125 

18 

19 
20 

6087 

5990 

5895 

5803 

5712 

5623 

5536 

5450 

5366 

5284 

5203 

5124 

19 
20 

0.6085 

5989 

5894 

5801 

5710 

5621 

5534 

5449 

5365 

5283 

5202 

5123 

21 

6084 

5987 

5892 

5800 

5709 

5620 

5533 

5447 

5364 

5281 

5201 

5122 

21 

22 

6082 

5985 

5891 

5798 

5707 

5618 

5531 

5446 

5362 

5280 

5199 

5120 

22 

23 

6081 

5984 

5889 

5796 

5706 

5617 

5530 

5445 

5361 

5279 

5198 

5119 

23 

24 

6079 

5982 

5888 

5795 

5704 

5615 

5528 

5443 

5359 

5277 

5197 

5118 

24 

25 

0.6077 

5981 

0886 

5793 

5703 

5614 

5527 

5442 

5358 

5276 

5195 

5116 

25 

26 

6076 

5979 

5884 

5792 

5701 

5613 

5526 

5440 

5357 

5275 

5194 

5115 

26 

27 

6074 

5977 

5883 

5790 

5700 

5611 

5524 

5439 

5355 

5273 

5193 

5114 

27 

28 

6072 

5976 

5881 

5789 

5698 

5610 

5522 

5437 

5354 

5272 

5191 

5112 

28 

29 
30 

6071 

5974 

5880 

5787 

5697 

5608 

5521 

5436 

5353 

5271 

5190 

5111 

29 
30 

0.6069 

5973 

5878 

5786 

5695 

5607 

5520 

5435 

5351 

5269 

5189 

5110 

31 

6067 

5971 

5877 

5784 

5694 

5605 

5518 

5433 

5350 

5268 

5187 

5108 

31 

32 

6066 

5969 

5875 

5783 

5692 

5604 

5517 

5432 

5348 

5266 

5186 

5107 

32 

33 

6064 

5968 

5874 

5781 

5691 

5602 

5516 

5430 

5347 

5265 

5185 

5106 

33 

34 
35 

6063 

5966 

5872 

5780 

5689 

5601 

5514 

5429 

5346 

5264 

5183 

5105 

34 

0.6061 

5965 

5870 

5778 

5688 

5599 

5513 

5428 

5344 

5262 

5182 

5103 

35 

36 

6059 

5963 

5869 

5777 

5686 

5598 

5511 

5426 

5343 

5261 

5181 

5102 

36 

37 

6058 

5961 

5867 

5775 

5685 

5596 

5510 

5425 

5341 

5260 

5179 

5101 

37 

38 

6056 

5960 

5866 

5774 

5683 

5595 

5508 

5423 

5340 

5258 

5178 

5099 

38 

39 

40 

6055 

5958 

5864 

5772 

5682 

5594 

5507 

5422 

5339 

5257 

5177 

5098 

39 

0.6053 

5957 

5863 

5771 

5680 

5592 

5506 

5421 

5337 

5256 

5175 

5097 

40 

41 

6051 

5955 

5861 

5769 

5679 

5591 

5504 

5419 

5336 

5254 

5174 

5095 

41 

42 

6050 

5954 

5860 

5768 

5677 

5589 

5503 

5418 

5335 

5253 

5173 

5094 

42 

43 

6048 

5952 

5858 

5766 

5676 

5588 

5501 

5416 

5333 

5252 

5172 

5093 

43 

44 
45 

6046 

5950 

5856 

5765 

5674 

5586 

5500 

5415 

5332 

5250 

5170 

6092 

44 

0.6045 

5949 

5855 

5763 

5673 

5585 

5498 

5414 

5331 

5249 

5169 

5090 

45 

46 

6043 

5947 

5853 

5761 

5671 

5583 

5497 

5412 

5329 

5248 

5168 

5089 

46 

47 

6042 

5946 

5852 

5760 

5670 

5582 

5496 

5411 

5328 

5246 

5166 

5088 

47 

48 

6040 

5944 

5850 

5758 

5669 

5580 

5494 

5409 

5326 

5245 

5165 

5086 

48 

49 
50 

6038 

5942 

5849 

5757 

5667 

5579 

5493 

5408 

5325 

5244 

5164 

5085 

49 

0.6037 

5941 

5847 

5755 

5666 

5578 

5491 

5407 

5324 

5242 

5162 

5084 

50 

51 

6035 

5939 

5846 

5754 

5664 

5578 

5490 

5405 

5322 

5241 

5161 

5082 

51 

52 

6033 

5938 

5844 

5752 

5663 

5575 

5488 

5404 

5321 

5240 

6160 

5081 

52 

53 

6032 

5936 

5843 

5751 

5661 

5573 

5487 

5402 

5320 

5238 

5158 

5080 

53 

54 
55 

6030 

5935 

5841 

5749 

5660 

5572 

5486 

5401 

5318 

5237 

5157 

5079 

54 

0.6029 

5933 

5839 

5748 

5658 

5570 

5484 

5400 

5317 

5235 

5156 

5077 

55 

56 

6027 

5931 

5838 

5746 

5657 

5569 

5483 

5398 

5315 

5234 

5154 

5076 

56 

57 

6025 

5930 

5836 

5745 

5655 

5567 

5481 

5397 

5314 

5233 

5153 

5075 

57 

58 

6024 

5928 

5835 

5743 

5654 

5566 

5480 

5395 

5313 

5231 

5152 

5073 

58 

59 

6022 

5927 

5833 

5742 

5652 

5564 

5478 

5394 

5311 

5230 

5150 

5072 

59 

0    A4 

[0       At 

»0   46 

0   47 

0   48 

0   49 

0   50 

0   51 

0   52 

0   53 

0   54 

0   65 

211 

TABLE  XXXIV. 

• 

PROPORTIONAL  LOGARITHMS. 

"   a 
1.  I 

1.     m.  1 

/  < 
1.   m.  ; 

> 

1.    m. 

1.    m. 

1.    m. 

1.    m. 

0         ' 

n.        m. 

O          f 

\\.           ID. 

o 

h.   m. 

•    1 

\k.        m. 

0         1 

h.   m. 

#1 

1. 

( 

)    56 

)   57  ( 

)   58  0   59| 

I    01    1| 

1    2 

1    3 

1    4 

1     5 

I    6 

1     7 

0  ( 

J. 5071 

4994 

4918 

4844 

4771 

4699 

4629 

4559 

4491 

4424 

4357 

4292   0  1 

1 

5070 

4993 

4917 

4843 

4770 

4698 

4628 

4558 

4490 

4422 

4356 

4291   1  1 

2 

5068 

4991 

4916 

4842 

4769 

4697 

4626 

'4557 

4489 

4421 

4355 

4290 

2 

3 

5067 

4990 

4915 

4841 

4768 

4696 

4625 

4556 

4488 

4420 

4354 

4289 

3 

4 
5 

5066 

4989 

4913 

4839 

4766 

4695 

4624 

4555 

4486 

4419 

4353 

4288 

4 
5 

0.5064 

4988 

4912 

4838 

4765 

4693 

4623 

4554 

4485 

4418 

4352 

4287 

6 

5063 

4986 

4911 

4837 

4764 

4692 

4622 

4552 

4484 

4417 

4351 

4285 

6 

7 

5062 

4985 

4910 

4836 

4763 

4691 

4621 

4551 

4483 

4416 

4350 

4284 

7 

8 

5061 

4984 

4908 

4834 

4762 

4690 

4619 

4550 

4482 

4415 

4349 

4283 

8 

9 

10 

5059 

4983 

4907 

4833 

4760 

4689 

4618 

4549 

4481 

4414 

4347 

4282 

9 

0.5058 

4981 

4906 

4832 

4759 

4688 

4617 

4548 

4480 

4412 

4346 

4281 

10 

11 

6057 

4980 

4905 

4831 

4758 

4686 

4616 

4547 

4479 

4411 

4345 

4280 

11 

12 

5055 

4979 

4903 

4830 

4757 

4685 

4615 

4546 

4477 

4410 

4344 

4279 

12 

13 

5054 

4977 

4902 

4828 

4756 

4684 

4614 

4544 

4476 

4409 

4343 

4278 

13 

14 
15 

5053 

4976 

4901 

4827 

4754 

4683 

4612 

4543 

4475 

4408 

4342 

4277 

14 
15 

0.5051 

4975 

4900 

4826 

4753 

4682 

4611 

4542 

4474 

4407 

4341 

4276 

16 

5050 

4974 

4899 

4825 

4752 

4680 

4610 

4541 

4473 

4406 

4340 

4275 

16 

17 

5049 

4972 

4897 

4823 

4751 

4679 

4609 

4540 

4472 

4405 

4339 

4274 

17 

18 

5048 

4971 

4896 

4822 

4750 

4678 

4608 

4539 

4471 

4404 

4338 

4273 

18 

19 
20 

5046 

4970 

4895 

4821 

4748 

4677 

4607 

4538 

4469 

4402 

4336 

4271 

19 
20 

0.5045 

4969 

4894 

4820 

4747 

4676 

4606 

4536 

4468 

4401 

4335 

4270 

21 

5044 

4967 

4892 

4819 

4746 

4675 

4604 

4535 

4467 

4400 

4334 

4269 

21 

22 

5043 

4966 

4891 

4817 

4745 

4673 

4603 

4534 

4466 

4399 

4333 

4268 

22 

23 

5041 

4965 

4890 

4816 

4744 

4672 

4602 

4533 

4465 

4398 

4332 

4267 

23 

24 

5040 

4964 

4889 

4815 

4742 

4671 

4601 

4532 

4464 

4397 

4331 

4266 

24 
25 

25 

0.5039 

4962 

4887 

4814 

4741 

4670 

4600 

4531 

4463 

4396 

4330 

4266 

26 

5037 

4961 

4886 

4812 

4740 

4669 

4599 

4530 

4462 

4395 

4329 

4264 

26 

27 

5036 

4960 

4885 

4811 

4739 

4668 

4597 

4528 

4460 

4394 

4328 

4263 

27 

28 

5035 

4959 

4884 

4810 

4738 

4666 

4596 

4527 

4459 

4393 

4327 

4262 

28 

29 
30 

5034 

4957 

4882 

4809 

4736 

4665 

4595 

4526 

4458 

4391 

4326 

4261 

29 
30 

0.5032 

4956 

4881 

4808 

4735 

4664 

4594 

4525 

4457 

4390 

4325 

4260 

31 

5031 

4955 

4880 

4806 

4734 

4663 

4593 

4524 

4456 

4389 

4323 

4269 

31 

32 

5030 

4954 

4879 

4805 

4733 

4662 

4592 

4523 

4455 

4388 

4322 

4268 

32 

33 

5028 

4952 

4877 

4804 

4732 

4660 

4590 

4522 

4454 

4387 

4321 

4256 

33 

34 
35 

5027 

4951 

4876 

4803 

4730 

4659 

4589 

4520 

4453 

4386 

4320 

4255 

34 
35 

0.5026 

4950 

4875 

4801 

4729 

4658 

4588 

4519 

4452 

4385 

4319 

4254 

36 

5025 

4949 

4874 

4800 

4728 

4657 

4587 

4518 

4450 

4384 

4318 

4253 

36 

37 

5023 

4947 

4873 

4799 

4727 

4656 

4586 

4517 

4449 

4383 

4317 

4252 

37 

38 

5022 

4946 

4871 

4798 

4726 

4655 

4585 

4516 

4448 

4381 

4316 

4261 

38 

39 
40 

5021 

4945 

4870 

4797 

4724 

4653 

4584 

4515 

4447 

4380 

4315 

4250 

39 
40" 

0.5019 

4943 

4869 

4795 

4723 

4652 

4582 

4514 

4446 

4379 

4314 

4249 

41 

5018 

4942 

4868 

4794 

4722 

4651 

4581 

4512 

4445 

4378 

4313 

4248 

41 

42 

5017 

4941 

4866 

4793 

4721 

4650 

4580 

4511 

4444 

4377 

4311 

4247 

42 

43 

5016 

4940 

4865 

4792 

4720 

4649 

4579 

4510 

4443 

4376 

4310 

4246 

43 

44 

45 

5014 

4938 

4864 

4791 

4718 

4648 

4578 

4509 

4441 

4375 

4309 

4246 

44 
45 

0.5013 

4937 

4863 

4789 

4717 

4646 

4577  ,  4508 

4440 

4374 

4308 

4244 

46 

5012 

4936 

4861 

4788 

4716 

4645 

iJ7.5 

4507 

4439 

4373 

4307 

4243 

46 

47 

5011 

4935 

4860 

4787 

4715 

4644 

4574 

4506 

4438 

4372 

4306 

4241 

47 

48 

5009 

4933 

4859 

4786 

4714 

4643 

4573 

4505 

4437 

4370 

4305 

4240 

48 

49 
50 

5008 

4932 

4858 

4785 

4712 

4642 

4572 

4503 

4436 

4369 

4304 

4239 

49 

0.5007 

4931 

4856 

4783 

4711 

4640 

4571 

4502 

4435 

4368 

4303 

4238 

50 

51 

5005 

4930 

4855 

4782 

4710 

4639 

4570 

4501 

4434 

4367 

4302 

4237 

61 

52 

5004 

4928 

4854 

4781 

4709 

4638 

4569 

4500 

4433 

4366 

4301 

4236 

52 

53 

5003 

4927 

4853 

4780 

4708 

4637 

4567 

4499 

4431 

4365 

4300 

4235 

53 

54 
55 

5002 

4926 

4852 

4778 

4707 

4636 

4566 

4498 

4430 

4364 

4298 

4234 

54 
55 

0.5000 

4925 

4850 

■4777 

4705 

4635 

4565 

4497 

4429 

4363 

4297 

4233 

56 

4999 

4923 

4849 

4776 

4704 

4633 

4564 

4495 

4428 

4362 

4296 

4232 

56 

57 

4998 

4922 

4848 

4775 

4703 

4632 

4563 

4494 

4427 

4361 

4295 

4231 

57 

58 

4997 

4921 

4847 

4774 

4702 

4631 

4562 

4493 

4426 

4359 

4294 

4230 

58 

59 

4995 

4920 

4845 

4772 

4701 

4630 

4560 

4492 

4425 

4358 

4293 

4229 

59 

0    56 

0   67 

0   58 

0   59 

1    0 

1    1 

1    2 

1    3 

1    4 

1    5 

1    6 

1    7 

212 

TABLE  XXXIV. 

PROPORTIONAL  LOGARITHMS. 

"  0 

'  c 

>   '  c 

>    '  O     '  |0    '  |0     '  |0    '  (O    '  |0    '  (O    '  1 

0    r,o        '1 

rr 

a.  k 

m.  b 

k.   la.  h 

L.    m.  fa 

m.  h 

m.  h 

m.  h 

m.  fa 

m.  h 

m.  fa 

m.  h.    in.|ti 

k.   m. 

1. 

1 

8] 

91 

101 

11  1 

121 

131 

141 

15  1 

161 

17  ] 

1811 

19 

0  0 

.4228 

4164 

4102 

4040 

3979 

3919 

3860 

3802 

3745  ■  3688  | 

3632 

3576 

0 

1 

4227 

4163 

4101 

4039 

3978 

3919 

3859 

3801 

3744 

3687 

3631 

3576 

1 

2 

4226 

4162 

4100 

4038 

3977 

3918 

3858 

3800 

3743 

3686 

3630 

3575 

2 

3 

4224 

4161 

4099 

4037 

3976 

3917 

3857 

3799 

3742 

3685 

3629 

3574 

3 

4 
5  C 

4223 

4160 

4098 

4036 

3975 

3916 

3856 

3798 

3741 

3684 

3628 

3573 

4 

(.4222 

4159 

4097 

4035 

3974 

3915 

3856 

3797 

3740 

3683 

3627 

3572 

5 

6 

4221 

4158 

4096 

4034 

3973 

3914 

3855 

3796 

3739 

3682 

3626 

3571 

6 

7 

4220 

4157 

4095 

4033 

3972 

3913 

3854 

3795 

3738 

3681 

3625 

3570 

7 

8 

4219 

4156 

4093 

4032 

3971 

3912 

3853 

3794 

3737 

3680 

3624 

3569 

8 

9 
10  ( 

4218 

4155 

4092 

4031 

3970 

3911 

3852 

3793 

3736 

3679 

3623 

3568 

9 
10 

).4217 

4154 

4091 

4030 

3969 

3910 

3851 

3792 

3735 

3678 

3623 

3567 

11 

4216 

4153 

4090 

4029 

3968 

3909 

3850 

3792 

3734 

3677 

3622 

3566 

11 

12 

4215 

4152 

4089 

4028 

3967 

3908 

3849 

3791 

3733 

3677 

3621 

3565 

12 

13 

4214 

4151 

4088 

4027 

3966 

3907 

3848 

3790 

3732 

3676 

3620 

3565 

13 

14 
15  ( 

4213 

4150 

4087 

4026 

3965 

3906 

3847 

3789 

3731 

3675 

3619 

3564 

14 

).4212 

4149 

4086 

4025 

3964 

3905 

3846 

3788 

3730 

3674 

3618 

3563 

15 

16 

4211 

4147 

4085 

4024 

3963 

3904 

3845 

3787 

3729 

3673 

3617 

3562 

16 

17 

4210 

4146 

4084 

4023 

3962 

3903 

3844 

3786 

3728 

3672 

3616 

3561 

17 

18 

4209 

4145 

4083 

4022 

3961 

3902 

3843 

3785 

3727 

3671 

3615 

3560 

18 

; 

19 
20 

4207 

4144 

4082 

4021 

3960 

3901 

3842 

3784 

3727 

3670 

3614 

3559 

19 
20 

! 

0.4206 

4143 

4081 

4020 

3959 

3900 

3841 

3783 

3726 

3669 

3613 

3558 

21 

4205 

4142 

4080 

4019 

3958 

3899 

3840 

3782 

3725 

3668 

3612 

3557 

21 

22 

4204 

4141 

4079 

4018 

3957 

3898 

3839 

3781 

3724 

3667 

3611 

3556 

22 

23 

4203 

4140 

4078 

4017 

3956 

3897 

3838 

3780 

3723 

3666 

3610 

3555 

23 

24 

25 

4202 

4139 

4077 

4016 

3955 

3896 

3837 

3779 

3722 

3665 

3610 

3555 

24 

0.4201 

4138 

4076 

4015 

3954 

3895 

3836 

3778 

3721 

3664 

3609 

3554 

25 

26 

4200 

4137 

4075 

4014 

3953 

3894 

3835 

3777 

3720 

3663 

3608 

3553 

26 

27 

4199 

4136 

4074 

4013 

3952 

3893 

3834 

3776 

3719 

3663 

3607 

3552 

27 

28 

4198 

4135 

4073 

4012 

3951 

3892 

3833 

3775 

3718 

3662 

3606 

3551 

28 

29 
30 

4197 

4134 

4072 

4011 

3950 

3891 

3832 

3774 

3717 

3661 

3605 

3550  29 

0.4196 

4133 

4071 

4010 

3949 

3890 

3831 

3773 

3716 

3660 

3604 

3549 

30 

31 

4195 

4132 

4070 

4009 

3948 

3889 

3830 

3772 

3715 

3659 

3603 

3548 

31 

32 

4194 

4131 

4069 

4008 

3947 

3888 

3829 

3771 

3714 

3658 

3602 

3547 

32 

33 

4193 

4130 

4068 

4007 

3946 

3887 

3828 

3770 

3713 

3657 

3601 

3546 

33 

34 
35 

4192 

4129 

4067 

4006 

3945 

3886 

3827 

3769 

3712 

3656 

3600 

3545 

34 

0.4191 

4128 

4066 

4005 

3944 

3885 

3826 

3768 

3711 

3655 

3599 

3545 

35 

[ 

36 

4189 

4127 

4065 

4004 

3943 

3884 

3825 

3768 

3710 

3654 

3598 

3544 

36 

37 

4188 

4126 

4064 

4003 

3942 

3883 

3824 

3767 

3709 

3653 

3598 

3543 

37 

38 

4187 

4125 

4063 

4002 

3941 

3882 

3823 

3766 

3709 

3652 

3597 

3542 

38 

39 
40 

4186 

4124 

4062 

4001 

3940 

3881 

3822 

3765 

3708 

3651 

3596 

3541 

39 

0.4185 

4122 

4061 

4000 

3939 

3880 

3821 

3764 

3707 

3650 

3595 

3540 

40 

; 

41 

4184 

4121 

4060 

3999 

3938 

3879 

3820 

3763 

3706 

3649 

3594 

3539 

41 

42 

4183 

4120 

4059 

3998 

3937 

3878 

3820 

3762 

3705 

3649 

3593 

3538 

42 

43 

4182 

4119 

4058 

3997 

3936 

3877 

3819 

3761 

3704 

3648 

3592 

3537 

43 

44 
45 

4181 

4118 

4056 

3996 

3935 

3876 

3818 

3760 

3703 

3647 

3591 

3536 

44 

0.4180 

4117 

4055 

3995 

3934 

3875 

3817 

3759 

3702 

3646 

3590 

3535 

45 

46 

4179 

4116 

4054 

3993 

3933 

3874 

3816 

3758 

3701 

3645 

3589 

3535 

46 

47 

4178 

4115 

4053 

3992 

3932 

3873 

3815 

3757 

3700 

3644 

3588 

3534 

47 

48 

4177 

4114 

4052 

3991 

3931 

3872 

3814 

3756 

3699 

3643 

3587 

3533 

48 

49 
50 

4176 

4113 

4051 

3990 

3930 

3871 

3813 

3755 

3698 

3642 

3587 

3532 

49 

0.4175 

4112 

4050 

3989 

3929 

3870 

3812 

3754 

3697 

3641 

3586 

3531 

50 

51 

4174 

4111 

4049 

3988 

3928 

3869 

3811 

3753 

3696 

3640 

3585 

3530 

51 

52 

4173 

4110 

4048 

3987 

3927 

3868 

3810 

3752 

3695 

3639 

3584 

3529 

52 

53 

4172 

4109 

4047 

3986 

3926 

3867 

3809 

3751 

3694 

3638 

3583 

3528 

53 

54 

4171 

4108 

4046 

3985 

3925 

3866 

3808 

3750 

3693 

3637 

3582 

3527 

54 

55 

0.4169 

4107 

4045 

3984 

3924 

3865 

3807 

3749 

3693 

3636   3581 

3526 

55 

56 

4168 

4106 

4044 

3983 

3923 

3864 

3806 

3748 

3692 

3635   3580 

3525 

56 

57 

4167 

4105 

4043 

3982 

3922 

3863 

3805 

3747 

3691 

3635  3579 

3525 

57 

58 

4166 

4104 

4U42 

3981 

3921 

3862 

3804 

3746 

3690 

3634 

3678 

3524 

58 

59 

4165 

4103 

4041 

3980 

3920 

3861 

3803 

3746 

3689 

3633 

3577 

3523 

59 

J 

Bl    < 

U   K 

)1   11 

[1     n 

il   U 

tl   14 

U   If 

il   16 

1     n 

1   18 

1   19 

i 

TABLE  XXXIV 

• 

213 

PROPORTIONAL  . 

LOGARITHMS 

-rr-i 

1     / 

.|< 

,,. 

/  o 

1     o 

f  " 

t     o 

/  = 

>l' 

'1 

1    1   1 

'1 

'/ 

*.    1 

1.    m.  h.   m.lli.   m.|l] 

I.    m.  b 

m.  h 

k.    m.  b 

I.    m.  b 

L.   m.  h.   m.|h.   m.|> 

1.    m.  h.    m.| 

1. 

] 

1     20 

I   21] 

I   22  1 

23  1 

24  1 

25  1 

26  1 

27  1 

28{] 

1   29  1   30  1   31| 

0  ( 

).3522 

.3468 

3415 

3362 

3310 

3259 

3208 

3158 

3108 

3059 

3010 

2962 

0 

1 

3521 

3467 

3414 

3361 

3309 

3258 

32Q7 

3157 

3107 

3058 

3009 

2062 

1 

2 

3520 

3466 

3413 

3360 

3308 

3257 

3206 

3156 

3106 

3057 

3009 

2961 

•2 

3 

3519 

3465 

3412 

3359 

3307 

3256 

3205 

3155 

3105 

3056 

3008 

2960 

3 

4 
5 

3518 

3464 

3411 

3358 

3306 

3255 

3204 

3154 

3105 

3056 

3007 

2959 

4 

3.3517 

3463 

3410 

3358 

3306 

3254 

3204 

3153 

3104 

3055 

3006 

2958 

5 

6 

3516 

3463 

3409 

3357 

3305 

3253 

3203 

3153 

3103 

3054 

3005 

2958 

6 

7 

3515 

3462 

3408 

3356 

3304 

3253 

3202 

3152 

3102 

3053 

3005 

2957 

7 

8 

3514 

3461 

3408 

3355 

3303 

3252 

3201 

3151 

3101 

3052 

3004 

2956 

8 

9 
10 

3514 

3460 

3407 

3354 

3302 

3251 

3200 

3150 

3101 

3052 

3003 

2955 

9 

10 

5.3513 

3459 

3406 

3353 

3301 

3250 

3199 

3149 

3100 

3051 

3002 

2954 

11 

3512 

3458 

3405 

3352 

3300 

3249 

3198 

3148 

3099 

3050 

3001 

2954 

11 

12 

3511 

3457 

3404 

3351 

3300 

3248 

3198 

3148 

3098 

3049 

3001 

2953 

12 

13 

3510 

3456 

3403 

3351 

3299 

3247 

3197 

3147 

3097 

3048 

3000 

2952 

13 

14 
15 

3509 

3455 

3402 

335) 

3298 

3247 

3196 

3146 

3096 

3047 

2999 

2961 

14 

0.3508 

3454 

3401 

3349 

3297 

3246 

3195 

3145 

3096 

3047 

2998 

2950 

15 

16 

3507 

3454 

3400 

3348 

3296 

3245 

3194 

3144 

3095 

3046 

2997 

2950 

16 

17 

3506 

3453 

3400 

3347 

3295 

3244 

3193 

3143 

3094 

3045 

2997 

2949 

17 

18 

3506 

3452 

3399 

3346 

3294 

3243 

3193 

3143 

3093 

3044 

2996 

2948 

18 

19 

20 

3505 

3451 

3398 

3345 

3294 

3242 

3192 

3142 

3092 

3043 

2995 

2947 

19 
20 

0.3504 

3450 

3397 

3345 

3293 

3242 

3191 

3141 

3091 

3043 

2994 

2946 

21 

3503 

3449 

3396 

3344 

3292 

3241 

3190 

3140 

3091 

3042 

2993 

2946 

21 

22 

.3502 

3448 

3395 

3343 

3291 

3240 

3189 

3139 

3090 

3041 

2993 

2945 

22 

23 

3501 

3447 

3394 

3342 

3290 

3239 

3188 

3138 

3089 

3040 

2992 

2944 

23 

24 
25 

3500 

3446 

3393 

3341 

3289 

3238 

3188 

3138 

3088 

3039 

2991 

2943 

24' 

0.3499 

3446 

3393 

3340 

3288 

3237 

3187 

3137 

3087 

3039 

2990 

2942 

25 

26 

3498 

3445 

3392 

3339 

3288 

3236 

3186 

3136 

3087 

3038 

2989 

2942 

26 

27 

3497 

3444 

3391 

3338 

3287 

3236 

3185 

3135 

3086 

3037 

2989 

2941 

27 

28 

3497 

3443 

3390 

3338 

3286 

3235 

3184 

3134 

3085 

3036 

2988 

2940 

28 

29 
30 

3496 

3442 

3389 

3337 

3285 

3234 

3183 

3133 

3084 

3035 

2987 

2939 

29 

0.3495 

3441 

3388 

3336 

3284 

3233 

3183 

3133 

3083 

3034 

2986 

2939 

30 

31 

3494 

3440 

3387 

3335 

3283 

3232 

3182 

3132 

3082 

3034 

2985 

2938 

31 

32 

3493 

3439 

3386 

3334 

3282 

3231 

3181 

3131 

3082 

3033 

2985 

2937 

32 

33 

3492 

3438 

3386 

3333 

3282 

3231 

3180 

3130 

3081 

3032 

2984 

2936 

33 

34 
35 

3491 

3438 

3385 

3332 

3281 

3230 

3179 

3129 

3080 

3031 

2983 

2935 

34 

0.3490 

3437 

3384 

3332 

3280 

3229 

3178 

3129 

3079 

3030 

2982 

2935 

35 

36 

3489 

3436 

3383 

3331 

3279 

3228 

3178 

3128 

3078 

3030 

2981 

2934 

36 

37 

3488 

3435 

3382 

3330 

3278 

3227 

3177 

3127 

3078 

3029 

2981 

2933 

37 

38 

3488 

3434 

3381 

3329 

3277 

3226 

3176 

3126 

3077 

3028 

2980 

2932 

38 

39 
40 

3487 

3433 

3380 

3328 

3276 

3225 

3175 

3125 

3076 

3027 

2979 

2931 

39 

0.3486 

3432 

3379 

3327 

3276 

3225 

3174 

3124 

3075 

3026 

2978 

2931 

40 

41 

3485 

3431 

3379 

3326 

3275 

3224 

3173 

3124 

3074 

3026 

2977 

2930 

41 

42 

3484 

3431 

3378 

3325 

3274 

3223 

3173 

3123 

3073 

3025 

2977 

2929 

42 

43 

3483 

3430 

3377 

3325 

3273 

3222 

3172 

3122 

3073 

3024 

2976 

2928 

43 

44 
45 

3482 

3429 

3376 

3324 

3272 

3221 

3171 

3121 

3072 

3023 

2975 

2927 

44 

0.3481 

3428 

3375 

3323 

3271 

3220 

3170 

3120 

3071 

3022 

2974 

2927 

45 

46 

3480 

3427 

3374 

3322 

3270 

3220 

3169 

3119 

3070 

3022 

2973 

2926 

46 

47 

3480 

3426 

3373 

3321 

3270 

3219 

3168 

3119 

3069 

3021 

2973 

2925 

47 

48 

3479 

3425 

3372 

3320 

3269 

3218 

3168 

3118 

3069 

3020 

2972 

2924 

48 

49 
50 

3478 

3424 

3372 

3319 

3268 

3217 

3167 

3117 

3068 

3019 

2971 

2924 

40 
50 

0.3477 

3423 

3371 

3319 

3267 

3216 

3166 

3116 

3067 

3018 

2970 

2923 

51 

3476 

3423 

3370 

3318 

3266 

3215 

3165 

3115 

3066 

3018 

2969 

2922 

51 

52 

3475 

3422 

3369 

3317 

3265 

3214 

3164 

3114 

3065 

3017 

2969 

2921 

52 

53 

3474 

3421 

3368 

3316 

3265 

3214 

3163 

3114 

3065 

3016 

2968 

2920 

53 

54 
55 

3473 

3420 

3367 

3315 

3264 

3213 

3163 

3113 

3064 

3015 

2967 

2920 

54 

0.3472 

3419 

3366 

3314 

3263 

3212 

3162 

3112 

3063 

3014 

2966 

2919 

55 

56 

3471 

3418 

3365 

3313 

3262 

3211 

3161 

3111 

3062 

3014 

2965 

2918 

56 

57 

3471 

3417 

3365 

3313 

3261 

3210 

3160 

3110 

3061 

3013 

2965 

2917 

57 

58 

3470 

3416 

3364 

3312 

3260 

3209 

3159 

3110 

3060 

3012 

2964 

2916 

58 

59 

3469 

3415 

3363 

3311 

3259 

3209 

3158 

3109 

3060 

3011 

2963 

2916 

59 

1    2( 

)1   2] 

1   2S 

1   23 

1   2< 

H   25 

1   26 

1   27 

1   28 

1   29 

1   30 

1   31 

214 

TABLE  XXXIV. 

PROPORTIONAL  LOGARITHMS. 

- 

tf    e 

1     '  c 

)    '  o    '  ( 

3     '  O     '  |( 

D    '  o    '  1 

o    ' 

o    ' 

o   ' 

o    ' 

o   ' 

n 

1.  b 

I.    m.  h 

m.  h.    m.  1 

1.    m.  '. 

1.   m. 

1.   m. 

h.   m.l 

h.   m. 

h.   m. 

h.    m. 

h.    m. 

h.    m. 

1. 

1 

32|] 

33  1   34 1   35 

1   36 

1   37  1   38j 

1   39 

1   40  1   41 

1   42 

1   43 

0  ( 

).2915 

2868 

2821 

2775 

2730 

2685 

2640 

2596 

2553 

2510 

2467 

2424 

0 

1 

2914 

2867 

2821 

2775 

2729 

2684 

2640 

2596 

2552 

2509 

2466 

2424 

1 

2 

2913 

2866 

2821) 

2774 

2729 

2684 

2639 

2595 

2551 

2508 

2465 

2423 

2 

3 

2912 

2866 

2819 

2773 

2728 

2683 

2638 

2594 

2551 

2507 

2465 

2422 

3 

4 
5 

2912 

2865 

2818 

2772 

2727 

2682 

2638 

2593 

2550 

2507 

2464 

2422 

4 
5 

3.2911 

2864 

2818 

2772 

2726 

2681 

2637 

2593 

2549 

2506 

2463 

2421 

6 

2910 

2863 

2817 

2771 

2725 

2681 

2636 

2592 

2548 

2505 

2462 

2420 

6 

7 

2909 

2862 

2816 

2770 

2725 

2680 

2635 

2591 

2548 

2504 

2462 

2419 

7 

8 

2909 

2862 

2815 

2769 

2724 

2679 

2635 

2591 

2547 

2504 

2461 

2419 

■  8 

9 
10 

2908 

2861 

2815 

2769 

2723 

2678 

2634 

2590 

2546 

2503 

2460 

2418 

9 

0.2907 

2860 

2814 

2768 

2722 

2678 

2633 

2589 

2545 

2502 

2460 

2417 

10 

11 

2906 

2859 

2813 

2767 

2722 

2677 

2632 

2588 

2545 

2502 

2459 

2417 

11 

12 

2905 

2859 

2812 

2766 

2721 

2676 

2632 

2588 

2544 

2501 

2458 

2416 

12 

13 

2905 

2858 

2811 

2766 

2720 

2675 

2631 

2587 

2543 

2500 

2458 

2415 

13 

14 
15 

2904 

2857 

2811 

2765 

2719 

2675 

2630 

2586 

2543 

2499 

2457 

2415 

14 
15 

0.2903 

2856 

2810 

2764 

2719 

2674 

2629 

2585 

2542 

2499 

2456 

2414 

16 

2902 

2855 

2809 

2763 

2718 

2673 

2629 

2585 

2541 

2498 

2455 

2413 

16 

17 

2901 

2855 

2808 

2763 

2717 

2672 

2628 

2584 

2540 

2497 

2455 

2412 

17 

18 

2901 

2854 

2808 

2762 

2716 

2672 

2627 

2583 

2540 

2497 

2454 

2412 

18 

19 
20 

2900 

2853 

2807 

2761 

2716 

2671 

2626 

2583 

2539 

2496 

2453 

2411 

19 
20 

0.2899 

2852 

2806 

2760 

2715 

2670 

2626 

2582 

2538 

2495 

2453 

2410 

21 

2898 

2852 

2805 

2760 

2714 

2669 

2625 

2581 

2538 

2494 

2452 

2410 

21 

22 

2898 

2851 

2805 

2759 

2713 

2669 

2624 

2580 

2537 

2494 

2451 

2409 

22 

23 

2897 

2850 

2804 

2758 

2713 

2668 

2624 

2580 

2536 

2493 

2450 

2408 

23 

24 

25 

2896 

2849 

2803 

2757 

2712 

2667 

2623 

2579 

2535 

2492 

2450 

2408 

24 
25 

0.2895 

2848 

2802 

2756 

2711 

2666 

2622 

2578 

2535 

2492 

2449 

2407 

26 

2894 

2848 

2801 

2756 

2710 

2666 

2621 

2577 

2534 

2491 

2448 

2406 

26 

27 

2894 

2847 

2801 

2755 

2710 

2665 

2621 

2577 

2533 

2490 

2448 

2405 

27 

28 

2893 

2846 

2800 

2754 

2709 

2664 

2620 

2576 

2533 

2489 

2447 

2405 

28 

29 
30 

2892 

2845 

2799 

2753 

2708 

2663 

2619 

2575 

2532 

2489 

2446 

2404 

29 
30 

0.2891 

2845 

2798 

2753 

2707 

2663 

2618 

2574 

2531 

2488 

2445 

2403 

31 

2891 

2844 

2798 

2752 

2707 

2662 

2618 

2574 

2530 

2487 

2445 

2403 

31 

32 

2890 

2843 

2797 

2751 

2706 

2661 

2617 

2573 

2530 

2487 

2444 

2402 

32 

33 

2889 

2842 

2796 

2750 

2705 

2660 

2616 

2572 

2529 

2486 

2443 

2401 

33 

34 
35 

2888 

2842 

2795 

2750 

2704 

2660 

2615 

2572 

2528 

2485 

2443 

2401 

34 
35 

0.2888 

2841 

2795 

2749 

2704 

2659 

2615 

2571 

2527 

2485 

2442 

2400 

36 

2887 

2840 

2794 

2748 

2703 

2658 

2614 

2570 

2527 

2484 

2441 

2399 

36 

37 

2886 

2839 

2793 

2747 

2702 

2657 

2613 

2569 

2526 

2483 

2441 

2398 

37 

38 

2885 

2838 

2792 

2747 

270] 

2657 

2612 

2569 

2525 

2482 

2440 

2398 

38 

39 
40 

2884 

2838 

2792 

2746 

2701 

2656 

2612 

2568 

2525 

2482 

2439 

2397 

39 
40 

0.2883 

2837 

2791 

2745 

2700 

2655 

2611 

2567 

2524 

2481 

2438 

2396 

41 

2883 

2836 

2790 

2744 

2699 

2655 

2610 

2566 

2523 

2480 

2438 

2396 

41 

42 

2882 

2835 

2789 

2744 

2698 

2654 

2610 

2566 

2522 

2480 

2437 

2395 

42 

43 

2881 

2835 

2788 

2743 

2698 

2653 

2609 

2565 

2522 

2479 

2436 

2394 

43 

44 
45 

2880 

2834 

2788 

2742 

2697 

2652 

2608 

2564 

2521 

2478 

2436 

2394 

44 

0.2880 

2833 

2787 

2741 

2696 

2652 

2607 

2564 

2520 

2477 

2435 

2393 

45 

46 

2879 

2832 

2786 

2741 

2695 

2651 

2607 

2563 

2520 

2477 

2434 

2392 

46 

'  47 

2878 

2831 

2785 

2740 

2695 

2650 

2606 

2562 

2519 

2476 

2433 

2391 

47 

48 

2877 

2831 

2785 

2739 

2694 

2649 

2605 

2561 

2518 

2475 

2433 

2391 

48 

49 
50 

2876 

2830 

2784 

2738 

2693 

2649 

2604 

2561 

2517 

2475 

2432 

2390 

49 

0.2876 

2829 

2783 

2738 

2692 

2648 

2604 

2560 

2517 

2474 

2431 

2389 

50 

51 

2875 

2828 

2782 

2737 

2692 

2647 

2603 

25.59 

2516 

2473 

2431 

2389 

51 

52 

2874 

2828 

2782 

2736 

2691 

2646 

2602 

2559 

2515 

2472 

2430 

2388 

52 

53 

2873 

2827 

2781 

2735 

2690 

2646 

2601 

2558 

2515 

2472 

2429 

2387 

53 

54 
55 

2873 

2826 

2780 

2735 

2689 

2645 

2601 

2557 

2514 

2471 

2429 

2387 

54 
55 

lo.2872 

2825 

2779 

2734 

2689 

2644 

2600 

2556 

2513 

2470 

2428 

2386 

56 

2871 

2825 

2779 

2733 

2688 

2643 

2599 

2556 

2512 

2470 

2427 

2385 

56 

57 

2870 

2824 

2778 

2732 

2687 

2643 

2599 

2555 

2512 

2469 

2426 

2384 

57 

58 

2869 

2823 

2777 

2732 

2687 

2642 

2598 

2554 

2511 

2468 

2426 

2384 

58 

59 

2869 

2822 

2776 

2731 

2686 

2641 

2597 

2553 

2510 

2467 

2425 

2383 

59 

1    32 

1   33 

1   34 

1   35 

1   36 

1   37 

1   38 

1   39 

1   40 

1   41 

1   42 

1   43 

215 

TABLE  XXXIV. 

PROPORTIONAL  LOGARITHMS. 

1.  1 

>     1  * 
\.           m. 

I    m. 

3            f 

[I.    ni. 

0          ' 

ti.    m. 

3          ' 

ti.    ra. 

1.    m. 

1.    m. 

O          f 

h.   ra. 

O          ( 

h.   in. 

•         r 

h.   m. 

h.    m. 

ti.    m. 

■. 

I    44 

I   45 

1   46 

1   47  1   48 

1   49 

1   50 

1    51 

1   52  1   53 

I   54 

1   55 

0 

J. 2382 

2341 

2300 

2259 

2218 

2178 

2139 

2099 

2061 

2022 

1984 

1946 

0 

1 

23SJ 

2340 

2299 

2258 

2218 

2178 

2138 

2099 

2060 

2021 

1983 

1945 

1 

2. 

2381 

2339 

2298 

2258 

2217 

2177 

2137' 

2098 

2059 

2021 

1982 

1944 

2 

3 

2380 

2339 

2298 

2257 

2216 

2176 

2137 

2098 

2059 

2020 

1982 

1944 

3 

4 
5 

2380 

2338 

2297 

2256 

2216 

2176 

2136 

2097 

2058 

2019 

1981 

1943 

4 
5 

0.2379 

2337 

22J6 

2256 

2215 

2175 

2136 

2U96 

2057 

2019 

1981 

1943 

b 

2378 

2337 

2296 

2255 

2214 

2174 

2135 

2096 

2057 

2018 

1980 

1942 

6 

7 

2378 

2336 

2295 

2254 

2214 

2174 

2134 

2095 

2056 

2017 

1979 

1941 

7 

8 

2377 

2335 

2294 

2253 

2213 

2173 

2134 

2094 

2055 

2017 

1979 

1941 

8 

9 
10 

2376 

2335 

2294 

2253 

2212 

2172 

2133 

2094 

2055 

2016 

1978 

1940 

9 
10 

0.2375 

2334 

2293 

2252 

2212 

2172 

2132 

2093 

2054 

2016 

1977 

1939 

11 

2375 

2333 

2292 

2251 

2211 

2171 

2132 

2092 

2053 

2015 

1977 

1939 

11 

12 

2374 

2333 

2291 

2251 

2210 

2170 

2131 

2092 

2053 

2014 

1966 

1938 

12 

13 

2373 

2332 

2291 

2250 

2210 

2170 

2130 

2091 

2052 

2014 

1975 

1938 

13 

14 
15 

2373 

2331 

2290 

2249 

2209 

2169 

2130 

2090 

2052 

2013 

1975 

1937 

14 
15 

0.2372 

2331 

2289 

2249 

2208 

2169 

2129 

2090 

2051 

2012 

1974 

1936 

16 

2371 

2330 

2289 

2248 

2208 

2168 

2128 

2089 

2050 

2012 

1974 

1936 

16 

17 

2371 

2329 

2288 

2247 

2207 

2167 

2128 

2088 

2050 

2011 

1973 

1935 

17 

18 

2370 

2328 

2287 

2247 

2206 

2167 

2127 

2088 

2049 

2010 

1972 

1934 

18 

19 
20 

2369 

2328 

2287 

2246 

2206 

2166 

2126 

2087 

2048 

2010 

1972 

1934 

19 
20 

0.2368 

2327 

2286 

2245 

2205 

2165 

2126 

2086 

2048 

2009 

1971 

1933 

21 

2368 

2326 

2285 

2245 

2204 

2165 

2125 

2086 

2047 

2009 

1970 

1933 

21 

22 

2367 

2326 

2285 

2244 

2204 

2164 

2124 

2085 

2046 

2008 

1970 

1932 

22 

23 

2366 

2325 

2284 

2243 

2203 

2163 

2124 

2085 

2046 

2007 

1969 

1931 

23 

24 
25 

2366 

2324 

2283 

2243 

2202 

2163 

2123 

2084 

2045 

2007 

1968 

1931 

24 

25 

0.2365 

2324 

2283 

2242 

2202 

2162 

2122 

2083 

2044 

2006 

1968 

1930 

26 

2364 

2323 

2282 

2241 

2201 

2161 

2122 

2083 

2044 

2005 

1967 

1929 

26 

27 

2364 

2322 

2281 

2241 

2200 

2161 

2121 

2082 

2043 

2005 

1967 

1929 

27 

28 

2363 

2322 

2281 

2240 

2200 

2160 

2120 

20C1 

2042 

2004 

1966 

1928 

28 

29 
30 

2362 

2321 

2280 

2239 

2199 

2159 

2140 

2081 

\  2042 

2003 

1965 

1928 

29 
30 

0.2362 

2320 

2279 

2239 

2198 

2159 

2119 

2080 

2041 

2003 

1965 

1927 

31 

2361 

2320 

2279 

2238 

2198 

2158 

2]  18 

2179 

2041 

2002 

1964 

1926 

31 

32 

2360 

2319 

2278 

2237 

2197 

2157 

2118 

2079 

2040 

2001 

19j63 

1926 

32 

33 

2359 

2318 

2277 

2237 

2196 

2157 

2117 

2078 

2039 

2001 

1963 

1925 

33 

34 
35 

2359 

2317 

2277 

2236 

2196 

2156 

2116 

2077 

2039 

2000 

1962 

1924 

34 

0.2358 

2317 

2276 

2235 

2195 

2155 

2116 

2077 

2038 

2000 

1962 

1924 

35 

36 

2357 

2316 

2275 

2235 

2194 

2155 

2115 

2076 

2037 

1999 

1961 

1923 

36 

37 

2357 

2315 

2274 

2234 

2194 

2154 

2115 

2075 

2037 

1998 

1960 

1923 

37 

38 

2356 

2315 

2274 

2233 

2193 

2153 

2114 

2073 

2036 

1998 

1960 

1922 

38 

39 
40 

2355 

2314 

2273 

2233 

2192 

2153 

2113 

2074 

2035 

1997 

1959 

1921 

39 

40 

0.2355 

2313 

2272 

2232 

2192 

2152 

2113 

2073 

2035 

1996 

1958 

1921 

41 

2354 

2313 

2272 

2231 

2191 

2151 

2112 

2073 

2034 

1996 

1958 

1920 

41 

42 

2353 

2312 

2271 

2231 

2190 

2151 

2111 

2074 

2033 

1995 

1957 

1919 

42 

43 

2353 

2311 

2270 

2230 

2190 

2150 

2111 

2072 

2033 

1994 

1956 

1919 

43 

44 

45 

2352 

2311 

2270 

2229 

2189 

2149 

2110 

2071 

2032 

1994 

1956 

1918 

44 
45 

0.2351 

2310 

2269 

2229 

2188 

2149 

2109 

2070 

2032 

1993 

1955 

1918 

46 

2350 

2309 

2268 

2228 

2188 

2148 

2109 

2070 

2031 

1993 

1955 

1917 

46 

47 

2350 

2309 

2268 

2227 

2187 

2147 

2108 

2069 

2030 

1992 

1954 

1916 

47 

48 

2349 

2308 

2267 

2227 

2186 

2147 

2107 

2068 

2030 

1991 

1953 

1916 

48 

49 
^  50 

2348 

2307 

2266 

2226 

2186 

2146 

2107 

2068 

2029 

1991 

1953 

1915 

49 
50 

0.2348 

2307 

2266 

2225 

2185 

2145 

2106 

2067 

2028 

1990 

1952 

1914 

51 

2347 

2306 

2265 

2225 

2184 

2145 

2105 

2066 

2028 

1989 

1951 

1914 

51 

,  52 

2346 

6305 

2264 

2224 

2184 

2144 

2105 

2066 

2027 

1989 

1951 

1913 

52 

53 

2346 

2304 

2264 

2223 

2183 

2143 

2104 

2065 

2026 

1988 

1950 

1913 

53 

54 
55 

2345 

2304 

2263 

2223 

2182 

2143 

2103 

2064 

2026 

1987 

1950 

1912 

54 
55 

0.2344 

2303 

226-2 

2222 

2182 

2142 

2103 

2064 

2025 

1987 

1949 

1911 

56 

2344 

2302 

2262 

2221 

2181 

2141 

2102 

2063 

2025 

1986 

1948 

1911 

56 

57 

2343 

2302 

2261 

2220 

2180 

2141 

2101 

2062 

2024 

1986 

1948 

1910 

57 

58 

2342 

2301 

2260 

2220 

2180 

2140 

2101 

2062 

2023 

1985 

1947 

1909 

58 

i  59 

2342 

2300 

2260 

2219 

2179 

2139 

2100 

2061 

2023 

1984 

1946 

1909 

59 

1    44 

1   45 

1   46 

1   47 

1   48 

1   49 

1   50 

1   51 

1   52 

1   53 

1   54 

1   55 

TABLE  XXXTV. 

PROPORTIONAL  LOGARITHMS 

I 

'/  c 

}      ( 

D     ' 

3     ' 

0    r. 

O            ' 

O     '  1 

o    ' 

o        ' 

o    ' 

o         ' 

o    ' 

J)   ' 

n 

•.   1 

I.     m.  . 

1.   m. 

ti.    m. 

b.    m.l 

1.    m. 

h.    m. 

h.   m. 

1.        xa. 

1.   m. 

h.        m. 

h.   m. 

h.        m. 

%. 

] 

I    56 

I   57 

1   581   59| 

2    0 

2     1 

2    2  2    3|2    4|2    5|2    6| 

2    7 

0  ( 

).1908 

1871 

1834 

1797 

1761 

1725 

1689 

1654 

1619 

1584 

1549 

1515 

0 

1 

1908 

1870 

1833 

1797 

1760 

1724 

1689 

1653 

1618 

1583 

1548 

1514 

1 

2 

1907 

1870 

1833 

1796 

1760 

1724 

1688 

1652 

1617 

1582 

1548 

1514 

2 

3 

1906 

186^» 

1832 

1795 

1759 

1723 

1687 

1652 

1617 

1582 

1547 

1513 

3 

4 
5  ( 

1906 

1868 

1831 

1795 

1759 

1722 

1687 

1651 

1616 

1581 

1547 

1512 

4 

3.1905 

1868 

1831 

1794 

1758 

1722 

1686 

1651 

1616 

1581 

1546 

1512 

6 

6 

1904 

1867 

1830 

1794 

1757 

1721 

1686 

1650 

1615 

1580 

1546 

1511 

6 

7 

1904 

1867 

1830 

1793 

1757 

1721 

1685 

1650 

1614 

1580 

1545 

1511 

7 

8 

1903 

1866 

1829 

1792 

1756 

1720 

1684 

1649 

1614 

1579 

1544 

1510 

8 

9 
10 

1903 

1865 

1828 

1792 

1755 

1719 

1684 

1648 

1613 

1578 

1544 

1510 

9 

3.1902 

1865 

1828 

1791 

1755 

1719 

1683 

1648 

1613 

1578 

1543 

1509 

10 

11 

1901 

1864 

1827 

1791 

1754 

1718 

1683 

1647 

1612 

1577 

1543 

1508 

11 

12 

1901 

1863 

1827 

1790 

1754 

1718 

1682 

1647 

1612 

1577 

1542 

1508 

12 

13 

1900 

1863 

1826 

1789 

1753 

1717 

1681 

1646 

1611 

1576 

1542 

1507 

13 

14 
15 

1899 

1862 

1825 

1789 

1752 

1717 

1681 

1645 

1610 

1576 

1541 

1507 

14 

0.1899 

1862 

1825 

1788 

1752 

1716 

1680 

1645 

1610 

1575 

1540 

1506 

15 

16 

1898 

1861 

1824 

1788 

1751 

1715 

1680 

1644 

1609 

i574 

1540 

1506 

16 

17 

1898 

1860 

1823 

1787 

1751 

1715 

1679 

1644 

1609 

1574 

1539 

1505 

17 

18 

1897 

1860 

1823 

1786 

1750 

1714 

1678 

1643 

1608 

1573 

1539 

1504 

18 

19 

20 

1896 

1859 

1822 

1786 

1749 

1714 

1678 

1643 

1607 

1573 

1538 

1504 

19 
20 

0.1896 

1859 

1822 

1785 

1749 

1713 

1677 

1642 

1607 

1572 

1538 

1503 

21 

1895 

1858 

1821 

1785 

1748 

1712 

1677 

1641 

1606 

1571 

1537 

1503 

21 

22 

1894 

1857 

1820 

1784 

1748 

1712 

1676 

1641 

1606 

1571 

1536 

1502 

22 

23 

1894 

1857 

1820 

1783 

1747 

1711 

1676 

1640 

1605 

1570 

1536 

1502 

23 

24 
25 

1893 

1856 

1819 

1783 

1746 

1711 

1675 

1640 

1605 

1570 

1535 

1501 

24 

0.1893 

1855 

1819 

1782 

1746 

1710 

1675 

1639 

1604 

1569 

1535 

1500 

25 

26 

1892 

1855 

1818 

1781 

1745 

1709 

1674 

1638 

1603 

1569 

1534 

1500 

26 

27 

1891 

1854 

1818 

1781 

1745 

1709 

1673 

1638 

1603 

1568 

1534 

1499 

27 

28 

1891 

1854 

1817 

1780 

1744 

1708 

1673 

1637 

1602 

1567 

1533 

1499 

28 

29 
30 

1890 

1853 

1816 

1780 

1743 

1708 

1672 

1637 

1602 

1567 

1532 

1498 

29 

0.1889 

18.52 

1816 

1779 

1743 

1707 

1671 

1636 

1601 

1566 

1532 

1498 

30 

31 

1889 

1852 

1815 

1778 

1742 

1706 

1671 

1635 

1600 

1566 

1531 

1497 

31 

32 

1888 

1851 

1814 

1778 

1742 

1706 

1670 

1635 

1600 

1565 

1531 

1496 

32 

33 

1888 

1850 

1814 

1777 

1741 

1705 

1670 

1634 

1599 

1565 

1530 

1496 

33 

34 
35 

1887 

1850 

1813 

1777 

1740 

1705 

1669 

1634 

1599 

1564 

1530 

1495 

34 

0.1886 

1849 

1812 

1776 

1740 

1704 

1668 

1633 

1598 

1563 

1529 

1495 

35 

36 

1886 

1849 

1812 

1775 

1739 

1703 

1668 

1633 

1598 

1563 

1528 

1494 

36 

37 

1885 

1848 

1811 

1775 

1739 

1703 

1667 

1632 

1597 

1562 

1528 

1494 

37 

38 

1884 

1847 

1811 

1774 

1738 

1702 

1667 

1631 

1596 

1562 

1527 

1493 

38 

39 
40 

1884 

1847 

1810 

1774 

1737 

1702 

1666 

1631 

1596 

1561 

1527 

1493 

39 
40 

0.1883 

1846 

1809 

1773 

1737 

1701 

1665 

1630 

1595 

1561 

1526 

1492 

41 

1883 

1846 

1809 

1772 

1736 

1700 

1665 

1630 

1595 

1560 

1526 

1491 

41 

42 

1882 

1845 

1808 

1772 

1736 

1700 

1664 

1629 

1594 

1559 

1525 

1491 

42 

43 

1881 

1844 

1808 

1771 

1735 

1699 

1664 

1628 

1593 

1559 

1524 

1490 

43 

44 
45 

1881 

1844 

1807 

1771 

5734 

1699 

1663 

1628 

1593 

1558 

1524 

1490 

44 
45 

0.1 88C 

1843 

1806 

1770 

1734 

1698 

1663 

1627 

1592 

1558 

1523 

1489 

46 

1880 

1843 

1806 

1769 

1733 

1697 

1662 

1627 

1592 

1557 

1523 

1489 

46 

47 

1879 

1842 

1805 

1769 

1733 

1697 

1661 

1626 

1591 

1556 

1522 

1488 

47 

48 

1878 

1841 

1805 

1768 

1732 

1696 

1661 

1626 

1591 

1556 

1522 

1487 

48 

49 
50 

1878 

1841 

1804 

1768 

1731 

1696 

1660 

1625 

1590 

1555 

1521 

1487 

49 
50 

0.1877 

1840 

1803 

1767 

1731 

1695 

1660 

1624 

1589 

1555 

1520 

1486 

51 

1876 

1839 

1803 

1766 

1730 

1694 

1659 

1624 

1589 

1554 

1520 

1486 

51 

52 

1876 

1839 

1802 

1766 

1730 

1694 

1658 

1623 

1588 

1554 

1519 

1485 

52 

53 

1875 

1838 

1802 

1765 

1729 

1693 

1658 

1623 

1588 

1553 

1519 

1h85 

53 

54 
55 

1875 

1838 

1801 

1765 

1728 

1693 

1657 

1622 

1587 

1552 

1518 

1484 

64 

0.1874 

1837 

1800 

1764 

1728 

1692 

1657 

1621 

1587 

1552 

1518 

1483 

55 

56 

1873 

1836 

1800 

1763 

1727 

1692 

1656 

1621 

1586 

1551 

1517 

1483 

56 

57 

1873 

1836 

1799 

1763 

1727 

1691 

1655 

1620 

1585 

1551 

1516 

1482 

57 

58   1872 

1835 

1798 

1762 

1726 

1690 

1655 

1620 

1585 

1550 

1516 

1482 

58 

59 

1871 

1835 

1798 

1762 

1725 

1690 

1654 

1619 

1584 

1550 

1515 

1481 

59 

1    5( 

31   5' 

n     5J 

Bl   5[ 

)2    ( 

)2    1 

2    i 

2    3 

2    4 

2    5 

2    6 

2    7 

1 

__ 

TABLE  XXXIV. 

..17 

PROPORTIONAL  LOGARITHMS 

• 

If       ( 

>    /  o   '  o   ' 

3    ' 

3   ' 

o   ' 

o  t 

o  ' 

o   ' 

o   ' 

o   ' 

o   ' 

o 

n 

1 

i<    m.  h.   m.  h.   m. 

1.   m. 

1.   ra. 

h.   ra. 

h.   m. 

h.   ra 

h.   m. 

h.   ra. 

h.   m. 

h.   m. 

h.   ni. 

s. 

I         82   92  10 

2  11 

2   12 

2   13  2   14|2   i5 

2   162   17 

2   18 

2  19 

2  20 

0 

0.1481 

1447 

1413 

138U 

1347 

1314 

1282 

1249 

1217 

1186 

1154 

1123 

1091 

0 

1 

1480 

1446 

1413 

1379 

1346 

1314 

1281 

1249 

1217 

1185 

1153 

1122 

1091 

1 

2 

1479 

1446 

1412 

1379 

1346 

1313 

1281 

1248 

1216 

1184 

1153 

1  1  22 

1090 

2 

3 

1479 

1445 

1412 

1378 

1345 

1313 

1280 

1248 

1216 

1184 

1152 

1121 

1090 

3 

4 

1478 

1445 

1411 

1378 

1345 

1312 

1280 

.1247 

1215 

1183 

1152 

1120 

1089 

4 

5 

0.1478 

1444 

1411 

1377 

1344 

1311 

1279 

1247 

1215 

1183 

1151 

1120 

1089 

5 

6 

1477 

1443 

1410 

1377 

1344 

1311 

1278 

1246 

1214 

1182 

1151 

1119 

1088 

6 

7 

1477 

1443 

1409 

1376 

1343 

1310 

1278 

1246 

1214 

1182 

1150 

1119 

1088 

7 

8 

1476 

1442 

1409 

1376 

1343 

1310 

1277 

1245 

1213 

1181 

1150 

.1118 

1087 

8 

9 

1476 

1442 

1408 

1375 

1342 

1309 

1277 

1245 

1213 

1181 

1149 

1118 

1087 

9 

10 

0.1475 

1441 

1408 

1374 

1342 

1309 

1276 

1244 

1212 

1180 

1149 

1117 

1086 

10 

11 

1474 

1441 

1407 

1374 

1341 

1308 

1276 

1243 

1211 

1180 

1148 

1117 

1086 

11 

12 

1474 

1440 

1407 

1373 

1340 

1308 

1275 

1243 

1211 

1179 

1148 

1116 

1085 

12 

13 

1473 

1440 

1406 

1373 

1340 

1307 

1275 

1242 

1210 

1179 

1147 

1116 

1085 

13 

14 

1473 

1439 

1406 

1372 

1339 

1307 

1274 

1242 

1210 

1178 

1147 

1115 

1084 

14 

15 

0.1472 

1438 

1405 

1372 

1339 

1306 

1274 

1241 

1209 

1178 

1146 

1115 

1084 

15 

16 

1472 

1438 

1404 

1371 

1338 

1306 

1273 

1241 

1209 

1177 

1146 

1114 

1083 

16 

17 

1471 

1437 

1404 

1371 

1338 

1305 

1273 

1240 

1208 

1177 

1145 

1114 

1083 

17 

18 

1470 

1437 

1403 

1370 

1337 

1304 

1272 

1240 

1208 

1176 

1145 

1113 

1082 

18 

19 

1470 

1436 

1403 

1370 

1337 

1304 

1271 

1239 

1207 

1175 

1144 

1113 

1082 

19 

20 

0.1469 

1436 

1402 

1369 

1336 

1303 

1271 

1239 

1207 

1175 

1143 

1112 

1081 

20 

21 

1469 

1435 

1402 

1368 

1335 

1303 

1270 

1238 

1206 

1174 

1143 

1112 

1081 

21 

22 

1468 

1435 

1401 

1368 

1335 

1302 

1270 

1238 

1206 

1174 

1142 

1111 

1080 

22 

23 

1468 

1434 

1401 

1367 

1334 

1302 

1269 

1237 

1205 

1173 

1142 

nil 

1080 

23 

24 

1467 

1433 

1400 

1367 

1334 

1301 

1269 

1237 

1205 

1173 

1141 

1110 

1079 

24 

25 

0.1467 

1433 

1399 

1366 

1333 

1301 

1268 

1236 

1204 

1172 

1141 

1110 

1079 

25 

26 

1466 

1432 

1399 

1366 

1333 

1300 

1268 

1235 

1204 

1172 

1140 

1109 

1078 

26 

27 

1465 

1432 

1398 

1365 

1332 

1300 

1267 

1235 

1203 

1171 

1140 

1109 

1078 

27 

28 

1465 

1431 

1398 

1365 

1332 

1299 

1267 

1234 

1202 

1171 

1139 

1108 

1077 

28 

29 

1464 

1431 

1397 

1364 

1331 

1298 

1266 

1234 

1202 

1170 

1139 

1108 

1076 

29 

30 

0.1464 

1430 

1397 

1363 

1331 

1298 

1266 

1233 

1201 

1170 

1138 

1107 

1076 

30 

31 

1463 

1429 

1396 

1363 

1330 

1297 

1265 

1233 

1201 

1169 

1138 

1106 

1075 

31 

32 

1463 

1429 

1396 

1362 

1329 

1297 

1264 

1232 

1200 

1169 

1137 

1106 

1075 

32 

33 

1463 

1428 

1395 

1362 

1329 

1296 

1264 

1232 

1200 

1168 

1137 

1105 

1074 

33 

34 

1461 

1428 

1394 

1361 

1328 

1296 

1263 

1231 

1199 

1168 

1136 

1105 

1074 

34 

35 

0.1461 

1427 

1394 

1361 

1328 

1295 

1263 

1231 

1199 

1167 

1136 

1104 

1073 

35 

36 

1460 

1427 

1393 

1360 

1327 

1295 

1262 

1230 

1198 

1167 

1135 

1104 

1073 

36 

37 

1460 

1426 

1393 

1360 

1327 

1294 

1262 

1230 

1198 

1166 

1135 

1103 

1072 

37 

38 

1459 

1426 

1392 

1369 

1326 

1294 

1261 

1229 

1197 

1165 

1134 

1103 

1072 

38 

39 

1459 

1425 

1392 

1359 

1326 

1293 

1261 

1229 

1197 

1165 

1134 

1102 

1071 

39 

40 

0.1458 

1424 

1391 

1358 

1325 

1292 

1260 

1228 

1196 

1164 

1133 

1102 

1071 

40 

41 

1458 

1424 

1391 

1357 

1325 

1292 

1260 

1227 

1196 

1164 

1132 

1101 

1070 

41 

42 

1457 

1423 

1390 

1357 

1324 

1291 

1259 

1227 

1195 

1163 

1132 

1101 

1070 

42 

43 

1456 

1423 

1389 

1356 

1323 

1291 

1259 

1226 

1195 

1163 

1131 

1100 

1069 

43 

44 

1456 

1422 

1389 

1356 

1323 

1290 

1258 

1226 

1194 

1162 

1131 

1100 

1069 

44 

45 

0.1455 

1422 

1388 

1355 

1322 

1290 

1257 

1225 

1193 

1162 

1130 

1099 

1068 

45 

46 

1455 

1421 

1388 

1355 

1322 

1289 

1257 

1225 

1193 

1161 

1130 

1099 

1068 

46 

47 

1454 

1421 

1387 

1354 

1321 

1289 

1256 

1224 

1192 

1161 

1129 

1098 

1067 

47 

48 

1454 

1420 

1387 

1354 

1321 

1288 

1256 

1124 

1192 

1160 

1129 

1098 

1067 

48 

49 

1453 

1419 

1386 

1353 

1320 

1288 

1255 

1223 

1191 

1160 

1128 

1097 

1066 

49 

50 

0.1452 

1419 

1386 

1352 

1320 

1287 

1255 

1223 

1191 

1159 

1128 

1097 

1066 

50 

51 

1452 

1418 

1385 

1352 

1319 

1287 

1254 

1222 

1190 

1159 

1127 

1096 

1065 

51 

52 

1451 

1418 

1384 

1351 

1319 

1286 

1254 

1222 

1190 

1158 

1127 

1096 

1065 

52 

53 

1451 

1417 

1384 

1351 

1318 

1285 

1253 

1221 

1189 

1158 

1126 

1095 

1064 

53 

54 

1450 

1417 

1383 

1350 

1317 

1285 

1253 

1221 

1189 

1157 

1126 

1095 

1064 

54 

55 

0.1450 

1416 

1383 

1350 

1317 

1284 

1252 

1220 

1188 

1157 

1125 

1094 

1063 

55 

56 

1449 

1416 

1382 

1349 

1316 

1284 

1252 

1219 

1188 

1156 

1125 

1094 

1063 

56 

57 

1449 

1415 

1382 

1349 

1316 

1283 

1251 

1219 

1187 

1156 

1124 

1093 

1062 

57 

58 

1448 

1414 

1381 

1348 

1315 

1283 

1250 

1218 

1187 

1155 

1124 

1092 

1062 

58 

59 

1447 

1414 

1381 

1348 

1315 

1282 

1250 

1218 

1186 

1154 

1123 

1092 

1061 

59 

2    8 

2   9 

2   10 

1 

2   11 

2   12 

2   13 

2   14 

2   15 

2   16 

2  17 

2   182  19 

2  20 

218 

TABLE  XXXIV 

PROPORTIONAL  LOGARITHMS. 

//   c 

»     '  ,0    '  |0    '  \0        '  lO    'I 

0         ' 

o   ' 

o   / 

o   '  o   ' 

o   ' 

o   ' 

o   ' 

ff 

a.    h.   m.  h.  m.  h.  m. 

1.   m.  h.   m. 

\.      m. 

h.   m. 

h.   m. 

h.   m.  h.   m. 

h.  m. 

h.  m. 

h.   m. 

a. 

2   212  22  2  23 

i     24  2  25 

2  26 

2  27  2  28 

2  29  2  30 

2  312  32 

2  33 

0  ( 

3.1061 

1030 

0999 

0969 

0939 

0909 

0880 

0850 

0821 

0792 

0763 

0734 

0706 

0 

1 

1060 

1029 

0999 

0969 

0939 

0909 

0879 

0850 

0820 

0791 

0762 

0734 

0705 

1 

2 

1060 

1029 

0998 

0968 

0938 

0908 

0879 

0849 

0820 

0791 

0762 

0733 

0705 

8 

3 

1059 

1028 

0998 

0968 

0938 

0908 

0878 

0849 

0819 

0790 

0762 

0733 

0704 

1 

4 

1058 

1028 

0997 

0967 

0937 

0907 

0878 

0848 

0819 

0790 

0761 
0761 

0732 

0704 

4 

5 

9.1058 

1027 

0997 

0967 

0937 

0907 

0877 

0848 

0818 

0789 

0732 

0703 

5 

6 

1057 

1027 

0996 

0966 

0936 

0906 

0877 

0847 

0818 

0789 

0760 

0731 

0703 

6 

7 

1057 

1026 

0996 

0966 

0936 

0906 

0876 

0847 

0817 

0788 

0760 

0731 

0703 

7 

8 

1056 

1026 

0995 

0965 

0935 

0905 

0876 

0846 

0817 

0788 

0759 

0730 

0702 

8 

9 

1056 

1025 

0995 

0965 

0935 

0905 

0875 

0846 

0816 

0787 

0759 

0730 

0702 

9 

10 

0.1055 

1025 

0994 

0964 

0934 

0904 

0875 

0845 

0816 

0787 

0758 

0730 

0701 

10 

11 

1055 

1024 

0994 

0964 

0934 

0904 

0874 

0845 

0816 

0787 

0758 

0729 

0701 

11 

12 

1054 

1024 

0993 

0963 

0933 

0903 

0874 

0844 

0815 

0786 

0757 

0729 

0700 

12 

13 

1054 

1023 

0993 

0963 

0933 

0903 

0873 

0844 

0815 

0786 

0757 

0728 

0700 

13 

14 

1053 

1023 

0992 

0962 

0932 

0902 

0873 

0843 

0814 

0785 

0756 

0728 

0699 

14 

15 

0.1053 

1022 

0992 

0962 

0932 

0902 

0872 

0843 

0814 

0785 

0756 

0727 

0699 

15 

16 

1052 

1022 

0991 

0961 

0931 

0901 

0872 

0842 

0813 

0784 

0755 

0727 

0698 

16 

17 

1052 

1021 

0991 

0961 

0931 

0901 

0871 

0842 

0813 

0784 

0755 

0726 

0698 

17 

18 

1051 

1021 

0990 

0960 

0930 

0900 

1871 

0841 

0812 

0783 

0754 

0726 

0697 

18 

19 

1051 

1020 

0990 

0960 

0930 

0900 

0870 

0841 

0812 

0783 

0754 

0725 

0697 

19 

20 

0.1050 

1020 

0989 

0959 

0929 

0899 

0870 

0840 

0811 

0782 

0753 

0725 

0696 

20 

21 

1050 

1019 

0989 

0959 

0929 

0899 

0869 

0840 

0811 

0782 

0753 

0724 

0696 

21 

22 

1049 

1019 

0988 

0958 

0928 

0898 

0869 

0839 

0810 

0781 

0752 

0724 

0695 

22 

23 

1049 

1018 

0988 

0958 

0928 

0898 

0868 

0839 

0810 

0781 

0752 

0723 

0695 

23 

24 

1048 

1018 

0987 

0957 

0927 

0897 

0868 

0838 

0809 

0780 

0751 

0723 

0694 

24 

25 

0.1048 

1017 

0987 

0957 

0927 

0897 

0867 

0838 

0809 

0780 

0751 

0722 

0694 

25 

26 

1047 

1017 

0986 

0956 

0926 

0896 

0867 

0837 

0808 

0779 

0751 

0722 

0694 

26 

27 

1047 

1016 

0986 

0956 

0926 

0896 

0866 

0837 

0808 

0779 

0750 

0721 

0693 

27 

28 

1046 

1016 

0985 

0955 

0925 

0895 

0866 

0836 

0807 

0778 

0750 

0721 

0693 

28 

29 

1046 

1015 

0985 

0955 

0925 

0895 

0865 

0836 

0807 

0778 

0749 

0721 

0692 

29 

30 

0.1045 

1015 

0984 

0954 

0924 

0894 

0865 

0835 

0806 

0777 

0749 

0720 

0692 

30 

31 

1045 

1014 

0984 

0954 

0924 

0894 

0864 

0835 

0806 

0777 

0748 

0720 

0691 

31 

32 

1044 

1014 

0983 

0953 

0923 

0893 

0864 

0834 

0805 

0776 

0748 

0719 

0691 

32 

33 

1044 

1013 

0983 

0953 

0923 

0893 

0863 

0834 

0805 

0776 

0747 

0719 

0690 

33 

34 

1043 

1013 

0982 

0952 

0922 

0892 

0863 

0834 

0804 

0775 

0747 

0718 

0690 

34 

35 

0.1043 

1012 

0982 

0952 

0922 

0892 

0862 

0833 

0804 

0775 

0746 

0718 

0689 

35 

36 

1042 

1012 

0981 

0951 

0921 

0891 

0862 

0833 

0803 

0774 

0746 

0717 

0689 

36 

37 

1042 

1011 

0981 

0951 

0921 

0891 

0861 

0832 

0803 

0774 

0745 

0717 

0688 

37 

38 

104l|  1011 

0980 

0950 

0920 

0890 

0861 

0832 

0802 

0774 

0745 

0716 

0688 

38 

39 

1041 

1010 

0980 

0950 

0920 

0890 

0860 

0831 

0802 

0773 

0744 

0716 

0687 

39 

40 

0.1040 

1009 

0979 

0949 

0919 

0889 

0860 

0831 

0801 

0773 

0744 

0715 

0687 

40 

41 

1040 

1009 

0979 

0949 

0919 

0889 

0859 

0830 

0801 

0772 

0743 

0715 

0686 

41 

42 

1039 

1008 

0978 

0948 

0918 

0888 

0859 

0830 

0801 

0772 

0743 

0714 

0686 

42 

43 

1039 

1008 

0978 

0948 

0918 

0888 

0858 

0829 

0800 

0771 

0742 

0714 

0686 

43 

44 

1038 

1007 

0977 

0947 

0917 

0887 

0858 

0829 

0800 

0771 

0742 

0713 

0685 

44 

45 

0.1037 

1007 

0977 

0947 

0917 

0887 

0857 

0828 

0799 

0770 

0741 

0713 

0685 

45 

46 

1037 

1006 

0976 

0946 

0916 

0886 

0857 

0828 

0799 

0770 

0741 

0712 

0684 

46 

47 

1036 

1006 

0976 

0946 

0916 

0886 

0856 

0827 

0798 

0769 

0740 

0712 

0684 

47 

48 

1036 

1005 

0975 

0945 

0915 

0885 

0856 

0827 

0798 

0769 

0740 

0711 

0683 

48 

49 

1036 

1005 

0975 

0945 

0915 

0885 

0855 

0826 

0797 

0768 

0740 

0711 

0683 

49 

50 

0.103£ 

1004 

0974 

0944 

0914 

0884 

0855 

0826 

0797 

0768 

0739 

0711 

0682 

50 

51 

1034 

1004 

0974 

0944 

0914 

0884 

0855 

0825 

0796 

0767 

0739 

0710 

0682 

51 

52 

1034 

[    1003 

0973 

0943 

0913 

0883 

0854 

0825 

0796 

0767 

0738 

0710 

0681 

52 

53 

1033 

1003 

0973 

0943 

0913 

0883 

0854 

0824 

0795 

0766 

0738 

0709 

0681 

53 

54 

1033 

1002 

0972 

0942 

0912 

0883 

0853 

0824 

0795 

0766 

0737 

0709 

0680 

54 

55 

0.1032 

1002 

0972 

0942 

0912 

0882 

0853 

0823i  0794 

0765 

0737 

0708 

0680 

55 

56 

1032 

1001 

0971 

0941 

0911 

0882 

0852 

0823 

0794 

0765 

0736 

0708 

0679 

56 

57 

1031 

1001 

0971 

0941 

0911 

0881 

0852 

0822 

0793 

0764 

0736 

0707 

0679 

57 

58 

1031 

1000 

0970 

0940 

0910 

0881 

0851 

0822 

0793 

0764 

0735 

0707 

0678 

58 

59 

103C 

1000 

0970 

0940 

0910 

0880 

0851 

0821 

0792 

0763 

0735 

0706 

0678 

59 

2   21 

2  22 

2  23 

2  24 

2  25 

2  26 

2  27 

2  28 

2  29 

2  30 

2  31 

2  32 

2  33 

J 


219 

TABLE  XXXIV. 

PROPORTIONAL  LOGARITHMS. 

It           0 

'  O   '  O    '  O   '  |0   '  |0    '  |o   '1 

D    ' 

3    '  O    ' 

0   ' 

0   ' 

0   ' 

ti 

s.     h 

in,  h.  m.  h>  m.  li 

I.   m.hi 

I.   m.lh.   m.  t 

1.  m. 

li.   m.  1 

ti.  m.  h.  m. 

d.  m. 

K.   m. 

h.   ni. 

1. 

2 

\       342  35  2  36  2  37|2  38(2  39|2  40|2  4l{ 

2  42  2  43 

2  44 

2  45 

2  46 

0  ( 

).0678 

0649 

0621 

0594 

0566 

0539 

0512 

0484 

0458 

0431 

0404 

0378 

0352 

0 

1 

0677 

0649 

0621 

0593 

0566 

0538 

05L1 

0484 

0457 

0430 

0404 

0377 

0351 

1 

2 

0677 

0648 

0621 

0593 

0565 

0538 

0511 

0484 

0457 

0430 

0403 

0377 

0351 

2 

3 

0676 

0648 

0620 

0592 

0565 

0537 

0510 

0483 

0456 

0430 

0403 

0377 

0350 

3 

4 

0676 

0648 

0620 

0592 

0564 

0537 

0510 

0483 

0456 

0429 

0403 

0376 

0350 

4 

5  ( 

).0675 

0647 

0619 

0591 

0564 

0536 

0509 

0482 

0455 

0429 

0402 

0376 

0349 

5 

6 

0675 

0647 

0619 

0591 

0563 

0536 

0509 

0482 

0455 

0428 

0402 

0375 

0349 

6 

7 

0674 

0646 

0618 

0591 

0563 

0536 

0508 

0481 

0454 

0428 

0401 

0375 

0349 

7 

8 

0674 

0646 

0618 

0590 

0562 

0535 

0508 

0481 

0454 

0427 

0401 

0374 

0348 

8 

9 

0673 

0645 

0617 

0590 

0562 

0535 

0507 

0480 

0454 

0427 

0400 

0374 

0348 

9 

10   1 

5.0673 

0645 

0617 

0589 

0562 

0534 

0507 

0480 

0453 

0426 

0400 

0374 

0347 

10 

11 

0672 

0644 

0616 

0589 

0561 

0534 

0507 

0480 

0453 

0426 

0399 

0373 

0347 

11 

12 

0672 

0644 

0616 

0588 

0561 

0533 

0506 

0479 

0452 

0426 

0399 

0373 

0346 

12 

13 

0671 

0643 

0615 

0588 

0560 

0533 

0506 

0479 

0452 

0425 

0399 

0372 

0346 

13 

14 

0671 

0643 

0615 

0587 

0560 

0532 

0505 

0478 

0351 

0425 

0398 

0372 

0346 

14 

15 

0.0670 

0642 

0615 

0587 

0559 

0532 

0505 

0478 

0451 

0424 

0398 

0371 

0345 

15 

16 

0670 

0642 

0614 

0586 

0559 

0531 

0504 

0477 

0450 

0424 

0397 

0371 

0345 

16 

17 

0670 

0641 

0614 

0586 

0558 

0531 

0504 

0477 

0450 

0423 

0397 

0370 

0344 

17 

18 

0669 

0641 

0613 

0585 

0558 

0531 

0503 

0476 

0450 

0423 

0396 

0370 

0344 

18 

19 

0669 

0641 

0613 

0585 

0557 

0530 

0503 

0476 

0449 

0422 

0396 

0370 

0343 

19 

20 

0.0668 

0640 

0612 

0585 

0557 

0530 

0502 

0475 

0449 

0422 

0395 

0369 

0343 

20 

21 

0668 

0640 

0612 

0584 

0557 

0529 

0502 

0475 

0488 

0422 

0395 

0369 

0342 

21 

22 

0667 

0639 

9611 

0584 

0556 

0529 

0502 

0475 

0448 

0421 

0395 

0368 

0342 

22 

23 

0667 

0639 

0611 

0583 

0556 

0528 

0501 

0474 

0447 

0421 

0394 

0368 

0342 

23 

24 

0666 

0638 

0610 

0583 

0555 

0528 

0501 

0474 

0447 

0420 

0394 

0367 

0341 

24 

25 

0.0666 

0638 

0610 

0582 

0555 

0527 

0500 

0473 

0446 

0420 

0393 

0367 

0341 

25 

26 

0665 

0637 

0609 

0582 

0554 

0527 

0500 

0473 

0246 

0419 

0393 

0366 

0340 

26 

27 

0665 

0637 

0609 

0581 

0554 

0526 

0499 

0472 

0446 

0419 

0392 

0366 

0340 

27 

28 

0664 

0636 

0609 

0581 

0553 

0526 

0499 

0472 

0445 

0418 

0392 

0366 

0339 

28 

29 

0664 

0636 

0608 

0580 

0553 

0526 

0498 

0471 

0445 

0418 

0392 

0365 

0339 

29 

30 

0.0663 

0635 

0608 

0580 

0552 

0525 

0498 

0471 

0444 

0418 

0391 

0365 

0339 

30 

31 

0663 

0635 

0607 

0579 

0552 

0525 

0498 

0471 

0444 

0417 

0391 

0364 

0338 

31 

32 

0663 

0634 

0607 

0579 

0552 

0524 

0497 

0470 

0443 

0417 

0390 

0364 

0338 

32 

33 

0662 

0634 

0606 

0579 

0551 

0524 

0497 

0470 

0443 

0416 

0390 

0363 

0337 

33 

34 

0662 

0634 

0606 

0578 

0551 

0523 

0496 

0469 

0442 

0416 

0389 

0363 

0337 

34 

35 

0.0661 

0633 

0605 

0578 

0550 

0523 

0496 

0469 

0442 

0415 

0389 

0363 

0336 

35 

36 

0661 

0633 

0605 

0577 

0550 

0522 

0495 

0468 

0442 

0415 

0388 

0362 

0336 

36 

37 

0660 

0632 

0604 

0577 

0549 

0522 

0495 

0468 

0441 

0414 

0388 

0362 

0336 

37 

38 

0660 

0632 

0604 

0576 

0549 

0521 

0494 

0467 

0441 

0414 

0388 

0361 

0335 

38 

39 

0659 

0631 

0603 

0576 

0548 

0521 

0494 

0467 

0440 

0414 

0387 

0361 

0335 

39 

40 

0.0659 

0631 

0603 

0575 

0548 

0521 

0493 

0466 

0440 

0413 

0387 

0360 

0334 

40 

41 

0658 

0630 

0602 

0575 

0547 

0520 

0493 

0466 

0439 

0413 

0386 

0360 

0334 

41 

42 

0658 

0630 

0602 

0574 

0547 

052t) 

0493 

0466 

0439 

0412 

0386 

0359 

0333 

42 

43 

0657 

0629 

0602 

0574 

0546 

0519 

0492 

0465 

0438 

0412 

0385 

0359 

0333 

43 

44 

0657 

0629 

0601 

0573 

0546 

0519 

0492 

0465 

0438 

0411 

0385 

0359 

0333 

44 

45 

0.0656 

0628 

i  0601 

0573 

0546 

0518 

0491 

0464 

0438 

0411 

0384 

0358 

0332 

45 

46 

0656 

.  0628 

!  060C 

0573 

0545 

0518 

0491 

0464 

0437 

0410 

0384 

0358 

0332 

46 

47 

065c 

>  0628 

i  060C 

0572 

0545 

0517 

049C 

0463 

0437 

0410 

0384 

0357 

0331 

47 

48 

065£ 

>  0627 

059£ 

0572 

!  0544 

0517 

049C 

0463 

0436 

0410 

0383 

0357 

0331 

48 

49 

065£ 

i  0627 

059E 

1  0571 

0544 

0517 

048S 

0462 

0436 

0409 

0383 

0356 

0330 

49 

50 

0.0654 

I  0626 

5  0598 

i  0571 

0543 

0516 

0489 

0462 

0435 

0409 

0382 

0356 

:330 

50 

51 

0654 

\    062f 

)  0598 

\    057C 

)  0543 

0516 

0489 

0462 

0435 

0408 

0382 

0356 

0329 

51 

52 

065: 

\    062; 

)  0597 

057C 

»  0542 

0515 

0488 

0461 

0434 

0408 

0381 

0355 

0329 

52 

53 

065: 

5  062; 

)  0597 

'  056C 

1  0542 

0515 

0488 

!  0461 

0434 

0407 

0381 

0355 

0329 

53 

54 

0655 

J  062- 

I  059f 

5  056£ 

1  0541 

0514 

0387 

0460 

0434 

0407 

0381 

0354 

0328 

54 

55 

0  0655 

l    062- 

\    059f 

5  0568 

\    0541 

0514 

0487 

0460 

0433 

0406 

0380 

0354 

0328 

55 

56 

065] 

062: 

\    059f 

)  0568 

\    0541 

0513 

0486 

•  0459 

0433 

0406 

0380 

0353 

0327 

56 

57 

0651 

062: 

5  059^ 

)  0568 

\    054C 

»  0513 

0486 

0459 

0432 

0406 

0379 

0353 

0327 

57 

58 

065( 

)  0621 

\    059; 

)  0567 

'  054C 

»  0512 

0485 

0458 

0432 

0405 

0379 

0353 

0326 

58 

59 

065( 

)  062S 

I    059^ 

1  0567 

'  053£ 

1  0512 

-  0485 

0458 

0431 

0405 

0378 

0352 

0326 

59 

2   3^ 

12  3. 

>2  3( 

52  37 

^2  38 

i2  35 

»2  4C 

12  41 

2  42 

2  43 

2  44 

2  45 

2  46 

220 

TABLE  XXXIV. 

PROPORTIONAL  LOGARITHMS. 

//     0 

'  o   '  o   '  c 

>   '  o   '  |0   /jo   '  1 

0       ' 

D          '    O          1 

o   ' 

o   ' 

o   ' 

It 

t.   fa 

m.  h.   EH*  h.   m.  h 

m.  i 

V.      mm.   m.  h.  m. 

i.   m 

1.   m.  h.   m. 

h.   m. 

h.  n. 

h.   m. 

t. 

i 

I       47  2  48  2  49  5 

I     50  2  51|5 

I     52|i 

I     53|2  54|2  55  2  56| 

2  57 

2  58  2  59 

0      ( 

).0326 

0300 

0274 

0248 

0223 

0197 

0172 

0147 

0122 

0098 

0073 

0049 

0024 

0 

1 

0325 

0299 

0273 

0248 

0222 

0197 

0172 

0147 

0122 

0097 

0073 

0048 

0024 

1 

2 

0325 

0299 

0273 

0247 

0222 

0197 

0171 

0146 

0122 

0097 

0072 

0048 

0023 

2 

3 

0324 

0298 

0273 

0247 

0221 

0196 

0171 

0146 

0121 

0096 

0072 

0047 

0023 

3 

4 

0324 

0298 

0272 

0247 

0221 

0196 

0171 

0146 

0121 

0096 

0071 

0047 

0023 

4 

5   ( 

3.0323 

0297 

0272 

0246 

0221 

0195 

0170 

0145 

0120 

0096 

0071 

0046 

0022 

5 

6 

0323 

0297 

0271 

0246 

0220 

0195 

0170 

0145 

0120 

0095 

0071 

0046 

0022 

6 

7 

0323 

0297 

0271 

0245 

0220 

0194 

0169 

0144 

0119 

0095 

0070 

0046 

0021 

7 

8 

0322 

0296 

0270 

0245 

0219 

0194 

0169 

0144 

0119 

0094 

0070 

0045 

0021 

8 

9 

0322 

0296 

0270 

0244 

0€19 

0194 

0169 

0143 

0119 

0094 

0069 

0045 

0021 

9 

10 

0.0321 

0295 

0270 

0244 

0219 

0193 

0168 

0143 

0118 

0093 

0069 

0044 

0020 

10 

11 

0321 

0295 

0269 

0244 

0218 

0193 

0168 

0143 

0118 

0093 

0068 

0044 

0020 

11 

12 

0320 

0294 

0269 

0243 

0218 

0192 

0167 

0142 

0117 

0093 

0068 

0044 

0019 

12 

13 

0320 

0294 

0268 

0243 

0217 

0192 

0167 

0142 

0117 

0092 

0068 

0043 

0019 

13 

14 

0319 

0294 

0268 

0242 

0217 

0192 

0166 

0141 

0117 

0092 

0067 

0043 

0019 

14 

15 

0  0319 

0293 

0267 

0242 

•0216 

0191 

0166 

0141 

0116 

0091 

0067 

0042 

0018 

15 

16 

0319 

0293 

0267 

0241 

0216 

0191 

0166 

0141 

0116 

0091 

0066 

0042 

0018 

16 

17 

0318 

0292 

0267 

0241 

0316 

0190 

0165 

0140 

0115 

0091 

0066 

0042 

0017 

17 

18 

0318 

0292 

0266 

0241 

0215 

0190 

0165 

0140 

0115 

0090 

0066 

0041 

0017 

18 

19 

0317 

0291 

0266 

0240 

0215 

0189 

0164 

'0139 

0114 

0090 

0065 

0041 

0017 

19 

20 

0.0317 

0291 

0265 

0240 

0214 

0189 

0164 

0139 

0114 

C089 

0065 

0040 

0016 

20 

21 

0316 

0291 

0265 

0239 

0214 

0189 

0163 

0139 

0114 

0089 

0064 

0040 

0016 

21 

22 

0316 

0290 

0264 

0239 

0213 

0188 

0163 

0138 

0113 

0089 

0064 

0040 

0015 

22 

23 

0316 

0290 

0264 

0238 

0213 

0188 

0163 

0138 

0113 

0088 

0064 

0039 

0015 

23 

24 

0315 

0289 

0264 

0238 

2013 

0187 

0162 

0137 

0112 

0088 

0063 

0039 

0015 

24 

25 

0.0315 

0289 

0263 

0238 

0212 

0187 

0162 

0137 

0112 

0087 

0063 

0038 

0014 

25 

26 

0314 

0288 

0263 

0237 

0212 

0187 

0161 

0136 

0112 

0087 

0062 

0038 

0014 

26 

27 

0314 

0288 

0262 

0237 

0211 

0186 

0161 

0136 

0111 

0087 

0062 

0038 

0013 

27 

28 

0313 

0288 

0262 

0236 

0211 

0186 

0161 

0136 

0111 

0086 

0062 

0037 

0013 

28 

29 

0313 

0287 

0261 

0236 

0211 

0185 
0185 

0160 

0135 

Olio 

0086 

0061 

0037 

0012 

29 

30 

0.0313 

0287 

0261 

0235 

0210 

0160 

0135 

Olio 

0085 

0061 

0036 

0012 

30 

31 

0312 

0286 

0261 

0235 

0210 

0184 

0159 

0134 

Olio 

0085 

0060 

0036 

0012 

31 

32 

0312 

0286 

0260 

0235 

0209 

0184 

0159 

0134 

0109 

0084 

0060 

0036 

0011 

32 

33 

0311 

0285 

0260 

0234 

0209 

0184 

0158 

0134 

0109 

0084 

0060 

0035 

0011 

33 

34 

0311 

0285 

0259 

0234 

0208 
0208 

0183 

0158 

0133 

0108 

0084 
0083 

0059 

0035 

0010 

34 

35 

0.0310 

0285 

0259 

0233 

0183 

0158 

0133 

0108 

0059 

0034 

0010 

35 

36 

0310 

0284 

0258 

0233 

0208 

0182 

0157 

0132 

0107 

0083 

0058 

0034 

0010 

36 

37 

0310 

0284 

0258 

0233 

0207 

0182 

0157 

0132 

0107 

0082 

0058 

0034 

0009 

37 

38 

0309 

0283 

0268 

0232 

0207 

0181 

0156 

0131 

0107 

0082 

0057 

0033 

0009 

38 

39 

0309 

0283 

0257 

0232 

0206 

0181 

0156 

0131 

0106 

0082 

0057 

0033 

0008 

39 

40 

0.0308 

0282 

0257 

0231 

0206 

0181 

0156 

0131 

0106 

0081 

0057 

0032 

0008 

40 

41 

0308 

0282 

0256 

0231 

0205 

0180 

0153 

0130 

0105 

0081 

0056 

0032 

0008 

41 

42 

0307 

0282 

0256 

0230 

0205 

0180 

0155 

0130 

0105 

0080 

0056 

0031 

0007 

42 

43 

0307 

0281 

0255 

0230 

0205 

0179 

0154 

0129 

0105 

0080 

0055 

0031 

0007 

43 

44 

0307 

0281 

0256 
02^5 

O230 
!  0229 

0204 

0179 

0154 

6129 

0104 

0080 

0055 

0031 

0006 

44 

45 

0.0306 

O280 

0204 

0179 

0153 

0129 

0104 

0079 

0055 

0030 

0006 

45 

46 

0306 

O280 

0254 

0229 

0203 

0178 

0153 

0128 

0103 

0079 

0054 

0030 

0006 

46 

47 

030£ 

0279 

0254 

022S 

0203 

0178 

0153 

0128 

0103 

0078 

0054 

0029 

0005 

47 

48 

0305 

0279 

0253 

0228 

0202 

0177 

0152 

0127 

0103 

0078 

0053 

0029 

0005 

48 

49 

030^ 

0279 

0253 

0227 

0202 

0177 

0152 

0127 

0102 

0077 

0053 

0029 

0004 

49 

50 

0.030^ 

0278 

0252 

0227 

0202 

0176 

0151 

0126 

0102 

0077 

0053 

0028 

0004 

50 

51 

0304 

0278 

0252 

0227 

0201 

0176 

0151 

0126 

0101 

0077 

0052 

0028 

0004 

51 

52 

0303 

0277 

0252 

0226 

0201 

0176 

0151 

0126 

0101 

0076 

0052 

0027 

0003 

52 

53 

0303 

0277 

0251 

0226 

0200 

0175 

0150 

0125 

0100 

0076 

0051 

0027 

0003 

53 

54 

0302 

0276 

0251 

0225 

0225 

0200 

0175 

0150 

0125 

0100 

0075 

0051 

0027 

0002 

54 

55 

0.0302 

•  0276 

0250 

0200 

0174 

0149 

0124 

0100 

0075 

0051 

0026 

0002 

55 

56 

0301 

0276 

0250 

022-1 

0199 

0174 

0149 

0124 

0099 

0075 

0050 

0026 

0002 

5Q 

57 

0301 

0275 

0250 

0224 

0199 

0174 

0148 

0124 

0099 

0674 

0050 

0025 

0001 

57 

58 

030C 

0275 

0249 

0224 

0198 

0173 

0148 

0123 

0098 

0074 

0049 

0025 

0001 

58 

— --- 

59 

030(1 

0274 

0249 

0223 

0198 

0173 

0148 

0123 

0098 

0073 

0049 

0025 

0000 

59 

2   47 

2  _  48 

2  49 

1 

2  50 

2  51 

2  52 

2  53 

2   54 

2  55 

2  56 

2   57 

2  t,>> 

e  59 

1 

FABLE  XXXV. 

22  i 

AMPLITUDES. 

DECLINATION. 

Lat. 

0° 

1° 

20 

3° 

40 

50 

6^ 

70 

8° 

9<^ 

10° 

no 

12° 

130 

140 

15°  . 

o 

o 

o 

o 

o 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

10 

20 

30 

40 

5-0 

60 

7-0 

8-0 

9-0 

10-0 

ll-O 

120 

13  0 

14-0 

150 

10 

0 

10 

2-0 

30 

4-1 

5-1 

6-1 

7-0 

8-1 

9-1 

10-1 

11-2 

12-2 

13-2 

14-.> 

15-2 

15 

0 

1-0 

21 

3-1 

4-2 

5-2 

6.2 

7-2 

8-3 

93 

10-4 

11-4 

12-5 

13-5 

14-5 

15-6 

20 

0 

1-1 

2-1 

3-2 

4-3 

5-3 

6-4 

7-5 

8-5 

9-6 

10-6 

11-7 

12-8 

13-8 

14-9 

160 

25 

0 

11 

2-2 

3-3 

4.4 

5-5 

6-6 

7.7 

8-8 

9-9 

111 

12-4 

13-3  14-4 

1 

15-5 

10-6 

30 

0 

1-2 

2-3 

3-4 

4-6 

5-8 

6-9 

8.1 

9-3 

10-3 

11-6 

12-7 

13-9 

150 

10-2 

17-4 

32 

0 

12 

2-4 

3-5 

4-7 

5-9 

71 

8-3 

9-5 

10-6 

11-8 

130 

14-2 

15-4 

16-6 

17-8 

34 

0 

1-2 

2-4 

3-6 

4-8 

6-0 

7-2 

8-4 

9-7 

10-8 

12-1 

13-3 

14-5 

15? 

17-0 

18-2 

35 

0 

1-2 

2-4 

3-7 

4-9 

6-1 

7-3 

8-5 

9-8 

110 

12-2 

13-5 

14-7 

15-9 

17-2 

18-4 

36 

0 

1-2 

2-5 

3-7 

4-9 

6-2 

7.4 

8-7 

9-9 

11-1 

12-4 

13-6 

149 

16-1 

17-4 

18-7 

37 

0 

1-2 

2-5 

3-7 

5-0 

6-3 

7-5 

8-8 

10-0 

11-3 

12-6 

138 

151 

16-4 

17-6 

18-9 

38 

0 

1-3 

2-5 

3-8 

51 

6-3 

7-6 

8-9 

10-2 

11-4 

12-7 

14-0 

15-3 

16-(; 

17-9 

19-2 

39 

0 

1-3 

2-6 

3-8 

51 

6-4 

7-7 

9-0 

10-3 

11-6 

12-9 

14-2 

15-5 

16-8 

18-1 

19-4 

40 

0 

1-3 

2-6 

3-9 

5-2 

6-5 

7-8 

91 

10-5 

11-8 

131 

14-4 

15-7 

17-1 

18-4 

19-7 

41 

0 

1-3 

2-6 

40 

5-3 

6-6 

8-0 

9-3 

10-6 

12-0 

13-3 

14-6 

16  0 

17-3 

18-7 

20-0 

42 

0 

1-4 

2-7 

40 

5-4 

6-7 

8-1 

9-4 

10-8 

121 

13-5 

14-8 

16-2 

17-6 

19-0 

20-4 

43 

0 

14 

2-7 

41 

5-5 

6-8 

8-2 

9-6 

110 

12-3 

13-7 

15-1 

16-5 

17-9 

19-3 

20-7 

44 

0 

1-4 

2-8 

4-2 

5-6 

7-0 

8-3 

9-7 

111 

12-6 

14-0 

15-4 

16-8 

18-2 

19-6 

21-1 

45 

0 

1-4 

2-8 

4-2 

5-7 

7-1 

8-5 

9-9 

11-3 

12-8 

14-2 

15-6 

17-1 

18-5 

20-0 

21-5 

46 

0 

1-4 

2-9 

4-3 

5-8 

7-2 

8-6 

10-1 

11-5 

130 

14-5 

15-9 

17-4 

18-9 

20-4 

21-9 

47 

0 

1-5 

2-9 

4-4 

5-8 

7-3 

8-8 

10-3 

11-8 

13-3 

14-7 

16-2 

17-7 

19-3 

20-8 

22-3 

48 

0 

1-5 

30 

4-5 

60 

7-5 

9-0 

10-5 

120 

13-5 

15-0 

16-6 

18-1 

19-5 

21-2 

22-7 

49 

0 

1-5 

3-0 

4-6 

6-1 

7-6 

9-2 

10-7 

12-2 

13-8 

15-3 

16-9 

18-5 

20-0 

21-6 

23-2 

50 

0 

1-6 

31 

4-7 

6-2 

8-8 

9-3 

10-9 

12-5 

14-1 

15-7 

17-3 

18-9 

20-5 

22  1 

23-7 

51 

0 

1-6 

3-2 

4-8 

6-4 

8-0 

9-6 

11-2 

12-8 

14-4 

160 

17-6 

19-3 

20-9 

22-6 

24-3 

52 

0 

1-6 

3-3 

49 

6-5 

8-1 

9-7 

11-4 

131 

14-7 

16-4 

18-0 

19-7 

21-4 

23  1 

24-9 

53 

0 

1-7 

3-3 

5-0 

6-7 

8-3 

100 

11-7 

13-4 

15-1 

16-8 

18-5 

20-2 

21-9 

23-7 

25-5 

54 

0 

1-7 

3-4 

5-1 

6-8 

8-5 

102 

12-0 

13-7 

15-4 

17-2 

18-9 

20-7 

22-5 

24-3 

26-1 

55 

0 

1-8 

3-5 

5-2 

70 

8-7 

10-5 

12-3 

14-0 

15-8 

17-6 

19-4 

21-2 

23-1 

24-9 

26-8 

56 

0 

1-8 

3-6 

5-4 

7-2 

9-0 

10-7 

12-6 

14-4 

16-2 

18-1 

19-9 

21-8 

23-7 

25-6 

27-6 

57 

0 

1-9 

3-7 

5-5 

7-4 

9-2 

HI 

12-9 

14-8 

16-7 

18-3 

20-5 

22-4 

24-4 

26-4 

28-4 

58 

0 

1-9 

3-8 

5-7 

7-6 

9-r. 

11-4 

13-3 

15-2 

17-2 

191 

211 

23-1 

25  1 

27-2 

29-2 

59 

0 

1-9 

3-8 

5-8 

7-8 

9-7 

12-0 

13-7 

15-7 

17-7 

19-7 

21-7 

23-8 

25-9 

28-0 

30-2 

60 

0 

2-0 

40 

60 

8-0 

10-0 

121 

14-1 

16-2 

18-2 

20-3 

22-4 

24-6 

26-7 

28-9 

31-2 

61 

0 

2-1 

41 

6  2 

8-3 

10-3 

12-5 

14-6 

16-7 

18-8 

2 10 

23-1 

25-4 

27-6 

29-0 
31  0 

32  2 

62 

0 

2-1 

4-3 

6-4 

8-5 

10-7 

12-9 

15-1 

17-3 

19-4 

21-9 

23-9 

26-3 

28-5 

33-4 

63 

0 

22 

4-5 

6-7 

8-8 

IM 

13-4 

15-6 

17-9 

20-1 

22-5 

24-8 

27-3 

29-6 

32-3 

34-7 

64 

0 

2-3 

4-6 

6-9 

91 

11-5 

13-9 

16-2 

18-5 

20-9 

23-3 

25-7 

28-3 

30-9 

33-5 

36-2 

65 

0 

2-4 

4-8 

71 

9-5 

11-9 

14-4 

16-8 

19-3 

21-7 

24-2 

26-8 

29-5 

32-5 

34-9 

3: -8 

to 

Note 
turn 

-— Th( 
those 

5  Amp 
teDths 

litudei 
into  u 

in  thi 
linatee 

sTabl 

k,  W«  D. 

e  are  t 
ultipb 

'xpressed  iu  degrees  and  tenth  parts  of  degrees  and 
^  tliem  by  six,  which  will  jjive  their  value  in  mini  tea. 

222 

TABLE  XXXV. 

AMPUTUDES. 

DECLINATION. 

Lat. 

16° 

161° 

170 

17^0 

18° 

18^o 

19° 

19i° 

200 

201° 

21° 

21^° 

22° 

22^0 

230 

2310 

o 

o 

o 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

16-0 

16-6 

17-0 

17-5 

18-0 

18-5 

190 

19-5 

20-0 

20-5 

21-0 

21-5 

22-0 

22-5 

23-0 

23-5 

10 

16-2 

16-7 

17-3 

17-8 

18-3 

18-8 

19-3 

19-9 

20-3 

20-8 

21-3 

21-8 

22-3 

22-9 

23-4 

23-9 

15 

16-6 

171 

17.-7 

18-1 

18-7 

19-2 

19.7 

20-2 

20-8 

21  3 

21-8 

22-3 

22-8 

23-3 

23-9 

24-3 

20 

17-1 

17-6 

18-1 

18-7 

19-2 

19-7 

20-3 

20-8 

21-3 

21-9 

22-4 

22-9 

23-5 

24-0 

24-6 

251 

25 

17-7 

18-3 

18-8 

19-4 

19-9 

20-5 

21-0 

21-6 

22-5 

22-7 

233 

23-8 

24-4 

24-6 

25-5 

26-1 

30 

18-6 

191 

19-7 

20-3 

20-9 

21-5 

22-1 

22.7 

23-3 

23-8 

24-4 

25  0 

25-6 

26-2 

26-8 

27-4 

32 

190 

196 

20-2 

20-8 

21-4 

22-0 

22-6 

23-2 

23-8 

24-4 

25-0 

25-6 

26-2 

26-8 

27-4 

28-0 

34 

19-4 

'lO-O 

20-6 

21-3 

21-9 

22-5 

23-] 

23-7 

24-4 

25-0 

25-6 

26-2 

26-8 

27-5 

281 

28-7 

35 

19-6 

20-3 

20-9 

21-5 

22-2 

22-8 

23-4 

240 

24-7 

25-3 

25-9 

26-6 

27-2 

27-8 

28-5 

29-1 

36 

19-9 

20-5 

212 

21-8 

22-4 

23-1 

23-7 

24-4 

250 

25-6 

26-3 

26-9 

276 

28-2 

28-9 

29-5 

37 

20-2 

20-8 

21-5 

22-1 

22-8 

23-4 

24-0 

24-7 

25-3 

26-0 

26-7 

27-3 

28-0 

28-6 

29-3 

29-9 

38 

20-5 

21-1 

21-8 

22-4 

231 

23-7 

24-4 

25-1 

25-7 

26-4 

27-0 

27-7 

28-4 

29-0 

29-7 

30-3 

39 

20-8 

21-4 

22-1 

22-8 

23-4 

241 

24-8 

25-4 

261 

26-8 

27-5 

28-1 

28-8 

29-5 

30-2 

30-8 

40 

21-1 

21-8 

22-4 

23-1 

23-8 

24-5 

251 

25-8 

26-5 

27-2 

27-9 

28-6 

29-3 

30-0 

30-7 

31-3 

41 

21-4 

22-1 

22-8 

23-5 

24-2 

24-8 

25-5 

26-2 

26-9 

27-6 

28-3 

290 

29-8 

30-5 

31-2 

31-8 

42 

21-8 

22-5 

23-2 

23-8 

24-6 

25-3 

260 

26-7 

27-4 

28-1 

28-8 

29-5 

30-3 

310 

31-7 

32-4 

43 

221 

22-8 

•23-6 

24-3 

25  0 

25-7 

26-4 

27-1 

27-8 

28-6 

29-3 

30-1 

30-8 

31-5 

32-3 

33  0 

44 

22-5 

23-2 

240 

24-7 

25-6 

26-2 

26-9 

27-6 

28-4 

291 

29-8 

30-6 

31-4 

321 

32-9 

33-6 

45 

22-9 

23-7 

24-4 

25-2 

25-9 

26-7 

27-4 

28-2 

28-9 

29-7 

30-4 

31-2 

320 

32-8 

33-5 

34-3 

46 

23-4 

241 

24-8 

25-6 

26-4 

27-2 

27-9 

28-7 

29-5 

30-3 

31-0 

31-8 

32-6 

33-4 

34-2 

35-0 

47 

23-8 

24-6 

25-4 

20-2 

26-9 

27-7 

28-5 

29-3 

30-1 

30-9 

317 

32-5 

33-3 

341 

34-9 

35-7 

48 

24-3 

251 

25-9 

26-7 

27-5 

28-3 

29-1 

29-9 

30-7 

31-6 

32-4 

33-2 

343 

34-8 

35-7 

36-5 

49 

24-8 

25-6 

26-5 

27-3 

28-1 

28-9 

29-7 

30H 

31-4 

32-3 

33- 1 

33-9 

34-8 

35-7 

36-5 

37-4 

50 

25-4 

26-2 

27-0 

27-8 

28-7 

29-6 

30-4 

31-3 

32-1 

33  0 

33-9 

34-8 

35-6 

36-5 

37-4 

38-3 

51 

26-0 

26-8 

27-7 

28-5 

29-4 

30-3 

311 

32-0 

32-9 

33-8 

34-7 

35-6 

36-5 

37-5 

38-4 

39-3 

52 

26-6 

27-5 

28-3 

29-2 

301 

310 

31-9 

32-8 

33-7 

34 '7 

35-6 

36-5 

37-5 

38-4 

39-4 

40-3 

53 

27-3 

28-2 

29-1 

30-0 

309 

31-8 

32-7 

33-7 

34-6 

35-6 

36-5 

37-5 

38-5 

39-5 

40-5 

41-4 

54 

28-0 

28-9 

29-8 

30-8 

31-7 

32-7 

33-6 

34-6 

35-6 

36-6 

37-6 

38-6 

39-6 

40-6 

41-7 

426 

55 

28-7 

29-7 

30-6 

31-6 

32-6 

33-6 

34-6 

35-6 

36-6 

37-6 

38-7 

39-7 

40-8 

41-8 

42-9 

44-0 

56 

29-5 

305 

31-5 

32-5 

33-5 

34-6 

35-6 

36-6 

37-7 

38-8 

39-8 

40-9 

421 

43-2 

44-3 

45-4 

57 

30-4 

31-4 

32-5 

33-5 

345 

35-6 

36-7 

37-8 

38-9 

400 

4M 

42-3 

43-4 

44-6 

45-8 

47-0 

58 

31-3 

32-4 

33-5 

34-6 

35-7 

36-8 

37-9 

39-0 

40-2 

41-7 

42-5 

43-8 

45-0 

46-2 

47-5 

48-7 

59 

32-3 

33-5 

34-6 

35-7 

36-8 

38-0 

39-2 

40-4 

41-6 

42-8 

441 

45-4 

46-7 

48-0 

49-3 

50-6 

60 

33-4 

34-6 

35-8 

370 

38-2 

39-4 

40-6 

41-9 

43-2 

44-5 

45-8 

471 

48-5 

49-9 

51-4 

52-8 

61 

346 

35-8 

37-1 

383 

39-6 

40-8 

42-2 

43-5 

44-8 

46-2 

47-7 

49-1 

50-6 

52-1 

53-7 

55-2 

62 

35-9 

37-2 

38-5 

39-8 

41-2 

42-5 

43-9 

45-3 

46-8 

48-2 

49-8 

51-3 

52-9 

54-6 

56-3 

58-0 

63 
•  64 

37-4 

38-7 

401 

41-5 

42-9 

44-3 

45-8 

47-3 

48-8 

50-5 

521 

53-8 

55-6 

57-4 

59-4 

61-3 

390 

40-4 

41-8 

43-3 

44-8 

46-4 

48-0 

49-6 

51  3 

53-0 

54-8 

56-7 

58-7 

60-8 

63-0 

65-3 

65 

40-7 

42-2 

43-8 

45-4 

47-0 

48-7 

50-4 

52-2 

54-0 

560 

58-0 

60-1 

62-4 

64-9 

67-6 

70-4 

223 

TABLE  XXXVI. 

THT?  FOLLOWING  TABLE  CONTAINS  EXTRACTS  FROM  THE  NAUTICAL  ALMANAC    I 

FOR  THE  YEAR  1864, 

FOR  THE  PURPOSE  OF  WORKING  OUT  THE 

EXAMPLE  GIVEN  IN  THIS  WORK  TO  SUIT  THOSE  WHO 

MAY  NOT  HAVE  AN  ALMANAC  AT  HAND. 

THE 

.  sun's  rioht  ascension,  declination,  (Ssc. 

Day  of  Month. 

Ap.  RAscen. 

Dit  1  Hr. 

App.  Declination. 

DitlHr 

Semid. 

Equa.  of  Time. 

Dif.  1  Hr. 

H.     M.     8. 

8. 

O       '       " 

If 

• 

/    // 

M.      8. 

• 

Jan. 

20 

20    7  38  S. 

33 

16  17 

(( 

21 

19  54  26  S. 

33.9 

16  17 

(( 

25 

18  57  58  S. 

37.5 

(( 

26 

18  42  58  S. 

38 

Feb. 

7 

21  23  36 

10 

+  14  27.32 

0.106 

t( 

8 

21  27  35 

10 

+  14  29.87 

072 

u 

9 

21  31  34 

10 

-f-  14  31.61 

039 

(( 

10 

21  35  32 

10 

+  14  32.55 

006 

(i 

11 

21  39  28 

10 

+  14  32.70 

025 

Maboh    5 

6     3  14  S. 

58 

16    9 

4-  11  45.76 

584 

(( 

6 

5  40     IS. 

58 

16    8 

+  11  31.74 

602 

(t 

10 

23  21  53 

9 

4     6  30  S. 

59 

-1-  10  31.55 

665 

u 

11 

23  25  33 

9 

3  42  59  S. 

59 

+  10  15.58 

679 

u 

23 

0     9  22 

9 

1     0  54  N. 

59 

+    6  45.27 

766 

u 

24 

0  13     0 

9 

1  24  32  N. 

59 

+    6  26.88 

767 

u 

25 

1  48     7  N. 

59 

-f-    6    8.46 

768 

u 

26 

2  11  40  N. 

58.9 

+    5  50.02 

768 

u 

27 

2  35  UN. 

58.6 

+    5  31.56 

768 

<( 

30 

3  45  22  N. 

58.2 

+    4  36.36 

763 

t( 

31 

4     8  S«  N. 

58 

+    4  18.06 

759 

April 

1 

4  31  35  N. 

58 

-1-    3  59.84 

755 

u 

2 

0  45  43 

9 

4  54  55  N. 

58 

+    3  41.71 

750 

« 

3 

0  49  21 

9 

5  17  56  N. 

57 

+    3  23.70 

745 

(( 

6 

1     0  18 

9 

+    2  30.50 

725 

u 

7 

1     3  57 

9 

+    2  13.11 

716 

M 

16 

-    0  11.87 

603 

(t 

17 

-    0  26.33 

586 

M 

21 

11  50  36  N. 

51 

—    1  20.06 

514 

M 

22 

12  10  53  N. 

50 

-    1  32.39 

494 

i( 

30 

14  45  32  N. 

46 

-    2  53.58 

328 

Mat 

1 

15     3  49  N. 

45 

~    3     1.44 

306 

M 

12 

3  15  50 

10 

18     7  27  N. 

37.4 

—    3  52.34 

053 

(( 

13 

3  19  45 

10 

18  22  25  N. 

36.7 

-    3  53.60 

028 

(i 

19 

19  45  36  N. 

32 

-    3  48.94 

116 

(4 

20 

19  58  19  N. 

31 

-    3  46.15 

140 

JlTNE 

1 

22     3  23  N. 

20 

-    2  31.92 

380 

(( 

2 

22  11  23  N. 

19 

-    2  22.80 

395 

(( 

3 

4  44  13 

10 

22  19     0  N. 

18 

15  48 

—     2  13.33 

410 

(( 

4 

6  52  41 

10 

22  26  13  N. 

17 

15  48 

— 

(( 

21 

23  27  32  N. 

0 

July 

3 

6  48  34 

10 

+    3  49.25 

455 

a 

4 

6  52  41 

10 

4-    4    0.18 

441 

(( 

12 

22     0  19  N. 

21 

+    5  14.40 

308 

(t 

19 

20  53  10  N. 

27 

+    5  56.28 

165 

C( 

20 

20  42     8  N. 

28 

+     6     0.25 

141 

Auo. 

4 

17  17     7  N. 

40 

+    5  50.21 

233 

ii 

5 

17     1     2  N. 

41 

-f    5  44.64 

258 

(( 

14 

9  34  48 

9 

14  24  30  N. 

46 

+    4  28.11 

469 

u 

15 

9  38  34 

9 

14     5  53  N. 

47 

+    4  16.80 

490 

(t 

21 

10    0  54 

9 

+    2  58.97 

610 

(( 

22 

10    4  36 

9 

-»-    2  44.34 

628 

( 

31 

8  41     ON. 

54 

15 


224 

TABLE  XXXVI. 

THE    sun's    RIGHT    ASCENSION,    DECLINATION,    &C. 

Day  of  Monti 

1.     Ap.  R-Ascea 

Dif.  1  Hr. 

App.  Declination. 

Dif.  1  Hr. 

Semid. 

Equa.  of  Time.    Dif  1  Hr.l 

H.     M.     8. 

8. 

o       '      " 

n 

/  n 

1 
M.      S. 

• 

Sept. 

1 

8  19  18  N. 

54 

a 

6 

6  28  51  N. 

56 

— 

1   41.97 

0.841 

n 

7 

6     6  26  N. 

56 

— 

2     2.14 

849 

li 

24 

0  2()     0  S. 

58 

— 

7  57.03 

854 

(i 

25 

0  49  26   S. 

58 

— 

8   17.52 

848 

(( 

26 

12  11   12 

9 

1   12  52  S. 

58 

— 

8  37.87 

840 

(( 

27 

12   14  48 

9 

1   36   17   S. 

58 

— 

8  58.04 

832 

a 

29 

2  23     5   S. 

58 

— 

9  37.78 

814 

u 

30 

2  46  27  S. 

58 

— 

9  57.32 

803 

Oct. 

3 

12  36  31 

9 

___ 

10  54.34 

767 

(( 

4 

12  40     9 

9 

— 

11    12.74 

753 

(( 

5 

12  43  47 

9 

— 

11   30.80 

738 

(( 

9 

6  14  42  S. 

57 

— 

12  39.01 

669 

(( 

10 

6  37  30  S. 

57 

— 

12  55.18 

647 

(( 

20 

10   19  47   S. 

53 

16  6 

— 

15     5.77 

406 

«( 

21 

10  41    18  S. 

53 

16  6 

— 

15   15.49 

378 

Nov. 

27 

21     8  34  S. 

27 



12  12.25 

842 

(( 

28 

21   19  21   S. 

26 

— 

11   52.04 

871 

Dec. 

5 

16  46  36 

11 

^_ 

9  12.43 

1.049 

Lb 

6 

16  50  58 

11 

— 

8  47.26 

1.071 

YEAR  1851.                                                              1 

April 

14 

1  28  37.65 

9.217 

0  22.71 

0.637 

u 

15 

1  32  18.87 

9.232 

0     7.42 

623 

July 

6 

6  59  47.73 

10.275 

4  17.99 

418 

(( 

7 

7     3  54.34 

10.260 

4  28.3 

402  1 

THE    moon's    right    ASCENSION,    DECLINATION,    &C. 

SEMID.          HOR.       PAR. 

RIGHT  ASCENSION. 

DECLINATION.                   MERID   1 

DATE 

1 

NOUN 

MID. 

NOON 

MID. 

NOON 

MID. 

NOON 

MID. 

PASS 

r      II 

'       // 

/      II 

1      1 

'     H,    M.  S. 

H.    M.  S. 

O       '      " 

O      '      " 

H.    M 

Feb. 

7 

14  46 

14  46 

54    8 

54    " 

^     4  59  57 

5  25  17 

23  28  49  N 

24  28  15  N 

March 

10 

14  57 

15     1 

54  47 

55     ( 

)    8  12  21 

8  38  20 

24  13  39  N 

23    3  42N 

(( 

23 

16    9 

59    e 

\ 

20  23  53 

23  51    2  S 

a 

24 

16    7 

59    3 

20  53  47 

22  19  53  S 

April 

23 

2159 

ii 

24 

15  31 

56  5( 

) 

0  51  12  S 

22  43 

u 

25 

15  26 

56  35 

2    2  14N 

June 

2 

15    7 

15  13 

55  24 

55  4.- 

) 

18  24    3  N 

16  1830N 

5  21 

(i 

3 

15    8 

15  03 

55  24 

55  \l 

j 

6    5 

u 

4 

15  19 

56    8 

57  1^ 

July 

3 

15  31 

15  38 

56  49 

1 

(.1 

4 

15  45 

57  41 

" 

11 

10  36 

61  n 

r 

21  21  34  S 

13  .58 

a 

12 

16  31 

61     6 

19    9  21   S 

14  56 

Aug. 

14 

15  15 

55  5S 

> 

2  52  13 

15  25  35  N 

u 

15 

15    9 

55  30 

3  16  29 

17  37  37  N 

(( 

16 

14  59 

14  55 

54  54 

54  4C 

21  26  15  N 

22  58  45  N 

IH    6 

(( 

17 

1!>54 

Sept. 

26 

15  53 

15  56 

58  11 

58  23 

15  26  42 

15  54  24 

18  52  48  S 

21    1  43  S 

Oct. 

1 

{( 

3 

16  12 

16  10 

50  21 

59  14 

22  27 

22  54    4 

15    9  45 

12  20  27 

8  11 

(( 

4 

16    8 

16    4 

59    5 

58  54 

23  20  24 

23  46    9 

9  22    4  S 

6  17  29  S 

1  Dec. 

sl 

13    3 

TABLE  XXXVl. 
YEAR  1851. 

226 

1 

THE  moon's  right  ASCENSION,  DECLINATION,  &C. 

DATE. 

SEMID,      HOR,     PAR. 

R.  ASCENSION. 

H.  DECLINATION 

DF.  10  m.  MERID. 

NOON 

MID. 

NOON 

MID. 

NOON 

MID. 

NOON 

MID.   MER.  PAH. 

April  14 
15 

t       n 

16  23 

16  26 

60  6 

t       It 

60  17 

» 

13 
14 

0  26  21.6  S  133.33 
0  .39  41.6  S  133.2.-:; 

H. 

11  17.9 

12  10.7 

Jolt   6 

7 

15  59 

15  55 

58  39.6  58  2.1.8 

11 

5  31  56.5  S  122.83 

6  40.5 

7  .32.0 

THE  PLANETS  1854. 

DATE, 

NAMES. 

merid.  passage. 

RIGHT  ASCENSION. 

DECLINATION. 

January 

1 

2 

28 

29 

Venus, 
Saturn 

H.  M. 

3  15.0 
3  15.0 
7  1.3 
6  57.0 

H.   M.  S. 

21  59  15 

22  2  33 
3  32  8 
3  32  9 

O    t       II 

13  4  40  S. 

12  39  60  S. 
17  2  12  N. 
17  2  33  N. 

February 

41 

1 
2 

u 

6  45.7 
6  41.8. 

3  32  15 
3  32  18 

17  3  47  N. 
17  4  15  N. 

April 

2 
3 
6 
7 
13 
14 

«( 
Venus 

Jupiter 

18  23.7 
18  20 

3  47  15 
3  47  41 
22  27  28 
22  29  44 
19  51  49 
19  52  36 

18  9  33  N. 
18  11  6  N. 

6  8  43  S. 

6  6  47  S. 
21  6  42  S. 
21  5  47  S. 

Junk 

6 

7 

Mars 

6  2 
5  59 

11  0  50 
11  2  28 

7  24  56  N. 
7  13  13  N. 

July 

3 

4 

Jupiter 

19  44  26 
19  43  55 

21  39  11  S. 
21  40  38  S. 

Septembeh 

.  24 
25 

7  4.6 
7  0.9 

19  17  43 
19  17  52 

22  44  27  S. 
22  44  12  S. 

October 

u 

3 
4 
5 

6  31. 
6  27.5 
6  23.8 

19  19  51 

19  20  7 

22  41  14  S. 
22  40  44  S. 
22  40  13  S. 

December 

5 

6 

« 

19  57  13 

19  58  4 

21  14  47  S. 
21  12  27  S. 

LUNAR  DISTANCES. 

date. 

NAMES. 

HOUR. 

DISTANCE. 

PRO  LOO. 

HOUB. 

DISTANCE. 

PRO.  LOG. 

JUNB 

3 
3 

Sun   W. 
Antares  E. 

VI. 

MID. 

86  48  23 
85  29  55 

.3208 
.2843 

IX. 

XV. 

88  14  23 
83  56  23 

.3193 

.2829 

July 

3 
3 

4 

Jupiter  E. 
Sun   W. 

Sun   W. 

III. 

XXI. 

NOON 

101  46  12 

100  13  12 

101  46  2 

.2t;i8 

.2876 
.2858 

VI. 

10 

0  7  41 

.2601 

August 

14 
14 
15 

Aldebaran  E. 

Sun    E. 
Sun    E. 

XVIIl. 
XXI. 

NOON 

19  57  36 
92  17  18 
90  51  50 

.3115 
.3235 
..3250 

XXI 

18  29  45 

.3175 

Septembei 

I  26 

Sun   W. 

XI. 

54  10  41 

.2769 

IX. 

55  45  50 

.2760 

January 

30 

Aldebaran  E. 

MID. 

85  38  28 

.2362 

XV. 

83  53  59 

.2378 

February 

7 

Sun   W. 

NOON 

117  47  51 

.3488 

I[I. 

11 

9  8  28 

.3489 

star's  right  ASCENSION  AND  DEC 

LINATION,  1851 

Spica, 
Arcturus 

Right  Ascension. 

u          u 

H.  M.   S. 

13  17  22 

14  8  .53 

Declination 

o 

10  2; 

19  5' 

5  1  S. 
r  43  N. 

226 

TABLE  XXXV 11. 

APPROXIMATE  VARIATION  OF  THE  COMPASS. 

N. 

WEST  LONGITUDE. 

O 

0 

0 

0 

C 

o 

o 

o 

o 

O 

o 

O 

O 

O 

o 

o 

o 

o 

o 

LAT. 

180 

170 

160 

150 

140 

130 

120 

110 

100 

o 

90 

80 

70 

60 

50 

40 

30 

20 

10 

0 

O 

O 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

o 

60  N 

17E 

20E 

23  k 

26  B 

26E 

27E 

27  E 

0 

0 

4W 

30W 

46  W 

46  W 

49  W 

48  w 

48  w 

41W 

32W 

28  W 

58 

17 

20 

22 

25 

25 

26 

26 

24 

46 

46 

49 

48 

48 

39 

31 

28 

56 

17 

19 

21 

24 

25 

25 

25 

19 

40 

42 

47 

47 

45 

37 

30 

26 

54 

17 

19 

21 

23 

23 

24 

24 

30 

42 

43 

44 

41 

35 

29 

25 

52 

16 

18 

20 

22 

22 

23 

23 

25 

36 

38 

40 

38 

34 

28 

25 

50 

16 

18 

20 

21 

21 

22 
22 

22 
21 

20 

29 

36 

36 

35 

32 

27 

25 

48 

16 

18 

20 

21 

21 

18 

24 

33 

33 

33 

30 

27 

25 

46 

16 

17 

18 

20 

21 

20 

20 

] 

VORTH 

4 

15 

22 

30 

30 

31 

29 

26 

25 

44 

16 

17 

18 

19 

20 

20 

19 

4 

15 

19 

28 

28 

30 

28 

26 

25 

42 

16 

17 

18 

18 

19 

18 

18 

America. 

2 

12 

17 

24 

26 

28 

27 

25 

24 

' 

40 

15 

16 

17 

17 

18 
17 

17 
16 

17 
16 

1 

9 

16 

21 

25 

26 

26 

24 

22 

38 

15 

16 

17 

17 

0 

6 

12 

20 

22 

25 

25 

23 

22 

36 

15 

15 

16 

16 

16 

15 

15 

1  E 

4 

10 

18 

20 

24 

25 

22 

34 

14 

15 

16 

16 

15 

14 

13 

2 

3 

8 

16 

19 

23 

24 

22 

32 

14 

14 

14 

15 

15 

14 

12 

3 

2 

6 

14 

17 

22 

24 

21 

30 

14 

14 
13 

13 

14 

13 
12 

12 
11 

12 
11 

8  E 

4 

2 

4 

13 

16 

21 

23 

21 

28 

13 

12 

13 

8 

4 

1 

3 

12 

15 

20 

23 

26 

13 

13 

12 

12 

11 

10 

10 

8 

4 

0 

2 

11 

13 

19 

22 

24 

12 

12 

11 

11 

10 

10 

10 

9 

5 

1  E 

1 

10 

12 

18 

21 

22 

12 

11 

10 

10 

9 

9 

9 

9 

5 

2 

0 

9 

11 

17 

21 

20 

12 

11 

10 

10 

9 

9 

9 

9E 

9E 
9 

9 

6 

3 

1  E 

8 

10 

16 

20 

AFkiuA. 

18 

12 

11 

10 

9 

9 

9 

9 

9 

9 

6 

4 

2 

7 

9 

15 

20 

16 

11 

10 

9 

9 

9 

9 

8 

8 

9 

9 

6 

4 

2 

6 

9 

15 

19 

14 

11 

10 

9 

8 

8 

8 

8 

8 

9 

10 

7 

5 

3 

5 

9 

14 

19 

12 

11 

10 

9 

8 

8 

8 

7 

8 

9 

10 

7 

5 

3 

4 

8 

14 

18 

10 

10 

9 

8 

8 

7 

7 

7 

8 

9 

10 

7 

5 

3 

3 

7 

13 

18 

8 

10 

9 

8 

7 

7 

7 

7 

8 

9 

10 

7 

2 

7 

12 

18 

6 

10 

9 

8 

7 

6 

7 

7 

8 

9 

10 

8 

0 

6 

12 

18 

20 

20 

4 

10 

9 

8 

7 

6 

6 

7 

7 

8 

9 

8 

5 

12 

17 

19 

20 

2 

10 

9 

8 

7 

6 

6 

6 

7 

8 

9 

8 

5 

11 

17 

19 

20 

0 

10 

9 

8 

7 

6 

6 

6 

7 

8 

9 

8 

5 

10 

17 

19 

20 

2S 

10 

9 

8 

6 

5 

6 

6 

7 

8 

9 

8 

1  E 

4 

9 

16 

18 

20 

4 

10 

9 

8 

6 

5 

6 

6 

7 

8 

9 

8 

South 

1 

4 

8 

14 

18 

20 

6 

10 

9 

8 

6 

5 

6 

6 

7 

8 

9 

8 

America. 

1 

3 

7 

12 

18 

20 

8 

9 

9 

8 

6 

5 

6 

6 

7 

8 

9 

8 

2 

3 

7 

12 

18 

20 

10 

9 

9 

8 

6 

5 

6 

6 
6 

7 

8 

9 

9 

2 

2 

7 

12 

18 

20 

12 

9 

9 

8 

6 

5 

6 

7 

8 

9 

9 

3 

2 

6 

11 

18 

20 

14 

9 

9 

8 

6 

5 

6 

6 

7 

9 

10 

9 

3 

1 

6 

11 

17 

20 

16 

10 

9 

8 

6 

5 

6 

6 

7 

9 

10 

10 

4 

1 

6 

11 

16 

20 

18 

10 

9 

8 

6 

5 

6 

6 

7 

9 

10 

10 

4 

0 

5 

10 

16 

20 

20 

10 

9 

8   6 

5 

6 

6 
6 

8 

10 

11 

11 

5 

1  E 

5 

10 
10 

16 

20 

22 

10 

9 

8   7 

6 

6 

8 

10 

11 

12 

5 

1 

5 

16 

20 

24 

10 

10 

9 

7 

6 

7 

7 

8 

10 

12 

13 

6 

3 

5 

10 

15 

19 

26 

10 

10 

9 

7 

6 

7 

7 

8 

11 

J2 

14 

10  E 

6 

2 

4 

9 

15 

19 

28 

11 

10 

9 

7 

6 

7 

7 

8 

11 

13 

15 

10 

7 

3 

4 

9 

15 

19 

30 

11 

10 

9 

8 

7 

7 

7 

7 

7 

8 
9 

11 
12 

13 

15 

11 

7 

3 

3 

8 

14 

19 

32 

12 

11 

9 

8 

7 

14 

16 

12 

8 

4 

3 

8 

14 

19 

34 

12 

11 

9 

8 

7 

8 

8 

9 

13 

15 

17 

13 

8 

4 

2 

7 

14 

19 

36 

13 

11 

9 

9 

8 

8 

8 

9 

13 

15 

17 

13 

9 

5 

1 

6 

14 

19 

38 

13 

12 

10 

9 

8 

9 

8 

10 

13 

16 

17 

14 

9 

5 

1 

6 

14 

19 

40 

14 

13 

10 

9 

8 

9 

8 

11 
11 

14 
14 

17 

18 

15 

10 

6 

0 

6 

14 

19 

42 

15 

14 

11 

10 

9 

9 

8 

17 

18 

16 

10 

6 

1  E 

5 

13 

18 

44 

15 

14 

12 

11 

10 

10 

9 

12 

15 

18 

19 

17 

11 

7 

2 

5 

13 

18 

46 

15 

14 

12 

11 

10 

10 

9 

13 

16 

19 

20 

18 

12 

8 

2 

5 

13 

18 

48 

15 

12 

13 

12 

11 

9 

13 

16 

19 

21 

19 

13 

9 

3 

5 

13 

18 

50 

13 

14 

13 

12 

10 
11 

14 
15 

17 
18 

20 

22 

20 

14 

9 

4 

4 

12 

17 

62 

15 

14 

13 

21 

23 

21 

15 

10 

5 

4 

12 

17 

54 

14 

13 

12 

16 

19 

22 

24 

21 

16 

11 

6 

4 

12 

17 

56 

14 

0 

12 

16 

19 

22 

25 

22  ' 

17 

12 

7 

4 

12 

17 

o 

o 

o 

nl 

0 

o 

o 

0 

0 

o 

o 

o 

o 

o 

0 

o 

o 

o 

LAT. 

180 

170 

160  1501 

140 

130 

120 

110 

100 

90 

80 

70   60 

50 

40 

30 

20 

10 

0 

S. 

WEST  LON 

GITUl 

OE. 



TABLE 

XXXV 11. 

227 

APPROXIMATE  VARIATION  OF  THE  COMPASS. 

N. 

IA8T  LONGITUDB.                                   1 

O 

o 

o 

o 

o 

o 

o 

o 

o 

O 

o 

O 

O 

o 

o 

o 

o 

o 

o 

LAT. 

0 

10 
o 

20 

30 

40 

50 

o 

60 

70 

80 

90 

100 

110 

120 

130 

140 

1O0160 

170 

180 

O 

0 

o 

o 

o 

o 

o 

o 

o 

o 

0 

o 

o 

o 

o 

1  ° 

o 

o 

60  N 

26W 

20-W 

15W 

3E 

7E 

12  E 

17E 

58 

25 

20 

15 

3 

12 

17 

56 

25 

20 

15 

3 

12 

17 

54 

24 

20 

15 

low 

» 

3 

12 

17 

52 

24 

20 

15 

10 

2 

12 

16 

50 

23 

19 
18 

15 

10 

2 

12 

16 

48 

22 

14 

10 

2 

12 

16 

46 

22 

18 

12 

11 

3 

12 

16 

44 

21 

17 

13 

11 

Asia 

1  w 

iw 

1  E 

3 

12 

16 

42 

21 

17 

13 

11 

1 

1 

3 

12 

16 

40 

2  • 

16 

13 

11 

2 

1 

3 

12 

16 
15 

38 

20 

16 

13 

11 

2 

1 

3 

7 

11 

36 

20 

16 

14 

12 

1 

0 

3 

6 

10 

14 

34 

16 

14 

12 

1 

0 

2 

3 

6 

10 

14 

32 

14 

13 

12 

0 

0 

2 

4 

6 

10 

14 

30 

12 

12 

0 

0 

2 

4 

7 

10 

13 

28 

IE 

1  E 

0 

0 

0 

2 

4 

7 

10 

13 

26 

3w 

0 

0 

1 

0 

0 

0 

2 

4 

7 

10 

13 

24 

Afk 

ICA. 

3 

0 

0 

1 

0 

0 

0 

3 

4 

7 

9 

12 

22 

3 

0 

0 

2 

1  ^ 

1  E 

0 

3 

5 

7 

9 

12 

20 

3 

0 

0 

2 

1  E 

3 

5 

7 

9 

11 

18 

3 

0 

0 

2 

2 

3 

5 

7 

9 

11 

16 

3 

0 

0 

2 

2 

3 

5 

6 

8 

10 

14 

3 

0 

0 

2 

3   4 

6 

7 

8 

10 

12 

12w 

8w 

3 

0 

0 

2 

2 

2 

2 

3 

4 

6 

7 

8 

10 

10 

12 

8 

3 

0 

0 

2 

2 

2 

2 

3 

4 

6 

7 

8 

10 

8 

12 

8 

3 

0 

0 

2 

2 

2 

2 

3 

4 

6 

7 

8 

10 

6 

20 

12 

8 

3 

0 

0 

2 

2 

2 

2 

3 

4 

6 

7 

8 

10 

4 

20 

12 

8 

3 

0 

0 

2 

2 

2 

2 

3 

4 

6 

7 

8 

10 

2 

20 

12 

8 

3 

0 

0 

2 

2 

2 

2 

3 

4 

6 

7 

8 

10 

0 

20 

13 

8 

4 

0 

0 

1 
1 

1 

2 

2 

3 

4 

6 

7 

8 

9 

2S 

20 

21 

22 

13 

8 

4 

0 

0 

1 

2 

2 

3 

4 

6 

7 

8 

9 

4 

20 

21 

22 

13 

8 

4 

2W 

0 

1 

1 

1 

1 

2 

4 

6 

7 

8 

9 

6 

20 

21 

22 

14 

9 

5 

2 

0 

0 

0 

0 

1 

2 

4 

6 

7 

8 

9 

8 

20 

21 

23 

15 

10 

6 

3 

0 

0 

0 

0 

0 

1 

4 

6 

7 

8 

9 

10 

20 

21 

23 

15 

10 

6 

3 

0 

0 

0 

0 

0 

1 

4 

6 

7 

8 

9 

12 

20 

21 

23 

16 

11 

7 

4 

2 

1  W 

0 

0 

0 

1 

4 

6 

7 

8 

9 

14 

20 

22 

24 

17 

12 

8 

4 

3 

1 

iw 

1  W 

1  W 

0 

4 

6 

7 

8 

9 

16 

20 

22 

24 

18 

14 

9 

6 

4 

2 

1 

1 

1 

0 

3 

fl 

7 

9 

10 

18 

20 

22 

24 

19 

14 

10 

7 

5 

3 

2 

1 

1 

0 

3 

6 

7 

9 

10 

20 

20 

22 

25 

20 

16 

12 

8 

6 

4 
5 

3 

2 

1 

0 

3 

6 

7 
8 

9 

10 

22 

20 

22 

25 

21 

17 

13 

9 

7 

4 

3 

2 

1  w 

4 

7 

0 

10 

24 

20 

22 

25 

22 

18 

15 

10 

8 

6 

5 

4 

2 

1 

4 

7 

8 

9 

10 

26 

19 

22 

26 

23 

19 

16 

11 

9 

7 

5 

3 

2 

1 

4 

7 

8 

9 

10 

28 

19 

22 

26 

24 

20 

17 

12 

10 

8 

6 

4 

3 

1 

4 

7 

8 

9 

10 

30 

19 

22 

26 

29 

25 

22 

19 

14 

12 

10 

7 

5 

3 

1 

6 

8 

9 

10 

11 

32 

19 

23 

27 

30 

26 

24 

20 

16 

14 

11 

9 

7 

4 

2 

5 

8 

9 

10 

11 

34 

19 

23 

27 

30 

27 

24 

21 

18 

16 

13 

10 

7 

4 

2 

5 

8 

9 

10 

12 

36 

19 

24 

28 

31 

28 

26 

23 

20 

18 

15 

11    7 

4 

2 

6 

9 

10 

11 

12 

38 

19 

24 

29 

32 

29 

26 

24 

21 

19 

16 

12 

9 

5 

3 

6 

9 

10 

12 

13 

40 

19 

24 

29 

32 

30 

28 
29 

26 

23 

21 

18 

14 

11 

5 

3 

7 

10 
10 

11 

12 

13 

42 

19 

25 

30 

33 

31 

28 

25 

23 

20 

16 

11 

6 

4 

7 

11 

13 

14 

44 

19 

25 

30 

33 

32 

30 

29 

27 

26 

24 

18 

12 

6 

4 

7 

10 

11 

14 

15 

46 

18 

24 

30 

33 

33 

30 

31 

29 

27 

26 

20 

14 

7 

5 

7 

10 

11 

14 

15 

48 

18 

24 

30 

33 

35 

34 

33 

31 

29 

28 

22 

16 

7 

5 

7 

10 

11 

14 

15 

50 

18 

24 

30 

33 
33 

36 

36 

35 

37 

33 

29 

30 

23 

17 

8 

6 

8 

11 

11 

14 

52 

17 

23 

30 

38 

37 

35 

34 

32 

23 

17 

8 

6 

8 

11 

12 

14 

54 

17 

23 

30 

33 

39 

38 

38 

36 

34 

33 

24 

17 

9 

7 

8 

11 

12 

56 

17 

23 

30 

33 

40 

40 

o 

39 

37 

34 

34 

26 

18 

9 

7 

8 

11 

0 

o 

0 

o 

0 

o 

o 

o 

0 

o 

o 

o 

o 

0 

o 

0 

o 

o 

LAT. 

0 

10 

20 

30 

40 

50 

60 

70 

80 

90 

100  110  1 

120 

130 

140 

150 

160 

170 

180 

s. 



EAS1 

'  LON 

GITITDE. 





_l 

228 


TABLE  XXXV 111. 
CONTAINING  THE  TIDE  HOURS,  OR  THE  TIMES  OF  HIGH  WATER, 


At  the  Full  and  Change  of  the  Moon,  (usually  called  the  Establishment  of  the  Port,)  at  the  principal  Porta  and 
Harbors  of  the  World,  with  the  Vertical  Rise  of  the  Tide  in  Feet,  in  both  Spring  and  Neap  Range.  The  first 
two  numbers,  connected  thus  -  in  the  Range  column,  denotes  the  Spring  Range,  the  second  the  Neap  Range 


PLAOE8. 


TIME. 


EANGE 


Abaco 

Abdl  Koory.. 
Aberdeen  .... 
Aberystwyth.. 

Abrolhos 

Acapulco  .... 

Achen.. 

Adelaide 

Aden 

Adenara. 

Agoada 

Akaroa. 

Akyab 

Albemarle.. . . 

Alderney , 

Amboyna.. ... 

Amoy 

Amsterdam.. . 

—  I^  LOc_.., 
Andamans  N. 

Harb 

Andrava  B.. . , 
Andrews,  St. . 
Augra,  Azores. 

—  Pequenha-. 
Ann,  Az. 

—  St.  I.,  Seych. 
Annapolis,  U.S. 

—  Nov.  Scot. . 
Anticosta,  W. 

Pt. 

Antongil  B.. . . 
Antonio,  Cuba. 

—  Port 

Antwerp 

Aor  Pulo 

Arbroath 

Apalachicola.-. 
Areachon  . . . . 
Areas 


H.  u. 

8     0 


80 

12 

31 

48 

6 

0 

44 

0 


10  30 

4  0 

9  46 

7  15 

6  46 

0  83 

ri2  SO 


8 
11 


Archangel. . . 
A  rdglass . . . . , 
Ardrossan. . , 

Arica 

Aroa. 

Arthur. 

Arundel 

Ascension.. . . 

Auckland 

Augustine  B„. 

—  U.  S. 

Awatcha. . . . 

A^yi- 


10  0 
8  80 

10  46 
12  82 

2  80 

11  69 
5  30 
4  48 

11     0 


FT. 

3 

8 
19-14 
13-6 

6 

H 

7 

6 

8 

8 

9- 

8 

9- 

7 
17-8 

7 
18-17 

18 

8 

9 
7 
25 

8 

18 

6 

2i 

80 


PLACES. 


3  80 

4  0 
9  30 

10  40 
4  25 

1  40 


87 

0 

18 


Kab  el  mandeb 

—  I 

Bahia 

Halfide .... 
Ualasore.. . 
Halbriggan, 

Ually 

Balta   

Baltimore.. 
Bananas  . . 
Bancoot. . . 

Banda 

Banff. 

Banks  . .. , 
Bantam. . . 
Ban  try  B_. 
B 


10  30 

11  54 
8     0 

7  52 

11  15 
6  30 
6  16 

4  30 

8  4 
8  80 

12  10 


11 
6 

H 

30-18 
14 
6 

14-8 
4 

12-7 

n 

2 
19 
10-8 
6 
10 
4 
16 
2 

10 
13 

4 

8-5? 


ar:>ara 


12 

11 

8 

6 

9 

10 

12 

9 

4 

8 

11 

4 

0 

8 

8 
U 


30 
30 
80 
30 
46 
40 
80 
46 
23 
16 
0 
0 
40 
42 

47 
16 


Barb* '  6     0     6- 


e 

8 

lo- 
ll 
11 
6-3 
12 

9 
12 

6! 
11-6 

8 

6 
10-6 

0 


Baifleur  .... 
Barnstable  . . 
Barren  Is.. .. 

Bas  Is 

Basseen 

Batanes 

Batchian ..... 

Bate 

Buthurst 

Bay  of  Is.. . . 

Bayonne 

Beachy  Hd.  . 
Beaumaris  . . 
Beaufort. . . . 

Belfast. 

Bell  Sound.. . 
Belle  Isle  .. . . 
Bambatooka. 
Bembridge  . . 
Bencoolen  .. . 
Benin 

Berbice 

Bergen  

Bergen  op  Z. . 
Bermuda. . . 
Berwick    on 
Tweed. . . 

Bilboa 

Bissao 

Blanco  C 

Blewfields. . . . 

Blyth 

Bodega 

Bojador 

Bombay 

Bi  luacca 

Bonny 

Bordeaux  .  . . . 

Boston,  U.  S... 

Botany  B 

Bow  I 

Boy anna  B. . . . 

Brava  

BrayHd 

Brehat  I 

Brest 

Bridgewater. . 

Biielle 

Brighton  .. . . . 

Bristol 

British  Sd.  . . . 

Bruny 

BiienoB  Ayres. 

Bulama  L 

Buncrana 

Bushire.. . 

Bussora. . 

Button  la. 


H.  M 

8  54 

11  0 
4  45 
6  15 

12  80 


TIME.   EANGE 


12     0 
8  10 


16 

15 

0 


10  32 
6  52 

10  43 
8  66 

11  30 
4  30 

11  40 

0  0 
4  16 
4  30 

1  30 
8  80 

7  or  8 


FT. 

9 

12 
27 
17 
4 
6 

14 
7 
6 

16 
21 
21-11 
7 
9-6 
3 
7 
16 


6  80 
11  46 

1  60 

2  48 

11  80 

12  0 
11   10 


18 
68 


9 
6 

6  55 

11  31 
8  0? 

2  40 
4  30 

4  30 
10  45 

5  27 

3  48 

6  60 

3  0 
10     6 

7  15 

4  0 
9? 

0  0 
4  80 
7  54 
7  30 

12  0 
6  60 


7 
11 


16 

291 

14 

6 

2 

14-10 

7 


PLACES. 


15-11 

u 

9 
14-11 

12 
7  or  4 

8 

15 

8 
12-7 

37 
19-9 
35-18 

14 

16 

40 

n 

9 

var. 
15 
17 
6 


Cadiz , 

Ciiernarvon. . , 

Cajeli 

Calcutta  . . . . . 
Calebar,  New, 

Callao 

Cameroons  R.. 
Camiguin  . . . , 
Campbell  I.  . . 
Campbelton.. , 
Campobello  . . 

Cambing 

CanBO,  Gut . . , 


2 

9  33 
1  0 
3  0 
6  0 
6  47 
6  0 
6  « 
12     Oi  43? 


12-8 

14-8 

6 

9 

4 
7 
6 


11  45 
11  19 
noon 


8-4 

21-16 

6 


8  80      8 


Cantin  C 

Canton 

Capricorn  C. . 
Cargados  Gar. 

Cardiff 

Carlingford. .. 

Carlos  St 

Carrickfergus . 

Car  tar  et 

Castlereagh  C. 
Catherine  St  . 
Catoehe,  C. . . . 

Cayenne  

Cayeux. 

Ceuta 

Chaguaramus. 
Champion  B. .. 
Charles,  0.  . . . 
Charleston  . . . 

Cliatham 

Chatte  C 

Chaussey  . . . , 

Cheduba 

Chepstow.. . . , 
Cherbourg  . . , 

Chester , 

Chichester. . 
Chignecto.  . , 
Chimmo  B.  . . , 
Chin-chew. . . 
Chin-Hae  . . . 
Cbittagong.. . 

Chosari 

Christmas. . . 

Chusan  

Circular  Hi. 
Clara,  Sta.. . . 

Coast,  C 

Cobija 

Cochin 

Cockburn  . . . 

Cod  C 

Colorado... 
Columbia  R. . 

Comoro 

Condore  .... 
Copiap6  .... 

Coquet  

Coquimbo... . 
Cordovan  . . . 

Coringa 

Corisco 

Coik 

Coruuna  .... 

Coupang 

Coy  Inlet  .  . 
Cracatoa  _. . . 
Cromer  _. . . . 
Crooked  I.. . . 
Crookhaven  . 
Curieuse.. . . . 
Curtis,    Port, 

Austr 

Cutch,  G 

Cuxhaven.. . . 

Dalrymple  . . . 
Damaun  Bar  . 
Dampier  Strait 
Dartmouth.. . 
Darnley  L. . , 
Darwin,  Port 


H.  M, 
10     0 


TIME.  EANGE 


2 
8 
2 

6 

11 


40 
0 
3 

59 
0 


11  46 

10  30 

2  60 

2  40 

8  45 

11  6 
1  55 

3  30 

9  10 
7  45 
7   16 

0  54 

12  0 

6  9 
11  30 

7  30 
7  49 

10  80 

11  45 

11  0 

12  25 
12  25 
12  10 

1  30 


PLACES. 


TIME.   RANGE 


7 
10 

11 

12 
4 
4 
9 


30 
0 
0 

0 
46 

54 


4  15 

11  30 
8  40 

12  15 


30 
0 


8  80 
5  45 


8 
37 
0 
0 
1 
0 
30 


FT. 


7 
4 

18-12 

19 

8 

6 

4 
6- 

1 

6 
27-16 

4 
1 
6 

8 

13 

30 

8 

70? 

17-8 

26 

14 

82 

16 

17- 

10 
15-10 

4 

12-6 

9 
7- 
7 
4 
6 

12 
13 
11 

1i 

12 

4 

5 

15-8 

6 

14-7 

5-3 

7 
11-7 


9  30 

7     0 


lltol 

0  44 

13     6 

1  30 

6     6 
9  80 

5  30 


7 

40 
4 

15-7 
2i 

12-8 
7 

10-6 
16 


10 

17 

11 
19-11 

10 
24-17 


Dauphin,  Fort 
Delagoa  .. 
Delaware  R.C. 

Hen.  c_. . . 
Delgado,  Az.. 

—  C _. 

Delhi,  R 

Demerara 

Desire 

Devonport-. 
Diamond  I.  . 
Diego  Gar.  . 

—  Ram.  . . . 

—  ot.  C  . , . 
Dieppe  ,.. . . 
Discovery  >. . 
Dislocation .. . 

Diu  I 

Divy 

Douglas 

Dover 

Dragon's  Mo... 
Dublin  Poolb, 

Dunbar 

Duncansby .. . 
Dundee  _. . . . 
Dunkirk  . . . . 
Dunraore. . . . 
Durnford.. . . . 
Durien,  Strait 

Easter  L  . . . . 
Edgar,  Port. . 
Egg  Harbor- . 

Elbe 

Elena  ....... 

Embden  . . . . 

Endeavor  R.», 

English  Rd 

Essington  Pt. 
Evangelists  . . 
Exmouth  . . . . 
Exuma.... .. . 


H.  M. 

4  30 
4  40 

8    0 

12  80 

4    0 

4    0 

4  30 
12  45 

5  43 

10  30 

1  30 
4  0 
4  30 

11  6 

2  80 

1  40 

2  0 

11     8 

11  12 
8    0 

10  30 
2    0 

10  0 
2  31 

12  8 
6  46 
4  46 
irr. 


Fairweath.  C. 
Falmouth. . . 

Famine . . . 

Faval„ 

Fear,  C 

Fernando  Nor. 

Ferrol , 

Finisterre  . . , 
Flamenco. . . 
Fleetwood  . ., 
Flushing  ... 
Folkstone  . . . 
Foreland,  N.  . 

Fowey 

Francisco,  St 
Funchal  . . . ., 
Fundy  B 


FT. 
7 

13 

4-3 

7 

16 
8 
9 
21 
16-7 
8 

6 

10 
27-16 

7 

4 

6 

6 
22-11 

20 

4 
IS-I 

9 
1&-7 
17-10 

16 

12 

10 


2 
7 
7 

12 
4 

12 
8 
7 
8 
1 


0 

15 

10 

0 

0 

0 

0 

30 

24 

0 

6  29 

7  20 


11  30 

7    0 


9  10 

10  63 
1    0 

11  15 
5  30 

11 

12  16 


Gaboon,  R.. . . 
Gallant,  Port, 
Gal  legos,  R.. . 
Galveston  . . . 

Gal  ;vay 

Gambia,  Bath- 

urst  .... 
Gambler  la. 
Gasp6  B. . . 
Gay  Hd 


6 

9 

8  601 


4  82 


6 

4 
12 
17 


5 
18 

5 
14-8 

28 
18 
9 

4i 
7 

6-5 


5 

28-21 

14- 
17 

16 

8-2 

9 

60 

8 
5 

48 

4 

15-7 


60 
60 
87 


8 
6 

7 


TAlil.E  XXXVlll. 
CONTAINING  THE  TIDE  HOURS,  OR  THE  TIMES  OF  HIGH  WATER. 


12V 


PLAOKS. 


TIME  EANGE 


Geby  I 

George,  St  ah , 
GeorgetowD  . . 

(ihei'iah 

Gibraltar  .... 

Glasgow 

Gloucester  . . , 

Goa , 

Good  Hope,  C. 
Good  Success  . 

Goree 

Gracias,  C.  . . . 
Graud,  Port  . . 
Granville  . . . . 
Greenock  . . . . 

(ruasco 

Guatulco 

Guaymes 

Guerusey  . . . . 

GuD  Cay 

Guayaquil. . . . 


Haarlem 

Hague 

Hakluyts  Hd.. 

Halifax.   

Hamburgh  . . . 
Hammerifest. . 
Hardy,  Port  . 
Hartlepool  . . . 

Harwich 

Hastings,  St.M 
Hatteras,  C.  .  • 

Havana 

Havre  _ 

Haytien,  C. .. 
Heligoland  . . . 
Helena,  St  B.. 

—  I 

Henlopen,  C. . 

Henry,  C 

Heraiiura,. . . , 
Hillsboro'  Inlet 
Hobarton  .... 
H<jkianga  .... 
Holmes'  Hole. 

Holy  L 

Holyhead  .... 
Honduras  Bay, 

Honfleur 

Hong  Ko 

Houtman'a  Ab. 
Hunoruru  . . . 

Horn,  C 

Howe,  C 

Huacho 

Hull     

Hunter,  Port 

Ilfracombe  . . 

Indus 

Inbambans. . . 
Inverness  . . . 
Iquiqua..    .. 

Islay , .. 

Ives,  St 


Jacinto  . .  . 
Jask  B-. .  , . 
JericoAcoard 

Jersey 

Jervig 

Jiddah 

Johanna  . . . 
John's,  St.  N.  FJ 


10  80 

7     0 


11  45 
3     0 


3 

48 


10  30 


6   13 


8  30 

1  30 

8  03 
6  30 

^ 

7 

9 
7 
1 
7 
5 
1 
8 
3 
0 
10  40 

9  0 

9  51 
6     0 


0 

0 
45 

30 
39 

0 
10 

0 
28 

6 


0 
30 


8  11 

8     0 


40 
8 

30 
0 

30 


11  48 

2  30 

10  26 


9  30 

11  30 
irr. 
4  40 
9  0 
4  44 
6  29 

10  45 

6  45 
irr. 

4  15 

12  1 
8  45 
8  53 
4  44 

6  80 
6     0 


11 

6 


6  46 
irr. 

8  80 

7  30 


FT. 

6- 

7 
4 
6 


5 

5 

9 
4 

2 

H 
37-17 
10-6 

5 

5 

6- 

35 

3 
11- 


21 

4 
8 

9 

12 

15-8 

11-7 

13- 

-5 

3 
22-12 

3 

9 

3 

4-3 

4 

6 

5 

4 

9 
2-1 

15 
16-8 

1 

18 
9- 

2 

2 

9 

6 

3 
22-13 

6 

32-13 
12-4 

10 
12-7 

5 

7 
21-10 

6 
6 
12 
33-14 
6 
2 
8 
7 


PLACES. 


John's,  St  N.B. 
Joseph,  St„. . 
Juan,  St  P.  R. 

—  Peru 

—  de  Nova. . 
Julian 


u.  M. 
11  23 


Karakakoa  B.. 

Katwyk 

Kedgeree  . . . . 
Keeling 


Keluug. 

Kilduin 

Kilrush 

Killibeg 

King  G's  Sd.. 

King's  I 

Kingston   .... 

Kiusale 

Kish  Lt 

Kishm  I 

Ki'acatoa 

Kuria  Muria.. 
Kykduin  _. . ., 

Lagos,  Afr.. . . 

—  Portugal  . . 
Lambeyeque.. 

Lamo 

Latham 

Leith 

Lerwick 

Leiibu  R 

Limerick 

Lindy 

Lintin 

Lisbon 

Liscombe  .... 
Liverpool  .... 

Loando  

Lobito 

Loheia 

Loire,  R,  mo.. 

Loraas 

Lombock . . . 
London  Bridge 
Loo  Choo,  Nap. 
Lopez,  C.  . . 
L'Orient . . . 
Los  Is.  de  . . 
Louis,  Port. 

—  Falk 

Low,  Port . . 
Lowestofft  . 

Lucas 

Lundy  I.. . . 


Macao  _. . . . 
Macowa  L. . 
Machias.. . . 
Macquarrie. 
Madame  . . . 
Madeira  . . . 
Madras  .... 
Magadoxa. . 
Magalhaen's  St 

E  entr... . 
Mahe  I.  . . . 

Mahon 

Magnetic  I.. 
Ma  jam  bo  . . 
Magtlalena  B.. 
Magdalen  Ib. 
Makuinba. . . 
Malacca  .... 


TIME. 


RANGE 


0 
20 
10 


10  45 


3 

2 

11 

4 


49 

30 

30 

0 


10  80 
7  0 


42 
45 


irr. 
irr. 
11  10 
4  43 

10  80 

11  0 

7  0 

8  20 
7  0 


4 
2 

4 
4 
4 
2 
9 

10 
7 
4 

12 
4 

11 

4 
2 
1 
3 
8 

2 
9 
4 
3 
6 
1 
6 
0 
9 
9 
6 

9 

12 
11 
7 
4 
12 
7 
4 

8 
8 
9 
3 

4 
7 
8 
4 
9 


0 

7 

0 

6 

0 

17 

45 

80 

58 

30 

0 

0 

16 
80 
20 
30 
45 
19 

7 

0 

80 

41 

35 

2 

0 

40 

61 

20 

15 

52 
80 

0 
80 

0 
48 
84 
30 

66 
45 
37 
10 
30 
85 
20 
45 
15 


FT. 

23-17 

8 

H 

3 
5 

30 


5 
3 

12 
16 

3 

12 
11-6 
11-7 

10 

12 

4 

6 

12 

6 
18 

3 
11 

10 
16-7 

8 

5 
17 
12 

8 

7-4 
25-14 

6 

5 

3 

19 

6 

7 
18- 

9 

20 
17-13 

2 

7 

7 
8-4 

9 
27-13 

8 
2 
12 
3 

5 
7 
8 
8 

46 

6 
6-4 
12 
16 

6 

3 
17 
8- 


PLAl'ES. 


TIME. 


Malaga, 

Maldives. .    . 

Malo,  St 

Malpelo  Pt. . 

Manila , 

Mhn  of-War 

Cay 

Manukau  . . . 
Maranham  . . 
Marblehead  . 
Marcouf,  St  . 

Marosse 

Martaban.. . . 
Martin,  Cove  .. 
Martin  Vas 
Mary,  St  C.  N. 

Scotia  .  . 
Matheson  Har. 
Massowah. . 

May,  C 

Mayotta  . . . 
Mazatlan. . . 
Mazeira. . . . 
Meiehow. ., 
Melinda .. . . 
Mergui  .... 

Merjee 

Miatau  .... 
Michael,  St  Az. 

Michel 

Milford  Haven 
Mindanao,  S.pt 

Mingan 

Min  R. 

Minow  L. . . . 
Miia  por  vos. 
Mississippi  . . 

Mobile 

Mocha 

Mogador  .. . . 
Molucca  Is.. . 
Mombaza  . . . 
Monganui  . . . 

MoDomy 

Monterey  . . . 
Monte  Video. 
Montrose. . . . 
Monts,  de. . . . 
Morebat  .... 

Moreno 

Morlaix 

Mossel  B.  . , . 
Mount  Desert 
Mourandova.. 
Mozambique. 
Mugeres  .... 
Musa 


H.  M. 

12     0 


Nagore 

Nancowry. . 
Nangasaki. . 

Nanka 

Nantucket  Shi 
Napakeang. . , 
Nareenda  B-. . 

Nassau 

Natal 

Negapatam . . . 

Negro  R. 

Nelson 

New  Bedford. 
Newbury  port. 
New  Calebar.. 
Newhaven  . . . 
—  U.  S 


RANOE 


3 
6 
4 
irr. 


10 
30 

0 
30 
55 

0 
20 
60 
45 


FT. 

3 

4 

35-17 

10 

3 

4 
12 
18 
12 
20 
5 
21 


9  30 
12  30 


0 
19 
46 


9  40 

10  48 
12  30 

4  15 

11  80 

11  0 

12  80 

5  46 
7  0 
1  80 

10  15 
5 
9  80 


2     0 


60 


11  30 

7  30 

irr, 

1  30 
12 

9 
10 

4  63 

3 
11   10 

4  45 

4  15 

9  30 


8  15? 
9  15 

7  52 

10  44 


6 
4 
7 

10 
6 

11 
9 
7 

11 
5 

11 

11 


30 
80 
30 

0 
0? 

0 

0 
55 
15 
30 

9 
16 


16 
17 
3 
6-4 
11 

H 

5 

17- 

11 

21- 

7 
7 
6 

22 

6 

7 

19- 

16 
8 

H 
2- 
4 
10 
3 
11 
8 
6 


18- 

12 

6 

4 
24-12 

6 

13 
12 
12 

6 

8 

8 
9-1 

12 

7 

15 

4-3 

8 

14 
11 

5-4 

10 

8 

19-14 

6-5 


PLACES. 


TIME. 


New  London 
Newport. . . 
N.  Providence 
N.  York  City. 
Nicholson. . . . 

Nicoya 

Ninepin  Is 

Noirmoustier. 
No  re  Light  . . 

Norfolk  I 

Noss  Bey .... 
Neuva  G 


RANGE 


Ociacocke  . 
Old  PtComft. 

—  Providence 

Oleron 

Oporto 

Orange  B . . . 

Ostend 

Otago 

Otaheite. . . . 
Otway,  Port. 

Padstow .... 
Palm  as  C.  . . 
Palmiras  Pt. 
Panama. . . . 

Paposo 

Para 

—  Entr 

Passamaquod. 
I'assandava. 
Patta. ..... 

Payta 

Pearl  Cays  . 
Peiho  R.  . . . 
Pelew  Is.. . . 

Pemba 

Pembroke  . . 
Penang  .... 
Penas  C.  . . . 
Peniche  .... 
Penmarc'h . . 
Pensacola  . . 
Pentlaud  Sker 
Pernambuco 
Peros  Banhos.. 
Pescadores  . 
Peterhead.. . 
Philadelphia 

Philip 

Pieliidanque 

Pillar  C 

Pisco 

Placeiitia. . . 
Pletteiiburg. 
Plymouth.U.S 
Pomba, . . . 

Poole 

Portland,  U.S. 
Porto  Rico . . 
Port  Royal  . 
Portsmouth, 

—  U.  S 

Post  Off.  B... 
Pouinipet  . . 

Praya  

Puget  Sound 
Pulicat  Shoals 


Quail  I 

Quebec  . . . . 
Quentin  St.. 
Quilca 


H.  M. 

9  30 
7  45 

7  3U 

8  37 
4  16 

2  56 
10  0 

3  2 
12  30 

7  46 

6  0 

7  10 

9  0 

8  27 
irr 
3  50 

2  30 

3  30 

0  20 

3  20 
noon 
noon 

4  40 
6  30 

9  30 

3  9 
9  40 

12  0 

10  0 

11  30 

5  0 

4  30 
3  20 

2  0 

3  30 

4  15 

6  12 

2  15 
6  42 

1  54 

3  16 

8  50 

4  23 
1  30 

10  30 

0  48 

1  22 

0  20 

9  20 

1  0 
4  50 
9  15 

3  10 

11  30 

4  0 
9  30 

11  10 

8  30 

5  46 
11  41 
11  30 

2  10 

6  0 
0  0 
6  0 

9  25 

4  0 

6  30 
9  5 
8  0 


FT. 

5-2 

6-3 

4-3 

6 

6 
10 

5 
17-16 
14- 

7 

15 

10 


4 
1? 
19 
10- 
5 

19-15 
9 
1 
6 

22-16 

6 
11-7 

5 
11 

25 
15 
10 

3 

2 

7 

6 

12 
21-10 

8 
12 


2 

8-3 

6 

5 

9-4 

11-6 

7-4 

3 

5 

6 

4 

8 

5 

11 

15-7 

5-2 

12 

1 

6 

12-6 

10 

6 

H 
5 

18 
3 

6 
17 
6 
6 


880 


TABLE  XXXVIII. 
CONTAINING  THE  TIDE  HOURS,  OR  THE  TIMES  OF  HIGH  WA.TER 


pi^osa 


Quillimane.. . . 
Qniloa 

Racbado  0.. . . 

Ragged  I 

—  Pt^  Borneo. 

Rainel 

Rajahpoor. . . . 

Rangoon  

Raa  el  Kbyma  1 

Realejo 

Rendezvous  L 
Resolution  Bay 

Marq 

Rio  Janeiro. . . 
Rochefort  .... 

Rochelle 

Rodriguez  ... 
Roque,  0.  St-. 
Rotterdam  . . . 

Royal  L 

Rush,  Port  . . . 


TIME.  SANGE 


a.  M. 

4  15 
4  46 


6 

8 

8 
11 
6 
1 
3 


8able  0.  . . . 

—  I.,  N.  side 

—  Ditto  S^side 

Saintes 

Saloombe  .... 

Saldanba 

Salem. 

San  Bias. 

Sandalwood  B. 
San  Carlos 

Falk- 

Sandy  Hook,  c. 
Sanguir  L. . . . 
San  Joeef .... 
Sta.  Onu. .... 


8 
10 
8 
6 
6 
2 
11 
9 
6 

1 

7 

10 

9 


80 
10 

0 
0 
30 
0 
6 


30 
0 
48 
89 
86 

46 

46 
60 

0 
80 
80 
46 
60 

0 
16 
46 

0 


0 
29 


FT. 

16 
12 

13- 

3- 

7 

10- 

12 
20-14 

11- 

8 

4 
6 

20 

6 
10-6 

8i 
7-4 

9 

7 
7 

19-11 

6 

11 

7- 

6-! 


8 

6-4 

6 

0180-20 
80I4O-I8 


PLACES. 


Sta.  Maria  Is. . 
Saperuah  B.. . 

Saugor  I 

Savannah  .... 
Saatander. . . . 
Scarborough . . 

Searbet  I 

Sea  Bear  B. . . 
Sebaet.  St.. . . . 
Second  Bar .. . 

Sein  I 

Selsea  Harb.. . 

Senegal 

Serrana 

Serranilla... . 
Shelburne. . .. 

Sheerness 

Sberbro' 

Shields 

Sierra  Leone  . 

Simons  B 

Singapore. . . . 

Sisal 

Sitka 

Sofala 

Spain,  Port .. . 
Spurn  Pt . . . . 

Staten  I 

Stephens   Port 

Falk. 

—  Austr.  .... 
Stirrup  Cay.. . 
Stonehaven. . . 
Stockton  ..... 
Stornoway  . . . 

Suez 

Sunderland... 
Supd. 


TUIE. 


H.U. 

10  20 


7  16 

8  30 
4  12 

1  30 
12  46 

2  0 
irr. 

8  21 
11  45 
10  30 

irr. 
8  30 


37 
0 
30 
60 
80 
0 

84 

0 
0 


6  20 
4  80 


46 
15 
0 
17 
80 


6  46 
0  SO 
8  28 
4  60 


aANGB 


FT. 
6 

6 

12 

Si 

18-10 

10 

20 

4 

7 
17-7 
14-5 

2 

2 

8 
16-11 

11 
16-11 

11 

6 

9 

2 

21- 

4 
28-14 

8 

7 

8 

4 
14-8 

18 
16-11 

6 
14-8 

8 


PLACES. 


TIME. 


Surat. . .., 
Surinam  . , 
Swan  R.  . , 
Swansea. . , 
Sydney.. . , 
—  Bret  I., 


Table  B. 

Tae-Chowls.. 
Talcuhuano. . . 

Tamar 

Tarnareed. . . . 
Tamatave. . .. 
Tang-tang .... 

Tanna  

Tarbert 

Tarifa 

Tavoy 

Teignmouth  . . 
Tenerife 

Tien  Pak 

Thomas,  St  L. 
Three  Pts.  C.  . 

Tiinoan 

Ting-Hae,  Ohu. 

Ban 

Tobago  

Tongatabou  . . 

Torbay  

Torres  Strait  . 

Triangles 

Trincomalee.. . 
Tristan  d'Ao, 
Tynemouth... 


10  14 
8     6 


aANQE 


B.  U. 


8  60 
6  36 


7 
9 

2 
10 


20 
18 
30 
85 
67 


1115? 
10     0 


0 
80 


6  46 
12  0 
8  26 
8  0 
6     0 

11  0 
irr. 
6  60 
6    0 


8  18 
2  60 


Union  B. 8  10 

Uprtart  C.  .. .',  9    pl 


FT. 

80 
6 
2 
30-15 
6 
6 

6 

16 

6 

6 

8 

8 

6 

3 
15-10 

8 

17 

13-7 

7 

6 

8 

4 

5 

7 

12-6 

3i 

4 

20 

6 

2 
8 
18 

ia-6 


PLACES 


TUOC  BANQB 


Uehant. 


Valdivia  . . . 
Valentia  . .  . 
Valparaiso  . 
Vera  Cruz. . 

Verd  0 

Versa vah.. . 
Vincent   Port 
Vingorla  . . . 
Virgin's  C. . 

Wahaay  . . . 
Walwich  . . . 
Wangaroa.. . 
Waterford . . 
Welseley  Is. 
Western,  Port 
Westport,. . 
Wexford  . . . 
Weymouth  . 

Whitby 

Whitehaven 
Wicklow.. . . 
Wilson's  Pro. 
Woosung-. . 

Yang-tze-ke- 

ang 

Yarmouth  ». 
Yellaboi  . . . 
Ylo. 

York  . . , 
Yooghal. 


B.M. 

8  82 

10  85 

8  45 

9  32 
irr. 

7  45 
12  15 

8  10 
10  80 

8  50 


!••••••• 


6 
1 
8 
6 
8 
1 
4 
6 
6 
8 
11 
10 
2 
1 


0 
54 
15 

6 

0 
10 
57 
80 
SO 
45 
14 
80 

0 
80 


Ziiuibar. 


10 
10 
20 
16 
26 


FT. 

19-8 

5 

17-7 

5 

3 

3 
16 

5 

6 
38 

3 

6 

7 
13-7 

12 

8 

13-6 

5-8 

7 

13 

23-12 

9-5 

10 

16 


15-10 

7-2 

10 

6 

14-10 

12-8 


4  20    10 


I 


TABLE   XXXIX.  2S) 

CONIAINING  THE  TRUE  POSITIONS  OF  THE  MOST  PROMINENT  AND  CONSPICUOUS  PLACES 

IN  THE  WORLD. 

Selected  on  account  of  their  height  (which  is  given  in  this  Table)  or  other  remarkable  appearance,  with  the  view 
of  their  being  readily  identified  by  the  Navigator  when  in  eight,  for  the  purpose  of  verifying  or  Rating  his  Chro- 
nometer, from  time  to  time  during  the  voyage.    (See  method  of  doing  this  at  page  155). 

The  Longitudes  are  reckoned  from  the  Meridian  of  Greenwich.     The  fractional  parts  of  Mmutes  of  Latitude 
and  Longitude  are  given  in  tenths,  which  multiplied  by  six,  will  produce  Seconds. 


E.  Coast  of  U.  S.  of  America. 


Lat.  N. 


44  57 
44  49  3 

44  34 

43  68 
43  46-4 
43  36 
43  13 

42  38-S 
42  31 
42  19 


NAMES  OF  PLACES. 

lel'd  of  Campo  Bello 

N.  end 

Quoddy  Head  Light 
Grand  Mannan  S.W 

end 

Mount  Desart  Rock 

Light  House. 
Martinicus  Island  It 
Portland  Lt.  House. 
Agaraenticus  Hill . . 
Cape  Ann,   Thatch 
churn  Island  lio:ht 
Salem  City  Hall 
Boston  Light  House 
Cambi'idge  Observa- 
tory  42  23 

Cape  Cod  Light... .  42    2 
Monomoy   Light. . .  41  33-5 
Nantucket  Har.  light  41  16-4 
New  Bedford  L.  H.  41  35-5 

Newport  Spire 41  292 

Point  Judith  Light.  41  216 
Block  Island  Light  41  lS-4 
New  London  L.'H..  41  19 
Moutauk  Point  L.  H.  41  4-2 
N.  Y.  City  Hall....  40  42-7 
Sandy  Hook  Light.  40  27-7 
Neversink  Lights. .  40  23-7 
Baruegat  Light  H.  39  46 
Little  Egg  Harb.  Lt  39  30-5 
Cape  May  Light. . .  38  55  8 
Cape  Henlop'n  L.  H.  38  46-6 
Phihidelphia  St.H. .  39  o6-9 
Smith's  Island  light  37    78 

Cape   Charles 37    7'3 

Cape  Henry  h'ght. .  36  55'5 

Richmond 37  82 

National  Obs'rvat'ry  38  53-6 
Cape   Hatteras....  35  15*2 

Cape  Lookout .34  37 

Cape  Fear 33  48 

George  Town  L.  H.  33  125 

Cape  Roman 33    1 

Charlestown  L.  H..  32  41-9 

Tybee   Light 32    0 

Light  on  St  Simon's 

Island 31    8 

Cumberland    Island 

Light 30  45 

St  Augustine  L.  H.  29  52  3 
Cape  Carneveral. . .  28  27 

Bald    Head 27     1 

Cape  Florida  Light  25  399 
Key  West  Light. .  24  33 
Tortugas  Island,  S. 

W.  end 24  31 

St  Mark's  Light  H.  30    4 
Cape  St  George. . .  29  35 
Pensacola  Light. . .  30  19 
Mobile  Point  Light.  30  ISS 
Mobile,  Barton's  Ac- 
ademy  30  41-4 

Mississippi  River. . 
"   a.  I.  Outre  Pass  29  14 

•♦  Balize 29  8  5 

"  S.  E.  Pass 29  6 

«  S.  Pass 28  59-7 

"  S.  W.  PasB...  28  68-5 


LoN.  W. 

o   / 


66  55 
66  57 


66  53 

68  8-5 

68  49 
70  12 
70  41 

70  34-7 
70  54 

70  53-6 

71  7-4 
70  8-3 

69  59  3 

70  44 

70  53-7 

71  18-5 
71  28.6 

71  34-2 

72  51 
71  511 
74  01 

73  59-8 

73  58-8 

74  6 
74  17-5 

74  f)7-3 

75  4-7 
75  8-7 
75  52-2 

75  57  9 

76  0-2 

77  27 
77  2-8 

75  30-9 

76  33 

77  57 
79  10 
79  24 

79  52-6 

80  52 

81  36 

81  37 
81  25 
80  33 
80  11 

80  5 

81  47-3 

83  7 

84  10 

85  4 

87  16-9 

88  05 

88  1-9 

89  0 
89  1-4 

88  57 

89  7-4 
89  20 


NAMES  OF  PLACES. 

New  Orleans 

Racoon  Point , 

Sabine  River  ent. , 
Galveston  entrance , 
Rio  Grande 


Lat.  N. 

o         / 

29  57-6 
%9    3 
29  40-6 
29  20-5 
25  56 


LoN.  W 


90    0 
90  57 

93  49 

94  45 
97  12 


NAMES  OF  PLAGES. 


Coast  of  California. 


St  Diego  Pt  Luma 
St  Catalina  Island. 
Santa   Cruz   Island- 

W.  end 

Point  Conception.. 
Mount   Buchon .... 

Point  Pinos 

Montery  Fort 

Farallones  Rocks  pk. 
San  Francisco  Fort, 

S.  side  entrance 
Mt   Bolbones   3765 
ft.  10  leag.  inland 

Cape  Mendocino 

Cape  Perpetua .... 
Pt  Adam  entrance, 

Columbo  River 
Cape  Disappointin't 
Astoria  City . . . 
Pacific  City .... 
Gray's    Harbor,    N. 

Head 

Cape  Flattery  S  side 
ent.  of  the  Straits 
of  Juan  de  Fnca 


32  38-8 

33  28 

34  10 

34  31 

35  18 

36  38-5 

36  36-4 

37  42 

37  48  5 

37  52.9 
40  29 
44  12 

46  12 
16  16 
46  10 

46  20 

47  0 


48  9 


117  14-7 

118  38 

119  47 

120  30 

120  60 

121  56 

121  53 

122  59 

122  28-5 

121  54-5 
124  32 
124  17 

124  1 
124  5 

123  49 

124  3 

124  7 


124  46 


Islands  in  the  West  Indies. 


Island  of  Trinidad, 
Point  Galiote. . 

"  Point  Galera.  . 

Tobago,  N.  E.  end 

Granada,  S.  end. 

Barbadoes.  E.  end 
"  Bridgtown  Engi- 
neer's wharf. . . 

St  Vincent,  Kingst'n 
"     N.E.  Point.. 

St  Lucia,  N.  Point. 

Martinique  Mt  Pele6 
4460  feet 

"  Fort  Royal 

Dominica,  N.  end . . 

Guadaloupe,  N.  end 
"  Mt  Souffriere, 
5500  feet 

Deseada,  N.  end. ... 

Antiqua,  S.  end. . . . 
"     Fort  James.. 

Montserrat-N.  E.  end 

Redonds  Isl'd  centre 

Nevis,  Charlestown. 

St  Kitts,  Mt  Misery,^ 
3711  feet 

Barbuda,  S.  E.  end 

St  Cruz  Observat'ry 

Anegada,  W.  end. 

St  Thomas,  Fort 
Christian 

Porto  Rico,  Cape  St 
John 

"  St  Augustine  Bat- 
tery  

"  Cape  Mala  Pasqua 


10  9 

10  50 

11  20 
11  59 
13  7 

13  4-2 
13  13 

13  18 

14  5 

14  48 

14  36 

15  38 

16  31 


16  5 

61  39 

16  20 

61  12 

16  69-5 

61  45 

17  6-7 

61  51-2 

16  50 

62  12 

16  55-5 

62  18-7 

17  8-8 

62  42 

1  22 

17  33 

1 7  44-5 

18  45 

18  20-4 

18  23 

19  29 
17  59 


60  59 
60  54 

60  27 

61  45 
59  30 

59  37 
61  15 
61  20 

60  67 

61  10 
61  4 
61  26 
51  35 


62  48 
61  43 
64  41 
64  21 

64  55  7 

65  36 

ee  7-1 
65  49 


Mona  Island,  E.  Pt. 
St  Domingo,    Cape 

Eugano 

"St  Domingo  City 

"  Cape  Tiberon. . . 

Jamaica,  Morant  Pt. 

"  Kingston 

"  Savannah  la  Mer. 
"  Montego  Bay.. . . 
"  Falmouth  Har  F't 
"  Port  Antonio.. 
Little  Cayman,  East 

end 

Grand  Cayman,  Fort 

George 

Cuba,   St   Jago  De 

Cuba 

"  Tarquina  P'k.,  10 

700  ft 

"  Cape  Cruz 

"  Manzanillo 

'  Isle  of  Pines,  Ca 

bellos 

"   S.  W.  Point 

"  Cape  St.  Antonio. 
"  Mt  of    Guagibon 

2532  feet  high 
"  Havana,  the  Moro 
"  Pan  of  Mantanzas 

1277  feet 

"  Matauzas .... 
Turks  Island,  N.  end 
North  Caycos,  centre 
Great  Heneaga,   N. 

E.  end 

Little   Heneaga,   E. 

Point 

Crooked  Isl.  S.  Point 
Rum  Key,  S.  Point 
St  Salvador,  E.  Pt., 
Land.p.ofColumb. 
New     Pro  v.  Nassau 

L.  House 

Andros  Isl.,  N.  end 
Bemiua  Island,  S.W. 

Point 

Little  Isaac,  centre. 
Great  Isaac,  centre. 
Gun  Key  Light. . . . 
Key  Lobas  Beacon. 

20  feet 

Tht-     Hole     in    the 

Wall  Lt  House.. 

Great   Bahama,   W, 

end 

"  East  end 

Double-headed  Shot 

Keys  Light. . . 
"  Salt  Key,  N.  Point 
AuKuilia  Isl.  E.  Pt 


LatN. 

18  5 

18  35 
18  28 
18  22 
17  56 

17  58 

18  12-3 
18  29-4 
18  30-6 

18  11-3 

19  42 
19  17-7 

19  55-9 

20  3 

19  504 

20  20 

21  57 
21  37 

21  51-5 

22  48 

23  9-4 

23  1-9 
23  3 
21  32 
21  56 

21  20 

21  29 

22  7 

23  37 


24  8 


25 

25 


56 

4 


LoN  W 

67  60 

68  20 
09  50 

74  28 
76  11 

76  46 

78  8-6 

77  56 
77  40 
76  27 

79  58 
81  23-ft 

75  50-6 


76  51 

77  45 
77  20 

82  53 

83  13 

84  57-2 

83  24 
82  22 

81  45 
81  40 

71  10 

72  0 

73  0 


25  41 

25  58-5 

26  2 

25  34 

22  225 

25  51-5 

26  42 

26  40 

23  66-6 

23  41-7 

23  30 

72  55 

74  21 
74  60 

75  17 

77  21-2 

77  57 

79  20 

78  51-3 

79  5 
79  18-4 

77  35-6 

77  10-6 

79  1 

77  48 

80  96-5 
8U  25 
79  32 


Coast  of  Mexico. 


Tampico,  N.  Point 

Cape  Roxo   

Vera  Cruz,  St  Juan 

de  Ulloa  Lt. . 
Ourizaba  Mt  17,400 

feet 

Oofre  del  Perote  Mt, 

13,400  ft 


22  15  5 
21  35 

19  11-9 

19    2-3 

19  29 


97  46 
97  17 

96  8 

97  13 
»7    7 


See  Position  of  Places,  Pages  244  and  245. 


283 


TABLE  XXXIX. 


NAMES  OF  PLACES. 

Port    Laguna    Brit 
Cous.  Ho 

Campeaeliy 

Sisal  Fort 

Cape  Catocbe  N.  Pt 
Jolbos  Isl 


Lat.  N. 

o        I 


18  38-4 

19  60 
21  101 

21  36 


LoN.  W. 

o  t 


91  50-7 
90  33 

90    2.7 

87    6 


Islands  in  Gulf  of  Mexico. 


Triaugles,  3  isl'ds.,  E. 
one 

Alaeraiies,  N.  Pt.. . 
Half  Moiin  Kev   Lt. 


20  54-9 
22  35 

17  12 


92  13 
89  49 

87  33 


British  Honduras. 


Belize,  Ft.  St.George 
Cockscomb  Mt.  4000 

feet 

Oraoa,  St.  Fernando 

Fort 

Saddle  Hill,  1760  ft. 
Cangrijo    Pk.,    8040 

feet 

Truxillo  Fort 

Cape  Honduras.  . 


17  29-3 

16  48 

15  47 

15  45 

15  38 

15  55-7 

16     2 

88  12 

88  38 

88    3 
79  58 

86  53 

85  69-6 

86  4 


Coast  of  Honduras. 


Pdit  Royal  barbor 
Bonacco  lal'd.  Sum. 

1200  feet 

Poyas  Pk.,  3700  ft. 

12  m.  inland 

C.  Gracias  a  Dios. . 


16  24-3 

16  28 

15  44 
14  59 


86  19-2 

85  55 

84  56 
83  11 


Mousquito  Coast, 


Caxones  or  Hobbies 
E.  Pt....      .... 

St.  Andrew's  fsl'd, 
S.  W.  cove 

Blewfield's  W.  Ptof 
Bluff , 

San  Juan  de  Nicara- 
gua, or  Grey  Town 


16    3 
13  21-7 
11  59-3 
10  55 


83    6 
81  44 
83  41-5 
83  43 


Gautemala,  N.  E.  Coast 
Point  Arenas. . . 


Mt  Cartago,  11,100 
feet 

High  Pk.,  5251  ft,  6 
m.  S.  S.  W.  from 
Buppan  Bluff. . . . 


10  56  7 
10    2 

8  42-7 


83  42.2 
83  48 

81  30 


Isth.  of  Panama,  N.  Coast. 


Cbagres,  Saa  Loreu- 
80  Fort 

Porto  Belle,  Fort  Je 
rt)nymo 

Cape  Tibei'un 


9  19-7 

9  32  5 
8  41 


79  59.2 

79  38.5 

77  25 


New  Granada. 


Cartbagena  Dome. . 
S'ta.  Martha  Morra. 

Pt  Gallinas 

Maracaybo,  bar.  eut 

Town  20  m.  up  the 

lake 


10  25-6 

11  15 

12  25 

11     2 

10  41 

75  34 
74  16 
71  44 
71  41 

71  40 


Coast  of  Venezuela. 


Los  Roques,  S.  E.  pt 

Light 

Porto  Oabello 


11  48 
10  29-4 


66  33 
68    0 


Garaccas. 


NAMES  OF  FLAOXS. 

Morro  of  Barcelona 
City 

Cumana  Fort  Boca, 

Pt.  Foleto  mouths 
of  the  Oronoco  R. 

"  East  Moutb,  Crab 
Island,  N.  pt.  . 


Lat.N. 
•    t 


10  13-5 
10  27-6 

10    0 

8  42 


LoN.  W 

o      I 


64  40 
64  11 

62  18 

60  55 


Guiana. 


Demarara  Bar  bea 
George  Town  L'ght 
Berbice  R.,  Crab  Isl 
River  Surinam,  Foit 

Amsterdam .  . . 
Paramaribo  Ch..  . 
Cayenne  Fort. . . 
Cape  Cachipour,  N. 

E.  point 

Cape  North,  ent  to 

the  Riv.  Amazon. 


6  58 
6  49-4 
6  21 

6  48 
5  44-3 
4  56-5 

3  46 

1   42 


58  14 
58  11-5 
57  33 

55    9 
55  13 

52  20 

51    3 

49  48 


Eiver  Amazon. 


Garaccas,  3000  feet, 

7  m   Inland 10  30 

Pk.  or  Silla  de  Ca- 
racoas,  6  m.  inland,  10  32 


66  54 

66  60 


Bailque  Isl.,  N.  pt. . 

1    4 

49  66 

Macapa  Fort 

0    0-8 

61    2 

Mexiana  Isl.  E.  pt...     0    0     1 

49  19 

Coast  of  New  Bruns-\ 

vick. 

St  Andrews,  S.  Pt 

Light 

45    4-3 

67    3 

C.  Lapreau  Lights.. 

45    37 

66  27 

St  Johns,  Partridge 

Island  Light 

45  141 

66    35 

Capfi  Spencer 

46  12 

66  65 

Cape  Enrage  Light. 

45  32 

64  46 

Annapolis  harb.  Pt.| 

Prim 

44  41 

65  45 

Bryer's  Isl.  Light. . 

44  16 

66  22 

Nova  Scotia. 

Seal  Isl.  S.  pt.  Light 

43  24 

65  58 

C.  Sable,  S.  E.  pt.. 

43  24 

65  36 

Shelburne  Har.  S.  E. 

pt  M'Nut  Isl.  L'ts. 

43  37-5 

65  16 

Sambro  Isl.  Light. . 

44  26-3 

63  Si 

Halifax  Dock  Yard 

Tablet: 

44  39-7 

63  35-6 

Cranberrv  Isl.  Light 

45  20 

60  56 

Cape  Causo 

15  18 

60  56 

Gut  of  Canso,  N.  W. 

entr.  Light 

45  41-8 

61  29-5 

Cape  St  George.. . 

45  52 

61  52 

Pictou  Har.  Light. . 

45  41-5 

62  40-2 

Anticosti  Island. 


Cape  Breton  Island. 


C.  St.  Lawrence... . 
Port  Hood.  Just   au 

Corps  Island  .... 
Caf)e  Hitehenbroke. 

Louishurg 

Scatary  Island  N.E. 

Point  Light,  .... 
Sidney   Harbor  Lt . 

Cape  North 

St  Paul's,  N.  ptlt.. 


47    2 

46    0 

45  34 

45  63 

46    2 

46  16 

47     3 

47  14 

60  38 

61  36 
60  42 
60    0 

69  41 
60  8 
60  25 
60    9 


Magdalen  Islands. 


Deadman's  Island.. 
Amherst  S.  W.  Pt. 

Entry  Island 

Cross  Island,  E.  Pt. 
Bird  Islands  E.  one . 


47  16 
47  14 
47  17 
47  48 
47  51 


62  14 
62    2 
61  42 
61  25-2 
61    9-7 


Prince  Edward's  Island. 


Charlotte  Town,  fort 

George , 

"  East  Point 

"  North  Cape 


46  14 

46  27 

47  4 


63  1 
61  68 

64  1 


NAMES  OF  PLACES. 

Heath  or  E.  Point . . 
S.  W.  Point  Light. . 


Lat.  N. 

49    5-4 

49  23.8 


LoN.  W 

o       ; 

61  45-2 
64  23-6 


Coast. 


Macquereau   Point 

Chaleur    Bay,    Car 
lisle 

Dalhousie  Island. . 

Miramichi,    Portage 
Island,  N.  Point 

Pt  Escumeuac  light 

Richibucto     Harboi 
mouth 

Fort  Monckton.  . . . 

Cape  Gaspe 

St    Anne's    Mounts, 
N.  E.  one  3973  ft 

Cape  Chatte  extre- 
mity  

Wolfe  and  Montcalm 
Monuments. . . 

Quebec,  N.E.  bastion 


48  12 

48    1 

48    4-4 

47  14 

47     6 

46  42 

46    3 

48  45-2 

48  52 

49    6 

46  48-6 

46  49-1 

64  48 

65  16 

66  22-2 

65  2 
64  46 

64  51 
64  4 
64  10 

66  49 

66  46 

71  1.3-5 
71  13-"; 


Newfoundland. 


Cape  St  George. . . 

Cnpe  Anguile 

Cape  Ray,  S.  W.  ex- 
tremity  

Miquelon,  Mt  Cal- 
vaire  at  N.  W.  Pt 

St  Pierre  Isl'd,  S.  E, 
Point 

Placentia  Har. castle 

Cape  Pine  Light. 

Cape  Race 

St  John's  Light  on 
South  Head. .  . 

Tiinity  Harbor, Hog 
Nose 

Cape  Bonavista  Gull 
Island  Light 

Cape  Bauld ....... 

Belle  Isle,  N.  E.  Pt 

Cape  Farewell. . . . 
Staten  hock 


48  29 
47  53 


59  16 
'59  25 


47  37 

69  18 

47    7 

56  25 

46  46 

56  12 

47  16 

64    4 

46  37 

53  36 

46  40 

53    7 

47  33-6 

52  43 

48  21 

53  24 

48  42 

53     8 

51  38 

65  24 

62     1 

55  17 

59  49 

43  54 

59  60 

40  39 

Iceland. 


Reikiavig I  64     8-4  I  21  55-2 

Mt  Heckla,  5364  ft.!  6.3  58     1 19  41 


Fa,roe  Islands. 


Fugloe  Island,  E.  Pt 
Monk   Rock 


62  20 
61  20 


6  13 
6  41 


Shetland  Islands. 


Fitful  Head,  929  ft. 
Fugloe  Skerry.... 
Balta  Island,  S.  end 
Noss  Head,  577  feet 

Lerwick   Fort 

Sumburgh  Head  Lt 
Fair  Island  summit 


59  54 

60  20-4 
eo  44-4 
60  8-3 
60  9-4 
59  51-3 
59  33 


1  24 
1  45 

0  47-7 

1  0-5 
1  8-7 
1  17 

1  88 


Orkney  Islands. 


Moul  Head  . . . 
Noup  Head . . . , 
N.  R<inaldsay  Island, 

E.  Point 

"  Stromness  or  S.  pt 

Start  Light 

Stronsa  Isl'd,  Lamb 

Head 

Stromness    Church . 
Kirkwall  Light. . . . 


69  23 
59  20 

59  23 
59  20 
59  16-6 

69    4-9 

68  57-8 
68  59-2 

2  53 

3  4-0 


24 
26 
22 

32 
17-5 

57-2 


TABLE  XXXIX. 


Names  of  plages. 
Old    Head 


Lax.  N. 


68  44-3 
57  36 
67  49 


Ruckal,  centre 

Stlvilda,  pk.l220ft. 
Flanueu  laid,  N,  W. 

extremity 58  13 

Roiia    Island,  S.   E.; 
suintnit,  360  feet,  59    7 


LoN.  W 

2  65  5 
13  41 
8  34-7 

7  87 

5  48-6 


Hebrides. 


Butt  of  L^wis. .  . , 
Stornaway  Lt.  house 
Shiant  lil'ds,  N.  W, 

oue 

Glass  Island  Light. 
S.  Uist,  East  Point. 
Barra  Hd.  Lt.  680  ft. 
Peiitrud  Sken-ies  It 


58  31 

6  14 

58  11-5 

6  22-2 

57  33 

6  24 

57  62 

6  33 

57  13 

7  11 

56  47-1 

7  39-2 

58  41-2 

2  65 

North  Coast  of  Scotland. 


Duncansby  Head . . 
Dunuit  hd.  It  346  ft 

Thurso 

Cape  Wrath  Light, 

400  feet 

Point  of  Aird 

Canna  Island,  W.  Pt 
Rum  Island,  S.  Pt.. 
Muck  Island,  W.  end 
Tirey  Island,  S.  end 
Skerry vore  Lt   150 

feet 

BeuMore,  3168  fp<^t 
Isle  of  Mal),:i.W. 

end 


58  89 

58  40-4 

68  33 

58  37-5 

67  39 

67  4 

56  56 

66  49 

67  27 

56  16-4 

56  26-5 

bi  36 

3     1 

3  21-2 

3  31 

4  59 
6  IS 
6  34 
6  23 
6  19 
6  66 


65 

0-7 


6  20 


Vi  en  Coast  of  Scotland. 


5er  Ife-is  i368  feet 
T^'or^  William... I 
LidiDore  Isl.  Lt  96  ft 
Oban  Free  Church. 
Rhinns  of  Isla  Light 
MuUofCautire  Lt_. 
Campbelton  Light. 
Glasgow  N.  Bridge. 
Greenock  Spire. . , . 
Cumbiae  Light. . . . 
Ardrossan  Lights . . 

Pladda  Lights 

Ailsa  Craig  summit 

1098  ft 

Corsewall  Pt  Light 
Mull  of  Galloway  Lt 
Mary  Port  S.  Pier. 
Workington  Lights. 
Whitehaven  Lights. 
St  Bees  Head  light 

333  feet 


56  48 
56  48 
56  27 
66  25  9 
55  40 
55  20 
65  26 

55  51-9 
65  66-9 

56  4-6 
55  38  7 

55  25-6 

65  15-2 

56  0-5 
34  38-1 
54  43 
54  38-9 
54  33-2 

54  30-8 


0 
5 

36 
31-7 
33 
49 
355 
16 
45-2 
59-7 
60-5 
7 


5  7 
5  9-6 
4  51-1 
3  30-6 
3  346 
3  35-7 

3  38 


Isle  of  Man. 


Peel  Light 

N.  Pt  Ayr  Pt  light 
Douglas  Light. . . ., 
Calf  of  Man  Lights. 


64  13-6 
64  25 
64    9 
54    3-2 


4  42 
4  22 
4  28 
4  50 


W.  Coast  of  England. 


Black  Comb,  1919  ft 
Walney  Isl.  S.  pt  It 

Crosby  Light 

Liverpool   Observa 

tory 

Bell  Beacon 

Formby  Ligiit. .  .. 
N.  W.  Light  vessel. 
Point  of  Air  Light. . 


54  15-5 

54  2-9 

53  31 

63  24-8 

53  31-2 

53  31 

53  27-4 

53  21-9 

19-6 

10-5 

4 

GO 

15-6 

9-5 

17-7 
190 


Coast  of  Wales. 


NAMES  OF  PLAGES. 

Great  Orme's  Head, 

signal  staff 

Point  Lynas  Light. 
Skerries  Light.... 
Holyhead   Light.,. 

S.  Stack  Light 

Caernarvon  Light. . 
Bardsey  Island  Lt. . 
Snowdon,  3580  feet 
Cardigan  Isl'd  sum 

mit , 

South  Bishop  Light, 
Small's  Rocks  light 
Pembroke  Dockyard 

N.  W.  corner. . 
Milford  Church.. 
St  Ann's  Lights. 
Caldy  Isl'd,  S.  pt  It. 
Worms  Head. . . 
Swansea  Pier  Light 
Mumbles  Light. . . . 
Cardiff  Custom  H.. 
Newport  Usk  Light 
Bristol  Cathedral. . 
Flatholm  Isl'd  light 
Bideford  or  Braun- 

ton  Lights 

Lundy  Isl'd  Lights. 
Pad  stow  Church. , . 
Trevose  Head  lights 
St  Ives  Steeple, .. . 
Cape  Cornwall 


Lat.  N. 

O     f 

63  20 

63  25 

53.26  8 

53  20 

53a8-3 

63  8-6 

52  45 

63  4-1 

52  7-9 

51  51-4 

51  43-3 

51  41-8 

51  42-7 

51  41 

51  37-9 

51  34 

51  37 

51  34 

51  28-6 

51  32-4 

51  26-8 

51  22-6 

51  4-5 

61  10-1 

50  32  5 

50  33 

50  12-8 

50  7-7 

LoN.  W 


8  51-2 


14-2 
36-5 
37 
42 
24-7 
48 
4-5 


4  41-6 

5  24-5 
5  40 

4  57-2 

5  1-5 

5  10-5 
4  41 

4  20 
8  66 
3  58-2 
8  10 
2  59-7 

2  36-6 

3  7 

4  12 

4  40-2 

4  56 

6  2 

5  26-5 
5  42-5 


Scilly  Islands. 


St.  Mary's  flag  staff,  49  55 
Saint  Martin's  Day 

Mark 49  58 

St  Agnes  Light... .  49  53-6 


6  19 

6  16 

6  20-7 


South  Coast  of  England. 


light 


Seven    Stones 

vessel 

Longships  Light. . . 
Wolf  Rock  Lt  to  be 
Penzance  Lt.  Pier. , 
Lizard  Lights. . . . , 
Falmouth,    Penden 

nis  Castle 

"  St  Anthony  light 
Deadman  sum.,  379 

feet 

Rame  Head 
Plymouth  Breakwa- 
ter, W.  end  Light 
Bolt  Head  flag  staff 
Start  Point  Light. 
Dartmouth  Liglit. 
Berry  Hd.  flag  staff 

Torquay 

Portland  Lights. . 
St  Albans  Head. 

Isle  of  Wight. 

Needles  Light. . . 
St  Catherine's  pt.  It. 
Cowes    Castle 


50    3 

50  41 
49  56-7 
60  71 
49  57-7 


50 
50 


8-8 
83 


Hurst  Lights. . , . 
Sou^mpton,  Saint 

Michael's  Spire 
Portsmouth,    R.   N. 

College 

Ower's  Light  vessel 
Brighton  Pier  Light 


50  13 
50  19 


7 
44-7 
48-2 
31-5 
12 

2-7 
1 

48 
13 


NAMES  OF  PLAGES. 

Beachy  Head  Light 
Duiigeness  Light. . . 
Dover  Castle  Light. 
S.  Foreland  Lights. 
S.  Sand  Hd.  Lt.  ves 
sel  Goodwin  sands 
N.  Sand  Lt  vessel  " 
Sandown  Cas.  ceutei 
Ramsgate  Pier  light 
N.  Foreland  Light. 
Mai'gate  Light. . . . 
Nore  Light  vessel. . 
Chatham  Dockyard 
Sheerness  flag  staff. 
Greenwich  Observa- 
tory  , 

London,    St    Paul's 
Cathedral. . , 


Lax.  N. 

»  / 

50  44-4 

60  55 

51  7-8 

61  8-4 

51  10 

51  19  5 

61  14.3 

51  22-5 

61  22-5 

51  ?8-4 

51  29 

61  23-8 

61  26-8 

61  28-6 

51  308 

23.S 
Lon.  £, 

0  12-7 

0  58 

1  19  0 
1  22-6 


28-2 
83  6 
24-2 
26-7 
26-7 
23-2 

0  48 

0  36 

0  44-7 

0    0-0 
W. 
0    5-7 


East  Coast  of  England. 


Mouse  Light  vessel . 
Swin  Middle  Lt  ves. 
Sunk  Light  vessel 
Kentish  Knock.. 
Shipwash  Lt  vessel 
Galloper  Lt  vessel. 
Harwich  Lights... 
Orfordness  Lights. . 
Aldborough  Steeple 
Pakefield  Light, , . . 
Lowestoft  Lights., 
Yarmouth  Spire . . , 
Winterton  Light, ,, 
Hasborough   Lights 

Cromer  Light 

Leman  and  Owen 
Light  vessel. . . . 
Dudgeon  light  vessel 
Spurn  Light  vessel. 
Spurn    Lights 


50  20-3 

4  9-5 

60  13-2 

8  48-7 

50  13-4 

8  38 

60  21 

3  38 

50  24 

3  28 

50  28 

8  30 
2  26-7 

50  31-4 

60  85 

2  8 

60  89-9 

1  34 

50  84-6 

1  18 

50  46 

1  17-7 

50  42-4 

1  82  7 

50  54 

1  24  2 

50  48 

1  6-2 

50  40 

0  40 

50  49 

0  8 

HuU  Citadel  , .  , 
Flamborough  Hd.  It 
Scarborough  Light. 
Whitby  Light... 
Redcar  Church. , 
Hartlepool  Pier  It's 
Sunderland,  N.  Pier 

Light 

Newc'stle  Bridge,  N. 

end 

Tyneniouth  Light . . 
Coquet  Island  Light 
Cheviot  Hill,  2668  ft 
Lougstoue  Light. . . 
Fame  Island  Lights 
Holy  Island  Castle. 
Berwick  Light 


51  31-8 

51  39 

51  46-7 

51  39-7 

52  1-5 

61  46 

61  56-6 

52  4-8 

52  9-2 

52  26-2 

52  29-8 

52  36-8 

52  48 

52  49-4 

52  55-7 

53  8-5 

53  15-2 

53  34 

53  34-7 

53  44-6 

E. 
1  0-2 
1  7 
1  28-2 
1  ?9-6 
1  37-7 
1  65-7 
17-5 


54    7 
54  17 
54  29-7 
54  36-9 
64  41-8 

54  54-5 

64  58-7 

65  1-3 
56  20-1 
65  29 

55  38-7 
55  37 
55  40-2 
55  46-2 


1 

1  34-2 
1  86 
1  43-5 
1  45-6 
1  43-7 
141 
1  82 

1  19 

2  1-6 
0  56-2 
0  18-5 
0    7-2 

W. 
0  20 
0    6 
0  23-6 

0  36-7 

1  3-5 
1  10-7 

1  22 

1  85-5 
1  26 

1  32-2 

2  9 

1  36-6 
1  39-2 

1  47 

2  0 


East  Coast  of  Scotland. 


St  Abb's  Head,  sig- 
nal staff 

Dunbar  Church   , . . 

Bass  Rock,  centre. . 

Inch  Keith  Light . , . 

Edinburgh  Observa- 
tory  

Leith  Pier  Lights. . 

May  Island  Light. . 

Bell  Rock  Ligk. . . 

Dundee  Lights. . . 

Buddoness  Lights. . 

Montrose  Lights... 

Girdleness  Lights. . 

Aberdeen    Lights.. 


65  55 

55  59  9 

66  47 

56  2 

55  57-4 

55  68-9 

56  111 
56  26 
56  27-6 

66  281 

56  42-6 

67  8-2 

57  8-9 


2    8 
2  31 

2  88-2 

3  8 


3  11 
3  10-6 
2  88-2 
2  28 
57-7 
46 
28 
80 
6-7 


J 


284 


TABLE  XXXIX. 


KAUSa  OF  PLACES. 


Lat.  N. 


BucbaDDesis  Light. .  67  28 
Pet'rh'ad,  Keith  Inch.  57  301 
Kinnaird's  Head  Lt|  57  41-7 

Burgh  Island 1 57  42-1 

Cromarty  Point  Lt.  67  41 
Tarbetness    Light..  57  509 
Noes  Head  Litrht.. .  58  28 


LoN.  W 

o  / 

1  46 

1  46 

2  1-5 

3  30 

4  2 

3  48-5 
3    4 


Shores  of  the  North  Sea. 


Dunkirk   Light. . . . 

51     31 

E. 
2  22 

Ostend  Lights 

51  141 

2  55 

Antwerp  Cathedral 

51  13-2 

4  24-2 

Brielle  Church 

51  54-2 

4  10-0 

Rotterdam  Church. 

51  55-3 

4  29-5 

Hague,  S.  James  Ch. 

52    4-3 

4  18-7 

Texel  Island  W.  Ft 

53    3 

4  42 

Haarlem,  Great  Ch. 

tower 

52  22-9 
54  10-8 

4  38-6 

Helgoland  Isl'd  Lt. 

7  53 

Elbe,  outer  Lt.  vessel 

54    0 

8  18 

Denmark. 

Cuxhaven  Light. . . 

65  53-7 

8  43 

Altona  Observatory 

53  32-7 

9  56-7 

The  Skaw  Ft.  Light 

67  43-8 

10  36-5 

Trindelen  Lt.  vessel 

67  26-6 

11  16 

Anholt  Island,  E.  Ft. 

Light. ...     .... 

56  44-3 

11  39-2 

Elsiueur,    Kronborg 

Light 

56     2-2 

12  37-5 

C-ipenhagen   Obser- 

toi-y 

55  40-9 

12  34  7 

Shores  of  the  Baltic. 


Moeu  Isl'd,  E.  Ft.  Lt 

Kiel  Observatory.. 

Lubeck,  St.  Mary's 
Church 

Wiamar,  St.  Mary's 
Church 

Rostock. 

Rugan  Island,  E.  Ft 

Swinemiinde  Light. 

Stettin 

Dantzig  Observat'ry 

Pillau  Light 

Memel  Light 

Lyserort 

Domesness  Lights. . 

Riga  Lights 

Pernau,  German  Ch 

Dagerort  Light .... 

Nargen  Island  Light 

Revel,  two  Lights. . 

Ekholm  Light 

Rothskar  Island  Lt. 

Hogland,  two  Lights 

Tolbouklia    Light 

Kronstadt  Cath.. 

St.  Petersburg    Ob- 
servatory   

Wiborg , 

Sommers  Isl'd  Lt's, 

Helsingfors  Obs'rva 
tory 

Sveaborg 

Ronskar   Light.... 

Lagskar 

Stockholm  Observa 
tory 

Gronskar  Light 

Gothland,  S.  Point. 

Gland,  N.  Hd.  Light 

Carlacrona 

Eartholms,  N.  Pt.  Lt 


64 
54 


67 
19-5 


53  621 


53 

.-,4 
54 
63 
53 
54 
54 
55 
57 
57 
56 
58 
58 
59 
69 
69 
59 
60 
60 
59 

69 
60 
60 

60 
60 
59 
69 

59 
69 
56 
57 
56 
65 


53-5 
5.5 

21 

66 

25 

21-3 

38-4 

43-7 

34 

45.6 

67 

231 

55 

36-4 

26-6 

41 

58 
6-3 
2-6 

59-7 

56-6 
42-7 
12-4 

9-7 
8-4 

56 

50-5 

20-6 
17 
55-2 
22 
9.7 
19 


12  33 
10  9 

10  41-6 

11  27-7 

12  9 

13  48 

14  17 
14  34 

18  41-2 

19  54 
21  6-2 

21  34 

22  37 
24  66 
24  30-2 
22  12 
24  31 

24  45-2 

25  49 

26  42 

26  58-5 
29  34 

29  46-5 

30  19 
28  47 

27  39-5 

24  67-5 
24  69-7 
24  24 
19  55-2 


18 
19 
18 
17 


3-7 
2 
9 
6 


15  35-6 
15  12 


NAMES  OF  PLACES. 

Bornholm,  N.  Ft  Lt 

S.  Point. 

Falsterbo   Light. . . 

Helsiugborg  Lt 

Warberg   Castle . . . 
Niddingen  two'Lt's. 


Lat.  N. 

o        / 

55  17-7 

64  69 

56  23 

56    2-7 

57     6-4 

57  18-2 

LoN.  E. . 

14  46 

15  5 

12  49-2 
12  42-2 
12  14-5 
11  54-3 


Coast  of  Norway. 


Wiugo  Light 

Gotteuburg 

Christiauia,  New  Ob 

sei'vatory 

Flekkero   Island... 

Naze  Light 

Fugloe 

Bergen . 

Chi-istiiiusuud  Light 
Rost  Islands,  middle 
Haramerfest  Church 
N.  Cape  of  Europe. 


57  38 

67  41-3 

59  54-7 

58    2 

57  57-8 

60     1 

60  24 

63    7 

67  31 

70  40 

71  10-3 

11  36-2 
11  54-5 

10  43-5 


57 

2 
59 
18 
39 

7 


23  42 
25  46 


White  Sea. 


Orlovsk  Light. . . , 
Onega,  St.  Michael's 

Church 

Archangel,    Trinity 

Churcli 

Moudiuga  Isl'd,  left 

entr'uce  R.  Dvina 


67  11-5 

63  53-6 

64  32-1 
64  55-8 


41  22-2 
34  38-7 
40  33-5 
40  16-2 


West  Coast  of  Ireland. 


Cape  Clear  Light. . 

Faslnet  Rk.  It.  to  be 

Mizen    Head 

Bear  Island,  summit 

Roanharrick  Isl'd  It. 

Skellig's  Lights. . 

Brea    Head 

Valentia  Fort  Light 

Great  Blaskett  N.  pt. 

Kerry  Head,  River 
Shannon 

Tarbert  Light 

Loup  Head  Light. . 

S.  Arran  Isl'd,  sum- 
mit of  Ilanmore  It. 

Black  Head 

Galway  Mutton  Isl'd 
Light 

Slyne  Head  Lights. 

Newport 

Achil  Hd.  2222  ft  . 

Eagle  Island  Lights 

Downpatrick    Head 


61  26 

51  23-3 

51  27 

51  37-5 

51  39  2 

51  46 

51  38 

51  56-8 

52     6 

52  23 

52  35-5 

62  34 

53    7-6 

53    9 

53  16-2 

53  24 

63  53 

63  68 

54  17 

54  20 

w. 

9  29 
9  36-3 
9  50 
9  62-2 
9  44-7 

:0  32 

10  25 

10  19 

10  "I 

9  55 
9  21-7 
9  56 

9  42 
9  17 

9  8-5 
10  14 
10  11 
10  16 
6 
21 


10 
9 


N.  W.  Coast  of  Ireland. 


Siigo  Bridge 

TiUen  Head  1415  ft 

summit 

Bloody  Farl'nd  1059 

feet 

Tory  Island  Light. 
Faunet  Point  Light, 
lunistraliul  Light. . 
Innishowen  Hd.  It's. 


54  16 

54  20 

65    8-2 

55  16-5 

55  16-6 

55  25  9 

55  13-8 

8  28 

8  45 

8  15-7 
8  15 
7  37-7 
7  13-7 
6  65-5 


N.  E.  Coast  of  Ireland. 


Londonderry  Bridge 
Port  Rush  Pier. . . . 
Giant's  Causeway  pt. 
Rachlin  Isl'd  It.  to  be 
KnocklaydMt.  1690 

feet 

Maiden  Rocks  lights 
Belfast  Spire. . . 


54  59  6 

55  12-4 

65  14-7 

55  17.6 

55    9-7 

64  55  8 

54  86-4 

7  19 
6  39  7 
6  30-7 
6  11-7 

6  15-2 
6  44  2 

6  56  2 


NAMES  OF  PLACES. 

Divis  Mt.  1800  feet. 

Copeland  Lights 

Slieve  Donard  2796 
feet 

Lambay  Island  sum. 


Lat.  N.  Lon."  W 


64  367 

54  41-7 

54  10-8 
53  29.6 


6    1 
6  31-2 

5  55-2 

6  10 


E.  Coast  of  Ireland. 


Howth  Bailey  light. 
Dublin  Observatory 
Kish  Light  vessel. . 
Great   Sugar    Loaf 

1651  feet 

Wieklow  Hd.  Lights 
Arklow  Light  vessel 
W'xford,  Rosslare  pt. 
Tiiskar  Rt)ck  Light. 
Saltees  Light  vessel 

Hook  Light 

Waterford  Bridge.  . 


63 

21-7 

53 

23-2 

53  19 

53 

9-2 

52  57-9 

52  42 

62 

10-9 

52 

121 

62 

2-3 

52 

7-4 

52 

16 

6    3 
6  20.3 
5  56-5 


9 

0 
59-7 
22-2 
12-2 
40 

6  55-7 

7  6 


S.  E.  Coast  of  Ireland. 


DuncanuoD  Fort  It' 
Roche  Point  Light 
Cork  Custom  House 

Barry  Head 

Kinsale,   Old   Head 

Light 

Galley  Head,  S.  Pt . 
Baltimore 


52  17-7 

51  47-5 

51  53-8 

51  42-1 

51  36-7 

51  31-8 

61  29 

6  56-5 
8  15-2 

8  27-7 
8  23-2 

8  32-2 

8  57-0 

9  22 


N.  W.  Coast  of  France. 


Gravelines  Light. . . 

Calais  Light 

Cape  Grisnez  Light 
Boulogne  Lt's  N.  E. 

Jetty 

Dieppe,  W.  Jetty  Lt. 
Cape  Ailly  Light. . 
Cape  de  la  Heve  It's 
Havre,  N.  Jetty  Lt. 
Paris  Observatory. 
Honfleur   Lights . . . 

La Hougue  Lights. . 
Cherbourg  Church. 
Cape  La  Hague  Lt. 


51     0.3 

50  57-6 

50  52-2 

50  43-9 

49  56 

49  65-1 

49  30-7 

49  29-3 

48  50-2 

49  25-6 

49  34-3 

49  38-6 

49  53-4 

E 
2  6-7 
1  61-2 
1  35-2 

1  35-2 

1  6-2 
0  57-7 
0  4-2 
0  6-7 

2  20-5 

0  13-7 

WJ 

1  16-2 
1  37-2 
1  57 


Channel  Islands. 


Alderney,  St.  Anne's 

Church 

Caskets  Lights. . 
Guernsey,  Jerbourg 

Tower, 390  feet.. 
"  Doyle  Fort,  N.  E. 

Point 

Jersey,  St.  Heller's 

Lights 

"   S.  E.  Pt.  Seymour 

Tower 


49  42-9 
49  43-4 

49  25  3 

49  30-1 

49  11-8 

49    9-4 


2  12-2 
2  22-5 

2  33 

2  31-2 

2    7 

2    M 


W.  Coast  of  France. 


Cape  Carteret  Light 
St.  Malo  Light.  . 
Cape  Frehel  sum.  It, 
Morlaix  Lights.. . . 

XJshant  Light 

Brest  Observatory 
Penmarc'h  Rocks  Lt 
L'Orient tower. . . . 
Port  Navalo  Pt.  Lt 
Port  Saint  Nazaire, 

Mole  Light 

Rochelle  LL  Tower . 
Rochford  Hospital. 
Bordeaux,  St.  Andr6 


49  22-4 
48  39 
48  411 
48  38  2 
48  28-5 
48  23.6 
47  47-9 
47  44-7 
47  32-9 

47  16  3 
46  9-4 
45  56-6 
44  50  8 


1  48-2 

2  1-6 

2  19 

3  53 

6     3-2 

4  29-2 
4  22-2 
8  21 

2  66 

2  11-7 
1  9-2 
0  67-7 
0  846 


TABLE  XXXIX. 


'iHt> 


North  Coast  of  Spain. 


NAMES  OF  PLACES. 

St.  Sebastian  Light 

Cape  Villaiio 

Bilbao  St  Nieh.  Cli. 
Santona  Mt.  sumniit 
Saiitander  mole  It's 

Cape  Blauco 

Island  Pancba,  West 

extremity..  . . 
Cape   Burela.  . . 
Cape  Vares  siimrait 
Cape  Ortegal  tower 

Ferrule  Mole 

Coi-una,  St.  Autouia 

Castle 

Cape  Finisterre  light 

to  be 

Mt.  Louro,  787  fe^t. 
Viana  Fort,  St  Jago 

Light  to  be 


Lax.  N.  Lo.\.  W 


43 
43 
43 


19-2 

27 
15-8 
43  27  5 
43  27-9 
43  36 

43  34-7 
43  42 
43  48 
43  45-2 
43  29-5 

43  22-5 

52  54 
42  44 

41  42-6 


2  0-5 
2  58 

2  54 

3  26 

3  48-7 
6  47 

6  59-2 

7  21 
7  41 

7  66 

8  12-7 

8  22-7 

9  15 
9  44 

8  43-2 


Coast  of  Portugal. 


Mt.  Oruellas,  high. 
Oporto  F(jrt,  St.  John 

Light 

Cantaros  Mt. summit 

6460  feet 

Cape  Mondego  light 

to  be 

Figueira  Light  to  be 
Burliug's  Light.  . 
Cape  RocaLt.  698  ft. 
Mt.   Ciutra  summit, 

1720  feet 

St.  Juhan  Fort  light 
Lisbon,  Marine  Ob- 
servatory  

Cape  Espichel  Light 

627  feet 

Selubal    Light,   490 

feet 

Mouchique  Mouat'ns 

summit  3830  feet. 
Cape  St.  Vincent  Lt 
Cape  Sta.  Maria  Lt. 
Mount  Figo,  2000  ft 
Cadiz  New  Obs'rt'ry 
C.Trafalgar  Tower. 
Tarifa   Light 


40  50 

41  8-8 
41     9-1 

40  19 

40  12 
40  10 
39  26 
38  46 

38  47-2 
38  40-3 

38  42-4 

38  24-9 

38  28-9 


8  21 
8  37-2 
8  37-5 

7  38 

8  64 

8  51 

9  80-7 
9  30 

9  25 

9  20-5 

9    8-2 
9  IS 
8  53 


37  20 

8  36 

37  2-9 

9  00 

36  56 

7  46 

37  10 

7  42 

36  27-7 

6  12 

36  10 

6  1 

36  0 

5  36 

N.  W.  Coast  of  Africa. 


Cape  Spartel  W.  Pt 
Mt  Habile,  3000  ft. 

Sallee 

N.  C.  Blanco,  170  ft. 

Mogador 

C.  Ghir,  1235  ft  pt 
Mt  Sum.  East  of  C. 

Ghir,  4400  feet.. 
Fogo  Pk,,  2970  ft. . . 
C.  Bajador,  W.  pt. . . 
Down    of  Cintra  or 

pk'd  aiud  hill.. . 

Senegal  Lt 

C.  V'erd,  extreme.. 
R.  Gambia  Bathurst 

flag-statf. 

M.  Kakulimah,2900 

feet 


35  48 
35  28 
34  2-7 
33  8 
31  30-5 
30  88 

30  39 

29  11 
26  7 

23  6 
16  0-8 
14  431 

13  28 

9  45-8 


5  55 

5  43 

6  46 

8  38 

9  46-2 
9  50 

9  33 

10  6 
14  29 

16  10 

16  33 

17  34 

16  36 
13  28 


Gulf  of  Guinea. 


C.  Sierra  Leone  Lt. 
Freetown  N.  Battery 
Bananas  Is'l  Gov.  ho. 
G.MouatPk.  1060  ft 


8  30       13  18 
8  29-9    13  14-5 
8    8       13  11-7 
6  43     111  21 


Liberia. 


NAMES  OF  PLACES. 


C.  Mesurada  Lt 

Monrovia  Gov't  ho., 

Mai'shall  Agts.  ho.  , 

Grand   Bassa  Amer. 

Agent's  ho 


Lat.  N. 


19 
191 
8'1 


5  54-1 


LoN.  W 

10  50 
10  49 
10  22-7 

10    4 


Grain  Coast. 


Trade  Town 

Mt.  Tobacco,  830  ft . 

Pt  Sanguin 

King  William  Town 

Eurp.  Factories 
Cape  Pal  mas  Lt. 


5  44 

5  47 

6  12-7 

4  49 
4  22-1 

9  54 
9  44 

9  20-2 

8  43 
7  44-2 


Ivory  Coast. 


Oval  Mt,  1315  ft.. 
King  George  Town. 

C.  Lahou 

Axiin,  Dutch  Ft. . . 
C.  Three  Pta.  S.  ex- 
tremity  


4  57 

4  58 

5  11 
4  52  3 

4  44-7 


6  48 
6  3 
4  31 
2  14-7 

2     6-7 


Gold  Coast. 


Dix  Cove  Fort. . 
Elmiua.  Dutch  Ft 
C.  Coast  Castle  Lt 
Camel's  Hump,  1200 
feet 


4  47-8 

5  4-8 

5  5-4 

5  37 

1  56-7 
1  22-2 
1  13-7 

0  31 


Bight  of  Benin. 


R.Volta  W.Ptent. 
Quitta.  Danish  Ft.. 
Why  dab  Flag-staff.. 
R.  Quorra,  or  Niger 

E.  Pt 

New  Calebar  R.  entr. 

W.  Pt 

Bonny  R.  entr.  E.  pt 
Old    Calebar,    Tom 

Shots  Pt 

Mt  Cameroons,  1376 

feet 

C.  Cameroons 

Rumby  Mont's  sum, 
The  Mitre,  3940  ft 

S.Sum 

Gaboon  R.  S.  pt  ent 
King  George  Tower 


N 

6  46 

6  65 

6  18 

4  17 

4  23 

4  23 

4  36 

4  13 

3  56 

4  57 

1  20 

0  22 

0  8 

E. 
0  41-2 

0  59-7 
2    6 

6  4 

1  1 

7  8 

8  19 

9  12 
9  30 
9  18 

9  57 
9  23 

9  44 


Islands  in  the  Bight  of  Biafra 


Fernando  Po.  C.  Bul- 

len,  or  N.  Pt 3  48 

•'  Peak,  10710  ft...  3  35 

"  S.  Pt  or  G.Barrow  3  13 
"  Clarence  Co.  Ade- 

hiide  Isle 3  46 

Princes  Isl'd  Ft  Sta. 

Anna 1  39-6 

"  Diamond  Rks.  off 

N.  E.  Pt  large  one.  1  407 
"  Brothers,  2  Isl  ds. 

S.  one 1  21*1 

St.  Thomas    Island, 

Sum.  7020  ft 0  14-7 

Ilha    das   Rollas  off  S. 

S.  Pt 0    0  5 

Anuobona,N.  Pt...  1  24-3 

"  S.  extr.  rock  off .  .  1  286 


8  43 
8  47 
8  43 

8  47-6 

7  26  5 

7  27-7 


7  17;6 
6  33 


6  30 
6  88-'2 
6  36-7 


Islands  in  the  N.  Atlantic 
Ocean.— Madeira. 


Desertaa  sm, 


1610  ft  32  31-3 


W. 

16  30-7 


NAMES  OF  PLACES. 

Madeira,  E.  Pt 

Funchal,  B.Cona'late 
Pico  Ruivo,  6100  ft. 
W .  End  or  Pargo  pt 
Great  Salvage  W.  S. 
Great  Piton  sum.. . . 
Alegrauza,     S.     W. 

sum.  939  ft 

Graceosa,  S.  W.  Pt. 
Lanzarote.N.  W.  Pt. 

S.  pt 
Fuerteveutura,  N.W 
Point 

"  Port  Cabras 

"  S.  PtorPtJandia 


Lat.  N. 

o    ( 

32  43-4 

32  37-7 
32  45 
32  48 
30  7-5 
30  1 

29  233 
29  12-7 

29  2-7 
28  60 

28  42 
28  29 
28  3 


LoN.  W. 

16  3«-6 
16  54-7 

16  67 

17  17 

15  61-;- 

16  0-2 

13  31-5 
13  32-7 

U  48 

13  47 

14  1 

13  51-7 

14  31 


Canary  Islands. 


Grand    Canary,    N. 

W.  Pt 

"  Palmas  mole  head 

"  South  Pt 

"  Isleta  sum.  847  ft 
Tenerife  Isl'd.,  N.  Pt 

Anaga  Rk 

"  Santa  Cruz,  Brit 

Consulate 

"  S.  PtorPtRasca 
"  Peak  12.172  ft. 
"  W.  extremity. . . 
Gomera  W.  Pt  sum. 

1440   ft 

Ferro    W.  extr.   (oi 
Merid.  of  Ferro) . . 

Palma,  N.  Pt 

"  Santa  Cruz,  Fort 

Sau  Miguel 

Corvo,  N.  Pt 

Flores,  N.  Extr 

Fayal,  W.  Pt 

"  Horta,  Sta.  Cruz 
Castle 


38  31.7 


28  9-6 

15  43-2 

287 

16  25 

27  43-8 

15  34 

28  10 

15  25-6 

28  36-6 

16  8-5 

28  28-2 

16  14-7 

28  0 

16  41-2 

28  16-5 

16  39 

28  20-5 

16  66 

28  6-7 

17  13-5 

27  42-5 

18  9-7 

28  61-3 

17  63-6 

28  40-5 

17  44-5 

39  43-5 

31  7-2 

39  31-6 

31  13 

38  36-6 

28  60-5 

28  28-5 


Azores  Islands. 


Pico  Peak,  8400  ft. 
St.  George,  S.  E.  end. 
Graciosa,  W.  Pt. . . 
Tercera  suul  3495  ft 
St  Michael,  E.  Pt. . 

"  Delgada  Lt 

"  W.  Pt.  or  Pt  Fer- 
raria  Lt 


S.  Mary  sum.  1660  ft  36  685    26    62 


38  28 

38  32-5 

39  4-2 
38  43-6 
37  48-3 
37  44-2 

37  51-7 


28  26 

27  46-7 

28  4-7 
27  10-5 
26  8-2 
26  40-7 

25  52-2 


Cape  Verd  Islands. 


St  Antonio,  N.  Pt .  . 

"  W.  Pt 

"  Summit  7400  ft.. 

"S.  Pt 

«E.  Pt 

St  Vincent,  S.  Pt.. 
St  Lucia,  N.Pt.... 

Bianca,  N.  Pt 

St  Nicholas,  N.  Pt. 

E.  Pt. 

S.  Pt. 

W.  Pt. 

Sal,  N.Pt 

"     Martinez  Peak, 

1340  ft 

«     South  Pt 

Bonavista,  N.  Pt. 

S.  Pt. 

W.  Pt. 

Mayo,  N.  Pt 


17  12 

17    4 
17    4 

16  54-7 

17  6-5 
16  47 
16  49 
16  41 
16  42 
16  346 
16  28 
16  37-7 
16  51 

16  49 
16  34 
16  14 
16  67 
16  2  3 
16  19 


26  6-7 

25  22-8 

26  17 
25  18-6 
24  59 
•24  69 
24  47 
24  416 
24  20-6 
24  0 
24  18-6 
24  26-2 
22  55 

22  66 

22  57 
22  67 
22  49-5 

22  69-6 

23  12 


236 


TABLE  XXXIX. 


NAMES  or  PLACES. 

Mayo,  S.  Pt 

"  English  town,  flag 

statf  bill , 

St  Jago,  E.  PL. . , 
«  Pt  Piaya, Quail  Is 
«  Mt   St   Antonia, 

7400  ft 

«  West  Pt  extr... 
"  N.  or  Bighude  Pt 

FogoN.  Pt 

"  Peak,  9760  ft 

Biava,  W.  Pt 

S.  Pt 


Lat.  N. 
15  66 


16 
16 


8-3 
1 


14  54 

15  2 

15  17-3 

16  19 
15  1-5 
14  66 
14  49-7 
14  46 


LoN.  W. 

a  I 

23  10  5 

23  13-2 
23  26 
23  30-7 

23  39 

23  48 

23  46 

24  21-6 
24  20 
24  46-2 
24  42-7 


S.  Coast  of  France. 


Bermuda  Islands. 


Dock  Yard  Cluck.. 

Wreck  hill 

Light  365  ft 


32  19 

32  16-3 

32  14-7 

64  62 
64  55 
64  52 


NAMES  OF  PLACES. 

0.  Bearn  Lt  751  ft. 

Fort  Brescon  Lt. . . 

Aigues  Mortes  Lt. 

Marseille,    St   John 

Fort 

"  Observatory.. . . 

Plaaier  Isl'd  Lt. . . 

Mt  St.  Michael,  Se- 
maphore, 1341  ft. 

C.  Side  Semaphore. 

Toulou  Observatory, 
"        Semaphore. 

Titan  Isl'd.  Lt.  246  ft 


Lat.  N. 

o   t 

42  31 

43  16-6 

43  32 

43  17-7 

43  17-8 

43  11-9 

43  13 

43  3-2 

43  7-5 

43  4-4 

43  2-8 

LoN.  E. 

o         / 

3    7-6 

3  30 

4  8 

6  21-7 

5  22-2 
5  14 

5  22 
5  61 
5  56 

5  66-6 

6  30-7 


Islands  in  the  Med.  below  Cape 
Bon. 


St.  Paul's  Islet. 


Penedo  de  San  Pe- 
dro, or  St  Paul's 
Mid.  Rk.,  60  ft. 


0  55-5 


29  23 


Coasts  of  Med.  Sea.— S.  Coast 
of  Spain. 


Palomos  Isl'd. .... 

Gibraltar  Mole 

Europa  Pt  Lt  150  ft 


36    4 
36  7-3 

36  6-7 


6  26 

5  21-2 

6  22 


Gulf  of  Genoa. 


L>'.CamaratLt426ft 
C.  Rouse  sum.  1600  ft 
Nice,  St  Frances  Ch 
Pt  Mala  Lt226ft. 

C.  St  Martin 

Mt  Grande,  3100  ft 

Savona  Citadel 

Genoa  3  Lights. ... 
Pt  Chiapa  sum. . . . 
Tino  Isl'd  Lt  384  ft 
Mouta  Altissimo, 
6213  ft 


43  12 
43  28 
43  42 
43  40 
43  43 

43  60 

44  18  4 
44  24-9 
44  20 
44    2-4 

44    3 


6  40-7 

6  65 

7  17 

7  19-5 
7  33 

7  37 

8  27-7 

8  63 

9  10.5 
9  62 

10  14 


NAMES  OF  PLACES. 

Maritime  Is.  2376  ft 


LoN.  N.  I  Lat.  E. 
37  59  6 '12    4 


Sardinia. 


Cape  Figari  sum... '40  69-9 
LimbarraPk.4331ft  40  51 
Mt     Geuuargeutua, 

6102  ft 40    1 

Mt  Seven  Brothers, 

3186  ft 39  18-6 

C.  Spartivento,  S.  pt  38  526 
Cape  Teulada  sum. 

725  ft 38  61-9 

Toro  Rock,  550  feet  38  51-6 
Mount  Arcueuto,  or 

Oristauo,  2713  ft.  39  367 
C.  Argentera  sum.. .  40  43-7 
Razzolellsl'd.Lt 41  183 


9  39-7 
9  11 

9  19 

9  26-6 
8  62-6 

8  39-2 
8  25-2 

8  33-6 

8  9-0 

9  20-7 


Minorca. 


Mahon  Mole  Lt.  to  be 
Cape  Cabaleria. . . . 
Cape  Dartuch 


39  52-6 

40  6 
39  65 


4  21 
4  7 
3  51 


Majorca. 


Coast  of  Morocco. 


S.  W.  Coast  of  Italy 


Ceuta  Lt 

Tangier  Consul's  ho, 
Lt 


36  64 


5  18 


36  47-2      5  48-6 


S.  Coast  of  Spain. 


Estepona 

Sierra  Berraeja  Mt 
Fuengiro  Castle . . . 
Malaga  Mole  Light, 
125  feet. ..... 

C.  Sacratif 

Corchuna,  Castle . 
Alineria,  Town . , 
Cape  De  Gath  Cas'le 

Pt.  Mesa  Tower. . 

O.DeCope 

MtRoldan 


36  26 
36  29 
36  32 

36  43-6 
36  41 
36  41 
36  60 
36  43 

36  56 

37  26 
37  26 


5  9 
5  12 
4  37 

4  26 
3  28 
3  25 
2  32 
2  12 

E. 
1  58 
1  32 
1     2 


E.  Coast  of  Spain. 


Pisa  Leaning  Tower 

Leghorn  Lt 

Gorgona  Isl'd  centre. 
Piombino  Palace. . . 
Mt.  Argentario  tele . 
Civita  Vecchia  Lt. 
Rome,St  Peter's  dm 
Monte   Circello,   St. 

Felix  Church. . . . 
Gseta  Lt,  Orlando  tr, 
Ischia  I.  Castle,  E.  pt 
Naples  Observ.  Capo 

di  Monte 

'    Mole  Lt 

Mt  Vesuvius,  3900  ft 
Castelamare  Lt. . . . 
Capr.   Isl'd,    S.   Pt 

(Lt  to  be) 

Mt  St  Angelo,  4680 

feet 

C.  Vaticano  Tower.. 
Scylla . 


Cartagena  Mole  Lt. 
C.  de  Pales  Tower. . 

0.  Cervera 

Plana  Isl'd,  E.  extre. 
Alicante  Castle  Lt.. 
Mt.  Roldan  Gap .... 
Cape  St  Antonio.. . 

ICape  CuUera  Tower 
Valencia  Lt 


37  36 

37  36-6 

38  0 
38  10 
38  20-7 
38  86 

38  48-6 

39  12 
39  28  6 


C.  Oropesa  Pt  tower 
Coluiiibretes  Islands 

N.  Rock 

Port  Alfaques,  San 

Carlos 

Tortosa  Cath 

Tarragona  Lt 

Barcelona  Mole  Lt . 
Monserrato  Mt. . . . 
■Cape  Tosa  Tower. . 
C.  St  Sebastian  sum 
0.  de  Creux,  E.  extr 

of  Spain. 


40    5-2 

39  64 

40  37-7 

40  48-8 

41  7 
41  22-6 
41  34 
41  43-2 

41  53 

42  19-2 


43  33-5 

10  24 

43  32-7 

10  17-7 

43  25-8 

9  53-6 

42  65-7 

10  31-7 

42  23.7 

11  10-5 

42  6-7 

11  44 

41  641 

12  27-2 

41  12-7 
41  12-4 
40  43-9 


13  5-2 
13  34-7 
13  57-7 


40  51-8 

14  15-5 

40  60-3 

14  15-7 

40  49 

14  26 

40  41-6 

14  28-2 

40  32 

14  11-7 

40  39 

14  31 

38  37-2 

15  52- 

88  14-5 

16  45 

E.  extr.  Cape  Pera.. 

Mt  Galatro 

Dragonera  Isl'd  sum 
S.  extr.  C.  Salinas.. 


39  42 
39  38 
39  36 
39  14 


3  27 
2  28 

2  18 

3  4 


Iviza«; 


Iriza  Castle 

Pt  Denserra,  N.  extr 
Port  St  Antonio,  N. 

Pt 

Formentera  Isl'd,  S, 

E.    Pt 


38  54-3 

39  8 

39    0-4 
38  38 


1  26-7 
1  32 

1  U 

1  36 


Lipari  Islands. 


Stromboli  Is.  2570  ft 
Volcano  Is.,  Sulphur 

Works 

Ustica  Isl'd  N.  E.  pt 

Fort 


38  46-7 
38  23-3 
38  43-3 


16  13-7 
14  56 
13  11-2 


Sicily. 


0  66 
0  40 
0  88 
0  26 
0  26 
0  12 
0  10 

W 
0  13 
0  24 

E. 
0  10 

0  44 

0  36 

0  33 

1  16 

2  11 

1  55 

2  58 

3  13 

3  20 


African  Coast. 


Ceuta  Lt 

Tetuan  Custom  Ho 

Alboran  Isl'd 

C.  Tres  Forca,  N.  pt. 

Mid 

Zafarine  Isl'd.  sum. 

W.  end 

Pt  Abuja,  2060  ft.. 

Algiers  Mole  Lt. . . 
MtAzafoun,  4360  ft 
Mt  Babor,  6200  ft . 
Philippsville  Lt. . . . 
Bona  Lions  Pt  Lt. 
Galita  Isl.  Pk.  1240 

feet 

Bizerta  Castle 

Cape  Cartilage  Lt 
Zembra  Island  sum. 

1661  ft 

C.Bon  Tower  1176 ft 


35  64 

36  37 
36  58 

35  28 

85  11 

35  53 

36  47-3 
36  50 
36  34 
36  52-8 

36  64-5 

37  31-2 
37  16-6 

36  52-4 

37  10 
37    4-8 


w. 

5  18 

6  18 

3  1 

8  0 

2  25-7 

0  29 

E. 

3  4-6 

4  25 

5  28 

6  63 

7  46'5 

Faro  Isl'd  Lt  on  E. 

extremity 

Messina  Lt 

Mt.  Etna,  10.874  ft 

Syracuse  Lt 

Passaro  Isl'd  Lt.  .  . 
Alicata  Castle  Light 
Girgenti  Mole,  2  Lts, 

Marsala  Lt 

Mt  St  Julian  2176  ft 
Palermo  Observat'y. 

Light 

Pantellaria  Is.  sum. 

2213   ft 

Liuosa  Isl'd.  centre. 
Lampion, centre. . . . 
Lampedusa  Is.  C'st 


33  15-8 

38  11 

37  43-6 

37  3 

36  41-6 

37  4 

37  15-6 

37  47-8 

38  3 

38  6-6 

38  8-2 

36  48 

35  51-8 

36  32-8 

36  29*2 

15  41-2 
15  34-7 
15  00 
15  16-0 
15  9 
13  56 
13  31-7 
12  26-2 

12  35-5 

13  21-2 
13  22-2 

12  2 
12  62 
12  20 
12  85'2 


Malta. 


8  65'5 

4  49-2 

10  20-2 


10  48 

11  35 


Valetta  Palace 35  53-8 

Spencer's  Monument' 35  63 

St  Elmo  Lt 36  64-1 

S.  E.  extre.  Pt  Delia 
Mare 


85  49-7 


14  31-2 
14  30-7 
14  31-6 

U  84-7 


Goza. 


N.  W.  Pt  or  Cape 
Demetri 


86    4 


14    8 


TABLE  XXXIX. 


287 


Coast  of  Naples. 


NAHES  OF  PLACES. 


0.  Spartivento 

C.  St.  Vito  Lt 

C.   Otranto,  (E.  Pt 
of  Italy) , . . 


Islands  in  the  Archipelago. 


W.  Coast  of  the  Adriatic. 


Aiii^elo 

IsTds   Mid 


Mt.  St. 
Tremiti 

Castle, 
CoUuiellasm.lOSOft. 
Aucoiia  Lt 
San  Marino,  2460  ft. 
Venice,    St    Mark.. 
Trieste  Lii^lit  Castle 


41  43 

42  7-3 

42  52-3 

43  37-7 

43  57 

45  25-9 

45  SS-6 

15  57 

15  30-5 
13  52 
13  30-5 
12  29 

12  2()"2 

13  46-5 


NAMES  OF  PLACES. 


sum 


E.  Coast  of  the  Adriatic. 


Sausogo    Isld    sum. 

35U  feet 

M.     Vella    Sti-azza, 

1070  feet 

St  Andrea  ia  Pelago 

1000   ft 

Meleda  Isl'd  W.  Pt. 
Molonta  Isl'd  sum. . 
Veterguach,  39tiO  ft. 
C.  Rod.mi,  400  feet.. 


44  30-9 

43  59 

43  1-7 

42  47 

42  29  9 

42  19 

41  37-6 

14  18-2 

15  2 

15  45-7 

17  IS 

18  23-5 

18  52 

19  28-2 


Coast  of  Albania. 


( 


C.  Liuguetta,  2290  ft 
Mt.  Ciea,  6300  ft,, 
Parga  Citadel. . . , 


40  26-7 

19  17-7 

40  15 

19  35 

39  16-4 

20  23-5 

Ionian  Islands. 


Hydia    Island 

1939    ft 

St.  George  S.E.  sum 

1085  ft. 
Zea  Isl'd,  Mount  St 

Elias.. . , 
"  Port  St.  Nicolau  It 
Herniia  Island  sum. 

900   feet 

Milo,  MtSt.  Ellas  uu 

S.  "W.  Pt  •24hO  ft. 
"  Port  W.  Pt  Point 

Vani 

Paros  Island,  Mt  St 

Elias,  mid.  2530  ft 
Syra  Island  sum.  E. 

side,   1415  ft. 
Audros   Island,    Mt 

Kovari,  3200  ft. 
C.  Dora,  islet  off. . 
Mt  Delphi,  6730  ft 
Skyros  Isl'd,  N.  end 

sum , 

•'  Grand  Port 
Mt  Pelion  (Patras), 

5310   ft 

Mt  Ossa  (Kessova), 

6407    ft 

Mt01ympu8,9754ft 

Salonika 

C.  Cassandra. 
Mt  Athos  sum.  6849 
Lemnos,  W.  Pt 
S.   Pt 


Fano  Isl'd  S.W.sum 
Corfu  Citadel  Lt. . 
M.  St  Giorgio,  1326 

feet 

Paxo  Isl'd  N.  W.  Pt 

Light 

Anti  paxo  Isl'd.  E.  Pt 
Mt  Nomali,  3750  ft 
Cephalonia,  N.  extr. 
Mt  Elato  sum.  5246 
Zante,  N.  Pt 

"  Mt  Teri,  2274  ft. 

"  MtSkopo.l439ft 


39  50-2 
39  37 

39  36-5 

39  13-2 
39  8-7 
38  41-6 
38  28-5 
38  8-5 
37  565 
37  50 
37  44-6 


19  20 
19  55-5 

19  48 

20  9 
20  5-7 
20  37-7 
20  33 
20  41 
20  41-5 
20  44.2 
20  57 


W.  Coast  of  Greece. 


Oxia  Is.  Pk.  1257  ft 
Lepanto  en.  Minaret 
Morea  Castle,  centre 

C.  Katakolo 

Stamfaues  Isl'd  Lt. 
Navarino  Mosque. . 
Mt  St.  Nieolo,  1627 

feet _. 

Sapienza  Isl'd  sum.. 
Mt  Makrino,  7900  ft 

C.  Matapan 

C.  St  Angelo 


Cerigo  Isld  N.  Pt . . 
•'  «  S.  Pt. . 
Ovo  Island,  550  ft.. 
Cerigottosm.  1230  ft 
Mt.  Kritluna,  2600  ft 

Kravi  Island 

Falconera  Isl'd  sum 
Bello  Poulo  sum.. . 


38  18-7 
38  23-4 
38  ls-5 
37  37-7 
37  15-3 
36  54-6 

36  63 
36  45 

36  57 
36  23 
36  26 
36  23 
36  7-7 
36    55 

35  50-1 

36  28-2 
36  461 
36  50-9 
36  64-9 


21  7 
21  50 
21  47 
21  19 
21  1-6 
21  41=7 

21  42 

21  41-2 

22  21  2 

22  29-2 

23  12 

22  67  2 
52  697 

23  0 
23  18 
23  8-2 
23  36-5 
23  53*7 

2  27-7 


Lat.  N. 

o   / 

37  19-6 
37  28 

37  37-3 

37' 39-4 

37  26-2 
36  40-6 

36  45-3 

37  2-7 
37  28-9 

37  601 

38  9-4 
38  37-4 

38  49-7 

38  46 

39  26-5 

39  48 

40  4-7 
40  38-8 

39  66-7 

40  9-6 
39  68-7 
39  46-6 


Coast  of  Asia  Minor. 


LoN.  E. 

o   / 


23  28 

23  66 

24  21-7 
24  20 

24  23-7 

24  23-5 

24  22-7 

25  11-5 

24  56-7 

24  50-5 
24  36-3 

23  60-7 

24  37-2 
24  37 

23  3 

22  42 
22  22 

22  67-2 

23  22-0 

24  20 

25  2 
25  21-5 


on 


NAMES  OF  PLACES. 

Tenedos  Isl'd  N.  W. 
sum 

Mt  Ida,  5750  feet 
Mitylene,  E.  Pt. . 
Smyrna     Mill, 

Daragaz  Pt. 
Sam  OS,  W.  sum 

"  M.  Kerki,4725ft 
Nicaria  Beacon  3390 

feet 

Patmos,  S.    Pt 

Mt  Samsouu,4130  ft 

Kos,    Mt.     Christos, 

2760  ft 

Rhodes  Lt. . . 
W.  Pt 


Lat.N. 

o        / 


39  50-2 
39  42 
39    0-7 

38  26-5 
37  43-8 
37  43-7 


Lon.  E 


26    5 
26  50-5 

26  37-7 

27  9-7 
26  38-5 
26  38-7 


37  32-2 

26  4-7 

37  16 

26  34-7 

37  39-8 

27  9 

36  60 

27  14-2 

36  26-9 

28  16-2 

36  8-7 

27  43-2 

Candia. 


Turkey. 


Dar(ianelles,  AsiaCs 

Gallipoli  Lt 

Marmora  Isl'd  S.  W. 

sum 

Constantinople,     St. 

Sophia! 

Papa,  or  Kalolimuo 

Isl'd  N.  sum 

Buyuk     Dereh,    N 

Minaret 

Bosphorus,  Europe  It 


40  9 

40  24 

40  36-5 

41  0-3 

40  33 

41  10  1 

41  14 

26  24-5 

26  39-7 

27  36 

28  69-2 
28  32 


29 
29 


3 

7*2 


Black  Sea. 


Coast  of  Greece. 


Piraeus,  2  Lts . . . , 
Athens  Parthenon , 
O.ColonuaTm.269ft 


37  56-2 
37  58  1 

37  38-8 


23  38-0 

23  43-7 

24  1-7 


Varna  Mosque,  raid. 
Danube  R.  Soulineh 

Mo.  Lt. 

Serpent  Island  Lt. . 

C.  Foutane  Lt 

Odessa   Cath 

Tendra  Isl'd  N.  end. 
0.  Khersones  Lt. . . 

Sevastopol  Ch 

Mt  Tchatirdag  S.W 

sum 

Kaffa,  ov  Theodosia. 

Cape  Takli  Lt 

Kertch  Ch 

Yenikaleh   Lt 

Taganrog  Ch 

Azov  Cath 

Anapa,  E.  Ch 

High  Summit,  4  ml'a 

inland 

C.  Batoum  Mosque. 
Trebizonde,  E,  extr. 

Si  nope  Castle 

Cape  Baba 

Asia  Lt.,  entr.  Bosp. 


43  12 

46  9-3 
46  15-6 
46  22-8 
46  28'9 

46  21-7 

44  35 
44  37-9 

44  44 

45  1-6 
45  6-9 
45  21-2 
45  23-1 

47  12-2 
47    7 
44  54'1 

43  17 
41  89-4 

41  1 

42  2-2 
41  20-9 
41  13 


27  26-5 

29  40-5 

30  14-2 
30  45-6 

30  54-5 

31  32 
33  22 

33  29-5 

34  17-2 

35  24 

36  27 
36  29-5 
36  39-2 

38  67 

39  26-6 
87  18-5 

40  r 

41  37 
89  46 
36  12  6 
81  26 
29    9-4 


Candia,  Minaret  Lt. 
"   E.  extr.  C.  Salo- 

ra.in 

'  Mt  Ida 

Gozza  Isl'd  W.Pt.. 
Boudroom  Castle. . 
Marmorice  Cape. . . 
Highestsum. 5980  ft 


36  21 

36  9-2 

35  13-3 

34  62 

37  2 

36  43-9 

36  31-8 

25  8-2 

26  19-6 
24  47 
24    2-2 

27  27-6 

28  20-7 

29  142 


Coast  of  Karamania. 


MtTakhtalu7800ft 

C.  Anamour,  S.  Pt. 
of  Asia  M. . . . 

Alexandretta  Con- 
sul flag  staff. . , 

C.  Khynzyr,  6650  ft 


36  31-7 

36    0-8 

36  36-3 
36  16 


30  28 

32  49 

36    9 
36  62 


Syria. 


Bairout  Brit  Con. . 
Tyre 

St.  John  d'Acre,  Bas- 
tion, Marine  gate. 


33  646 
33  17 

32  65 


36  28-2 
36  12-7 

36    2-5 


Island  of  Cyprus. 


West  extr.  C.  Epi- 
phanius 

N.  and  E.  extr. C.St 
Andrea 

S.  and  E.  extr.  0. 
Gatto 


35  6-3 

35  41-7 

34  32-8 

32  14-5 


84  36-5 


32  59-7 


Egypt. 


Rosetta,  EngL  Cons . 
Aboukir  Castle.. . . 
Alexandria   Pt  Eu- 

Dostos  Lt 

Arabs  Tower. 

C.  Razat 


31  24-3 
31  20-5 

31  11-5 

30  57-7 

32  57 

30  28 
30    5-7 

29  51-6 
29  83-2 
21  38 


Barbary. 


Jebel   Zawan,  3917 
feet 

Tripoli,  Pasha's  Cas. 
Jebel  Thelj,  N.   E. 

sum 

Kuryah  Isl'ds,  N.  E. 
Pt.  sum 


36  23 
32  53-9 

34  25 

35  48 


10  5 
18  11-0 

9  52 

11  8 


Shores  of  the  S.  Atlantic  Ocean 
— W.  Coast  of  Africa. 


Cape  Lopez 

Loango  River  ent. . 
Congo  River,  S.  ent 


s. 

J 

0  36 

8  43 

4  89-5 

11  46 

6  46 

12  15 

K 


238 


TABLE  XXXIX. 


NAMES  OF  PLACES. 

St.  Paul  de  Loando, 

flag  staff 

St.   Philip  de   Ben- 

guela  flag  staff. . 
Cape  Negro,  200  ft. 

Diaz's    pillar. . . . 
Mt.  Colquhoun,  11  or 

18  L.  Inland 
Walvisch  B.  Pelican 

point 

HoUam's  Bird  Island 
Angra  Pequena,  Pe 

destal  point 


Lat.  S. 


8  48-1 

12  33-9 

15  40'7 

22  33 

22  52-5 
24  34-7 

26  38-4 


Cape   Voltas |  28  44 


LoN.  K 


13  13-5 


13  24 


11  58 

11  58 

14-27 
14  32 


15  8 

16  32 


S.  Coast  of  Africa. 


Koussie  R.,  limits  of 
Cape  Colony. . 

Elephant's  River. 

Cape  Deseada. . . 

St.  Helena  B.,  Point 
St.  Martin .... 

Saldanha  Bay,  N.  Pt 

Dassen  Island . . . 

Robben  Island,  S.  pL 

Table  B.,  Green  Pt 
two    Lights 

Deril's  Peak,  3315  ft 

Cape   Observatory . 

Cape  of  Good  Hope 
Point,  800  feet. 

"  Lion's  Head. . . 

Simon's  B.  dockyard 

Cape  Hangklip  Pt 
1800  feet 

Dyer  Island  centre. 

Quoin  Point 

Cape  Agulhas,  S.  ex- 
tremity of  Africa 
Light 


29  40 
81  38 
32  18 

32  40 

33  1-7 
33  26-2 
33  48-2 

33  53-2 
33  67-2 

33  56 

34  22 

33  56 

34  11-3 

34  23-8 
34  43-7 
34  48-8 


34  49-7 


17  10 

18  12 
18  23 

17  59 

17  54 

18  6-7 
18  22-7 

18  24-5 
18  81-7 

18  28-7 

18  29 
18  24 
18  26 

18  50-9 

19  28-2 
19  41-7 


20  0-7 


E.  Coast  of  South  America. 


Maranham  Cath.. . 

Fort  St.  Marcas  Lt 

Mt  Melancias  Peak, 
sand  bill 

Point  Macoripe  Lt 

Morro  Tibao,  Red 
sand  hill 

Cape  St  Roque. 

Pernambuco,  Fort 
Picao 

C.  St  Augustin  Ch. 
summit 

Mt  Sellada,  S.  Peak 

Mo'nt  Masarandupio 
lOm.  inland. . 

Bahia,  St.  Antonio 
Light . . 

Abrolhos  Isl'ds.,  lar- 
gest E.  summit. 

Mt  Pascoal  summit 

Morrc  San  Juan,  iso- 
lated  , 

Cape  Frio,  S.  Pt  Lt 

Cape  Negro  Point 

Rio  Janeiro,  foi-t  Vil- 
iagagnan 

St  Sebastian  Island, 
Sjiuth  Point. . 

St  Catherine  Island, 
North  Point. . 

Rio  Grande  de  Sul, 
E.  Point  Light 


S. 
2  31-7 

2  29 

3  12 

3  41 

4  49 

5  28 

* 

8 


3-6 


8  21 
8  25 

12  24 

13  0-7 

18  6 
16  54 

22  32-5 

23  1-3 
22  57 

22  54-7 

23  57 
27  22-5 
32  7 


W 
44  18-7 

44  18 

39  18 
38  29 

37  18 
35  16 

34  51-7 

34  56 

35  11 

38  4 
38  31-7 

38  42 

39  20 

42  0 

41  58-2 

42  39 

43  9 

45  15 
48  25-7 
52  8 


NAMES  OF  PLACES. 

Great  Castillos  rock 
(like  a  schooner) 

Cape  St  Mary .... 

Maldonado  Tower. 

Flores  Islands  Light 

Monte  Video  Rat  Isl 
*'         summit. . 

Colonia  Light 

Buenos  Ayres  mole 
landing  place. . 

Pt   Indio 

Sierra  Ventana,3500 
feet 

Sierra  de  San  An- 
tonio, 1700  feet. . 

Pt.  Delgada,  200  ft 
S.  E.  cliff 


Lat.  S. 


34  24 
34  39 
34  53-5 
34  56 
34  53-3 
34  53 
34  28 

34  35-5 

35  16 

38  11-7 
41  41 


LoN.  W. 
»  / 

53  46 

64  9 

54  57-7 

55  55 
66  13-6 

66  15 

57  49-7 

58  22 

67  9 

61  565 

65  12 


42  46   63  37 


E.  Coast  of  Patagonia. 


Salamanca  Pk.,  700 

feet 

C.  Three  Pfs  2000  ft 
Monte  "Video,  300  ft 

4m.  inland 

Wood  Mt,  visible  11 

leagues. ...... 

C.  Fairweather,  300 

feet,  S.  Pt 

0.   Possession,    mid. 

300  feet 

Orange  Peak 

Port  Famine  observ, 
Mt  Saimento,  6800 

feet,  two  Peaks 
MtBuckland4000ft 

Cape  Tamar 

Staten  Island  C.  St 

John 

Cape  Horn  500  feet 


45  34 

47  6 

48  14 

49  13-7 

51  321 

52  17 

52  28-3 

53  38-3 

54  27-2 

54  26 
53  56-5 

53  43-5 

55  59 


67  20 

65  51 

66  26 

67  45 

68  55-5 

68  56-7 

69  25-5 

70  58-2 

70  51-5 
70  22-7 
73  48-5 

64  44' 8 
67  16 


Islands  in  S.  Atlantic  Ocean. 


Ascension,    Barrack 

square 

Green  Mt'n  2820  ft 
Cross  Hill  850  feet. 
St  Helena,  Diana's 

Pk.  2700  feet. . 
Obs'rvat'ry,  showing 

G.  M.  T. 

Fernando   Noronha, 

S.  W.  Pt 

"  Pk.  on  S.  E.  side. 
Trinidad  Isl'd  S.  Pt 
Martin   Vas   Rocks, 

large  one 

Tristan       d'Acunha 

waterfall  N.  side 

middle 

Inaccessible  Islands, 

West  one 

Nightingale  Island. 
Gough's   Isl'd    4385 


55-5 

57 

65-7 


15  57 

16  65 

3  52 

3  60-4 
20  31 

20  28 


37    6 


37 

27 


16 
26 


ft  N.  Point 1 40  19 


14  25-5 
14  21 
14  25 

5  42 

544 

32  28 
32  25-5 
29  19 

28  51 


12    2 

12  52 
12    8 

9  44 


Falkland  Islands. 


W.   Falkland,    Port 

Steph'ns  entrance 

E  Pt  summit. . . 

0.  Tamer  N.  cliff  sum 

Eddystone  Rk  200  ft 

East  Falkland,  Port 

Salvador, 

Island  entrance . 

0.  Carysford,  N.  E, 

cliff 


Shag 


52 
51 
51 


11 

17 
10 


61  23-7 


51  25-2 


60  41-2 
60  52 
69    2-5 


58  19 
57  50-6 


NAMES  OF  PLACES. 

Port    Louis    Settle 

ment  flag  staff. . 
C.  Pembroke  beacon 

on  S.  E 

Port  William,  Gov. 

Store  House   .... 
Beachene  Isl'd,  200 

feet  S  Point. ... 


Lat.  S.  Lon.  W. 


51  32 
51  40-7 

51  41 

52  55-7 


68    'J 
57  42 
67  61-6 
59  12-7 


Shores  of  the  Indian  Ocean. 


Cape  Agulhas,  S.  ex- 
tremity of  Africa 

C.  St  Blaize,  S.  Pt 
of  Mossel  Bay. . . 

Plittenburg  B.  S.  Pt 

Cape  St  Francis. . , 

Cape  Recif  Light. , 

Algoa  B.  Command 
ant  House 

"  St  Croix  Isl'd  Pk. 

Bird  Island,  E.  one. 

Port  Hood 

Cape  Natal. 

Port  Natal,  S.  Pt  of 

■    Bay.. 

Cape  Vidal 

St  Mary's  Isl'd  N.pt 

P.  Melville,Elephant 
Isl'd,  S.W.  side,  N.) 
Point 

Cape  Corrientes. 

Mt.    Cockburn. . . 

Port  Mocamba,  N. 
Pt  Pk,  2000  ft 

Mozambique,  Saint 
George's  Island 

Mount  Pao 

Loguua  Peak. ... 

C.  Paman,  Hull  Rk. 


S, 

34  49-7 

34    6-9 
34    4-8 
34  10 
34    2-2 

33  57  5 


as  47-6 
33  521 

33  3-8 

29  53 

29  53 

28  96 

25  58-2 

25  58 

24  7-5 

16  29 

15  6 

15  2-2 

14  60 

14  21 

10  10 

E. 
20    0-7 

22  11-7 

23  22-6 

24  52-7 

25  41-2 


25  39-5 

25  46-5 

26  18 

27  58 

31  2-2 

81    2 

32  88 

33  2-6 


32  57-6 
35  30-6 
38  66 

40  36 

40  48-5 
40  25 
40  37-6 
40  10 


Madagascar  Island. 


S.  extremity  of  Cape 

St  Mary 

Leven  Island,  centre 
Murderer's   Bay,  N 

Point •. . 

Cape  St  Vincent. . 
N.  W.  extremity,  or 

Cape  St  Audi'ew 
Cape  St  Sebastian, 

(Island  om.  off  the 

Point)   

Woody  Island. . . 
Amber  Mountain 
Port  Leven  Lingo  rk 
Mananhar  Table  Hill 
Tangtang  flag  staff 
Plum  Island,  visible 

6  leagues 

Port    Dauphin   flag 

staff 


12  26-2 
12  16-7 
12  34-5 
12  46-5 
14  39-7 
16  42-5 

18    2-8 

25    1-3 


48  45-7 

48  41-2 

49  11 

49  54-2 

50  15-7 
49  46-2 

49  29-2 

47    2-2 


Isl'ds  in  Mozambique  Channel. 


Europa     Island,    or 

Bassas  da  India 
St  Juan  da  Nova. . 
Mayotta,   Valentine 

Peak 

Johanna  Isl'd  Pk.  E. 

Point 

Comoro,  S.  E.  Point 
Assumption   island, 

hummock  on  S.E. 

part 


22  22-5 
17    35 

12  64 

12  16 
11  64 


40  24-2 

42  50 

45  16 

44  29-6 

43  83 


25  38-9 
25  12-5 

46  7 
44  18 

22  12-5 
21  54-4 

43  18 
43  20-6 

16  11-4 

44  31 

9  46    U6  34 


TABLE  XX XIX. 


289 


Coast  of  Africa  (Continued.) 


NAMES  OF  PLACES. 

MtTiiuiclaclel200ft 
Zanzibar  Isl'd  S.  Pt. 
Waseeu  Peaks,  mid- 
dle one 

Mt  Gibbous 


MurotHill 

K  extreiu.  of  Africa 
Ras  Hafoon  600  ft, 
East  Point 

C.  Guiirdafui,  N.  K 
extrem.  of  Africa. 

Tocotra,  W.  extrem 
ity  Point 

"  S.  W.  Point,  Ras 
Kattanie,  summit 
1466  feet 

Ras  Feluk  800  feet. 


Lat.  S. 

o         t 

10    4 

6  27-7 

4  30 

1  12-2 
N. 

5  41-3 


10  26-8 

11  60 

12  .S3 


12  22-5 
12    0 


LoN.  E. 

o         » 

39  44 
39  33 

39  22 
41  28' 
E. 
46  17-2 


61  22 
61  16 
63  18 


53  32 

50  51 


S.  Coast  of  Arabia. 


a  St  Antony  2772 
feet 

C.  Aden,  sum.  1776 

feet 

N.  Barnlike  Pk  6284 

feet 

JebelJinjeri  1300  ft 
Kuria  Muria  Islands, 

W.  one,  Haski  pk 
Mazeira  Isl'd,  S.  Pt. 
0.  Mussendom,  N.  pt 
Great  Quoin  300  ft 
Asses  Ears  5m.  inl'd 
Hummocks  of  Kenn, 

S. one 

High  Clay  Pk.  white 

Conical  Hill 

Cambay  flag  staff 
St  John's  Highland 
Terrpore  Point..  . 
Bombay  Obs'rvat'ry 
"  Lighthouse 
Rajapour  Harbor  or 

Rajah  Point. . . . 
Goa,  St  Ann's  light 
Barsalore  Pk.  4452 

feet 

Mount  Dilly 

Calicut  Lt  flag  atafif 
C.  Coniorin  Point,  S. 

extremity  of  India 
"  Peak 


12  41 
12  46 

14  4 
17    8 

17  27-2 
20    7-6 
26  24 
26  80 
28  29 

28  4 
25  23 
20  57 
22  17 
20  2 
19  62 

18  63-7 
18  51-7 

18  16 

15  28-3 

18  50 
12  2 
11  15-2 

8    5 
8  23-2 


44  10 

45  3 

47  32 
54  58 

56  35-7 
58  33 
56  34 
56  33 
51  14 

61  41 

62  30 

71  18 

72  35  5 
72  43 

72  40 
72  48 

72  47-7 

73  0 

73  51-2 

74  51 
76  11 

76  45-5 

77  80 
77  30-5 


Island  of  Ceylon. 


Calpeutyn  Fort. . . . 
Colombo  Liijht. . . . 
Pt  de  Galli  fl.  stlt 
Adam's  Pk.,  7000  ft 
S.  extr.  Doudra  Hd. 
Elephant  Rk.  inland 

Friar's  Hood 

Tiineomalee  Light. 
Palmyra  Point. . . . 


15 
561 
1-8 
52 
55 
24 
29 
337 
49 


79  46 

79  49 

80  11 
80  29 

80  84 

81  32 
81  40 
81  14-7 
80  14 


Islands  in  the  Arabian  Sea.- 
Lacadive  Islands. 


Aticutta,  mid . 
Kittan,  S.  Pt. 


lU  51 
11  25 


72  10 

73  0 


Maldives. 

Containing  19  AtolU,  or  Oroups. 


Malcolm  Atoll,  N.E 

extr 

Powell's  Is'lds  N.  one 


6  24-6 
5  29 


72  40 
72  54 


names  ok  PLACEa 

Male  Atoll,  E.  extr. 
"  Kings   Is'ld   flag- 
staff, N.  side 


LoN.  N. 


4  27 


4  10 


Lat.  E. 


73  42 


73  29 


Almirante  Islands. 


St  Joseph  Island . 


S. 


5  27 


E. 
53  30 


Seychelle  Archipelago. 


Frigate  Isl'd,  E.  extr 

550  feet 

Foquet  Isl'd,  S.  extr. 


4  35-2 

5  27 


56    1-2 

71  46 


Chagos  Gro^p. 


Diego  Garcia,  S.  Pt|    7  26     |72  23 


Cargados  Garajos. 


Frigate  Island . 
Siren  Island..  . 


16  36 

16  28 


59  33 
59  37 


Islands  in  the  Indian  Ocean. 


Rodrigue 

Round  Isl'd,  1049  ft 
Mauritius,        Peter 

Botte,2600ft 

"  Port,  L.  Cooper's 

Island 

Bourbon  Isl'd,  S.  ex. 
Bouvet's  Island. . 
Thompson's  Isl'd. 
Prince  Edward's  Is. 

N.  Pt 

Marion  and  Crozet's 

Island 

Kerguelen's  Land,  N. 

Pt 

C.  St  George. . . 
St  Paul,  700  ft. . 
Amsterdam  summit, 

2760  ft 

Keeling    Island,    S. 

Group,  S.  Pt 

Direction  Isl'd  S.  W. 

Pt 

Christmas  Isl'd. . . . 


19  41 

19  60 

20  11-7 

20  9-7 

21  24 
64  20 
63  66 

46  46 

46  9 

48  41 

49  54 
38  43-8 

37  62 

12  12-6 

12  6-4 

10  31 


63  25 
57  60 

67  36-7 

67  31-7 

65  40 

6  24 

5  30 

87  18 

60  28 

69  6 

70  10 
77  38 

77  36 

96  54 

96  63 
105  38 


NAMES  OF  PLACES. 

Rangoon  city,  Dagon 


Pagoda.. 


Martiiban 

Maulmain  Pagoda. . 
Amherst  Lt.,  to  be. 
Mt  sum.  inland. . . . 
The  cone,  vis'ble  161 
Tenasserim  Island. . 
Juukseilon,  H.  Mt  S 

Pt 

Pulo  Pera 

Penang  Island  sum 

2713  ft 

"   Cornwallis  fl.  st. 

Pulo  Dinding 

Salangore  Hill  and 

Fort 

Parcler  Hill  sum. 
C.  Rachado,  vis.  7  1. 
Malacca  flag  st. . . 
Mt  Moar  sum... 
Mount  Formosa. . . 
Pulo  Kissang,  200  ft 
Singapore  Battery 
Barbukit  Hill,  645  ft 
Pedra     Branca,     or 

Horsburgh  Lt . . 
Bintang  hill,  1200  ft 
Preparis  Isl'd  Cow  <fe 

Calf,   N.  end.. 
Great  Andaman,  N. 

Pt,  or  C.  Price., 
Saddle  Hill,  visible 

20  1.  N.  Pk... 
Narcondam  vis.  161, 
LittleNicobarN.pt 
G.  Nicobar,  S.  Pt. 


Lat.  N. 


16  47 
16  32 
16  30 
16  6 
16  ] 
14  1 
12  34 


46 

42 

25 

251 

16 

20 
62 

26 
10-5 
59 
49 

28 
17 
24 

20 
6 


14  66 

13  84 

13  10 

13  36 

7  26 

6  46 


LoN.  K. 


96  10 

97  36 
97  37 
97  33 

97  35 

98  24 

97  49 

98  18 
98  56 

100  14 
100  19-7 

100  35 

101  22 
101  25 

101  50 

102  14-2 
102  40 

102  54 

103  13 

103  60 

104  11 

104  23 
104  26 

93  88 

93  4 

98  4 

94  18 
93  42 
93  54 


S.  W.  Coast  of  Sumatra. 


Queen's 


Coromandel  Coast. 


Negapatam  flag  st. 
Five  White  pagodas 
Pondicherry  Lt. . 
Madras  Observ. . 
"  Light  Ft  St  Geo. 
Coringa,  town  Lt. 
Jugurnaut  Pagodas, 

large 

Black  Pagoda 

False  Pt  Lt 

Mypurra  Isl'd,  S.  Pt 

Pt  Palmiras 

Lower  float'g  It  ves. 
Upper  float'g  It  ves. 
Kedgeree  Lt. . . . 
Saugor    Island    Lt 

tripod , 

Calcutta,  Fort  Wm. 
Chittagong  fliig  staff 
Table  land,  8300  ft. 
Akyab  harb.  fl.  st. . 
Great  Savage  Lt. . . 
Keiiain  kown  pk  .  . . 
Cheduba  Isl'd,  S.  pk. 

170U   ft 

Elephant  Pt  Pagoda 


N. 
10  45-6 

10  49 

11  56-7 
13  41 
13    4-7 


19  60 

19  52 

20  19-4 

20  41  3 

20  41 

21  3 

21  26 

21  60-8 

21  37-2 

22  33-6 

22  20 

21  9 

20  8-4 

20  5-2 

19  48 

18  40 

16  28 

E. 
79  50-6 
79  50 

79  49-2 

80  14 
80  16-2 
82  12 

85  66 

86  8 

86  44 

87  7 

87  9 

88  12 
88  4 
87  55-7 


Golden,   or 

Mt8280 

Achen  Head 

Goonung      Loose, 

11000  ft 

Sinkel    Pt 

Pulo  Babi 

Mt  Ophir,  vis.  37  1. 

Padang  head  fl.  st. . 
Bencoolen,  Ft  Marl- 
borough. 
Rajah  Bassa,  1600  ft 
KrakatoaPk.2690ft 

South  end.. . 

Anjer  flag  staff 

Bauca,     Parmesang 

hill,   1250  ft 

'  Monopin  h.  1 640  fj 

"  Goonung  h.  2600  f 


6  22 
6  36 

3  47 
2  15 
1  44 
0    6 


S. 
0  66 

3  47-6 
6  49 


9 
3-2 


2  38 
2  0 
2  36 


95  46 

96  11 

97  15 
97  46 
97  37 
99  67 

E. 
100  20 

102  19 
106    4 

105  29 
105-57 

105  53 

105  12 

106  49 


Coast  of  Java. 


Java  Head 

Bantam  flag  staff 
Mt  Karang,  6000  ft 
Batavia  Obser.. . 
Mt  Cede,  9380  feet 
Mt  Chermair  Peak, 

88    1         9730   ft 

88  19-2  Mt  Fegal,  11000  ft 

91  47-7  MtSoumbing  10.700 

92  23         feet  

92  54     Samarang  flag  Mi.tff 

92  53-7  C.  Sedano  Pt  4480  ft 

93  28     Mt  Idjeng,  9600  ft 
SemiruMt  12.000  ft 

93  41     Arjuno  Mt  11.930  ft 
96  21     Lomboek  P.  11.400  f 


6  47 
6  1-7 
6  16 
6  8 
6  46 

6  66 

7  14 

7  21 

6  67  8 

7  49 

8  3 
8  8 

7  48 

8  26 


105  13 

106  10'7 
106  6 

106  60 

107  0 

108  26 

109  15 

110  4 
110  27 
114  30 
114  14 
112  68 
112  87 
116  25 


16 


240 


TABLE  XXXIX. 


Coast  of  China. 


Lat.  N. 

NAMES  OF  PLACES.  o       / 

Great  Lema,  E.  Pt.  22    6 
Lautao  Pk.  3050  ft.  22  16 

Macao  flag  staff 22  11-4 

Canton  Eng.  factory  23    6-9 
Hong  KoDg  summit, 

N.W.  Pt.  1825  ft  22  15 
A  high  sum.  2810  ft  22  31 
Table  Hill,  1767  ft.  23  39 

Amoy  citadel 24    2'8 

Mt.  Keu-sau  pagoda 

760  feet 24  48 

Double    Peak    Isl'd, 

W.  Pk.  1190  feet.  26  36 
Montague  Isl'd,  E.  pt 

740  feet 29  10 

Ohusan  Isl'd  S.  extr.  29  36 
«  Chookeainoft.  29  54 


LoN.  E. 

o        / 

114  19 
113  58 
113  32 

113  15 

114  22 
114  32 

117  9 

118  4 

118  38 
120  11 


NAMES  OF  PLAGES. 


12  1 


Bald  Head  vis, 

S.  Point... 
King  George's  Sound 

Gov.  buildings . 
Bald  Island  summit 
Port  Hood 


pt 


S. 


122 
122 
122 


5 

8 
25 


Formosa. 


Formosa  S.  Point. 
Table  Hill,  360  feet 
Sum.  Eastw'rd  2800 

feet 

K  extr.  of  Formosa. 
Mt  Morrison,  10,800 

feet 

Double  Pk.,  3m.  in 

land,  vis.  17  leag. 


21  54 
24  53-5 


11 
2 


23  50 


22  60 


120  55 

120  69 

121  31 

122  2 

120  43 

121  8 


Lat.  N. 


35    7 

35    2.2 
34  65 
34  24 

S. 


Borneo. 


Mt.  Tatau,  1900  feet 
Mt.Silungunl600ft. 
ML  Mulu  8000  feet. 

Borneo  City 

Labuan  Isl'd,  W.  pt. 
Castle  Pk.,  1600  ft. 
Kiiii  Balu  Mountain, 
13,700  feet 


2 
60 

7 
50 
16-5 
47 


6    8 


12  59 
118  49 
115  10 

114  58 

115  7 

116  1 

116  36 


Mindora. 


High  Mt'n  3126  feet 
Mt.  Calavite  2000  ft 


13  23 
13  28 


120  48 
120  34 


Philippines. 


Pt  San  Diego... 
Manilla  Oath,  and  Lt 


13  58 

14  86 


120  88 

121  0 


Coast  of  New  Guinea. 


Cape  Sapey,  summit 
8020  feet 

island  C.  Katomun 
summit  8940  feet 

Lamancbiri  hill,  N. 
W.  sum.  8225  ft. 

Lakahia  Mt  4564  ft. 

A  high  sum.  9000  ft. 

Mt  Oornwallis  visi- 
ble 9  leagues. . , . 

Aird  Hill,  1260  feet 

Mt  Victoria  10  1.  in 

C.  Rodney,  S.  E.  extr, 


3  87 

8  59 

3  46 

4  18 
4    9 

9  27 

7  28 

8  9 
10  15 


E, 
182  80 
182  44 

184    3 

184  52 

185  88 

142  36 
144  35 
146  60 
148  30 


Esperance  B.  W 

Islaud 

Mondrain  Island, 

summit 

Middle  Island,  S.W. 

summit. . 
C.  Pasley  sum.,  l^m. 

inland ... 

Hd.  of  Great  Austra 

lian  Bight 

Island  of  St  Peter 

S.  W.  Point 
C.  Radstock. . 
Pearson's  Isl'd  2  pk's 
Greenly  Isl'd  Peak, 

680  feet. 
Beagle  Island,  small 
Thistle  Island,  vis.  12 
leagues,  S.  Point 
High  Isl'ds  vis.  4  L 
C.  Donnington. . . . 
Mt  Brown,  3000  ft 
Tronbridge   Hill. 
P'rt  Adelaide,  It  ves 

"    Town 
Mt  Lofty,  2200  feet 
Glenelg  flag  staff 
Kangaroo  Isl'd,  Mt. 

Torrens 

Mt  Gambier, . , 

C.  Otway  Lt  303  ft. 

Port  Philip,  Pt  Ne- 

pean.  .. . 
"  Melbourne,    Bate- 
man's  hill 

S.  Pt  of  Australia. 
Mt  Wilson,  2350  ft. 
C.  Wickham,  N.  Pt 

summit  695  feet 

Bl'k.  Pyramid,  240  ft 

Curtis  Isl'd  1060  ft 

Peak 

KentlsLS.W.endlt 
Barren  Island,  Mt 
Munro  2300  feet. 


33  66 


34  10 


34  8 


LoN.  K 


118  1 

117  53-7 

118  27 

119  34 
E. 

121  46 

122  14 

123  8 


Australia  (Continuea 


;i 


NAMES  OF  PLACES. 


Wellington. 


Lat.  S. 


31  28 

32  22 

33  12 
38  67 

34  35 

34  49 

36  6 

35  22 

34  43 
32  80 

35  8 
34  48 
84  56 
34  58-6 
34  58-6 

46  5o 

37  52 

38  61 

38  18-5 

37  48-6 

39  8 
39  4 

39  85 

40  28 


38  66   128  28 


131  7 

133  27 

134  16 
134  13 

134  47 
134  49 

136  11 

136  8 

136  67 
138  1 

137  41 

138  28 
138  36 
138  43-7 
138  32-7 

136  38 
140  42 

143  33 

144  42-7 

144  67-7 
146  23 
146  24 

143  67 

144  21 

146  40 

137  19 

148  6 


39  28 

39  30-2 

40  23 


Van  Dieman's  Land. 


W.  Coast  of  Australia. 


N. 
Steep  pt.  W.  extrem- 
ity of  Australia.  .26    5 
Mt  Fairfax,  582  feet  ?8  45'4 
Wizard  Peak  640  ft.  zS  29-7 
Mt  Peron,  3.  1.  inl'd  80    7 
Swan  R.  Scott's  jetty  32    8-8 
•  Perth  Got.  House  81  67-4 
.0.  Chatham,  vis.  10 1.86    2 


E. 

112  57 
114  41-7 

114  47 
116  9 
116  45-6 

115  62-7 

116  28 


Mt  de  Witt  vis.  12 
leagues 

S.  W.  Cape  1000  ft. 

C.  Bruny  Lt  839  ft. 

Hobarton  Fort  Mul- 
grave 

Port  Arthur,  Sema 
phore 

Maria  I.  sum.  3500  ft 

Mt  Cameron  8  L  in 
land,  1780  ft 

Cape  Portland. .... 

Mt  Arthur  5  1.  in- 
land, 4300  ft 

Port  Dalrymple  Lt 
"  Georgetown  fl.  st, 

Valentine  pk.  7  1.  in 
land,  4000  ft 

Rooky  Cape  sum.  2 
m.  inland,  1000  ft. 

Albatross  Is.  125  ft 
sum 


43  9 
48  38 
43  28-7 

42  68-6 

48    91 
42  86 

40  69 
40  44 


41 
41 
41 


16 
8-4 
6-8 


41  22 


40  63 


40  22 


145  48 

146  1 

147  8 


Cape 

Mt  Dromedary  vis. 

16  LN.  Pt 

Jarvis,   B.    Pt    per 
pendicular,  650  ft 
Botany  Bay,  N.  Pt 

entr 

Pt  Jackson  Lt  350  f 
Sydney,  Fort  Mac 

quarrie 

Paramatta  Observ.. 
Pt  Hunter,  Court  ho 

G.  Hawke 

C.  Byron,  E.  Pt  Aus. 

A  High  Peak 

Round  Hill 

C.  Keppel 

Peaked  Island 

Pt  Bowen,  N.  P.  en. 
Long  Hill,  2333  feet 
C.  Hillsborough  sum 

966  feet 
Cumberland    Island, 
Shaw's  pk.  N.  Pt 
1601  feet. , 
M.Dryander,4666ft 
Mt  Abbott  3460  ft 
Mt  Eliot  4075  fl^. 
Mount  Hitchinbrook, 

3500   ft 
Fitz  Roy  Isl'd,  N.  E. 

pk.  550  feet 
C.  Tribulation  finger 

pk.  8350  feet 

C.    Flattery,   2  pks, 

866  feet 

Lizard  I.  sm,  1200  ft 

C.  Bowen 

C.    Weymouth,    Re 

storation  Isl'd  pk. 

360  ft  W.  Pt 

Forbes  I.  sm.  340  ft 

Orfordness,  Pudding 

pan  hill,  354  feet. 

Mt  Adolphus,  548  ft 

Mt  Bremer,  420  ft 

N.  extr.  of  Australia 

C.  York 

Murray  Isl'd  gr 

pk.  700  feet 

Balls  Pyramid  V.  121 

Lord  Howe  I.  2600  f 

Prince  of  Wales  Is. 

N.  E  T>t  Ecrued 

Hili,  4S0  feet 


39  4 


36  16 

35  6 

34  0 
33  51  2 

83  51-7 
33  48-7 
32  55-8 
32  14 
28  38 
26  20 
24  16 
23  27 
22  40 
22  29 
21  84 

20  64 


20  28 
20  14 
20  3 
19  38 


LoN.  E 


146  SO 


160  13 


151  2 


161 
161 


16 

18-2 


151 
161 
151 


147  21-5 

147  50-7 

148  8 

147  66 

147  57 

147  17 
146  48-2 
146  50  2 

146  46 

145  29 

144  89 


,  one 


18  22 
16  66 
16  4 

14  62 

14  41-4 
14  34 


12  37-5 
12  16 

11  19 

10  37 
10  41 

10  41-6 

9  66-6 
31  48 
81  87 


14 
1 

48-7 

152  35 

153  40 
152  56 
151  66 
161  7 
151  0 
150  48-6 
149  20 

149  e 


149  7 
148  31 
147  48 
146  69 

146  17 

146  0 

146  26 

146  21 

145  28-6 
144  41 


143  27-5 

143  27 

142  51 
142  41 
142  85 

142  34 

144  5 
169  20 
169  14 


'10  57  1142  18 


Torres  Straits. 


Post 


Booby  L  80  ft 

Office •. 

Darnley  I.  hill  680  ft 
Turtle  Backed  Isl'd, 

368  feet 
Mt  Ernest,  807  feet 


Mt  Augustus,  1810  f|l0    9 


10  86-7 
9  86-8 

9  54 

10  16 


141  66 
143  49 

142  48 
142  31 
142  21 


Gulf  of  Carpentaria. 


Wellesly  Is.  Sweers 
Island  Inspection 
Hill,  105  feet 

C.  Shield 

Mt  CaledoD 

C.  Arnheim. 

C.  Wilberforce 

Pt  Dale 


17  8-2 

189  41 

18  20 

136  28 

12  53 

136  88 

12  17 

187 

11  53 

186  84 

11  86 

136  7 

TABLE  XXXIX. 


241 


N.  Coast  of  Australia. 


Lat.  s.  Lon.  e. 

NAMES  OP  PLACES.  or  of 


C.  Cockburn 

Pt  EssiiigtoQ  gov. 


h. 


C.  Don. 

Cape    Hothara 

Bathurst  Is'ld  S.  extr 

C.  FourciDy 

P.Darwiu.  P.  Emery 

on  E.  side  of  eutr. 
Pt.    Blaze 


11  18 
11  22-3 

11  19 

12  3 

11  61 

12  27 
12  61 


132  51 
132  10-7 
131  48 
131  20 

129  57 

130  51 
no  11 


N.  W.  Coast. 


Mt.  Gasuariua 

C.  Beinier , 

C.  Talbot.. 

Port       Wariauder, 

Chrystal  Hd 

Port  Nelson  CareeO' 

ing    beach 

Pr.  Regent,   R.   ML 

Trafalgar  summit 

C.  Borda. 

C.  Baskerville 

C.  Vellaret,  150  ft.. 
C.  Jaubert,  46  feet.. 

Mt.  Blaze,  60  ft 

Depuch   Island,  614 

feet 

C.Lambert 

C.  Preston 

Barrow    Island,    N 

Pt 


14  23 

14  0 

13  47 

14  28 

15  6 

16  16-6 

16  36 

17  9 

18  19 

18  68 

20  0 

20  38-4 

20  36 

20  30 

20  40 

127  40 
127  28 
126  46 

126  58 

1^  4 

125  7 
122  49 
122  19 
122  7 
121  40 
119  38 

117  46 
117  11 
116    6 

115  27 


New  Zealand. 


Cape  Farewell.. . 

Cape  Foul  wind. . , 

The  Five  Fingers., 

Bold  Head 

Cape    Patersoru. . 

Cape  West 

Pt.  Maequarrie.. . 

South  Cape , 

Molyneux  Har.  N.  pt. 

Saddle  Hill , 

E;i8t  extreme  Pt. , 

Mt  Tako,  a  high  pk. 

Pt  Hardy,  Nelson's 
Monument  at  entr. 

Nelson,  Aglionby  pt 

G.  Egmout,  or  Borul 

M.  Egmont.  8.9000  f 

Entry    Isl'd    W.   Pt 
1800    ft 

Port  Nicholson,  Pen- 
carrow  Head. , , , 

Black   Hd 

C.  Gable 

Mt  IkourangL 

Mt  Edgecumbe. ... 

Guvier  Isl'd  sm. . . . 

Auckland  flag  staff. 

C.  Tewara  Pt 

C.  Motou-aro 

Wangaroa  Hb.  N.  lid 

Mt  Ohoura  or  Camp- 
bell  

C.  Otou,  or  N.  Cape 

Three  Rings,  I.  one. 

Mt  Manganui 

Lymoud's  Hb.  Bea- 
con Bluff. 

Kawia  Harb.  Alba 
tross  Pt 


40  31 

172  47 

41  46 

171  29 

42  4 

171  25 

42  67 

170  40 

46  24 

166  30 

45  56 

166  8 

46  20 

168  10 

47  17 

167  32 

46  25 

169  55 

45  56 

170  31 

43  46 

173  14 

41  42 

174  25 

40  44 

41  14 
39  20 

39  15 

40  64 


41  27 

174  53 

40  14 

176  55 

38  31 

178  26 

37  55 

178  16 

38  0 

177  2 

36  26 

176  42 

36  51-5 

174  45 

35  51 

174  35 

35  26 

174  27 

35  0 

173  45 

84  49 
84  24 
34  18 
36  62 

ST    6 

38    6 


173  67 
173  16 

173  39 

174  4 

174  65 


173    2 

173  1 
172  10 
178  40 

174  82 
174  62 


Loo-Choo  Islands. 


Lat.  N. 

NAMES  OF  PI.ACES.  o      / 


Koomisang,  N.W.  Pt 
Loo-Choo,  Gr.  Isl'd 

vis.  19  L 

E.  extr.  C.  Sidmouth 
Herbert  Isl'd  entr.  to 

Pt  Melville.  .. 
Sugar-loaf,  mark  for 

Pt  Melville 

Montgomery  Island 

N.  Pt..." 


26  24 

26  12-5 
26  47 


26  44 


26  48 

27  4 


Lon.  E 
126  47 


127  41-6 

128  21 

127  58 

127  48 

128  2 


Coast  of  China 

Nankin  city.porcel'n 

Tower 

Uih  Taou,  or  Staun- 
ton Isl'd 

Saddle  Island.. . . 

Great   Wall 

S.  extr.  of  Coast 
Rock  like  a  Junk., 
Lindsay  I.  S.  W.  Pt 
Gape  Basil,  Basil  bay 


(continued.) 


32    2 


36  60 

122  15 

37  24 

119  53 

40  5 

120  0 

38  40 

121  11 

38  56 

122  49 

36  26 

126  28 

36  8 

126  61 

118  49 


Japan  Islands. 


Asses  Ears,  S.  one, 
Nangasaki,    mid.   of 

City 

C.  Nomo 

Horner  Peak 

0.  Tschitschagoff,  S. 

extr.  of  Japan  I'ds 

C.  Cochrane 

G.   Misaki,    W.    Pt, 

Sikok   Island..., 

Nipbon  S.  Pt 

«    N.  E.  C.  Nambu. 

"   N.  Pt   

C.  Greig 

Russian  Promontory 

W.  Pt 

Zach  Mt 


32     2 

32  44-8 

32  86 
31     9 

30  67 

31  51 

33  18 
33  26 
41  23 
41  32 

41     9 

39  52 
35  26 


128  36 

129  62 

129  42 

130  28 

130  36 

131  27 

132  17 
136  47 
141  30 
140  60 
140    8 

139  38 
132  20 


Jesso. 


C.  Spanberg 

N.  extr.  C.Soya.. 
C.  Malespina. ... 
Pyramid  Rk.  off  the 
N.  EPt 


44  35 

45  31 
43  42 

46  17 


145  0 
141  51 
141  18 

150  30 


Eamtschatka. 


Kronotskypk  10,610 
feet 

Kluchevsky  volcano 
16,600  feet 

Behring  Isl'd  W.  Pt. 
«    ■  S.  Pt. 

Copper  Isl'd.  3.  Pt. 


54  45 

56  "8 

55  17 

54  21 

54  33 

160  33 

160  41 

165  46 

166  44 
168  11 


N.  W.  Coast  of  N.  America. 


C.  Douglas  E.  Pt 
Mt  St  Augustine  am 
C.  Elizabeth,  E.  Pt 
Montague  Isl'd,  Port 

Chambers,  E.  cove 

"  S.  Point 

Mt  St  Elias,  14.917 

feet,  seen  50  1.  off, 
Mt   Fairweather. 
C.  Fairweather.. . 
C.   Edgecumbe..  . 


N. 


68  64 

59  22 

69  9 

60  16 

69  46 

60  17 

68  64 

.58  61 

67  2 

W. 
152  51 
163    0 
151  18 

146  60 

147  30 

140  52 
137  38 
137  50 
135  45 


Russian  America. 


names  ok  places. 

Sitka  Arsenal  Light 
C.  Ommanney. . . 
C.  Addiugton.. . . 
C.  Muzon 


Lat.  N. 

o   / 

67  2.9 
66  9 
66  27 
64  43 


Lon.  W. 

o    / 

135  17-: 
134  34 
133  48 
132  42 


N.  W.  Coast  (Continued.) 


Queen  Charlotte  s  Is. 
Cape  Henry 

"  Pt  North 

"  C.St  James,  S.pt 
Port  Simpson 


52  52 
64  20 
51  56 
64  33 


132  25 

133  11 
131  2 

130  18 


Vancouver's  Island. 


NootkaSo'ud  friend- 
ly cove 

Esquimalt  harbor. 
Islet  entrance. .. 

Port  Discovery  W. 
Head 

Port  Neah,  S.  W.  Pt 

Gray's  Harb.  N.  Hd. 

Fort  George 

C.  Perpetua 

C.  Mendocino 


49  35 

48  25-6 

48  6-6 

48  22-5 

47  0 

46  11-5 

44  12 

40  29 

126  35-6 
128  37-7 

122  64-5 
124  S6-7 

124    7 

123  51 

124  17 
124  32 


Coast  of  California. 


Mt  Bolbones,    3765 

feet,  10  1.  inland 
St   Francisco    Fort 

S.  side 

See  also  the  Sea  coast  s 
of  the  United  States 
for  more  particulars. 
Monterey  Fort. . 
Pt.   Conception. . 

San  Juan 

St  Diego,  Pt  Loma 
C.  Goluett,  S.  W.  Pt 
Pt  St  Bartholomew 

N.Head 

C.  St.  Lazaro  Mount 

1300  feet , 

C.  Palmo 


37  52-9 
37  48-5 


36  364 
34  31 
32  53 
32  38-8 
30  69 

27  39-S 

24  47 
23  22 


121  54-6 

122  28  6 


121  53 
120  30 
117  44 
117  14-7 
116  15 

114  53-5 

112  16 
109  17 


Gulf  of  California, 


Santa  Ciuz  Island. 

C.  St  Gabriel 

C.  Haro 

Pt.  Rosa 


25  22 
28  35 
27  50 

26  42 


110  49 
112  46 
110  54 
109  50 


Mexico,   West  Coast. 


Pt  Arbolado 

Mazatlau  Custom  H. 
San  Bias  Arsenal. 
Mt  St  Juan,  6220  ft 

6  leagues  inland. 
Port   Navidad  sum 

S'luth  Head 

Colima  Volcano  12- 

000  feet 

Acapulco,  Fort  St 

Di«go 


23  33 
23  11-8 
21  32-6 

21  27 

19  12 

19  26 

16  50-8 


106  48 
106  28-7 
106  15-6 

104  56-6 

104  46 

103  38 

99  62 


Central  America. 


Libertad  vill.  fl.  st. 
Pt  Consequina  Vol- 
cano, 3800  feet. , 
Volcan,Viejo5662ft 
Port  St  Juan  S.  bluff 


13  80 

12  58 
12  41 
11  15-2 


89  17 

87  37 
86  58 
85  63 


Panama. 


Bahia  Honda  Senti 

Del  Isl'd  at  eat . . . 

PtMala 


7  436 
7  26 


81  SI 

80    S 


242 


TABLE  XXXIX. 


NAMES  07  PLACES. 

Panama,  N.  E.  Baa- 

LlOIi  ■•■•••••■    I 

0.  Corrientes...., 
lel'd  Gorgona,  N.  pt. 
1296  feet 


Lat.  N. 


8  66-9 
6  33 

3    0 


LoN.  W 


79  31-2 

77  29-5 

78  9 


Peru. 


S. 

W 

0.  Passado 

0  21 

80  32 

C.  St.  Lorenzo 

1     3 

80  67 

Guayaquil  Arsenal. 

2  12-4 

79  52  7 

Saddle     of    Payta 

1300  feet 

5  12 

81  10 

Eten  Hill  640  feet 

a  mark 

6  56 

79  54 

Mt.  Sulivan  5000  ft 

I7m.  inland 

7  17 

79  21 

Truxillo    Ch,    l^m 

inland 

8   7-6 
8  27 

79    42 

Guanape  Hill,  700  ft 

78  67 

Mt.  Division  3  pks. 

1880  feet 

9  11 

78  88 

Mt.  Mongon  summit. 

3900  feet 

9  88 

78  22 

Darwin  pk.,  5800  ft 

10  30 

77  60 

Peseador  Isl'ds  large 

one 

1147 
12    8 

77  20 

Lima  Bridge 

77    6 

Callao  Arsenal  3.  st. 

12    4 

77  13-7 

San  Lorenzo  Island, 

1284  ft.,  N.  PL  or 

C.  St  Lorenzo. .. 

12    4 

77  19 

Ohincha  Isl'ds  N.  pt. 

13  38 

76  28 

Mt.  Quemado  2070  ft 

14  20 

76  11 

Mt.  Camana  (like  a 

fort) 

16  37 

72  45 

Islay,  port  of  Are- 

quipa  Custom  H. 

17    0 

72  10-6 

MorroofSama,8890 

feet 

17  59 

18  28 

70  56 
70  24 

Arica   mole 

Carrasco  Mt  5620  ft 

4m.  inland 

20  58-5 

70  10 

Cobija  Pk.  3330  feet 

22  32 

70  18 

Mt.  Mexillones  2560 

feet,  3m.  inland. . 

23    6-5 

70  35 

Mt  Moreno  4160  ft 

23  28-6 

70  88-6 

Grande  Pt  W.  sum- 

mit 1572  feet. ... 

25    7 

70  84 

Port  Caldera,  W.  hd. 

27    3 

70  66-2 

Copiapo  (landing  pL) 

27  19-5 

71    2 

Herradura  Point. . . 

28    6 

71  16 

Guasco   port 

28  27 

71  19 

Ooquimbo  Signal  hill 

Mt  Edward's  Ho. 

29  54-2 

71  19 

Mt  Talinay,  2300  ft 

80  51 

7142 

Valparaiso  Lt  on  N. 

"V.    Pt,    fort  St 

Antonio 

88    1-9 

71  41-6 

Aconcagua  23,200  ft 

26  leagues  inland 

S2  88-5 

70    1 

Bell  of  Quillota  6200 

ft.  7  leagues  inl'nd 

82  67-2 

71  10-5 

Talcabuano,       Fort 

Galvez 

86  42 
86  49-6 

78  10-2 
78    6-6 

Coneepcion  City  mid 

Paps  of  Bio  Bio,  800 

feet  S.  W.  summit 

86  48 

78  16 

Mocha  Isl'd  summit, 

1250  feet 

88  28 

78  59 

Valdivia  City  mid.. 

39  49 

78  19 

Chayapiran  Volcano 

8000  feet 

42  48 

72  84-7 

Oorcobado  Volcano, 

7600  feet 

43  11-8 

72  49 

Obiloe  Island,  W.  pt 

43  17 

74  26 

NAMES  OF  PLAOE& 


w 


Huafo  Isl'd,  N. 

Pt  800  feet. 
C.  Taytao,  3000  feet 

W.  Point. 
G.  Tres  Montes  2000 

feet  Pt. . . 
Port  Otway,  S.  ent 

summit. . 
Dome  of  St  Paul's, 

2284  feet 

Port   Sta.   Barbara 

W.  Head 

0.  Montague  W.  cliff 
0.  Three  Pts.  2000  ft 

Diana  Peak 

Westminster  Hall. 

C.   Deseado 

0.  Noir,  600  ft.  S.  pt 
0.  Desolation  Pks.  pt 
York  Minster 
Diego  Ramirez  Isl'd 

middle. . . 
Ildefonsa  Isl'd  100  ft 

middle. ,. . 
False  C.  Horn 
Orange  Bay,  Brunt 

Island. . . . 
Cape  Horn  500  feet 


Lat.  S. 


43  86 

45  53 

46  59 
46  49-5 
46  36 

48  2 

49  7 
60  2 
52  8 
52  37 
52  55-6 
84  30 

64  46 

65  25 

56  25 

55  62 
65  43 

55  30-8 
55  69 


LoN.  W. 


74  49 

75  8 

75  28 

75  18-2 

76  14 

75  80 
75  37 
75  21 
74  48 
74  24 
74  38 
73  6 
71  37 
70    5 

68  44 

69  19 
68    6 

68  2 
67  16 


Islands  in  S.  Pacific  Ocean. 


Bishop  and  Clerk. . 
Macquarrie  Isl'd,  N. 

Point     

Campbell  Isl'd,  1500 

feet  S.  harbor,  N, 

Head  

Auckland  Islands,  S. 

Cape 

"  W.  extreme. . . 
Mt  Eden,  1325  feet 
Enderby  Isl'd  E.  pt 
Peuantipode  Island, 

small 

Bounty  Islands  . 

Chatham  Islands,  S. 
Isle,  like  a  Pyra 
mid 

Juan  Fernandez  Isl'd 
N.  side  Cumber- 
land B.  Fort.. 
S.  Pt  Sta.  Clara 
Island 

St  Ambrose,  vis.  10 
leagues  W.  Pt. 

Easter  Island,  N.  E. 
Peak,  1323  feet 

Pitcairn  Island  2500 
feet 

Gambier's  Isl'd,  Mt 
Duff... 

Encarnacion   Island 

St  Elmo. 

Aurora  Isl'd  250  iL 
N.  Point 

Otaheite  Isl'd,  vis.  12 
1.,  Pt  Venus  fl.  St. 
Summit  7000  feet 
Papeta  Harb.  fl.  st. 

Eimeo  Isl'd  perfora 
ted  Pk.  4041  feet 

Marquesas  E.  extr. 
Ariadne  Rk.  10  ft 

"  Madalena  Island 
8700  feet  S.  Pt. . 


S. 
56  15 

64  19 

52  34-4 

50  56 
50  60 
60  35 
60  30 

49  82 

47  44 


44  20 

83  87-6 
88  46 

26  21 

27  6 
25    8-6 

28  8 
24  46 
21  20 

15  60 

17  29-2 
17  89 
17  821 

17  80 

10  21 

10  31 


E. 
168  56 

158  56 


169  12-7 

166    7 

165  55 

166  10 
166  19 

179  42 

179    7 
W. 


176    4 

78  68 

79  2 

80  10 
109  17 
180    8 


NAMES  OF  PLACES. 

St  Pedro  Isl'd  1700 

feet  E.  Pt 

Sta.  Christina  3000  f. 
Hood  Isl'd  1200  ft. 
Washington   Island, 

2000ftS.Pt.. 
Nukahiva,3600feet 
Robert's  Isl'd  2000  i. 
Norfolk    Island   Mt 

Pitt  2000  ft. . 
Verraders  Isl'd  2006 

feet 

Manua  Isl'd,  2600  ft 

summit 

Apolima  Isl'd  472  ft 
Home  Isl'ds,  2500  ft 
Pylslaart  Isl'd  700  ft 
Eoa  Isl'd  600  ft  mid 
Kao  Isl'd  Pyr,  5000  f 
Tofona  Isl'd,  2800  ft. 
Latte  Isl'd,  1600  ft. 
Lakamba  Isi'd,  1200 

ft  mid, 

Niau  I.  seen  15  Lsm. 


Lat.  S.  Lon.  W. 


9  57 
9  66 

9  25 

8  56 
8  65-3 
8    0 

28  58 

16  54 

14  15 

13  49 

14  18 
23  34 
21  24 
19  42 
19  45 
18  49 

18  14 

17  59 


188  45 
139  10 

138  67 

139  33 

140  6 

140  48 

167  46 

173  48 

169  26 
172  3 
178  18 
176    4 

174  57 

175  0 
175  3 
174  35 

178  51 

179  2 


Eejee  Islands. 


Vanua  Levou  1. 2070 

ft.  E.  orUndap., 

Dana's  Peak. . 

Moala  Isl'd,  1800  ft 
S.  Pt 

Mitre  Isl'd,  vis.  41.. 

Ticopia,  vis.  10  leags 


16  8 
16  46 

18  41 

11  65 

12  21 


179  56 

178  49 

179  53 
170  9 
168  48 


New  Caledonia. 


New  Caledonia,  E.  p 

C.  Colnett 

"  W.  extr.  Pt  Ton 
nerre 


S. 


22  16 
20  29 

20  24 


E. 
166  56 
164  44 

164    0 


New  Hebrides. 


Tanna   Isi'd,  Cook's 

Pyramid 19  809 

"  Volcano,  4  m.  in- 
land  19  81 

Sandwich  Isl'd  S.W. 
Pt 17  46 

Pentacote  Isl'd  S.  pt  16  69 

Vanikoro  Isl'd,  sum. 
8081  ft Ill  87 

Volcano  Isl'd  sum. .  10  23 


169  28-7 

169  24 

168    9 
168  19 

166  49 
166  49 


Solomon  Islands. 


184  56 
186  40 
143  60 

148  11 

149  29 
149  80 
149  34 

149  47 

188  29 

138  48 


Guadalcanar  Isl'd  K 

Pt 

"  Mt  Lammas. . 
Isabel  Isl'd,  S.  Pt  C. 

Prieto 

«M.Marescot,8901 

feet 

Eddystone  Rk.  1086 

feet 

Bougainville  Isl'd  Mt 

Balbi,  10.062  ft  6 

L  inland 

N.  Pt.  0.  I'Averdi.. 
Bouka  Isl'd,  N.  Pt. . 

"       Summit. . . . 
Garret  Denys,  8200 

ft  the  highest  of 

these  Islands. . 
Gardner's  Isl'd,  2000 

ft  N.  Pt , 


9  60 
9  50 

8  84 

8  14 

8  18 


6  66 
6  80 
6  1 
6  18 


8    4 
2  34 


160  64 
160  20 

169  64 

169  88 

166  81 


164  29 

165  7 
164  40 
164  89 


162  84 
61  64 


TABLE  XXXIX. 


248 


New  Ireland. 


MAKES  OP  FIACES. 

New  Ireland,  E.  Pt. 

C.  SL  Mary 

Cape  St.  George 


Lat.  S. 


4    2 

4  51 


LoN.  R 


153  18 
152  56 


New  Britain 

N.  Pt.  0.  Stephens.. 

4  12 

152    0 

S.  E.  Pi.  C.  Orford. 

S.  E.  extr 

5  24 

152    4 

Pt  Roebuck 

6  16 

150  33 

C.  Gloucester,  2  p'ks 

5  28 

148  23 

Lotteu   Isl'd,  above 

3000  ft 

5  20 

147  36 

Volcano,  above  4000 

feet 

6  32 

148  17 

Dischamps  pk.  8  m. 

inland 

6    6 

151  28 

Galapagos  Islands. 


NAMES  OF  PLACES. 

Chatham  Isl'd,  1650 
ft.  E.  Pt  Mt  Pitt, 

800  feet 

"  S.  side  watering- 
place 

Charles  Isl'd  1780  fl 
Post-Office  on  N. 
W.  side.  Daylight 
Pt 

Gardner  Isl'd,  760  ft 

Albemarle  Is.  3780 
ft.  Iguana  Cove, 
S.   W.  side 


Lat.  S. 

044 
0  66-4 


1  16-4 

r2i 


0  69 


LoN.  W. 

o      t 


89  20 
89  88-7 


90  81-7 
9  28 


91  32  5 


NAMES  OP  PLACES. 


N.  Coast  of  New  Guinea. 


Cape  Rodney 

Cape  King  William 

13000  ft 

Dampier  Is'l  5000  ft. 
Vulcan  Isl'd,  conical 
Garnot  Isl'd,  conical 
D'Urville    Isl'd    pk. 

near  W.  end 

Mt  Julian,  2  1.  inla'd 
E\  ries  Mt  very  high 

sum.  8  1.  inland 
Cyclops  Mt  vis.  20  L 

E.  sum 

Lesson  Isl'd,  a  high 

C0D3 

Jobie  bl'd,  vis.  20  1 

E.  Pt 

Arfak   Mts.   S.  one, 

9520    ft. 

»  N.  one,  8610  feet 

Bee-hive  Mt , 

Mt.  Diceras,  8  m.  in 

laud. 


10    2 


16 

40 

6 

80 

20-1 
6 

50 

81 

7 

48 

8.9 
61 
44 


0  82 


148  30 

147  40 
145  58 
145  1 
144  85 

143  31-! 

144  26 

141  15 

140  80 

189  27 

136  60 

138  64 
133  64 
133  25 

182  16 


Isl'ds  in  the  N.  Pacific  Ocean. 


Redondo  Rk.  86  ft 
Towers  Isl'd,  211  ft. 

E.  P 

Abingdon  Isl'd  S.  pt 

mid.  1930  ft. . . 
Wenman  Isl'd,  830  ft 
Culpepper  I.  550  ft 
Malpelo  Island  sum. 

1200  ft 

Socorro  Isl'd,  2000  ft 

S.  E.  Pt 

Benedicito  Isl'd  1100 

feet  mid 

Guadalupe  Isl'ds,  W, 

one,  8400  feet .... 


N. 
0  14 

0  21 

0  84 

1  28 
1  40 

4  0 

18  48 

19  20 
28  64 


W. 
91  40 

90  0 

90  49 

91  64 

92  4 

81  82 
110  52 
110  86 
118  20 


Lat.  N. 


Sandwich  Islands. 


Owhyhee  Isl'd,  S.  pt 

"  Mowna  Rou  Mt 
13.175  feet 

"  East  Pt 

"  West  Pt 

Mowee  Isl'd,  K  Pt. 

"  W,  sum.  6126  ft. 


19    6 

19  28 
19  84 

19  42 

20  44 
20  48 


166  49 

155  88 
164  56 
166  6 
166  68 
166  14 


Morotoi  Isl'd,  E.  Pt. 

W.  Pt. 

Woahoo  Isl'd,  E.  Pt 

"  S.  or  Diamond  pt 

"  Honoruru  Fort. 

«  S.  W.  extreme.. 

-  W.  Pt 

«  N.  Pt 

Atoor  Isl'd,  EPt.. 
"  Hanalae,  B.  Brit 

Cons.  K  side.. 

"  N.  Pt 

Oneehow  Island,  K 

Pt 

"  S.  Pt 

Necker  Island,   800 

feet 

Rica  de  Oro  Rk.  or 

Lot's  wife,  850  ft 
Volcanoes,  8  Sulph'r 

Islands 

"  N.  Isl'd  San  Ales- 

sandro 

«  S.  Isl'd,  San  Dio 

nisio,  896  feet. . . , 

Forfana  Island 

Rota  Isl'd,  800  ft  E, 

Pt 

Assumption    Island, 

2026   ft 

Guam  Isl'd,  N.  Pt 
Oalan    Island,    Mt 

Crozer  about  2000 

Mao  Askill  Islands, 
S.  one 

Pouiuipet  Isl'd  sum, 
2861  ft 

The  highest  land  yet 
discovered  is  Mt 
Erebus,  which  is 
12.400  ft  above 
the  sea,  and  is  an 
active  volcano  in 


21  9 
21  7 
21  20 
21  15 
21  18-2 
21  17 
21  86 

21  43 

22  8 

22  14 
22  16 

22    0 
21  45 

28  84 

29  61 

24  48 

25  14 

24  22 

26  84 

14    9 
19  41 

18  89 


6  19 


6  IS 


6  68 


LoN.  W 

o 

156  5] 
167  24 
167  37 

157  48 

167  56 

168  7 

158  15 
157  68   I 

159  20    I 

159  82  I 

169  81 

160  6 

160  18 

164  87 

167    4 

141  20 

141  18 

141  28 
148    0 

145  18 

146  27 

144  63 


163    4-7 
160  47 
168  24 


S. 


77  88 


K 
166  68 


f'244 
COF 


TABLE  XL. 


CONTAINmG  THE   POSITIONS  OF  PLACES  (OMITTED  IN  TABLE  XXXIX.)  ON  THE  COAST  OF 
THE  UNITED  STATES  OF  AMERICA  AND  WEST  INDIES,  TAKEN  FROM 

THE  LATEST  SURVEYS. 


E.  Coast  of  U.  S.  of  America. 


Seal  laland  Lights 
Libby  Island  Liglit 
Baker's  Island  Lt, 
Petite  Manan  Is.  Lt. 

Isle  an  Haute 

Cashes  Ledge. .  . . 
Manegan  Isl'd  Lt.  . 
Penmaguid  Pt.  Lt. . 
Bantam  Ledge .... 
Seguin  Island  Lt. . . 

Cape  Small 

Cape  Elizabeth  Lt.. 
Wood  Island  Light 
Goat  Island  Light 
Cape  Neddeck  . . . 
Boone  Island  Light 

New  Hampshire. 

White  Island  Light 
Portsm'th  Outer  Lt. 
Great  Boar's  Head. 

Massachusetts. 

Newburyport  Light 

on  Plumb.  Isl'dL. 
Annis  Squam  Lt.. . 

Cape  Ann 

Gloucester  Hr.  Lt. 
Baker's  Island  Lt. . 
Nahant,  east  pt.  of 

Boston  Harbor. 
Scituate  Har.  Light 

Braat  Point. 

Gurnet  Pt.  Lt,  ent. 

to  Plymouth .... 
Beach  Pt  Lt,  ent  to 

Barnstable  Bay . 
Race  Point  Light . . 
Nausette  Light . . . 
Chatham  Hr.  Light 
Great  Point  Light 
Sankaty  Hd.  Light 

Smith's  Point 

Cape  Poge  Light. . 
No  Man's  Land. . . . 
Gay  Head  Light . . 
Cuttyhunk  IsL  Lt . 
Sangkornet  Point . 

Nantitcket  Shoals. 

McBlair's  Shoal . . . 
Old  South  ShoaL . . 
Davis'  Sho.  Lt  Ship 

Georges  BhoaU. 

S.  R  Point 

W.  Point 

N.  R  Point 

North  Shoal 

Third  ShoaL 

East  ShoaL 


Lat.  N.  Lon.  W. 


u 

29 

44 

34 

44 

14 

44 

22 

43 

59 

42 

66 

43 

45 

43 

45 

43 

44 

43 

42 

43 

41 

43 

34 

43 

28 

43 

21 

43 

10 

43 

7 

42 

68 

43 

04 

42 

55 

42 

49 

42 

40 

42 

39 

42 

35 

42 

32 

42 
42 
42 


25 
12 
06 


42  00 


Rhode  Island. 

Brenton's  Reef. . . . 
Beaver  Tail  Point . 
Watch  Hill  Pt  Lt. 
Block  IsL  S.  R  Pt. 

New    York   and 
Connecticut. 

Montauk  Pt  Light 
Fire  Island  Light. . 


41 
42 
41 
41 
41 
41 
41 
41 
41 
41 
41 
41 


44 
04 
52 
40 
24 
17 
18 
25 
15 
21 
25 
27 


24 

04 


41 
41 
40  67 


41  88 
41  42 
41  48 
41  68 
41  61 
41  47 


41  26 
41  27 
41  18 
41  09 


41  04 

40  38 


68 
68 
69 
69 
69 
69 
69 
70 
70 
70 


36 
51 
17 
28 
36 
44 
50 
11 
19 
25 


70  36 
70  28 


70  88 
70  41 
70  47 


70  49 
70  41 
70  35 
70  89 
70  47 

70  54 
70  43 
70  88 

70  86 

70  16 
70  15 
69  57 

69  57 

70  03 

69  57 

70  17 
70  27 
70  49 
70  50 

70  67 

71  11 


New  Jersey  and 
Pennsylva7iia. 

67  06  Barnegat  Light  . . 

67  23  Little  Egg  Hr.,  o 

68  08  Tucker's  Isl.  Lt 
67  62  Chincoteague  Lt . 

Carolina  and 
Georgia. 

Currituck  Inlet. . . , 
Roddy's  Isl'd  Light 
Ocracock  Light  . . , 
Doboy  Bar  ....«.., 
Amelia  Isl'd  Light. 

Florida. 

St.  John's  Light. . . 
CarysfortRf.  LtSh, 
Sand  Key  Lt  Bea. 

Cape  Romano 

Carlos  Bay  Ent. . . 
Tampa  Bay  Ent  Lt 
Dog  Island  Light. . 
Cape  St.  Bias  Lt. . 

Islands  in  the  West 
Indies. 

Barbadoes  N.  Pt . . 
Martinico  S.  R  Pt. 
Mariegalanta  S.  Pt. 
Saintes  Isl'd  W.  Pt 
Guadaloupe,  Petite 

Terre  Light 

t  Austatia,  N.  Pt 

Saba,  W.  Pt 

Aves  or  Bird  Island, 

N.  Pt 

Berbuda,  N.  end  . . 
St  Bartholom's,  N. 
St  Martin's,  S.RPt 
Anguilla  Custom  H. 
Dog  &  Prickly  Pear 

Sombrero 

Virgin  Gorda,E.Pt 
Santa  Cruz,  R  ecd. 
Frenchman's  Cap.  . 

Sail  Rock 

Crab  IsL,  R  end.. . 
Porto    Rico,    Saint 

Juan  Lt  

Pt   Brugen,   or  N 

W.  Pt 

Cape  Roxo 

Monico  Island 

Zecheo  Island 


69 
69 
69 


48 
51 
51 


67  89 
67  69 
67  47 
67  48 
67  26 
67  19 


71  21 
71  24 
71  51 
71  33 


71  51 

73  18 


Lat.  N, 

O    t 

39  46 


39  30 

37  55 


36  23 
35  47 

35  7 
31  20 
30  40 


30  20 

25  13 
24  27 

26  61 

26  32 

27  35 
29  46 
29  40 


St.  Domingo 
Island. 

Saona  IsL,  E.  Pt.. 

Beata  Island 

Altovela. 

Cape  Jaqnemel. . . 
Isle  a  Vache,  R  end. 
Navassa  IsL,  Mid.. 

Jeremife 

C.  Nichola,  Mole  . . 

Tortuga,  R  Pt 

Port  Paix. 

Pt  Picolet 

Grange  Pt 

Port  de  Plata 

Old  Cape  Francois. 

Cape  Samana 

Cape  Raphael 


13  19 

14  80 

15  52 

15  52 

16  10 

17  32 
17  89 

15  41 

17  43 

17  54 

18  5 
18  13 
18  17 
18  36 
13  30 

17  45 

18  14 
18  16 
18  7 

18  29 

18  32 

17  56 

18  9 
18  24 


18  12 
17  87 

17  28 

18  13 
18  6 
18  25 

18  40 

19  49 

20  1 
19  56 
19  47 
19  66 
19  46 
19  42 
19  18 
19  3 


LoN.  W, 
74  6 

74  17 

75  21 


75  55 

75  32 

76  68 
81  22 


Jamaica. 

Morant  Pt  Lt 

Portland  Pt 

S.  Negril 

Morant  Keys 

Portlan  Rock 

Pedra  Shoals,  N.  Pt 
South  Rocks,  above 

water 

Camanbrack,  E.  Pt 
Swan  IsL,  R  Pt . . . 


Cuba. 

81  36  jTrinidad. 

Jardines,  S.  E.  Key. 

Cape  Antonia  Lt . . 
81  33    Pt  Hyecos  Lt 

80  13    French  Cay,  N.  Pt. 

81  52    Neuvitas  Lt 

81  56  Pt  deMulas 

82  15  Bara-o 

82  47  Cape  Maize 

84  48  Cumberland  Hr. . . 

86  28  3t  Jaco  de  Cuba  Lt. 


59  46 

60  60 

61  24 
61  45 

61  7 
63  5 
68  19 

63  87 

61  52 

62  48 

63  6 
63  4 
68  17 

63  28 

64  14 
64  34 

64  52 

65  8 

65  18 

66  7 

67  8 
67  10 
67  56 
67  28 


68  31 
71  32 

71  40 

72  33 

73  31 
75  3 

74  5 
73  27 
72  36 
72  46 
72  12 
71  42 
70  46 

69  65 
69  6 
68  50 


Turks  and  Caicos 
Islands. 

Baho  de  Navidad.. 
Silver    Key   Bank, 

—  S.  W.  end  .... 

—  N.  end. .... 

—  N.  R  end  . . 


Square  Handkerc'f, 

S.  W.  end. 

N.  R  end. 


Grand  Turk  Lt . , 

Salt  Key , 

Sand  Key 

Philips'  Reef 

N.  W.  Caycos  . . , 
West  Caycos... . , 
South  Caycos  . . . , 


Bahamas. 

Gt  Inagua,   S.  W, 
end. 

Hogsties,  E.  end. . . 
Mayaguana,  E.  end. 
S.  W.  end 


French  Key,  R  Pt 
Aclin'sIsL.N.Rend 
Bird  Rock,  N.   W. 

end  of  Crooked  Is, 
Miraporvos,  S.E  end 

Castle  Isl 

Atwood's  Keys,  R 

end 

Watling'sIsL.N.  R 

Pt.... 

Conception   IsL,  S. 

Pt 

Long  IsL,  N.  Pt  . . . 
Eluethera   Isl'd,  Si 

Pt,— Ship  Chan'l 
Harbor  IsL,  N.  end. 
Gt    Abaco,   N.    R 

Pt  (keys  off.)... 
Mantanilla  Reef. . . 

Memory  Rock 

Gt  Bahama,  S.  R 

Pt 

Stiriup  Keys. 

Berry  IsL,  E 

Orange  Keys  N.  end 


Lat.  N, 

17  56 

17  44 

18  16 
17  26 
17  7 
17  40 


16  60 
19  45 

17  25 


21  43 
21  40 

21  61 
23  11 

22  50 
21  40 
21  10 
20  21 
20  15 
19  55 
19  57 


20  13 

20  18 
20  55 
20  35 

20  52 

21  9 
21  31 
21  19 
21  14 
21  43 
21  52 
21  37 
21  3 


20  65 

21  40 

22  23 
22  21 
22  35 
22  45 

22  51 
22  00 

22  7 

23  6 

24  7 

23  47 
iS   42 

24  37 
26  35 

26  88 

27  81 
26  55 

26  28 

25  50 

25  28 
24  56 


LoN.  W, 


76 

77 


11 

10 


7«  25 
75  57 

77  27 

78  54 

78  20 


79  42  1 

83 

50 

80 

6 

81 

12 

84  67  1 

81 

9 

79 

30 

77 

15 

75 

55 

74 

80 

74 

7 

75 

15 

76  2 


68  62 

69  68 
69  52 

69  18 

70  65 

70  26 

71  5 
71  10 
71  11 

71  20 

72  16 
72  27 
71  46 


73  89 
78  51 

72  42 

73  9 
73  28 


73 

50 

74 

22 

74 

28 

74  20  1 

73 

87 

74  26  1 

75 

8 

75 

18 

76 

9 

76  45  1 

76 

50 

79 

8 

79 

3 

78 

10 

77 

55 

77 

42 

7c 

9 

TABLE   XL. 


245 


Ridding  Rocks,  S . 

Mexico. 

Pasa  de  Cabello . . 
Brazo  de  Santiago 
St  Fernando  River, 

ent 

River  Tampieo,  ent. 

Cape  Rojo 

Tamiagua  Bar. .... 

Boca  de  Lima 

Alvarado  Bar 

Pt  Morillos. 

Barilla 

River  St.  Ann 

IsL  Carmen,  W.  Ft 
IsL  Real,  W.  Ft .    . 

Ytteatan. 

Ft  Piedras 

B0CO8  Del  Rio  La 

gartos. 

Los  Arcos 

Bajo  Nnevo 

IsL  Arenas. 

Mogeres  IsL,  &  Pt. 


Lat.  N 


26  12 


LoN.  W. 

O  f 

79  10 


21  11 

21  86 

20  13 

21  60 

22  8 
21  18 


28  20 

96  22 

26  6 

97  12 

25  20 

97  30 

22  15 

97  48 

21  35 

97  20 

21  13 

97  17 

20  30 

96  57 

18  47 

95  43 

18  38 

94  54 

18  10 

94  32 

18  11 

93  51 

18  38 

91  48 

18  62 

91  22 

90  10 

88  14 

91  69 

92  6 
91  26 
86  45 


IsL  Contoy,  N.  Pt . 
IsL  Cozurael,  N.  Pt 

South  Pt 

N.  Ti'iangle 

South  end. . . . 

Mauger  Key  Light 
Turneff  Reef,  S.  Pt 
Half  Moon  KeyLt. 
Glover's  Reef,  N.Pt 
Cape  Three  Points. 
UtillalsL.R  Ft... 
Rattan  IsL,  R  Ft. . 

West  Point... 

Barburet  Island. . . 
Cape  Camaron.... 

JVew  Oranada. 

Fort  Sabanilla,  ent 

—  Hacha    

Cape  La  Vela 

Ft  Galinas 

IsLOniba.N.W.Pt 

—  S.  R  Point... 
Cape  St  Roman . . . 
Curaco  IsL,  N.  Pt. 
St  Ann's  Bay  .... 


Lat.  N. 

o    f 

21  82 

20  85 

21  15 
18  46 
18  23 
17  36 
17  JO 

17  12 
16  55 

18  58 
16  7 
16  27 
16  17 
16  26 
16  00 


11 
11 


1 
88 


12  10 
12  25 
12  86 
12  24 
12  11 

12  21 

13  6 


Lon.  W 

o  / 

86  51 

86  44 

87  00 
87  20 
87  20 

87  46 

88  00 
87  34 

87  45 

88  88 
86  53 
86  12 
86  88 
86  9 
85  8 


76  1 
72  66 
72  14 
71  44 
70  12 
70  1 
70  7 
69  10 
68  54 


Little  Curacoa  .... 
Buen  Ayre,  N.  Pt . 

P.  Rosa  Light 

Bird  Island,  E  . . . . 

Western  end  . 

Laguira 

Cape  Codera 

Orchilla  IsL,W.  end. 
Blanco  Island,  N  . . 
Los  Hermanos,  S.  Ft 
Tortuga  Salada,  R 

Point 

Margarita,  R  end. . 
W.  end 


Testigos  IsL,  mid 
Dragon's    Mouth — 

Point  Pera  .... 
9erpant's  Mouth,- 

Point  YeacoB.. , 

Ouiana. 

Mouth  of  Essequibo 

—  LeanwsnIsI 
Cape  Nassau. . . . 
Pt  Baja. 


Lat.  N 

• 

12  2 
12  19 
12  2 

11  67 

12  00 
10  87 

10  86 

11  50 
11  56 
11  42 

10  68 

11  00 

10  68 

11  23 

10  44 
10  4 

7  00 

7  86 
9  25 


Lou.  W. 

o    ( 

ee  38 

6»  31 

68  17 

67  82 

67  46 

66  56 

66  8 

66  14 

64  37 

64  29 

65  15 

63  60 

64  28 
^^98  10 

61  58 

61  58 


58  18 

58  f« 
60  48 


?46 

■AMrdiBC  to  Aot  of  OoBCTMa,  in  th*  year  one  thooiand  eieht  hnadred  and  Afty-MTen,  by  JAMBS  H.  BROWKI.UW.  La 
tk«  Clark's  Offio*  of  th«  Diitriet  Court  of  th*  United  State*,  for  th*  Soathem  DUtrtot  of  New  York. 


NEW   TIME  TABLES 

♦  «ICH  FURNISH  THE  SHORTEST  METHOD  OF  FINDING  THE  TIME  AT  SHIP  (AND  THENlJl 
THE  LONGITUDE  BY  CHRONOMETER),  AT  ABOUT  8  O'CLOCK  IN  THE  MORNING, 

OR  4  O'CLOCK  IN  THE  AFTERNOON. 

By  James  H.  Beowklow,  Teacher  of  Practical  Navigation  amd  Nautical 

Astronomy,  92  Madison  Street,  N&w  York, 


EXPLANATION    AND    USE    OF   THE    TABLES. 


Table  A,  in  Two  Parts. 

Th«  first  part  contains  the  True  Altitude  of  the  Sun's  centre,  at  the  instant  it  is  8  hours,  A.  M.,  ot 
\  hours,  P.  M.,  apparent  time,  when  the  Latitude  and  Declination  are  of  the  same  name.  The  second 
f^art  contains  the  same,  when  the  Latitude  and  Declination  are  of  different  names.  These  tables  are 
entered  with  the  degree  of  Declination  at  the  top,  and  the  degree  of  Latitude  at  the  side,  and  the  angla 
of  meeting  gives  the  True  Altitude  required.  If  there  are  miles  of  Latitude  and  Declination,  two  pro- 
portions  are  necessary,  which  may  be  made  either  meataiiy,  or  by  the  aid  of  Table  B. 

Ti^BLE    B, 

For  finding  the  proportion  of  Altitude  for  the  milet  ^f  Latitude  and  Declination,  as  follow*  •  Enter  thu 
table  with  the  difference  of  Altitude  for  1°  of  Lat;'.;4e  at  the  top,  and  the  miles  of  Latitude  at  the  aide, 
«nd  the  angle  of  meeting  gives  the  proportion  of  Altitude  required,  in  miles  and  tenths,  which  must  b« 
added  to  the  Altitude  taken  from  Table  A,  if  the  Altitude  was  increasing  with  the  Latitude ;  or  aub- 
tracted,  if  decreasing.  Again,  enter  this  table  with  the  difference  of  Altitude  for  1**  of  Declination  at  th« 
top,  and  the  miles  of  Declination  at  the  side,  and  take  out  the  proportion  of  Altitude,  to  be  added  to  the 
Altitude  taken  from  Table  A,  if  it  was  increasing  with  the  Declination,  or  subtracted  if  decreasing,  will 
^[ive  the  true  Altitude  of  the  Sun's  centre,  from  which  subtract  the  joint  correction  for  Semidiameter,  Dip, 
&c.,  (which  is  usually  taken  at  10')  to  obtain  the  Observed  Altitude  of  the  Sun's  lower  limb  :  now  •ct 
the  Quadrant  to  this  Altitude,  and  when  the  Sun  arrives  at  it,  note  the  time  by  Chronometer,  to  w&ich 
Apply  the  error,  if  any,  and  you  have  the  Mean  Time  at  Greenwich,  and  Apparent  Time  at  Ship,  whjch 
is  either  8  hours,  A.  M.,  or  4  hours  P.  M.  To  the  Apparent  Time  at  Ship  apply  the  Equation  of  Time, 
which  will  give  the  Mean  Time  at  Ship,  the  difference  between  which  and  the  Mean  Time  at  Greenwich 
te  the  Longitude  in  time,  turned  into  space  at  the  rate  of  15*  to  the  hour,  or  T  to  4  seconds  of  time. 

EXAMPLE. 

September  10th,  1857,  in  Latitude  30*  29'  N.,  and  Longitude  by  D.  R.  60*  W.,  the  height  of  the  eye 
being  18  feet,  required  the  Altitude  at  which  to  set  my  Quadrant,  so  as  to  observe  the  Altitude  of  the 
Sun's  lower  limb  at  8  o'clock  in  the  morning,  Apparent  Time,  and  by  noting  the  time  by  Chronometer, 
find  the  Longitude. 

The  Sun's  Declination  on  September  10th,  is  4*  62'  N.,  and  Latitude  30°  29'  N.,  being  of  the  same 
name,  I  enter  first  part  of  Table  A  with  4°  of  Declination  and  30°  of  Latitude,  which  gives  the  Altitude 
87'  50',  and  under  the  same  degree  of  Declination,  but  opposite  31°  of  Latitude,  the  Altitude  is  27*  37', 
(rhich  gives  the  Difference  of  Altitude  for  1*  of  Latitude  to  be  13'  decreasing.  Again,  entering  Table 
A,  with  5°  of  Declination  and  30°  of  Latitude,  gives  the  Altitude  28'  21',  which  gives  the  Difference  of 
Altitude  for  1°  of  Declination  to  be  31'  increasing.  Now  enter  Table  B,  with  13'  at  top,  and  29'  of 
Latitude  at  the  side,  and  take  out  the  proportion  of  Altitude  for  29'  of  Latitude,  which  is  6'  3  tenths,  tc 
be  subtracted  from  Altitude  27*  50'.  Again  enter  Table  B,  with  31'  at  top,  and  52'  of  Declination  at  th« 
•ide,  and  take  out  the  proportion  of  Altitude  for  52'  of  Declination,  which  is  26'  9  tenths,  to  be  added  \4 
Altitude  27*  50'.  As  the  greater  of  these  two  proportions  is  additive,  and  the  lesser  one  subtractiye, 
take  the  difference  between  them,  which  is  20'  6  tenths  (or  21'),  and  add  it  to  27*  50',  will  give  the  tnw 


NEW    TIME    TABLES.  S4I 

Altitude  of  the  Sun's  centre  28*  11',  from  which  subtract  '.O'for  Semidiameter,  Dip^  &c.,  girec  the 
Observed  Altitude  of  the  Sun's  lower  limb  28*  1',  to  which  I  set  my  Quadrant,  and  when  the  Sun 
arrives  at  that  Altitude,  note  the  time  by  Chronometer;  which  suppose  to  be  llhrs.  58m.  lOseo.,  A.  M^ 
Mean  Time  at  Greenwich,  the  Longitude  is  found  as  follows . 

Apparent  Time  at  Ship 8h.     OOti.     OOsec,  A.  M. 

Equation  of  Time,  to  subtract 3  10 

Mean  Time  at  Ship "T       56         50  A.  M. 

Mean  Time  at  Greenwich II        58  10  A.M. 

Longitude  in  Time 4  1  20  in  degreet  60*  20'  W. 

» 

Rkm&rk. — As  the  above  method  of  setting  the  Quadrant  to  the  Altitude,  and  waiting  until  the  Sob 
arrives  to  that  Altitude,  may  be  considered  somewhat  inconvenient,  Table  C  ha«  been  oonstnioted  U> 
obviate  that  necessity.  ^ 

Table  C,  in  Two  Parts. 

The  first  part  of  this  table  is  used  when  the  Latitude  and  Declination  are  of  the  same  name  ;  the 
second  part,  when  they  are  of  different  names.  They  are  entered  with  the  Declination  at  top,  and  Latitude  at 
the  side,  and  the  angle  of  meeting  gives  the  time  (in  seconds  and  hundredth  parts  of  a  second)  corres- 
ponding to  a  change  of  the  Sun's  Altitude  of  one  mile  at  8hrs.,  A.  M.,  or  4hrs.,  P.  M.  The  Declination 
is  given  only  for  every  other  degree,  as  the  change  tor  1°  is  small,  and  the  proportion  for  the  intermediate 
degree  of  Declination,  or  for  miles  of  Latitude  and  Declination,  can  be  made  either  mentally  or  by 
Table  B,  in  the  same  manner  as  the  proportion  of  Altitude  is  found  for  miles  of  Lat.  and  Dec. 

By  Table  C,  then,  we  obtain  the  time  corresponding  to  a  change  of  Altitude  of  one  mile  at  8hrs.,  A.  M., 
or  4hr8.,  P.  M.  Now,  if  we  observe  the  Sun's  Altitude  within  a  few  minutes  of  those  times,  say  within 
to  minutes  of  them,  either  before  or  after,  note  the  time  by  Chronometer  ;  and,  after  correcting  th« 
Observed  Altitude,  as  usual  to  obtain  the  True  Altitude,  take  the  difference  in  miles  between  it  and  the 
Altitude  taken  from  Table  A,  and  multiply  this  difference  of  Altitudes  by  the  time  corresponding  to  ou« 
mile,  taken  from  Table  C,  and  we  have  the  time  either  before  or  after  Shrs.,  A.  M.,  or  4hrs.,  P.  M.,  according 
as  the  Altitude  observed  is  greater  or  less  than  the  Altitude  taken  from  Table  A.  In  the  morning,  if 
the  Altitude  observed  (after  correcting  it)  is  greater  than  the  one  taken  from  Table  A,  the  time  corres- 
ponding to  the  difference  of  Altitude  must  be  added  to  Shrs. ;  but  if  the  Altitude  observed  be  less,  th« 
time  must  be  subtracted  from  Shrs.  In  the  afternoon,  if  the  Altitude  observed  be  greater  than  the  one 
from  Table  A,  the  time  must  be  subtracted  from  4hr8. ;  but  if  the  Altitude  observed  be  less,  the  time 
must  be  added  to  4hr8 

Suppose,  in  the  preceding  example,  the  Sun's  Altitude  had  been  observed  a  few  minutes  after  8  o'clock 
to  be  30°  r,  and  the  time  by  Chronometer  12hr8.  7m.  39sec.,  A.  M.,  the  work  to  find  the  Longitude  woul'' 
0"  as  follows : 

Sun's  UDs.  Alt 30°   1'  The  time  corresponding  to  a  change  of  Alt.  of  one 

Corr.  for  Semid.,  Dip,  Ac,  to  add..         10  mile,  at  8hrs.,  from  Table  C 4.74 

True  Alt.  by  Observation WTl  Difference  of  Altitude 120 

True  Alt.,  from  Table  A 28  11  6O)568.$0(9m.  28g 

Diff.ofAIt8 2°     or  120  miles.  540 

_28 

NoTB. — If  the  difference  of  Altitude  does  not  exceed  Note — Multiply  the  4sec.  and  74  hundredths   by 

60  or  60  miles,  it  is  enough,  to  take  out  the  time  from      120  miles,  cut  off  the  two  right  hand  figures,  and  tha 
Table  O  for  the  nearest  degree  of  Declination  and  Lati-      remaining  figures  are  seconds. 
tude. 

Time  for  Diff.  of  Alts 9m.  28sec. 

App.  Time  from  Table  A 8h.   0        00  A.  M. 

App  Time  at  Ship 8       9        28  A.  M 

Equation  of  Time,  subt 3        10 

Mean  Time  at  Ship 8       6        Ts  A.  M. 

Mean  Time  at  Greenwich 12       7        39  A.M. 

Longitude  in  Time 4       1        21  or  60*  20'  W. 

Kkhark. — When  the  Ship  is  on  the  Equator,  and  the  Sun  is  also  on  the  Equator,  that  is,  when  hii 
Declination  is  0,  the  Sun  rises  and  sets  vertically.  In  this  case,  the  Sun's  change  of  Altitude  is  uni- 
formly 1  mile  in  4  seconds  of  time,  throughout  the  entire  day.  But,  under  any  other  circumstances,  the 
lime  corresponding  to  a  change  of  the  Sun's  Altitude  of  1  mile,  is  more  than  4  seconds. 

When  the  Lat.  and  Dec.  are  under  3°,  the  time  from  Table  C  may  be  assumed  the  same  for  2hrB. 
»  "  u  u  jQ"  u  ((  u  ((  u  'i  J  T^ 

20-  "  »  «  "  «  «     40minut«a 

When  the  Lat.  is  under        "  30*  "  "  "  "  «  "15        " 

"  "  '<  «  50*  "  "  "  «  «  u      JQ         u 

"  «<  «  •»  gQ»  «  «  «  (i  u  "7         " 


248                    TABLE  A.— Part  I. 

Thia  Table  shows  the  True  Altitude  of  the  Sun's  Centre  at  the  instant  it  is  8  o'Clock  in  the  Morning,  or  4 
©'Clock  in  the  Afternoon,  Apparent  Time,  for  more  readily  finding  the  Longitude  by  Chronometer.' 

DECLINATION  AND  LATITUDE  OF  THE  SAME  NAMK 

Lat 

o<> 

r 

2° 

3' 

4» 

6" 

6" 

7° 

8' 

9' 

10' 

11* 

12' 

• 

o    / 

O    1 

°  1 

o   f 

•  / 

o    / 

o    / 

o    / 

o     1 

o    / 

o   / 

•  1 

o   / 

0 

30  0 

30  0 

29  59 

29  57 

29  55 

29  52 

29  49 

29  45 

29  41 

29  36 

29  30 

29  24 

29  17 

1 

30  0 

30  1 

30  1 

30  1 

30  0 

29  58 

29  56 

29  53 

29  50 

29  46 

29  42 

29  37 

29  31 

2 

29  59 

30  1 

30  2 

30  3 

30  4 

30  3 

30  2 

30   1 

29  59 

29  56 

29  53 

29  49 

29  44 

3 

29  57 

30  1 

30  3 

30  5 

30  7 

30  8 

30  8 

30  8 

30  7 

30  5 

30  3 

30  1 

29  57 

4 

29  55 

30  0 

30  4 

30  7 

30  10 

30  12 

30  13 

30  14 

30  14 

30  14 

30  13 

30  12 

30  10 

5 

29  52 

29  58 

30  3 

30  8 

30  12 

30  15 

30  18 

30  20 

30  21 

30  22 

30  23 

30  22 

30  21 

6 

29  49 

29  56 

30  2 

30  8 

30  13 

30  18 

30  22 

30  25 

30  28 

30  30 

30  31 

30  32 

30  32 

7 

29  45 

29  53 

30   1 

30  8 

30  14 

30  20 

30  25 

30  30 

30  34 

30  37 

30  39 

30  41 

30  43 

8 

29  41 

29  50 

29  59 

30  7 

30  14 

30  21 

30  28 

30  34 

30  39 

30  43 

30  47 

30  50 

30  53 

9  '29  36 

1 

29  46 

29  56 

30  5 

30  14 

30  22 

30  30 

30  37 

30  43 

30  49 

30  54 

30  58 

31   2 

10 

29  3U 

29  42 

29  53 

30  3 

30  13 

30  23 

30  31 

30  39 

30  47 

30  54 

31  0 

31   6 

31  11 

11 

29  24 

29  37 

29  49 

30  1 

30  12 

30  22 

30  32 

30  41 

30  50 

30  58 

31   6 

31  13 

31  19 

12 

29  17 

29  31 

29  44 

29  57 

30  10 

30  21 

30  32 

30  43 

30  53 

31   2 

31  11 

31  19 

31  26 

13 

29  9 

29  25 

29  39 

29  53 

30  7 

30  20 

30  32 

30  44 

30  55 

31   5 

31  15 

31  25 

31  33 

14 
15 

29   1 

29  18 

29  33 

29  49 

30  3 

30  17 

30  31 

30  44 

30  66 

31   8 

31  19 

31  30 

31  39 

28  53 

29  10 

29  27 

29  43 

29  59 

30  15 

30  29 

30  43 

30  57 

31  10 

31  22 

31  34 

31  45 

16 

28  44 

29  2 

29  20 

29  38 

29  55 

30  11 

30  27 

30  42 

30  57 

31  11 

31  25 

31  38 

31  50 

17 

28  34 

28  54 

29  13 

29  31 

29  50 

30  7 

30  24 

30  41 

30  57 

31  12 

31  27 

31  41 

31  54 

18 

28  24 

28  44 

29  5 

29  25 

29  44 

30  3 

30  21 

30  38 

30  55 

31  12 

31  28 

31  43 

31  58 

19 

28  13 

28  35 

28  56 

29  17 

29  37 

29  57 

30  17 

30  35 

30  54 

31  11 

31  28 

31  45 

32   1 
32  3 

20 

28  1 

28  24 

28  47 

29  9 

29  31 

29  52 

30  12 

30  32 

30  51 

21  10 

31  28 

31  46 

21 

27  50 

28  14 

28  37 

29  0 

29  23 

29  45 

30  7 

30  28 

30  48 

21  8 

31  28 

31  47 

Ai     5 

22 

27  37 

28  2 

28  27 

28  51 

29  15 

29  38 

30  1 

30  23 

30  45 

31   6 

31  26 

31  46 

32  6 

23 

27  24 

27  50 

28  16 

28  41 

29  6 

29  31 

29  54 

30  18 

30  40 

31   3 

31  24 

31  46 

32  6 

24 

27  11 

27  38 

28  5 

28  31 

28  57 

29  22 

29  47 

30  12 

30  36 

30  59 

81  22 

31  44 

32  6 

25 

26  57 

27  25 

27  53 

28  20 

28  47 

29  14 

29  40 

30  5 

30  30 

30  55 

31  19 

31  42 

32  5 

26 

26  42 

27  12 

27  40 

28  9 

28  37 

29  4 

29  31 

29  58 

30  24 

30  50 

31  15 

31  89 

32  3 

27 

26  27 

26  58 

27  27 

27  57 

28  26 

28  54 

29  22 

29  50 

30  17 

30  44 

31  10 

31  36 

32  1 

28 

26  12 

26  43 

27  14 

27  44 

28  14 

28  44 

29  13 

29  42 

30  10 

30  38 

31   5 

31  32 

31  58 

29 
30 

25  56 
25  40 

26  28 

27  0 

27  31 

28  2 

28  33 

29  3 

29  33 

30  2 

30  31 

80  59 

31  27 

31  54 

26  13 

26  45 

27  18 

27  50 

28  21 

28  53 

29  23 

29  54 

30  23 

30  53 

31  22 

31  50 

31 

25  23 

25  57 

26  30 

27  4 

27  37 

28  9 

28  41 

29  13 

29  45 

30  15 

30  46 

Z\    16 

31  46 

32 

25  5 

25  40  26  15 

26  49 

27  23 

27  57 

28  30 

29  3 

29  35 

30  7 

30  38 

31  9 

31  iO 

33 

24  48 

25.23  25  59 

26  34 

27  9 

27  43 

28  18 

28  51 

29  25 

29  58 

30  30 

31  2 

31  34 

34 

24  29 

25  6 

25  42 

26  19 

26  54 

27  30 

28  5 

28  39 

29  14 

29  48 

30  21 

30  54 

31  27 

35 

24  11 

24  48 

25  26 

26  3 

26  39 

27  16 

27  52 

28  27 

29  2 

29  37 

30  12 

30  46 

31  19 

36 

23  52 

24  30 

25  9 

25  46 

26  24 

27  1 

27  38 

28  14 

28  50 

29  26 

30  2 

30  37 

31  11 

37 

23  32 

24  11 

24  50 

25  29 

26  7 

26  46 

27  23 

28  1 

28  38 

29  15 

29  51 

30  27 

31  3 

38 

23  12 

23  52 

24  32 

25  12 

25  51 

26  30 

27  9 

27  47 

28  25 

29  3 

29  40 

30  17 

30  53 

39 

22  52 

23  33 

24  13 

24  54 

25  34 

26  14 

26  53 

27  32 

28  11 

28  50 

29  28 

30  6 

30  44 

40 

22  31 

23  13 

23  54 

24  35 

25  16 

25  57 

26  37 

27  17 

27  57 

28  37 

29  16 

29  55 

30  33 

41 

22  10 

22  53 

23  35 

24  17 

24  58 

25  40 

26  21 

27  2 

27  43 

28  23 

29  3 

29  43 

30  22 

42 

21  49 

22  32 

23  15 

23  58 

24  40 

25  22 

26  4 

26  46 

27  27 

28  9 

28  49 

29  30 

30  10 

43 

21  27 

22  11 

22  55 

23  38 

24  21 

25  4 

25  47 

26  30 

27  12 

27  54 

28  35 

29  17 

29  58 

44 

21  5 

21  49 

22  34 

23  18 

24  2 

24  46 

25  29 

26  13 

26  56 

27  38 

28  21 

29  3 

29  45 

45 

20  42 

21  28 

22  13 

22  58 

23  42 

24  27 

25  11 

25  55 

26  39 

27  23 

28  6 

28  49 

29  32 

46 

20  19 

21  5 

21  51 

22  37 

23  22 

24  7 

24  52 

25  37 

26  22 

27  6 

27  50 

28  34 

29  18 

47 

19  56 

20  43 

21  29 

22  16 

23  2 

23  48 

24  33 

25  19 

26  4 

26  49 

27  34 

28  19 

29  3 

48 

19  33 

20  20 

21  7 

21  54 

22  41 

23  27 

24  14 

25  0 

25  46 

26  32 

27  18 

28  3 

28  48 

49 
50 

19  9 

19  57 

20  45 

21  32 

22  20 

23  7 

23  54 

24  41 

25  28 

26  14 

27  0 

28  47 

28  32 

18  45 

19  33 

20  22 

21  10 

21  58 

22  46 

23  34 

24  21 

25  9  25  56 

26  43 

27  30 

28  16 

51 

18  20 

19  9 

19  58 

20  47 

21  36 

22  24 

23  13 

24  1 

24  49  25  37 

26  25 

27  12  28  0  1 

52 

17  56 

18  45 

19  35 

20  24 

21  14 

22  3 

22  52 

23  41 

24  29  25  18 

26  d 

26  54 

27  42 

53 

17  31 

18  21 

19  11 

20  1 

20  51 

21  41 

22  30 

23  20 

24  9 

24  58 

25  47 

26  36 

27  25 

54 

S5 

17  5 

17  56 

18  47 

19  37 

20  28 

21  18 

22  8 

22  58 

23  48 

24  88 

25  28 

26  17 

27  7 

16  40 

17  31 

18  22 

19  13 

20  4 

20  55 

21  46 

22  37 

23  27 

24  18 

25  8 

25  58 

26  48 

56 

16  14 

17  6 

17  58 

18  49 

19  41 

20  32 

21  23 

22  15 

23  6 

23  57 

244  7 

25  38 

26  29 

57 

15  48 

16  40 

17  33 

18  25 

19  17 

20  9 

21  0 

21  52 

22  44 

23  35 

24  27 

25  18 

26  9 

58 

15  22 

16  15 

17  7 

18  0 

18  52 

19  45 

20  37 

21  30 

22  22 

23  14 

24  6 

24  57 

25  49 

59 

14  55 

15  49 

16  42 

17  35 

18  28 

19  21 

20  14 

21  6 

21  59 

22  51 

23  44 

24  36 

25  28 

60 

14  29 

15  22 

16  16  17  9| 

18  3 

18  56 

19  50 

20  43 

21  36 

22  29 

23  22 

24  15 

25  8 

TABLE  . 

A..— Part  I. 

249 

This  Table  shows  the  True  Altitude  ot  the  Su 

n's  Centre  at  the  instant  it  is  8  o'CIock  in  the 

Morninff.  or  4  1 

o'clock 

in  the  Afternoon,  Apparent  Time,  for  more  readily  finding  the  Longitude 

>  by  Chronometer.     1 

DECLINATION  AND  LATITUDE  OF  THE  SAME  NAME. 

Lat. 

13° 

14 

"15 

°16 

17° 

18° 

19' 

20' 

21" 

22° 

23* 

24*    1 

• 

0 

29 

9 

29 

1 

28 

53 

o 

28 

44 

• 

28 

34 

o 

28 

/ 

24 

O 

28 

13 

o 

28 

1 

27 

60 

• 

27 

/ 

37 

27 

24 

• 

27 

1 
11 

1 

29 

25 

29 

18 

29 

10 

29 

2 

28 

54 

28 

44 

28 

35 

28 

24 

28 

14 

28 

2 

27 

50 

27 

38 

2 

29 

39 

29 

33 

29 

27 

29 

20 

29 

13 

29 

5 

28 

56 

28 

47 

28 

37 

28 

27 

28 

16 

28 

5 

3 

29 

53 

29 

49 

29 

43 

29 

38 

29 

31 

29 

25 

29 

17 

29 

9 

29 

0 

28 

51 

28 

41 

28 

31 

4 

30 

7 

30 

3 

29 

59 

29 

55 

29 

50 

29  <44 

29 

37 

29 

31 

29 

23 

29 

16 

29 

6 

28 

57 

5 

30 

20 

30 

17 

30 

15 

30 

11 

30 

7 

30 

3 

29 

57 

29 

52 

29 

45 

29 

38 

29 

31 

29 

22 

6 

30 

32 

30 

31 

30 

29 

30 

27 

30 

24 

30 

21 

30 

17 

30 

12 

30 

7 

30 

1 

29 

54 

29 

47 

7 

30 

44 

30 

44 

30 

43 

30 

42 

30 

41 

30 

38 

30 

35 

30 

32 

30 

28 

30 

23 

30 

18 

30 

12 

8 

30 

55 

30 

56 

30 

57 

30 

57 

30 

57 

30 

55 

30 

55 

30 

51 

30 

48 

30 

45 

30 

40 

30 

36 

9 

31 

5 

31 

8 

30 

10 

31 

11 

31 

12 

31 

12 

31 

11 

31 

10 

31 

8 

31 

6 

31 

3 

30 

59 

10 

31 

15 

31 

19 

31 

22 

31 

25 

31 

27 

31 

28 

31 

28 

31 

28 

31 

28 

31 

26 

31 

24 

31 

22 

11 

31 

25 

34 

30 

31 

34 

31 

38 

31 

41 

31 

43 

31 

45 

31 

46 

31 

47 

31 

46 

31 

46 

31 

44 

12 

31 

33 

31 

39 

31 

45 

31 

50 

31 

54 

31 

58 

32 

1 

32 

3 

32 

5 

32 

6 

32 

6 

32 

6 

13 

31 

41 

31 

49 

31 

55 

32 

2 

32 

7 

32 

12 

32 

16 

32 

20 

32 

22 

32 

26 

32 

26 

32 

27 

14 

31 

49 

31 

57 

32 

5 

32 

13 

32 

19 

32 

25 

32 

31 

32 

35 

32 

39 

32 

43 

32 

46 

32 

48 

15 

31 

55 

32 

5 

32 

14 

32 

23 

32 

31 

32 

38 

32 

45 

32 

61 

32 

56 

33 

0 

33 

4 

33 

7 

16 

32 

2 

32 

13 

32 

23 

32 

33 

32 

42 

32 

50 

32 

58 

33 

5 

33 

12 

33 

17 

33 

23 

33 

27 

17 

32 

7 

32 

19 

32 

31 

32 

42 

32 

52 

33 

2 

33 

11 

33 

19 

33 

27 

33 

34 

33 

40 

33 

46 

18 

32 

12 

32 

25 

32 

38 

32 

50 

33 

2 

33 

13 

33 

23 

33 

32 

33 

41 

33 

50 

33 

57 

34 

4 

19 

32 

16 

32 

31 

32 

45 

32 

58 

33 

11 

33 

23 

33 

34 

33 

45 

33 

55 

34 

5 

34 

13 

34 

21 

20 

32 

20 

32 

35 

32 

51 

33 

5 

33 

19 

33 

32 

33 

45 

33 

67 

34 

8 

34 

19 

34 

29 

34 

38 

21 

32 

22 

32 

39 

32 

56 

33 

12 

33 

27 

33 

41 

33 

55 

34 

8 

34 

21 

34 

33 

34 

44 

34 

54 

22 

32 

25 

32 

43 

33 

0 

33 

17 

33 

34 

33 

50 

34 

5 

34 

19 

34 

33 

34 

46 

34 

58 

35 

10 

23 

32 

26 

32 

46 

33 

4 

33 

23 

33 

40 

33 

57 

34 

13 

34 

29 

34 

44 

34 

58 

35 

12 

35 

24 

24 

32 

27 

32 

48 

33 

7 

33 

27 

33 

46 

34 

4 

34 

21 

34 

38 

34 

54 

35 

10 

35 

24 

35 

39 

25 

32 

27 

32 

49 

33 

10 

33 

31 

33 

51 

34 

10 

34 

29 

34 

47 

35 

4 

35 

21 

35 

37 

36 

52 

26 

32 

27 

32 

50 

33 

12 

33 

34 

33 

55 

34 

15 

34 

35 

34 

54 

35 

13 

35 

31 

35 

48 

36 

5 

27 

32 

26 

32 

50 

33 

13 

33 

36 

33 

58 

34 

20 

34 

41 

36 

1 

35 

21 

36 

40 

35 

59 

36 

16 

28 

32 

24 

32 

49 

33 

14 

33 

38 

34 

1 

34 

24 

34 

46 

35 

8 

35 

29 

36 

49 

36 

9 

36 

28 

29 

32 

21 

32 

48 

33 

13 

33 

39 

34 

3 

34 

27 

34 

51 

35 

13 

35 

36 

35 

57 

36 

18 

36 

38 

30 

32 

18 

32 

46 

33 

12 

33 

39 

34 

5 

34 

30 

34 

54 

35 

18 

35 

42 

36 

4 

36 

26 

36 

48 

31 

32 

14 

32 

43 

33 

11 

33 

38 

34 

5 

34 

32 

34 

57 

35 

22 

35 

47 

36 

11 

36 

34 

36 

57 

32 

32 

10 

32 

40 

33 

9 

33 

37 

34 

5 

34 

33 

34 

59 

36 

26 

35 

51 

36 

16 

36 

41 

37 

5 

33 

32 

5 

32 

35 

33 

6 

33 

35 

34 

4 

34 

33 

35 

1 

35 

28 

35 

55 

36 

21 

36 

47 

37 

12 

34 

31 

59 

32 

31 

33 

2 

33 

33 

34 

3 

34 

33 

35 

2 

35 

30 

35 

58 

36 

26 

36 

52 

37 

19 

35 

31 

53 

32 

25 

32 

58 

33 

29 

34 

1 

34 

32 

35 

2 

35 

31 

36 

1 

36 

29 

36 

57 

37 

24 

36 

31 

46 

32 

19 

32 

53 

33 

26 

33 

58 

34 

30 

35 

1 

35 

32 

36 

2 

36 

32 

37 

1 

37 

29 

37 

31 

38 

32 

13 

32 

47 

33 

21 

33 

54 

34 

27 

35 

0 

35 

32 

36 

3 

36 

34 

37 

4 

37 

34 

38 

31 

29 

32 

5 

32 

41 

33 

16 

33 

50 

34 

24 

34 

58 

36 

30 

36 

3 

36 

35 

37 

6 

37 

37 

39 

31 

21 

31 

57 

32 

34 

33 

10 

33 

45 

34 

20 

34 

55 

35 

29 

36 

2 

36 

35 

37 

8 

37 

40 

40 

31 

11 

31 

49 

32 

26 

33 

3 

33 

39 

34 

15 

34 

51 

35 

26 

36 

1 

36 

35 

37 

8  37 

41    J 

41 

31 

1 

31 

40 

32 

18 

32 

56 

33 

33 

34 

10 

34 

47 

35 

23 

36 

68 

36 

34 

37 

8 

37 

42 

42 

30 

50 

31 

30 

32 

9 

32 

48 

33 

26 

34 

4 

34 

42 

35 

19 

35 

55 

36 

32 

37 

7 

37 

42 

43 

30 

39 

31 

19 

31 

59 

32 

39 

33 

18 

33 

57 

34 

36 

35 

14 

35 

51 

36 

29  37 

6 

37 

42   ^^ 

44 

30 

27 

31 

8 

31 

49 

32 

30 

33 

10 

33 

50 

34 

29 

35 

8 

35 

47 

36 

25 

37 

3 

37 

40    \ 

45 

30 

14 

30 

56 

31 

38 

32 

20 

33 

1 

33 

42 

34 

22 

35 

2 

36 

41 

36 

21 

37 

0 

37 

38 

46 

30 

1 

30 

44 

31 

27 

32 

9 

32 

51 

33 

33 

34 

14 

34 

65 

35 

36 

36 

16 

36 

66 

37 

36 

47 

29 

47 

30 

31 

31 

15 

31 

58 

32 

41 

33 

23 

34 

6 

34 

47 

35 

29 

36 

10 

36 

51 

37 

31 

48 

29 

33 

30 

18 

31 

2 

31 

46 

32 

30 

33 

13 

33 

56 

34 

39 

35 

21 

36 

3 

36 

45 

37 

27 

49 

29 

18 

30 

3 

30 

49 

31 

33 

32 

18 

33 

2 

33 

46 

34 

30 

35 

13 

35 

56 

36 

39 

37 

21 

60 

29 

3 

29 

49 

30 

35 

31 

20 

32 

6 

32 

51 

33 

36 

34 

20 

35 

4 

35 

48 

36 

31 

37 

15 

51 

28 

47 

29 

34 

30 

20 

31 

7 

31 

53 

32 

39 

33 

24 

34 

10 

34 

55 

35 

39 

36 

23 

37 

7 

52 

28 

30 

29 

18 

30 

5 

30 

52 

31 

39 

32 

26 

33 

12 

33 

58 

34 

44 

35 

30 

36 

15 

37 

0 

53 

28 

13 

29 

1 

29 

50 

30 

37 

31 

25 

32 

12 

33 

0 

33 

46 

34 

33 

35 

19 

36 

5 

36 

51 

54 

27 

56 

28 

45 

29 

33 

30 

22 

31 

10 

31 

58 

32 

46 

33 

34 

34 

21 

36 

8 

35 

65 

36 

4S 

55 

27 

38 

28 

27 

29 

17 

30 

6 

30 

55 

31 

44 

32 

32 

33 

21 

34 

9 

34 

57 

35 

44 

36 

32 

56 

27 

19 

28 

9 

28 

59 

29 

49 

30 

39 

31 

28 

32 

18 

33 

7 

33 

56 

34 

44 

35 

33 

36 

21 

57 

27 

0 

27 

51 

28 

42 

29 

32 

JO 

22 

31 

13 

32 

2 

32 

52 

33 

42 

34 

31 

35 

20 

36 

9 

58 

26 

41 

27 

32 

28 

23 

29 

14 

30 

5 

30 

56 

31 

47 

32 

37 

33 

27 

34 

17 

35 

7 

35 

67 

59 

26 

21 

27 

13 

28 

4 

28 

56 

29 

48 

30 

39 

31 

30 

32 

21 

33 

12 

34 

3 

34 

53 

35 

44 

60 

26 

0 

26 

53 

27 

45 

28 

37  29 

29 

30 

21 

31 

13 

32 

5 

32 

56 

33 

48 

34 

39 

36 

30 

250                   TABLE  A.— Part  II. 

TIuB  Table  ahowi  the  True  Altitude  of  the  Sun's  Centre  at  the  instant  it  is  8  o'CIock  in 

the  Morninsr,  or  4 1 

o'clock  in  the  Afternoon,  Apparent  Time,  for  more  readily  finding  the  Longitude  by  ChronometerT 

DECLINATION  AND  LATITUDE  OF  DIFFERENT  NAMES. 

Lat. 

Qo 

1' 

2' 

Z" 

4' 

5* 

6' 

7 

O 

8° 

9» 

10* 

ir 

12* 

. 

e  t 

o  1 

o    / 

0        1 

•  / 

o    / 

•  / 

0 

/ 

•  1 

o   / 

o 

/ 

• 

1 

O    / 

0 

30  0 

30  0 

29  59 

29  57 

29  55 

29  52 

29  49 

29 

45 

29  41 

29  36 

29 

30 

29 

24 

29  17 

1 

30  0 

29  58  29  56! 

29  53 

29  50 

29  46 

29  42 

29 

36 

29  31 

29  25 

29 

18 

29 

10 

29  2 

2 

29  59 

29  56 

29  53 

29  49 

29  44 

29  39 

29  34 

29 

27 

29  20 

29  13 

29 

5128 

56 

28  47 

3 

29  57 

29  53 

29  49 

29  44 

29  38 

29  32 

29  25 

29 

17 

29  9 

29  1 

28 

51 

28 

42 

28  31 

4 

29  55 

29  50 

29  44 

29  38 

29  31 

29  24 

29  16 

29 

7 

28  58 

28  48 

28 

38 

28 

27 

28  15 

5 

29  o2 

29  46 

29  39 

29  32 

29  24 

29  15 

29  6 

28 

56 

28  46 

28  35 

28 

23 

28 

11 

27  59 

6 

29  49 

29  42 

29  34 

29  25 

29  16 

29  6 

28  55 

28 

44 

28  33 

28  21 

28 

8 

27 

55 

27  41 

7 

29  45 

29  36 

29  27 

29  17 

29  7 

28  56 

28  44 

28 

32 

28  20 

28  6 

27 

53 

27 

38 

27  24 

8 

29  41 

29  31 

29  20 

29  9 

28  58 

28  46 

28  33 

28 

20 

28  6 

27  51 

27 

37 

27 

21 

27  5 

9 

29  36 

29  25 

29  13 

29   1 

28  48 

28  35 

28  21 

28 

6 

27  51 

27  36 

27 

20 

27 

3 

26  47 

10 

29  30 

29  18 

29  5 

28  51 

28  38 

28  23 

28  8 

2? 

'^Z 

27  37 

27  20 

27 

3 

26 

45 

26  27 

11 

29  24 

29  10 

28  56 

28  42 

28  27 

28  11 

27  55 

27 

38 

27  21 

27  3 

26 

45 

26 

27 

26  8 

12 

29  17 

29  2 

28  47 

28  31 

28  15 

27  59 

27  41 

27 

24 

^7  5 

26  47 

26 

27 

26 

8 

25  48 

13 

29  9 

28  54 

28  37 

28  21 

28  3 

27  45 

27  27 

27 

8 

26  49 

26  29 

26 

9 

25 

48 

25  27 

14 

29   1 

28  45 

28  27 

28  9 

27  51 

27  32 

27  12 

26 

53 

26  32 

26  11 

25 

50 

25 

28 

25  6 

15 

28  53 

28  35 

28  16 

27  57 

27  38 

27  18 

26  57 

26 

36 

26  15  25  53 

25 

31 

25 

8 

24  45 

16 

28  44 

28  24 

28  5 

27  45 

27  24 

27  3 

26  41 

26 

19 

25  57 

25  34 

25 

11 

24 

47 

24  23 

17 

28  34 

28  14 

27  53 

27  32 

27  10 

26  48 

26  25 

26 

2 

25  39 

25  15 

24 

51 

24 

26 

24   1 

18 

28  24 

28  2 

27  40 

27  18 

26  55 

26  32 

26  9 

25 

45 

25  20 

24  55 

24 

30 

24 

4 

23  38 

19 

28  13 

27  50 

27  28 

27  4 

26  40 

26  16 

25  51 

25 

26 

25  1 

24  35 

24 

9 

23 

42 

23  15 

20 

28  1 

27  38 

27  14 

26  50 

26  25 

26  0 

25  34 

25 

8 

24  41 

24  14 

23 

47 

23 

19 

22  52 

21 

27  50 

27  25 

27  0 

26  35 

26  9 

25  42 

25  16 

24 

49 

24  21 

23  53 

23 

25 

22 

57 

22  28 

22 

27  37 

27  12 

26  46 

26  19 

25  52 

25  25 

24  57 

24 

29 

24  1 

23  32 

23 

3 

22 

33 

22  4 

23 

27  24 

26  58 

26  31 

26  3 

25  35 

25  7 

24  38 

24 

9 

23  40 

23  10 

22 

40 

22 

10 

21  39 

24 

27  11 

26  43 

26  15 

25  47 

25  18 

24  49 

24  19 

23 

49 

23  19 

22  48 

82 

17 

21 

46 

21  14 

25 

26  57 

26  28 

25  59 

25  30 

25  0 

24  30 

23  59 

23 

28 

22  57 

22  25 

21 

53 

21 

21 

20  49 

26 

26  42 

26  13 

25  43 

25  12 

24  41 

24  10 

23  39 

23 

7 

22  35 

22  3 

21 

30  20 

57 

20  24 

27 

26  27 

25  57 

25  26 

24  54 

24  23 

23  51 

23  18 

22 

46 

22  13 

21  39 

21 

6  20 

32  19  58  1 

28 

26  12 

25  40 

25  8 

24  36 

24  3 

23  30 

22  57 

22 

24 

21  50 

21  16 

20 

41  20 

6  19  32  1 

29 
30 

25  56 

25  23 

24  51 

24  17 

23  44 

23  10 

22  36 

22 

1 

21  27 

20  52 

20 

16 

19 

41 

19  5 

25  40 

25  6 

24  32 

23  58 

23  24 

22  49 

22  14 

21 

39 

21   3 

20  27 

19 

51 

19 

:.-) 

18  38 

31 

25  23 

24  48 

24  13 

23  39 

23  3 

22  28 

21  52 

21 

16 

20  39 

20  3 

19 

26 

18 

48 

18  11 

32 

25  5 

24  30 

23  55 

23  19 

22  42 

22  6 

21  29 

20 

52 

20  15 

19  38 

19 

0 

18 

22 

17  44 

33 

24  48 

24  12 

23  35 

22  58 

22  21 

21  44 

21   6 

20 

29 

19  51 

19  12 

18 

34 

17 

55 

17  16 

34 

24  29 

23  52 

23  15 

22  37 

22  0 

21  22 

20  43 

20 

5 

19  26 

18  47 

18 

8 

17 

28 

16  49 

35 

24  11 

23  33 

22  55 

22  16 

21  38 

20  59 

20  20 

19 

40 

19  1 

18  21 

17 

41 

17 

1 

16  20 

36 

23  52 

23  13 

22  34 

21  55 

21  15 

20  36 

19  5Q 

19 

16 

18  35 

17  55 

17 

14 

16 

33 

15  52 

37 

23  32 

22  53 

22  13 

21  33 

20  53 

20  12 

19  32 

18 

51 

18  10 

17  28 

16 

47 

16 

5 

15  24 

38 

23  12 

22  32 

21  51 

21  11 

20  30 

19  48 

19  7 

18 

25 

17  44 

17  2 

16 

20 

15 

37 

14  55 

39 

40 

22  52 

22  11 

21  30 

20  48 

20  6 

19  24 

18  42 

18 

0 

17  17 

16  35 

15 

62 

15 

9 

14  26 

22  31 

21  50 

21   7 

20  25 

19  43 

19  0 

18  17 

17 

34 

16  51 

16  8 

15 

24 

14 

41 

13  57 

41 

22  10 

21  28 

20  45 

20  2 

19  19 

18  35 

17  52 

17 

8 

16  24 

15  40 

14 

56 

14 

12 

13  27 

42 

21  49 

21   6 

20  22 

19  38 

18  54 

18  10 

17  26 

16 

42 

15  57 

15  12 

14 

28 

13 

43 

12  68 
12  2^ 

43 

21  27 

20  43 

19  59 

19  14 

18  30 

17  45 

17  0 

16 

15 

15  30 

14  45 

13 

59 

13 

14 

44 

21  5 

20  20 

19  35 

18  50 

18  5 

17  19 

16  34 

15 

48 

15  2 

14  17 

13 

30 

12 

44 

11  58 

45 

20  42 

19  57 

19  11 

18  26 

17  40 

16  54 

16  7 

15 

21 

14  35 

13  48 

13 

2 

12 

15 

11  28 

46 

20  19 

19  33 

18  47 

18   1 

17  14 

16  27 

15  41 

14 

54 

14  7 

13  20 

12 

32 

11 

45 

10  58 

47 

19  56 

19  10 

18  23 

17  36 

16  48 

16  1 

15  14 

14 

26 

13  39 

12  51 

12 

3 

11 

15 

10  27 

48 

19  33 

18  45 

17  58 

17  10 

16  22 

15  35 

14  47 

13 

59 

13  10 

12  22 

11 

34 

10 

45 

9  57 

49 

19  9 

18  21 

17  33 

16  45 

15  56 

15  8 

14  19 

13 

31 

12  42 

11  53 

11 

4 

10 

15 

9  26 

50 

18  45 

17  56 

17  8 

16  19 

15  30 

14  41 

13  52 

13 

2 

12  13 

11  24 

10 

34 

9 

45 

8  55 

51 

18  20 

17  31 

16  42 

15  53 

15  3 

14  14 

13  24 

12 

34 

11  44 

10  54 

10 

4 

9 

11 

8  24 

52 

17  56 

17  6 

16  16 

15  26 

14  36 

13  46 

12  56 

12 

6 

11  15 

10  25 

9 

34 

8 

44 

7  53 

53 

17  31 

16  41 

15  50 

15  0 

14  9 

13  18 

12  28 

11 

37 

10  46 

9  55 

9 

4 

8 

13 

7  22 

54 

17  5 

16  15 

15  24 

14  33 

13  42 

12  51 

11  59 

11 

8 

10  17 

9  25 

8 

34 

7 

42 

6  61 

55 

16  40 

15  49 

14  57 

14  6 

13  14 

12  22 

11  31 

10 

39 

9  47 

8  55 

8 

4 

7 

12 

6  20 

66 

16  14 

15  22 

14  30 

13  38 

12  46 

11  54 

11   2 

10 

10 

9  18 

8  25 

7 

33 

6 

41 

5  48 

57 

15  48 

14  56 

14  3 

13  11 

12  18 

11  26 

10  33 

9 

41 

8  48 

7  55 

7 

2 

6 

9 

5  17 

58 

15  22 

14  29 

13  36 

12  43 

11  50 

10  57 

10  4 

9 

11 

8  18 

7  25 

6 

32 

5 

38 

4  45 

59 

14  55 

14  2 

13  9 

12  15 

11  22 

10  29 

9  35 

8 

42 

7  48 

6  54 

6 

1 

5 

7 

4  14 

60 

14  29 

13  35 

12  41 

11  47 

10  54 

10  0 

9  6 

8 

12 

7  18 

6  24 

5 

30 

4 

36   3  42  1 

TABLE  A.— Part  II 


251 


Thi«  T*bie  •hows  the  Trae  Altitude  of  the  Sun's  Centre  at  the  instant  it  is  8  o'Clock  in  the  Mornine  or  4 
o'Clocit;  in  the  Aaernoon,  Apparent  Time,  for  more  readily  finding  the  Longitude  by  Chronometer.' 


DECLINATION  AND  LATITUDE  OF  DIFFERENT  NAMEa 


Lat. 

130 

14° 

15^ 

16' 

17° 

18' 

19" 

20° 

21° 

22° 

23* 

24' 

• 

e   / 

0   > 

o  t 

•  f 

•  / 

o    / 

o   f 

o   / 

o    / 

o   / 

O   f 

•  / 

0 

29  9 

29  1 

28  53 

28  44 

28  34 

28  24 

28  13 

28  1 

27  50 

27  37 

27  24 

27  11 

1 

28  54 

28  45 

28  35 

28  24 

28  14 

28  i 

27  50 

27  38 

27  25 

27  12 

26  58 

26  43 

2 

28  37 

28  27 

28  16 

28  5 

27  53 

27  40 

27  28 

27  14 

27  0 

26  46 

26  31 

26  16 

3 

28  21 

28  9 

27  57 

27  45 

27  32 

27  18 

27  4 

26  50 

26  35 

26  19 

26  3 

25  47 

4 

28  3 

27  51 

27  38 

27  24 

27  10 

26  55 

26  40 

26  25 

26  9 

25  52 

25  35 

25  18 

6 

27  45 

27  32 

27  18 

27  3 

26  48 

26  32 

26  16 

26  0 

25  42 

25  25 

25  7 

24  49 

6 

27  27 

27  12 

26  57 

26  41 

26  25 

26  9 

25  51 

25  34 

25  16 

24  57 

24  38 

24  19 

7 

27  8 

26  53 

26  36 

26  19 

26  2 

25  45 

25  26 

25  8 

24  49 

24  29 

24  9 

23  49 

8 

26  49 

26  32 

26  15 

25  57 

25  39 

25  20 

25  1 

24  41 

24  21 

24  1 

23  40 

23  19 

9 

26  29 

26  11 

25  53 

25  34 

25  15 

24  55 

24  35 

24  14 

23  53 

23  32 

23  10 

22  48 

10 

26  9 

25  50 

25  31 

25  11 

24  51 

24  30 

24  9 

23  47 

23  25 

23  3 

22  40 

22  17 

11 

25  48 

25  28 

25  8 

24  47 

24  26 

24  4 

23  42 

23  19 

22  57 

22  33 

22  10 

21  46 

la 

25  27 

25  6 

24  45 

24  23 

24  1 

23  38 

23  15 

22  52 

22  28 

22  4 

21  39 

21  14 

13 

25  6 

24  44 

24  21 

23  58 

23  35 

23  12 

22  48 

22  23 

21  59 

21  33 

21   8 

20  42 

14 

24  44 

24  21 

23  57 

23  33 

23  9 

22  45 

22  20 

21  55 

21  29 

21   3 

20  37 

20  10 

15 

24  21 

23  57 

23  33 

23  8 

22  43 

22  17 

21  52 

21  26 

20  59 

20  32 

20  6 

19  38 

16 

23  58 

23  33 

23  8 

22  42 

22  16 

21  50 

21  23 

20  56 

20  29 

20  1 

19  33 

19  5 

17 

23  35 

23  9 

22  43 

22  16 

21  50 

21  22 

20  55 

20  27 

19  59 

19  30 

19  1 

18  32 

18 

23  12 

22  45 

22  17 

21  50 

21  22 

20  54 

20  26 

19  57 

19  28 

18  58 

18  29 

17  69 

19 

22  48 

22  20 

21  52 

21  23 

20  55 

20  26 

19  56 

19  27 

18  57 

18  27 

17  56 

17  26 

20 

22  23 

21  55 

21  26 

20  56 

20  27 

19  57 

19  27 

18  56 

18  26 

17  55 

17  23 

16  62 

21 

21  59 

21  29 

20  59 

20  29 

19  59 

19  28 

18  57 

18  26 

17  54 

17  22 

16  50 

16  18 

22 

21  33 

21   3 

20  32 

20  1 

19  80 

18  58 

18  27 

17  55 

17  22 

16  50 

16  17 

16  44 

23 

21  8 

20  37 

20  5 

19  33 

19  1 

18  29 

17  56 

17  23 

16  50 

16  17 

15  43 

15  10 

84 

20  42 

20  10 

19  38 

19  5 

18  32 

17  59 

17  2€'  16  52 

16  18 

16  44 

15  10 

14  35 

25 

20  16 

19  43 

19  10 

18  37 

18  3 

17  29 

16  55 

16  20 

15  46 

15  11 

14  36 

14  1 

26 

19  50 

19  16 

18  42 

18  8 

17  33 

16  58 

16  23 

15  48 

15  13 

14  37 

14  2 

13  26 

27 

19  23 

18  49 

18  14 

17  39 

17  3 

16  28 

15  52 

15  16 

14  40 

14  4 

13  27 

12  61 

28 

18  56 

18  21 

17  45 

17  9 

16  33 

15  57 

15  21 

14  44 

14  7 

13  30 

12  53 

12  16 

29 

18  29 

17  53 

17  16 

16  40 

16  3 

15  26 

14  49 

14  11 

13  34 

12  56 

12  18 

11  40 

30 

18  2 

17  25 

16  47 

16  10 

15  32 

14  55 

14  17 

13  39 

13  0 

12  22 

11  44 

11  6 

31 

17  34 

16  56 

16  18 

15  40 

15  2 

14  23 

13  45 

13  6 

12  27 

11  48 

11  8 

10  29 

32 

17  6 

16  27 

15  49 

15  10 

14  31 

13  51 

13  12 

12  33 

11  53 

11  13 

10  34 

9  64 

33 

16  37 

15  58 

15  19 

14  39 

13  59 

13  20 

12  40 

12  0 

11  19 

10  39 

9  58 

9  18 

34 

16  9 

15  29 

14  49 

14  9 

13  28 

12  48 

12  7 

11  26 

10  45 

10  4 

9  23 

8  42 

35 

15  40 

14  59 

14  19 

13  38 

12  57 

12  15 

11  34 

10  53 

10  11 

9  29 

8  48 

8  6 

36 

15  11 

14  30 

13  48 

13  7 

12  25 

11  43 

11   1 

10  19 

9  37 

8  55 

8  12 

7  30 

37 

14  42 

14  0 

13  18 

12  35 

11  53 

11  10 

10  28 

9  45 

9  2 

8  20 

7  37 

6  54 

38 

14  12 

13  30 

12  47 

12  4 

11  21 

10  38 

9  55 

9  11 

8  28 

7  44 

7  1 

6  17 

39 

13  43 

12  59 

12  16 

11  32 

10  49 

10  5 

9  21 

8  37 

7  53 

7  9 

6  25 

5  41 

40 

13  13 

12  29 

11  '45 

11   1 

10  16 

9  32 

8  48 

8  3 

7  19 

6  34 

5  49 

5  5 

41 

12  43 

11  58 

11  14 

10  29 

9  44 

8  59 

8  14 

7  29 

6  44 

5  59 

6  13 

4  28 

42 

12  13 

11  28 

10  42 

9  57 

9  11 

8  26 

7  40 

6  55 

6  9 

5  23 

4  37 

3  52 

43 

11  42 

10  57 

10  11 

9  25 

8  39 

7  53 

7  6 

6  20 

5  34 

4  48 

4  1 

3  15 

44 

11  12 

10  25 

9  39 

8  52 

8  6 

7  19 

6  32 

5  46 

4  59 

4  12 

3  25 

2  38 

45 

10  41 

9  54 

9  7 

8  20 

7  33 

6  46 

5  58 

5  11 

4  24 

3  36 

2  49 

2  2 

46 

19  10 

9  23 

8  35 

7  48 

7  0 

6  12 

5  24 

4  37 

3  49 

3  1 

2  13 

1  25 

47 

9  39 

8  51 

8  3 

7  15 

6  27 

5  39 

4  50 

4  2 

3  14 

2  25 

1  37 

0  48 

48 

9  8 

8  20 

7  31 

6  42 

5  54 

5  5 

4  16 

3  27 

2  38 

1  49 

1   1 

0  12 

49 

8  37 

7  48 

6  59 

6  10 

5  20 

4  31 

3  42 

2  52 

2  3 

1  14 

0  24 

50 

8  6 

7  16 

6  26 

5  37 

4  47 

3  57 

3  7 

2  18 

1  28 

0  38 

51 

7  34 

6  44 

5  54 

5  4 

4  14 

3  23 

2  33 

1  43 

0  52 

0  2 

52 

7  3 

6  12 

5  22 

4  31 

3  40 

2  49 

1  59 

1   8 

0  17 

53 

6  31 

5  40 

4  49 

3  58 

3  7 

2  15 

1  24 

0  33 

54 
55 

5  59 

5  8 

4  16 

3  25 

2  33 

1  41 

0  50 

5  28 

4  36 

3  44 

2  52 

2  0 

1   7 

0  15 

56 

4  56 

4  3 

3  11 

2  18 

1  26 

0  33 

57 

4  24 

3  31 

2  38 

1  45 

0  52 

58 

3  52 

2  59 

2  5 

1  12 

0  19 

59 

3  20 

2  26 

1  32 

0  39 

60 

2  AH 

1  54 

1   0 

0   6 

1 

252 

TABLE  B. — Sexagesimal  Proportional  Table 

For  finding  the  proportion 

of  Altitude  for  Miles  oi  Latitude  and 

Declination,  to  be  applied  to  the 

Altitude  taken 

from  Table  A. 

Mile* 

of 
Lat. 

or 
Decli. 

DIFFERENCE  OF  ALTITUDE  FOB 

.  r  OF  LATITUDE  OR  DEOLUfATION. 

r 

3' 

5' 

7' 

9' 

11' 

13' 

15' 

17' 

19' 

21' 

23' 

25' 

27' 

r 
1 

0.0 

0.1 

0.1 

1 
0.1 

0.2 

/ 

0.2 

0.2 

0.3 

0.3 

/ 

0.3 

> 
0.4 

0.4 

0.4 

0.6 

2 

0.0 

O.i 

0.2 

0.2 

0.3 

0.4 

0.4 

0.5 

0.6 

0.6 

0.7 

0.8 

0.8 

0.9 

3 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

1.0 

1.1 

1.2 

1.3 

1.4 

4 

0.1 

0.2 

0.3 

0.5 

0.6 

0.7 

0.9 

1.0 

1.1 

1.3 

1.4 

1.6 

1.7 

1.8 

5 

0.1 

0.3 

0.4 

0.6 

0.8 

0.9 

1.1 

1.3 

1.4 

1.6 

1.8 

1-9 

B.l 

2-3 

6 

0.1 

0.3 

0.5 

0.7 

0.9 

1.1 

1.3 

1.5 

1.7 

1.9 

2.1 

2.3 

2.5 

2.7 

7 

0.1 

0.4 

0.6 

0.8 

1.1 

1.3 

1.5 

1.8 

2.0 

2.2 

2.6 

2.7 

2.9 

3.2 

8 

0.1 

0-4 

0.7 

0.9 

1.2 

1.5 

1.7 

2.0 

2.3 

2.5 

2.8 

3.1 

3.3 

3.6 

9 

0.2 

0.5 

0.8 

1.1 

1.4 

1.7 

2.0 

2.3 

2.6 

2.9 

3.2 

3.5 

3.8 

4.1 

10 

0.2 

0.5 

0.8 

1.2 

1.5 

1.8 

2.2 

2.5 

2.8 

3.2 

3.5 

3.8 

4.2 

4.5 

11 

0.2 

0.6 

0.9 

1.3 

1.7 

2.0 

2.4 

2.8 

3.1 

3.5 

3.9 

4.2 

4.6 

6.0 

12 

0.2 

0.6 

1.0 

1.4 

1.8 

2.2 

2.6 

3.0 

3.4 

3.8 

4.2 

4.6 

5.0 

5.4 

13 

0.2 

0.7 

1.1 

1.5 

2.0 

2.4 

2.8 

3.3 

3.7 

4.1 

4.6 

6.0 

6.4 

5.9 

14 

0.2 

0.7 

1.2 

1.6 

2.1 

2.6 

3.0 

3.5 

4.0 

4.4 

4.9 

6.4 

5.8 

6.3 

15 

0.3 

0.8 

1.3 

1.8 

2.3 

2.8 

3.3 

3.8 

4.3 

4.8 

6.3 

5.8 

6.3 

6.8 

16 

0.3 

0.8 

1.3 

1.9 

2.4 

2.9 

3.5 

4.0 

4.6 

5.1 

6.6 

6.1 

6.7 

7.2 

17 

0.3 

0.9 

1.4 

2.0 

2.6 

3.1 

3.7 

4.3 

4.8 

5.4 

6.0 

6.5 

7.1 

7.7 

18 

0.3 

0.9 

1.5 

2.1 

2.7 

3.3 

3.9 

4.5 

6.1 

5.7 

6.3 

6.9 

7.5 

8.1 

19 

0.3 

1.0 

1.6 

2.2 

2.9 

3.5 

4.1 

4.8 

6.4 

6.0 

6.7 

7.3 

7.9 

8.6 

20 

0.3 

1.0 

1.7 

2.3 

3.0 

3.7 

4.3 

5.0 

5.7 

6.3 

7.0 

7.7 

8.3 

9.0 

21 

0.4 

1.1 

1.8 

2.5 

3.2 

3.9 

4.6 

5.3 

6.0 

6.7 

7.4 

8.1 

8.8 

9.6 

22 

0.4 

1.1 

1.8 

2.6 

3.3 

4.0 

4.8 

6.5 

6.2 

7.0 

7.7 

8.4 

9.2 

9.9 

23 

0.4 

1.2 

1.9 

2.7 

3.5 

4.2 

5.0 

5.8 

6.5 

7.3 

8.1 

8.8 

9.6 

10.4 

24 

9.4 

1.2 

2.0 

2.8 

3.6 

4.4 

5.2 

6.0 

6.8 

7.6 

8.4 

9.2 

10.0 

10.8 

25 

0.4 

1.3 

2.1 

2.9 

3.8 

4.6 

5.4 

6.3 

7.1 

7.9 

8.8 

9.6 

10.4 

11.3 

26 

0.4 

1.3 

2.2 

3.0 

3.9 

4.8 

5.6 

6.5 

7.4 

8.2 

9.1 

10.0 

10.8 

11.7 

27 

0.5 

1.4 

2.3 

3.2 

4.1 

5.0 

6.9 

6.8 

7.7 

8.6 

9.5 

10.4 

11.3 

12.2 

28 

0.5 

1.4 

2.3 

3.3 

4.2 

5.1 

6.1 

7.0 

7.9 

8.9 

9.8 

10.7 

11.7 

12.6 

29 

0.5 

1.5 

2.4 

3.4 

4.4 

5.3 

6.3 

7.3 

8.2 

9.2 

10.2 

11.1 

12.1 

13.1 

30 

0.5 

1.5 

2.5 

3.5 

4.5 

5.5 

6.5 

7.5 

8.5 

9.5 

10.6 

11.5 

12.6 

13.5 

31 

0.5 

1.6 

2.6 

3.6 

4.7 

5.7 

6.7 

7.8 

8.8 

9.8 

10.9 

11.9 

12.9 

14.0 

32 

0.5 

1.6 

2.7 

3.7 

4.8 

5.9 

6.9 

8.0 

9.1 

10.1 

11.2 

12.3 

13.3 

14.4 

33 

0.6 

1.7 

2.8 

3.9 

5.0 

6.1 

7.2 

8.3 

9.4 

10.6 

11.6 

12.7 

13.8 

14.9 

34 

0.6 

1.7 

2.8 

4.0 

5.1 

6.2 

7.4 

8.6 

9.6 

10.8 

11.9 

13.0 

14.2 

15.3 

35 

0.6 

1.8 

2.9 

3.0 

4.1 

5.3 

6.4 

7.6 

8.8 

9.9 

11.1 

12.3 

13.4 

14.6 

15.8 

36 

0.6 

1.8 

4.2 

6.4 

6.6 

7.8 

9.0 

10.2 

11.4 

12.6 

13.8 

15.0 

16.2 

37 

0.6 

1.9 

3.1 

4.3 

5.6 

6.8 

8.0 

9.3 

10.6 

11.7 

13.0 

14.2 

16.4 

16.7 

38 

0.6 

1-.9 

3.2 

4.4 

5.7 

7.0 

8.2 

9.5 

10.8 

12.0 

13.3 

14.6 

16.8 

17.1 

39 

0.7 

2.0 

3.3 

4.6 

5.9 

7.2 

8.5 

9.8 

11.1 

12.4 

13.7 

15.0 

16.3 

17.6 

40 

0.7 

2.0 

3.3 

4.7 

6.0 

7.3 

8.7 

10.0 

11.3 

12.7 

.14.0 

15.3 

16.7 

18.0 

41 

0.7 

2.1 

3.4 

4.6 

6.2 

7.5 

8.9 

10.3 

11.6 

13.0 

14.4 

15.7 

17.1 

18.5 

42 

0.7 

2.1 

3.5 

4.9 

6.3 

7.7 

9.1 

10.5 

11.9 

13.3 

14.7 

16.1 

17.6 

18.9 

43 

0.7 

2.2 

3.6 

5.0 

6.5 

7.9 

9.3 

10.8 

12.2 

13.6 

15.1 

16.5 

17.9 

19.4 

44 

0.7 

2.2 

3.7 

5.1 

6.6 

8.1 

9.5 

11.0 

12.5 

13.9 

16.4 

16.9 

18.3 

19.8 

45 
46 

0.8 

2.3 

3.8 

5.3 

6.8 

8.3 

9.8 

11.3 

12.8 

14.3 

15.8 

17.3 

18.8 

20.3 

0.8 

2.3 

3.8 

5.4 

6.9 

8.4 

10.0 

11.5 

13.0 

14.6 

16.1 

17.6 

19.2 

20.7 

47 

0.8 

2.4 

3.9 

5.5 

7.1 

8.6 

10.2 

11.8 

13.3 

14.9 

16.5 

18.0 

19.6 

21.2 

48 

0.8 

2.4 

4.0 

5.6 

7.2 

8.8 

10.4 

12.0 

13.6 

15.2 

16.8 

18.4 

20.0 

21.6 

49 

0.8 

2.5 

4.1 

5.7 

7.4 

9.0 

10.6 

12.3 

13.9 

15.5 

17.2 

18.8 

20.4 

22.1 

50 
51 

0.8 

2.5 

4.2 

5.8 

7.5 

9.2 

10.8 

12.5 

14.2 

16.8 

17.5 

19.2 

20.8 

22.5 

0.9 

2.6 

4.3 

6.0 

7.7 

9.4 

11.1 

12.8 

14.5 

16.2 

17.9 

19.6 

21.3 

23.0 

52 

0.9 

2.6 

4.3 

6.1 

7.8 

9.5 

11.3 

13.0 

14.7 

16.5 

18.2 

19.9 

21.7 

23.4 

53 

0.9 

2.7 

4.4 

6.2 

9.0 

9.7 

11.5 

13.3 

15.0 

16.8 

18.6 

20.3 

22.1 

23.9 

64 

0.9 

2.7 

4.5 

6.3 

9.1 

9.9 

11.7 

13.6 

15.3 

17.1 

18.9 

20.7 

22.5 

24.3 

55 

66 

0.9 

2.8 

4.6 

6.4 

9.3 

10.1 

11.9 

13.8 

16.6 

17.4 

19.3 

21.1 

22.9 

24.8 

0.9 

2.8 

4.7 

6.5 

9.4 

10.3 

12.1 

14.0 

16.9 

17.7 

19.6 

21.5 

23.3 

26.2 

57 

1.0 

2.9 

4.8 

6.7 

9.6 

10.5 

12.4 

14.3 

16.2 

18.1 

20.0 

21.9 

23.8 

25.7 

58 

1.0 

2.9 

4.8 

6.8 

9.7 

10.6 

12.6 

14.6 

16.4 

18.4 

20.3 

22.2 

24   2 

26.1 

59 

1.0 

3.0 

4.9 

6.9 

9.9 

10.8 

12.8 

14.8 

16.7 

18.7 

20.7 

22.6 

24.6 

26.6 

60 

1.0 

3.0 

5.0 

7.0 

9.0 

11.0 

13.0 

15.0 

17.0 

19.0 

21.0 

23.0 

25-0 

27.0 

TABLE  B. — Sexagesimal   Proportional  Table 

253 

For  finding  the  proportion  of  Altitude  for  Miles 

of  Latitude  and 

Declination,  to 

be  applied  to  the        1 

Altitudf 

3  taken 

from  Table  A. 

Milst 

of 
Lkt. 

or 
DwU 

DIFFERENCE  OF  AT.TITUDE  FOE 

.  r  OF  LATITUDE  OR  DECLINATION. 

29' 

31' 

33' 

35' 

37' 

39' 

41' 

43' 

45' 

47' 

49' 

51' 

53' 

55' 

1 

0.5 

t 

0.5 

1 
0.6 

1 
0.6 

0.6 

/ 

0.7 

0.7 

,   0.7 

0.8 

/ 

0.8 

0.8 

0.9 



/ 

0.9 

1 
0.9 

2 

1.0 

1.0 

1.1 

1.2 

1.2 

1.3 

1.4 

1.4 

1.5 

1.6 

1.6 

1.7 

1.8 

1.8 

3 

1.5 

1.6 

1.7 

1.8 

1.9 

2.0 

2.1 

2.2 

2.3 

2.4 

2.5 

2.6 

2.7 

2.8 

4 

1.9 

2.1 

2.2 

2.3 

2.5 

2.6 

2.7 

2.9 

3.0 

3.1 

3.3 

3.4 

3.5 

3.7 

5 

2.4 

2.6 

2.8 

2.9 

3.1 

3.3 

3.4 

3.6 

3.8 

3.9 

4.1 

4-3 

4.4 

4.6 

6 

2.9 

3.1 

3.3 

3.5 

3.T 

3.9 

4.1 

4.3 

4.5 

4.7 

4.9 

5.1 

5.3 

5.5 

7 

3.4 

3.6 

3.9 

4.1 

4.3 

4.6 

4.8 

5.0 

5.3 

5.5 

5.7 

6.0 

6.2 

6.4 

8 

3.9 

4.1 

4.4 

4.7 

4.9 

6.2 

5.5 

5.7 

6.0 

6.3 

6.5 

6.8 

7.1 

7.3 

9 

4.4 

4.7 

5.0 

5.3 

5.6 

5.9 

6.2 

6.5 

6.8 

7.1 

7.4 

7.7 

8.0 

8.3 

10 

4.8 

5.2 

5.5 

5.8 

6.2 

6.5 

6.8 

7.2 

7.5 

7.8 

8.2 

8.5 

8.8 

9.2 

11 

5.3 

5.7 

6.1 

6.4 

6.8 

7.2 

7.5 

7.9 

8.3 

8.6 

9.0 

9.4 

9  7 

10.1 

12 

5.8 

6.2 

6.6 

7.0 

7.4 

7.8 

8.2 

8.6 

9.0 

9.4 

9.8 

10.2 

10  6 

11.0 

13 

6.3 

6.7 

7.2 

7.6 

8.0 

8.5 

8.9 

9.3 

9.8 

10.2 

10.6 

11.1  . 

11.5 

11.9 

14 

6.8 

7.2 

7.7 

8.2 

8.6 

9.1 

9.6 

10.0 

10.5 

11.0 

11.4 

11.9 

12.4 

12.8 

15 

7.3 

7.8 

8.3 

8.8 

9.3 

9.8 

10.3 

10.8 

11.3 

11.8 

12.3 

12.8 

13.3 

13.8 

16 

7.7 

8.3 

8.8 

9.3 

9.9 

10.4 

10.9 

11.5 

12.0 

12.5 

13.1 

13.6 

14.1 

14.7 

: 

17 

8.2 

8.8 

9.4 

9.9 

10.5 

11.1 

11.6 

12.2 

12.8 

13.3 

13.9 

14.5 

15.0 

15.6 

18 

8.7 

9.3 

9.9 

10.5 

11.1 

11.7 

12.3 

12.9 

13.5 

14.1 

14.7 

15.3 

15.9 

16.5 

' 

19 

9.2 

9.8 

10.5 

11.1 

11.7 

12.4 

13.0 

13.6 

14.3 

14.9 

15.5 

16.2 

16.8 

17.4 

20 

9.7 

10.3 

11.0 

11.7 

12.3 

13.0 

13.7 

14.3 

15.0 

15.7 

16.3 

17.0 

17.7 

18.3 

21 

10.2 

10.9 

11.6 

12.3 

13.0 

13.7 

14.4 

15.1 

15.8 

16.5 

17.2 

17.9 

18.6 

19.3 

22 

10.6 

11.4 

12.1 

12.8 

13.6 

14.3 

15.0 

15.8 

16.5 

17.2 

18.0 

18.7 

19.4 

20.2 

23 

11.1 

11.9 

12.7 

13.4 

14.2 

15.0 

15.7 

16.5 

17.3 

18.0 

18.8 

19.6 

20.3 

21.1 

> 

24 

11.6 

12.4 

13.2 

14.0 

14.8 

15.6 

16.4 

17.2 

18.0 

18.8 

19.6 

20.4 

21.2 

22.0 

25 

12.1 

12.9 

13.8 

14.6 

15.4 

16.3 

17.1 

17.9 

18.8 

19.6 

20.4 

21.3 

22.1 

22.9 

■ 

26 

12.6 

13.4    U.3 

15.2 

16.0 

16.9 

17.8 

18.6 

19.5 

20.4 

21.2 

22.1 

23.0 

23.8 

27 

13.1 

14.0 

14.9 

15.8 

16.7 

17.6 

18.5 

19.4 

20.3 

21.2 

22.1 

23.0 

23.9 

24.8 

■ 

28 

13.5 

14.5 

11'. 4 

16.3 

17.3 

18.2 

19.1 

20.1 

21.0 

21.9 

22.9 

23.8 

24.7 

25.7 

29 

14.0 

15.0 

16.0 

16.9 

17.9 

18.9 

19.8 

20.8 

21.8 

22.7 

23.7 

24.7 

25.6 

26.6 

30 

14.5 

15.5 

16.5 

17.5 

18.5 

19.5 

20.5 

21.5 

22.5 

23.5 

24.5 

25.5 

26.5 

27.5 

31 

15  0 

16.0 

17.1 

18.1 

19.1 

20.2 

21.2 

22.2 

23.3 

24.3 

25.3 

26.4 

27.4 

28.4 

32     15.5 

16.5 

17.6 

18.7 

19.7 

20.8 

21.9 

22.9 

24.0 

25.1 

26.1 

27.2 

28.3 

29.3 

33 

16.0 

17.1 

18.2 

19.3 

20.4 

21.5 

22.6 

28.7 

24.8 

25.9 

27.0 

28.1 

29.2 

30.3 

34 

16.4 

17.6 

18.7 

19.8 

21.0 

22.1 

23.2 

24.4 

25.5 

26.6 

27.8 

28.9 

30.0 

31.2 

35 

16.9 

18.1 

19.3 
19.8 

20.4 

21.6 

22.8 

23.9 

25.1 

26.3 

27.4 

28.6 

29.8 

30.9 

32.1 

36 

17.4 

18.6 

21.0 

22.2 

23.4 

24.6 

25.8 

27.0 

28.2 

29.4 

30.6 

31.8 

33.0 

37 

17.9 

19.1 

20.4 

21.6 

22.8 

24.1 

25.3 

26.5 

27.8 

29.0 

30.2 

31.5 

32.7 

33.9 

38 

18.4 

19.6 

20.9 

22.2 

23.4 

24.7 

26.0 

27.2 

28.5 

29.8 

31.0 

32.3 

33.6 

34.8 

39 

18.9 

20.2 

21.5 

22.8 

24.1 

25.4 

26.7 

28.0 

29.3 

30.6 

31.9 

33.2 

34.5 

35.8 

40 

19.3 

20.7 

22.0 

23.3 

24.7 

26.0 

27.3 

28.7, 

30.0 

31.3 

32.7 

34.0 

35.3 

36.7 

41 

19.8 

21.2 

22.6 

23.9 

25.3 

26.7 

28.0 

29.4 

30.8 

32.1 

33.5 

34.9 

36.2 

37.6 

42 

20.3 

21. 7 

23.1 

24.5 

25.9 

27.3 

28.7 

30.1 

31.5 

32.9 

34.3 

35.7 

37.1 

38.5 

43 

20.8 

22.2 

23.7 

25.1 

26.5 

28.0 

29.4 

30.8 

32.3 

33.7 

35.1 

36.6 

38.0 

39.4 

44 

21.3 

22.7 

24.2 

25.7 

27.1 

28.6 

30.1 

31.5 

33.0 

34.5 

35.9 

37.4 

38.9 

40.3 

45 
46 

21.8 

23.3 

24.8 

26.3 

27.8 

29.3 

30.8 

32.3 

33.8 

35.3 

36.8 

38.3 

39.8 

41.3 

22.2 

23.8 

25.3 

26.8 

28.4 

29.9 

31.4 

33.0 

34.5 

36.0 

37.6 

39.1 

40.6 

42.2 

47 

22.7 

24.3 

25.9 

27.4 

29.0 

30.6 

32.1 

33.7 

35.3 

36.8 

38.4 

40.0 

41.5 

43.1 

48 

23.2 

24.8 

26.4 

28.0 

29.6 

31.2 

32.8 

34.4 

36.0 

37.6 

39.2 

40.8 

42.4 

44.0 

49 

23.7 

25.3 

27.0 

28.6 

30.2 

31.9 

33.5 

35.1 

36.8 

38.4 

40.0 

41.7 

43.3 

44.9 

50 

24.2 

25.8 

27.5 

29.2 

30.8 

32.5 

34.2 

35.8 

37.5 

39.2 

40.8 

42.5 

44.2 

45.8 

51 

24.7 

26.4 

28.1 

29.8 

31.5 

33.2 

34.9 

36.6 

38.3 

40.0 

41.7 

43.4 

45.1 

46.8 

52 

25.1 

26.9 

28.6 

30.3 

32.1 

33.8 

35.5 

37.3 

39.0 

40.7 

42.5 

44.2 

45.9 

47.7 

53 

25.6 

27.4 

29.2 

30.9 

32.7 

34.5 

36.2 

38.0 

39.8 

41.5 

43.3 

45.1 

46.8 

48.6 

54 

26.1 

27.9 

29.7 

31.5 

33.5 

35.1 

36.9 

38.7 

40.5 

42.3 

44.1 

45.9 

47.7 

49.5 

55 

26.6 

28.4 

30.3 

32.1 

33.9 

35.8 

37.6 

39.4 

41.3 

43.1 

44.9 

46.8 

48.6 

50.4 

66 

27.1 

28.9 

30.8 

32.7 

34.5 

36.4 

38.3 

40.1 

42.0 

43.9 

45.7 

47.6 

49.5 

51.3 

57 

27.6 

29.5 

31.4 

33.3 

35.2 

37.1 

39.0 

40.9 

42.8 

44.7 

46.6 

48.5 

50.4 

52.3 

58 

28.0 

30.0 

31.9 

33.8 

35.8 

37.7 

39.6 

41.6 

43.5 

45.4 

47.4 

49.3 

51.2 

53.1 

59 

88.5    30. 5| 

32.5 

34.4 

36.4 

38.4 

40.3 

42.3 

44.3 

46.2 

48.2 

50.2 

52.1 

54.1 

60 

29.0 

31.0 

33.0 

35.0 

37.0 

39.0 

41.0 

43.0 

45.0 

47.0 

49.0 

51. C 

53.0 

55.0 

254 

TABLE  C— First  Pabt. 

The  Time  ( 

in  seconds  and  hundredth  parts  of  seconds)  corresponding  to  a  change  of  the  Sun 

*s  Altitude  of    1 

1  milC;  at  8  o'clock,  A.  M.,  or  4  o'clock,  P.  M.,  and  which  may  be  assumed  the  same  for  20  minutes;     \ 

that  is,  10  minutes  either  before  or  after  8,  A.  M.,  or  4,  P.  M.     (See  Remark  at  bottom  of 

page  247 

■•) 

DECLINATION  AND  LATITUDE  OF  THE  SAME  NAME.                                      | 

Lat. 

0' 

2'. 

4' 

6' 

8° 

10° 

12° 

14° 

16° 

18° 

20° 

22* 

24° 

• 

s. 

s. 

s. 

s. 

s. 

*. 

s. 

s. 

5. 

s. 

s. 

s. 

5. 

0 

4.00 

4.00 

4.01 

4.03 

4.05 

4.08 

4.12 

4.16 

4.22 

4.28 

4.34 

4.42 

4.60 

1 

.00 

.00 

.01 

.03 

.05 

.08 

.11 

.15 

.21 

.27 

.33 

.40 

.48 

2 

.00 

.00 

.01 

.02 

.04 

.07 

.10 

.14 

.18 

.25 

.31 

.38 

.46 

3 

.00 

.01 

.01 

.02 

.04 

.06 

.10 

.14 

.18 

.24 

.30 

.38 

.45 

4 

.01 

.01 

.01 

.02 

.04 

.06 

.09 

.13 

.17 

.23 

.29 

•35 

.44 

5 

4.02 

4.02 

4.02 

4.03 

4.04 

4.06 

4  "^9 

4.13 

4.17 

4.22 

4.28 

4.34 

4.43 

6 

.03 

.02 

.02 

.03 

.04 

.06 

.Od 

.12 

.16 

.21 

.27 

.34 

.42 

7 

.04 

.03 

.03 

.04 

.05 

.06 

.09 

.12 

.16 

.21 

.27 

.33 

.41 

8 

.05 

.04 

.04 

.04 

.05 

.07 

.09 

.12 

.16 

.20 

.26 

.32 

.40 

9 

.07 

.06 

.05 

.05 

.06 

.08 

.10 

.12 

.16 

.20 

.26 

.32 

.39 

10 

4.08 

4.07 

4.06 

4.06 

4.07 

4.08 

4.10 

4.13 

4.17 

4.21 

4.26 

4.32 

4,38 

11 

.10 

.08 

.07 

.07 

.08 

.09 

.11 

.13 

.17 

.21 

,26 

.32 

,38 

12 

.12 

.  .10 

.09 

.09 

.09 

.10 

.12 

.14 

.18 

.22 

,26 

.32 

,38 

18 

.14 

.12 

.11 

.10 

.10 

.11 

.13 

.15 

.18 

.22 

,26 

.32 

,38 

14 
15 

.16 

,14 

.13 

.12 

.12 

.13 

.14 

.16 

.19 

.23 

.27 

.32 

.38 

4.19 

4.17 

4.15 

4.14 

4.14 

4.15 

4.16 

4.18 

4,20 

4.24 

4,28 

4.32 

4.38 

16 

.22 

.19 

.17 

.16 

.16 

.17 

.18 

.19 

,22 

.25 

,29 

.33 

,39 

17 

.25 

.22 

.20 

.18 

.18 

.19 

.20 

.21 

.24 

.27 

.30 

.34 

.40 

18 

.28 

.25 

.23 

.21 

.20 

.21 

.22 

.23 

.25 

.28 

.31 

.35 

,41 

19 

.31 

.28  1 

.26 

.24 

.23 

.23 

.24 

.25 

.27 

.30 

.33 

.36 

,42 

20 

4.34 

4.31 

4.29 

4.27 

4.26 

4.26 

4.26 

4.27 

4.29 

4.31 

4.34 

4.38 

4.43 

21 

.38 

.34 

.32 

.30 

.29 

,29 

.29 

.30 

.31 

.33 

.36 

.40 

.44 

22 

.42 

.38 

.35 

.34 

.32 

.32 

.32 

.32 

.33 

.35 

.38 

.42 

.46 

23 

.46 

.42 

.39 

.37 

.36 

.35 

.35 

.35 

.36 

.38 

.40 

.44 

.48 

24 

.50 

.46 

.44 

.42 

.40 

.38 

.38 

.38 

.39 

.41 

.43 

.46 

.50 

25 

4.55 

4.51 

4.48 

4.46 

4.44 

4.42 

4.42 

4.42 

4.42 

4.44 

4.46 

4.48 

4.52 

26 

.60 

.56 

.52 

.50 

.48 

.46 

.46 

.46 

.46 

.47 

.49 

.51 

.65 

27 

.65 

.61 

.57 

.54 

.52 

.50 

.50 

.50 

.50 

.50 

.52 

.54 

.58 

28 

.70 

.66 

.62 

.59 

.57 

.55 

.54 

.54 

.54 

.54 

.55 

.57 

.61 

29 

.75 

.71 

.67 

.64 

.62 

.60 

.58 

.58 

.58 

.58 

.59 

.61 

.64 

30 

4.81 

4.77 

4.73 

4.69 

4.67 

4.65 

4.63 

4.63 

4.63 

4.63 

4.63 

4.65 

4.68 

31 

.87 

.83 

.79 

.75 

.72 

.70 

.68 

.68 

.68 

.68 

.68 

.70 

.72 

32 

.93 

.89 

.85 

.81 

.78 

.76 

.74 

.73 

.73 

.73 

.73 

.74 

.76 

33 

5.00 

.95 

.91 

.87 

.84 

.82 

.80 

.78 

.78 

.78 

.78 

.78 

.80 

34 

.07 

5.02 

.98 

,94 

.90 

.88 

.86 

.84 

.83 

.83 

.83 

.84 

.85 

35 

5.14 

5.09 

5.05 

5.01 

4.97 

.95 

4  93 

4.91 

4.90 

4.89 

4.89 

4.89 

4.90 

36 

.22 

.17 

.13 

.09 

5.05 

5.02 

5.00 

.98 

.96 

.95 

.95 

.95 

.96 

37 

.30 

.25 

.21 

.17 

.13 

.10 

,07 

5.05 

5.03 

5.01 

5.01 

5.01 

5.02 

38 

.39 

.33 

.29 

.25 

.21 

.18 

,14 

.12 

.10 

.08 

.08 

.08 

.08 

39 

.48 

.42 

.38 

.34 

.30 

.26 

.22 

.20 

.18 

.16 

.15 

.15 

.15 

40 

5.58 

5.52 

5.47 

5.43 

5.39 

5.35 

5.31 

5.28 

5.26 

5.24 

5.23 

5.23 

6.23 

41 

.68 

.62 

.57 

.52 

.48 

.44 

.40 

.37 

.35 

.33 

.31 

.30 

.30 

42 

.78 

.72 

.67 

.62 

.58 

.54 

.60 

.46 

.44 

.42 

.40 

.38 

,38 

43 

.89 

.83 

.77 

.72 

.68 

.64 

.60 

.56 

.53 

.51 

.49 

.47 

.47 

44 

6.00 

.94 

.88 

.83 

.78 

.74 

.70 

.66 

.63 

.61 

,59 

.58 

,56 

45 

6.12 

6.06 

6.00 

5.94 

5.89 

5.85 

5.81 

5.77 

5.74 

5.71 

5,69 

5,67 

6.66 

46 

.25 

.18 

.12 

6.06 

6.01 

.97 

.93 

.89 

.86 

.82 

,80 

,78 

,77 

47 

.38 

.81 

.25 

.19 

.14 

6.10 

6.06 

3.02 

.98 

.94 

,92 

.90 

.88 

48 

.52 

.45 

.39 

.33 

.27 

•   .23 

.19 

.15 

6.11 

6.07 

6,05 

6.03 

6,01 

49 
50 

.66 

.60 

,54 

.48 

.42 

.36 

.32 

.28 

.24 

.21 

.18 

.15 

,13 

6.81 

6.75 

6.69 

6.63 

6.59 

6.51 

6.46 

6.42 

6.38 

6.34 

6.32 

6.29 

6.27 

51 

.97 

.91 

.85 

.79 

.73 

.67 

.61 

.57 

.53 

.49 

.47 

.44 

,42 

52 

7.14 

7.08 

7.02 

.96 

.90 

.84 

.78 

.73 

.69 

.65 

.63 

.60 

,58 

53 

.33 

.26 

.20 

7.14 

7.08 

7.02 

.96 

.91 

.87 

.83 

.80 

.76 

.74 

54 

.53 

.45 

,39 

.33 

.27 

.22 

7.15 

7.10 

7.06 

7.02 

.98 

.94 

.91 

55 

7.74 

7.66 

7.59 

7.53 

7.47 

7.41 

7.35 

7.29 

7.25 

7.21 

7.17 

7.13 

7.09 

56 

.96 

.88 

.81 

.74 

.68 

.62 

.56 

.50 

.45 

.41 

.37 

.33 

.29 

57 

8.19 

8.11 

8.04 

.98 

.92 

.86 

.80 

.74 

.18 

.62 

.58 

.64 

.60 

58 

.44 

.36 

.28 

8.22 

8.16 

8.10 

8.14 

.98 

.92 

.86 

.81 

.77 

.73   . 

69 

.70 

.62 

.54 

.47 

.41 

.35 

.29 

8.23 

8.17 

8.11 

8.06 

8.02 

.98 
8.25  i 

60         .98 

.90 

.82 

.75 

.69 

.63 

.57 

.51 

.45 

.38 

.33 

.29 

TABLE  C— Second  Part.                                            255 

The  Time 

'in  seconds  and  hundredth  parts  of  seconds)  corresponding  to  a  change  of  the  Sun's  Altitude  of 

1  mile,  at  8  o'clock,  A.  M.,  or  4  o'clock,  P.  M.,  and  which  may  be  assumed  the  same  for  20  minutes :     ! 

that  is, 

10  mmutes  either  before  or  after  8,  A.  M.,  or  4,  P.  M.     (See  Remark  at  bottom  of  page  247).          i 

DECLINATION  AND  LATITUDE  OF  DIFFERENT  NAMESL                                     | 

Lat. 

1* 

3° 

5° 

7' 

9° 

ir 

13' 

15" 

17° 

19' 

21* 

23* 

24' 

o 

s. 

s. 

s. 

s. 

5. 

s. 

5. 

s. 

s. 

s. 

5. 

s. 

s. 

1 

4.00 

4.01 

4.03 

4.05 

4.08 

4.11 

4.16 

4.20 

4.26 

4.32 

4.39 

4.47 

4  62 

2 

.00 

.02 

.04 

.06 

.09 

.12 

.16 

.22 

.28 

.34 

.41 

.49 

.64 

3 

.01 

.03 

.05 

.07 

.10 

.13 

.18 

.24 

.30 

.36 

.43 

.51 

.56 

4 

.02 

.04 

.06 

.08 

.11 

.14 

.19 

.26 

.32 

.38 

.45 

.54 

.69 

5 

.03 

.05 

.07 

.09 

.12 

.16 

.21 

,28 

.34 

.40 

.47 

•56 

61 

6 

4.04 

4.06 

4.08 

4.11 

4.14 

4.18 

4.23 

4.30 

4.36 

4.42 

4.50 

4.59 

4.64 

7 

.05 

.07 

.09 

.13 

.16 

.20 

.25 

.32 

.38 

.44 

.52 

.61 

.66 

8 

.06 

.08 

.11 

.15 

.18 

.22 

.27 

.34 

.40 

.47 

.55 

.64 

.69 

9 

.08 

.10 

.12 

.16 

.20 

.24 

.29 

.36 

.42 

.50 

.58 

.67 

.72 

10 

.09 

.11 

.14 

.18 

.22 

.26 

.32 

.38 

.45 

.53 

.61 

.70 

.75 

11 

4.11 

4.13 

4.16 

4.20 

4.24 

4.29 

4.35 

4.41 

4.48 

4.56 

4.64 

4.74 

4.79 

12 

.13 

.15 

.18 

.22 

.26 

.32 

.38 

.44 

.51 

.59 

.67 

.77 

.82 

13 

.15 

.18 

.21 

.25 

.29 

.35 

.41 

.47 

.54 

.62 

.70 

.80 

.85 

14 

.17 

.21 

.24 

.28 

.33 

.39 

.45 

.51 

.58 

.66 

.74 

.84 

.89 

15 
16 

.20 

.24 

.28 

.32 

.36 

.41 

.47 

.54 

.61 

.69 

.78 

.87 

.93 

4.23 

4.37 

4.31 

4.35 

4.39 

4.44 

4.50 

4.57 

4.65 

4.73 

4.82 

4.92 

4.97 

17 

.26 

.30 

.34 

.38 

.42 

.48 

.54 

.61 

.69 

.77 

.86 

.96 

6.01 

18 

.29 

.33 

.37 

.41 

.46 

.52 

.58 

.65 

.73 

.81 

.90 

5.00 

.05 

19 

.32 

.36 

.40 

.44 

.50 

.56 

.62 

.69 

.77 

.85 

.95 

.05 

.10 

20 

.35 

.39 

.43 

.48 

.54 

.60 

.66 

.74 

.82 

.90 

5.00 

.10 

.16 

21 

4.39 

4.43 

4.47 

4.52 

4.58 

4.64 

4.70 

4.78 

4.86 

4.95 

5.05 

5.15 

6.20 

22 

.43 

.47 

.51 

.56 

.62 

.69 

.75 

83 

.91 

5.00 

.10 

.20 

.26 

23 

.47 

.51 

.56, 

.61 

.67 

.74 

.80 

.88 

.96 

.05 

.15 

.25 

.30 

24 

.52 

.56 

.61 

.66 

.72 

.79 

.85 

.93 

5.01 

.10 

.20 

.30 

.36 

25 

.57 

.61 

.66 

.71 

.77 

.84 

.91 

4.99 

.07 

.16 

.26 

.36 

.42 

26 

4.62 

4.66 

4.71 

4.76 

4.82 

4.89 

4.97 

5.05 

5.13 

5.22 

5.32 

5.42 

6.48 

27 

.67 

.71 

.76 

.82 

.88 

.95 

5.03 

.11 

.19 

.28 

.38 

.48 

.54 

28 

.72 

.76 

.81 

.87 

.94 

5.01 

.09 

.17 

.25 

.34 

.44 

.54 

.60 

29 

.77 

.82 

.87 

.93 

5.00 

.07 

.15 

.23 

.31 

.41 

.51 

.61 

.67 

30 

.83 

.88 

.93 

.99 

.07 

.14 

.22 

.30 

.38 

.48 

.58 

.68 

.74 

31 

4.89 

4.95 

5.00 

5.06 

5.14 

5.21 

5.29 

5.37 

5.45 

5.55 

5.65 

5.75 

6.81 

32 

.96 

5.02 

.07 

.13 

.21 

.28 

.36 

.44 

.52 

.62 

.72 

.82 

.88 

33 

5.03 

.09 

.14 

.20 

.28 

.35 

.43 

.51 

.59 

.69 

.79 

.90 

.96 

34 

.10 

.16 

.21 

.27 

.35 

.42 

.50 

.58 

.67 

.77 

.87 

.98 

6.04 

35 
36 

.17 

.24 

.29 

.35 

.43 

.50 

.58 

.66 

.75 

.85 

.95 

6.07 

.13 

5.25 

5.32 

5.37 

5.43 

5.51 

5.58 

5.66 

5.74 

5.83 

5.93 

6.03 

6.15 

6.22 

37 

.33 

.40 

.45 

.52 

.60 

.67 

.75 

.83 

.92 

6.02 

.12 

.24 

.31 

38 

.42 

.48 

.54 

.61 

.69 

.76 

.84 

.92 

6.01 

.11 

.21 

.33 

.40 

39 

.51 

.57 

.63 

.70 

.78 

.85 

.93 

6.02 

.11 

.21 

.31 

.43 

.49 

40 

.61 

.67 

.73 

.80 

.88 

.95 

6.03 

.12 

.21 

.31 

.41 

.53 

.59 

41 

5.71 

5.77 

5.83 

5.90 

5.98 

6.05 

6.13 

6.23 

6.32 

6.42 

6.52 

6.63 

6.69 

42 

.81 

.87 

.93 

6.01 

6.09 

.16 

.24 

.34 

.43 

.53 

.63 

.74 

.80 

43 

.92 

.98 

6.04 

.12 

.20 

.27 

.35 

.45 

.54 

.64 

.74 

.86 

.91 

44 

6.03 

6.09 

.16 

.23 

.31 

.39 

.47 

.57 

.66 

.76 

.86 

.97 

7.03 

45 

46 

.15 

.22 

.29 

.37 

.45 

.53 

.61 

.71 

.88 

.93 

.98 

7.09 

.16 

6.28 

6.35 

6.42 

6.50 

6.58 

6.66 

6.74 

6.84 

47 

.41 

.48 

.55 

.63 

.71 

.79 

.87 

7.97 

48 

.55 

.62 

.69 

.77 

.85 

.93 

7.01 

.11 

49 

.69 

.76 

.83 

.91 

.99 

7.07 

.15 

.25 

50 

.84 

.91 

.99 

7.07 

7.15 

.23 

7.00 

7.07 

7.15 

7.23 

7.31 

7.39 

52 

.17 

.24 

.32 

.40 

.49 

.57 

53 

.36 

.43 

.51 

.59 

.68 

.76 

54 

.56 

.63 

.71 

.79 

.87 

.95 

55 
66 

.77 

.84 

.92 

8.00 

7.99 

8.06 

8.14 

8.22 

57 

8.22 

.30 

.38 

.46 

58 

.47 

.55 

.63 

.71 

59 

.73 

.81 

.89 

97 

60 

.01 

.09 

.18 

.25 

TO 

EXTRACTS    FROM   NAUTICAL  ALMANAC,   FOR   1854. 
WORK  EXAMPLES   OF  LATITUDE   BY   THE    MOON,   ON  PAGES   102, 

•103. 

Date. 

Semid. 

Hor.   Par. 

Declination. 

Equation 
Of  Time. 

Meridian. 

Noon. 

Mid. 

Noon. 

Mid. 

Noon. 

Mid. 

Passase. 

July  11 
"     12 

/     // 

16  0 

60  0 

o      / 

19  9  S. 

o      / 

21    21  S. 

—  6  m. 

h.  m. 

13  58 

14  56 

April  23 
"     24 
"     25 

t    It 
16  0 

1 

/    // 

57  0 

2  2  N. 

0  51  S. 

+  2  m. 

21  59 

22  43 

April  4 
"     6 

15  0 

54  0 

26  0  N. 

26   13  N. 

—  3  m. 

5  30 

6  21 

April  1 

"      2 

15  0 

55  0 

18  46  K 

20  36  N. 

—  4  m. 

3     3 
3  51 

April  12 
«      13 

16  0 

69  0 

7  27  S. 

4  25  S. 

—  1  m. 

11  63 

12  42 

FROM 

TO   1^ 

LARGE 

^ORK   SAW 

NAUTICAL  ALMANAC. 
R   EXAMPLES   AS    ABOVK. 

Date. 


July  11 
"      12 


April  23 
"     24 

"      25 


April    4 
"       5 


April    1 

"        2 


April  12 
"     13 


Semld. 


Noon. 


16  32 


15  27 


14  49 


15     2 


16     5 


Mid. 


/      // 

16  37 


16  31 


16     0 


Hor.    Par. 


Noon. 


t      n 

60  32 


56  85 

14  49 

64  16 

14  58 

65     3 

58  64 


Mid. 


/    // 

60  61 


66  50 


64  15 


64  60 


68  86 


Declination. 


At  19  h. 


o      /      // 

20  6  34    S, 


At  17  h. 


0  21   16  N. 


At7h. 


26  9  62  N. 


AtTh. 


19  52  23  K 


At  18  h. 


4  40  12    S. 


DIffi 


10  m. 


112 


145 


91 


162 


£q  nation 
of  Time. 


m.  S. 
—   67 


+   1  67 


—  36 


—  40 


0  50 


Meridian, 


Passage.     | 

h. 

m. 

13 

58 

14 

56 

h.   m. 

21  69 

22  43 


6  30 
6  21 


3     4 
3  61 


11  54 

12  43 


TO  WORK   EXAMPLES  OF  LATITTJDE  BY   PLANETS,    ON  PAGE   106. 


Date. 


January  1 
2 


II 


June  6 

"    7 


April  18 
"     14 


'teoB 


February  1 
«        2 


Names. 


Venus. 


Mars. 


Jupiter. 


(( 


Saturn, 


Meridian  Passage. 


h.  m. 
3  16 


6     2 


18  24 


6  46 


Declination. 


13     6  S. 
12  40  S. 


7  26  N. 
7  13  K 


21 
21 


7  S. 
6  S. 


17 
17 


4  N. 
4  N. 


EqoAtion. 


m. 
—    4 


+     2 


—    1 


-  14 


TO   WORK   EXAMPLES   OF   LATITUDE   BY   STARS, 

PAGES    107,    108. 

Date. 

Names.                     1           Meridian  Passage. 

Declination.                | 

February  27 

Aldebaran 

h.    m. 

5     48 

o          / 

16     13 

N. 

February  28 

Antares 

17     36 

26        6 

s. 

Marc 

b  21 
h26 

Sirius 

6     34 

16      31 

s. 

Marc 

Vega 

'is     12 

38     39 

N. 

May  1 

Vega 

15     59 

38     39 

N. 

June  21 

Cross-Foot  Star 

6     21 

62      17 

S. 

April  1 

Castor 

6     43 

32      12 

N. 

TO   WORK   LATITUDE   BY    POLAR  STAR,   PAGE   109. 

I>«t«.                   I     Meridian  Passage.     | 

Right  Ascension. 

Declination. 

Equation. 

July  1 

h.     ra. 
18     26 

h.    m. 

0 

88 

32  N. 

July  20 

17       9 

88 

32  N. 

January  20 

20     9 

February  10 

21  36 

m. 

—     15 

TO   WORK  EXAMPLES  OF  TIME  BY  MOON, 

PAGE   133. 

DkUL 

Seml-I 
DiuB. 

/ 

15 

Hm. 
Par. 

/' 

55 

Right  Atcatulon. 

DeellnaUoB. 

KqoatloB  of 
Tim.. 

Dlt 
Ih. 

Son's  Right 
A»cenilon. 

Dit 

I   h. 

6. 

9l 

Noos. 

Mid. 

Noon. 

Mid. 

Mar.  10 

b.  m.  8. 
8  12  21 

h.  m.  B. 
8  38  26 

0         / 

24  14  N. 

O        / 

23  4  N. 

m. 
10 

8. 

31.55 

.665 

h. 

23  5 

m.  8. 
21  53 

TO   WORK  EXAMPLES   OF  TIME  BY   PLANETS,   PAGE   135 

Data. 

Eight  Ascen. 

Declination. 

Equation. 

Dlff.  1  h. 

Sun's  R.  A. 

Dlff  Ih. 

April  6 

"     7 

h.  Ttl.    s. 
22  27  28 
22  29  44 

0     / 

6  7S. 

m.      8. 
2  30.50 

8. 

.725 

b.  in.  8. 
1  0  18 

8. 

9 

December  5 
«          6 

19  57  13 
19  58     4 

21   16  S. 

9  12.43 

1.049 

16  46  36 

11 

TO  WORK  EXAMPLES  OF  TIME  BY  STARS,   ON  PAGE   137. 

IHt«. 

Bight  Asceiu 

Declination. 

Equation. 

Dlff.  1  h. 

Sim's  E.  A- 

Ditt  Ih. 

February  S 

h.   m.    S. 
6  38  43 

0     / 
16    31  S. 

m.       8. 
14  31.61 

.39 

k.   m.  8. 
21  81  34 

8. 

10 

May  IS 

!    16  20  24 

26     6  S. 

3  52.34 

.53 

h.   m.  8. 
3  15  50 

10 

The  foUovmtg  wre  a  few  from  among  the  ncmy  recommendations  of  the  work  r$- 
Deived  by  the  Publishers  : — 

New  York,  April  5,  1856. 

Mb.  Shaw, — Dear  Sir, — Ha  nng  used  the  new  treatise  on  the  Practice  of  Navigation 
«t  Sea,  by  Captain  William  Thorns,  during  ten  passages  across  the  Atlantic,  I  am  oi 
opinion  that  it  is  the  most  clear,  simple,  and  practical  work  on  the  subject  I  have  yet 
geen,  containing  all  that  is  requisite  to  the  navigator,  without  being  encumbered  with 
pages  of  useless  matter. 

For  the  learner  I  consider  it  most  especially  desirable,  for  evervthing  necessary 
for  finding  a  ship's  place  on  the  Ocean  is  so  simply  and  clearly  explamed,  and  illustra 
ted  by  diagrams,  that  it  must  clear  the  mist  and  doubts  that  so  often  hang  over  him. 

1  am  fully  of  opinion  that  this  work  will,  in  time,  be  duly  appreciated,  and  generally 
adopted   by   our   sea-faring  community.     Very  respectfully, 

P.  E.  Le  Fevre,  Master  Steamship  ArieL 


New  Yokk,  December  26,  1855. 
Mb.  R.  L.  Shaw, — Dear  Sir, — Captain  Eldridge,  of  the  Steamship  Pacific,  in   con- 
versation with  me,  after  having  used  Thorns'  Practical  Navigation,  said  :    "  The   book 
recommends  itself,  publish  it,  it  is  sure  to  go." 

Jas.  H.  Brownlow,  Teacher  of  Namgation. 


New  York,  April  5,  1856. 
Mb.  Shaw, — Dea/r  Si/r, — Having  used  the  work  on  Navigation  published  by  Captain 
William  Tlioms,  I  can  cheerfully  recommend  it  to  all  those  interested  in  navigation,  in 
being  the  most  simple  and  easy  method  of  calculations.     Yours, 

Thos.  D.  Ewan,  Master  of  Steamship  Southerner. 


Mb.  R.  L.  Shaw, — I  have  used  Tlioms'  Navigator  for  several  voyages,  and  prefer  it 
to  any  other  I  have  had  before,  and  recommend  it  to  all  classes  of  navijrators,  being 
more  explicit,  and  best  adapted  to  the  general  practice  of  navigation  at  s'ea. 

J.  Westervelt,  Master  of  Schooner  Pea/rl. 

Nkw  York,  Ma/rch  12,  1856. 


New  York,  April  V,  1856. 
Mb.  R.  L.  Shaw, — Dea/r  Sir, — I  have   used  Thorns'   Navigation  for  three   voyagfti 
-id  prefer  it  to  any  others  I  have  seen. 

John  Hardy,  Master  of  Schooner  D.  Dc^.^d^soH. 


OPINION  OF  THE  WORK, 

From  Men  of  Experience, 


Wk,  the  undersigned,  Captains  of  Ships,  and  others,  having  examined  thi 
Manuscript  of  a  new  Treatise  on  the  Practice  of  Navigation,  and  Nautical 
Astronomy,  by  Capt.  Wm.  Thoms,  are  of  opinion  that  it  is  the  most  simple 
and  practical  work  on  the  subject  we  have  yet  seen,  especially  for  the  learner, 
who  will  be  greatly  assisted  in  obtaining  a  knowledge  of  the  Science  by  the 
numerous  Diagrams  which  illustrate  the  subject,  and  is  particularly  adapted  for 
Seamen,  as  it  treats  on  those  subjects  only  which  have  reference  to  the  Ship's 
Place  on  the  Ocean,  (or  Navigation  proper.)  Many  new  problems  have  also 
been  introduced,  which  will  be  found  of  much  practical  value  to  many  Captains 
of  Ships,  who  may  not  have  had  an  opportunity  of  previously  becoming  acquainted 
with   them. 

We  are  therefore  of  opinion,  that  if  the  work  is  published  in  its  present 
style,  it  will  be  duly  appreciated  by  our  seafaring  community,  and  would  in 
time   be  extensively   used   by   them   throughout   this   large   maritime   country. 


Names. 


Vessels  Attached  to. 


S.  McKAY,  Great  Republic. 

THOMAS  DIXON,         Fidelia. 
EDWARD  MURRAY,  Balance. 


Blon. 
Cornelia. 
Telegraph. 
S.  Austin. 
S.  B.  Strong. 


WM.  BRAGDON, 

JOHN  T.  FRENCH, 

JOHN  STRAKER, 

J.  H.  CASWELL, 

ISAAC  LYNCH, 

WILLIAM  P.  JONES,  Kensington. 

GUNDER  KRABEL,  Chief  Mate. 

FRANCIS  PATTERSON,     " 

JOHN  W  HOLMES,  R.  DeWolfb. 

CHaS.  ANDERSON,  Mar.  Vineyard. 

JAMES  SAFFORD,  Helene. 

JOHN  KIRKPATRICK,  Mate. 

AND.  ARMSTRONG,  Cora  Linn, 

C.  E.  LUCAS, 

A.  B.  CLAUSSE, 

RICHARD  LLOYD, 

A.  P.  FOSTER, 

JAMES  W.  TAYLOR,  D.  B.  Warner. 

J.  W.  JEROLOMON,  Alexander  Law. 

ALF.  B.  LOWBER,  S.  S.  Ericsson. 

JOHN  R.  CAVARLY,  Am.  Eagle. 

JOSEPH  C.  DO  WD,  Wm.  Rathbone. 

RICH'D.  B.  MORSE,  George  Ratner. 

HENRY  W.  DODGE,  T.    &     P.Wood- 

W.  R.  FOREMAN,  Ohio.         [ward. 

MARTIN  ALLEN,  Rapu>. 

PET.  BORGESTONE,  H.  W.  Mosoubk. 


Mate. 
Sword  Fish. 
Gloucester,  Mass. 
Adela  Swift. 


Names. 

J.  WILSON  COMBY, 
WILLIAM  HOWARD, 
VICTOR  VIEROUS, 
CHARLES  LIDBECK, 
WILLIAM  DALY, 
JAMES  NEWBERY, 
THOMAS  McLEAVY, 
C.  FERD.  BROWN, 
G.  DOUGHTY, 
JOS.  G.  WOODSIDE, 
FRED.  WIELMANN, 
JOSEPH  D.  HUGHES, 
EDWARD  MOORE, 
RUFUS  BROWN, 
B.  F.  TAYLOR, 
LEWIS  E.  JACKSON, 
WM.  L.  KEMPTON, 
B.  FRANCIS, 
ZACHEUS  KEMPTON, 
J.  H.  ROGERS, 
WILLIAM  LYDDON, 
CHAS.  E.  MERRY, 
G.  RICE, 

J.  R.  McDOUGALL, 
JOSHUA  E.  SMITH, 
M.  NICHOLAS, 
JOHN  MOONEY, 
PETER  WIXEN, 
EDWARD  ABEEL, 
CHAS.  ANDERSON, 


Vessels  Attached  t& 

Calhoun. 

Lucy  Watts 

H.  T.  L. 

Abrasia. 

Gazellb. 

Jasper. 

Mary  Morrm*. 

e.  bulklet. 

Anstiss. 

Contest. 

Vulture. 

Uranus. 

Augusta. 

Mongolia. 

Anna  Tift, 

Hollander. 

St.  Joseph. 

Cataract. 

Horatio. 

S.  B.  Strong. 

J.  N.  Cooper. 

Skylark. 

B.  N.  Hawkins. 

John  Stroud. 

Ann  Elizabeth. 

Unattached. 

Governor  Brow» 

North  Wind. 

Isaac  Wright. 

Qitktxax  Mom. 


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